Daily Papers

Natural language inference (NLI) is critical for complex decision-making in biomedical domain. One key question, for example, is whether a given biomedical mechanism is supported by experimental evidence. This can be seen as an NLI problem but there are no directly usable datasets to address this. The main challenge is that manually creating informative negative examples for this task is difficult and expensive. We introduce a novel semi-supervised procedure that bootstraps an NLI dataset from existing biomedical dataset that pairs mechanisms with experimental evidence in abstracts. We generate a range of negative examples using nine strategies that manipulate the structure of the underlying mechanisms both with rules, e.g., flip the roles of the entities in the interaction, and, more importantly, as perturbations via logical constraints in a neuro-logical decoding system. We use this procedure to create a novel dataset for NLI in the biomedical domain, called BioNLI and benchmark two state-of-the-art biomedical classifiers. The best result we obtain is around mid 70s in F1, suggesting the difficulty of the task. Critically, the performance on the different classes of negative examples varies widely, from 97% F1 on the simple role change negative examples, to barely better than chance on the negative examples generated using neuro-logic decoding.

With the emergence of advanced reasoning models like OpenAI o3 and DeepSeek-R1, large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, their ability to perform rigorous logical reasoning remains an open question. This survey synthesizes recent advancements in logical reasoning within LLMs, a critical area of AI research. It outlines the scope of logical reasoning in LLMs, its theoretical foundations, and the benchmarks used to evaluate reasoning proficiency. We analyze existing capabilities across different reasoning paradigms - deductive, inductive, abductive, and analogical - and assess strategies to enhance reasoning performance, including data-centric tuning, reinforcement learning, decoding strategies, and neuro-symbolic approaches. The review concludes with future directions, emphasizing the need for further exploration to strengthen logical reasoning in AI systems.

Neural decoding, the process of understanding how brain activity corresponds to different stimuli, has been a primary objective in cognitive sciences. Over the past three decades, advancements in functional Magnetic Resonance Imaging and machine learning have greatly improved our ability to map visual stimuli to brain activity, especially in the visual cortex. Concurrently, research has expanded into decoding more complex processes like language and memory across the whole brain, utilizing techniques to handle greater variability and improve signal accuracy. We argue that "seeing" involves more than just mapping visual stimuli onto the visual cortex; it engages the entire brain, as various emotions and cognitive states can emerge from observing different scenes. In this paper, we develop algorithms to enhance our understanding of visual processes by incorporating whole-brain activation maps while individuals are exposed to visual stimuli. We utilize large-scale fMRI encoders and Image generative models pre-trained on large public datasets, which are then fine-tuned through Image-fMRI contrastive learning. Our models hence can decode visual experience across the entire cerebral cortex, surpassing the traditional confines of the visual cortex. We first compare our method with state-of-the-art approaches to decoding visual processing and show improved predictive semantic accuracy by 43%. A network ablation analysis suggests that beyond the visual cortex, the default mode network contributes most to decoding stimuli, in line with the proposed role of this network in sense-making and semantic processing. Additionally, we implemented zero-shot imagination decoding on an extra validation dataset, achieving a p-value of 0.0206 for mapping the reconstructed images and ground-truth text stimuli, which substantiates the model's capability to capture semantic meanings across various scenarios.

Large language models (LLMs) continue to face challenges in reliably solving reasoning tasks, particularly those that require precise rule following, as often found in mathematical reasoning. This paper introduces a novel neurosymbolic method that improves LLM reasoning by encoding hidden states into neurosymbolic vectors, enabling problem-solving within a neurosymbolic vector space. The results are decoded and merged with the original hidden state, significantly boosting the model's performance on numerical reasoning tasks. By offloading computation through neurosymbolic representations, this method enhances efficiency, reliability, and interpretability. Experimental results demonstrate an average of 88.6% lower cross-entropy loss and 15.4 times more problems correctly solved on a suite of mathematical reasoning tasks compared to chain-of-thought prompting and supervised fine-tuning (LoRA), without degrading performance on other tasks. We make our code available at: https://github.com/vdhanraj/Neurosymbolic-LLM.

We propose NEURONA, a neuro-symbolic framework for fMRI decoding and concept grounding in neural activity. Leveraging image- and video-based fMRI question-answering datasets, NEURONA learns to decode interacting concepts from visual stimuli based on patterns of fMRI responses, integrating symbolic reasoning and compositional execution with fMRI grounding across brain regions. We demonstrate that incorporating structural priors (e.g., compositional predicate-argument dependencies between concepts) into the decoding process significantly improves both decoding accuracy over precise queries, and notably, generalization to unseen queries at test time. With NEURONA, we highlight neuro-symbolic frameworks as promising tools for understanding neural activity.

Despite their linguistic competence, Large Language models (LLMs) often exhibit limitations in their ability to reason reliably and flexibly. To address this, we propose a neurosymbolic approach that prompts LLMs to extract and encode all relevant information from a problem statement as logical code statements, and then use a logic programming language (Prolog) to conduct the iterative computations of explicit deductive reasoning. Our approach significantly enhances the performance of LLMs on the standard mathematical reasoning benchmark, GSM8k, and the Navigate dataset from the BIG-bench dataset. Additionally, we introduce a novel dataset, the Non-Linear Reasoning (NLR) dataset, consisting of 55 unique word problems that target the shortcomings of the next token prediction paradigm of LLMs and require complex non-linear reasoning but only basic arithmetic skills to solve. Our findings demonstrate that the integration of Prolog enables LLMs to achieve high performance on the NLR dataset, which even the most advanced language models (including GPT4) fail to solve using text only.

Decoding continuous language from neural signals remains a significant challenge in the intersection of neuroscience and artificial intelligence. We introduce Neuro2Semantic, a novel framework that reconstructs the semantic content of perceived speech from intracranial EEG (iEEG) recordings. Our approach consists of two phases: first, an LSTM-based adapter aligns neural signals with pre-trained text embeddings; second, a corrector module generates continuous, natural text directly from these aligned embeddings. This flexible method overcomes the limitations of previous decoding approaches and enables unconstrained text generation. Neuro2Semantic achieves strong performance with as little as 30 minutes of neural data, outperforming a recent state-of-the-art method in low-data settings. These results highlight the potential for practical applications in brain-computer interfaces and neural decoding technologies.

Logical reasoning, i.e., deductively inferring the truth value of a conclusion from a set of premises, is an important task for artificial intelligence with wide potential impacts on science, mathematics, and society. While many prompting-based strategies have been proposed to enable Large Language Models (LLMs) to do such reasoning more effectively, they still appear unsatisfactory, often failing in subtle and unpredictable ways. In this work, we investigate the validity of instead reformulating such tasks as modular neurosymbolic programming, which we call LINC: Logical Inference via Neurosymbolic Computation. In LINC, the LLM acts as a semantic parser, translating premises and conclusions from natural language to expressions in first-order logic. These expressions are then offloaded to an external theorem prover, which symbolically performs deductive inference. Leveraging this approach, we observe significant performance gains on FOLIO and a balanced subset of ProofWriter for three different models in nearly all experimental conditions we evaluate. On ProofWriter, augmenting the comparatively small open-source StarCoder+ (15.5B parameters) with LINC even outperforms GPT-3.5 and GPT-4 with Chain-of-Thought (CoT) prompting by an absolute 38% and 10%, respectively. When used with GPT-4, LINC scores 26% higher than CoT on ProofWriter while performing comparatively on FOLIO. Further analysis reveals that although both methods on average succeed roughly equally often on this dataset, they exhibit distinct and complementary failure modes. We thus provide promising evidence for how logical reasoning over natural language can be tackled through jointly leveraging LLMs alongside symbolic provers. All corresponding code is publicly available at https://github.com/benlipkin/linc

Neural decoding, a critical component of Brain-Computer Interface (BCI), has recently attracted increasing research interest. Previous research has focused on leveraging signal processing and deep learning methods to enhance neural decoding performance. However, the in-depth exploration of model architectures remains underexplored, despite its proven effectiveness in other tasks such as energy forecasting and image classification. In this study, we propose NeuroSketch, an effective framework for neural decoding via systematic architecture optimization. Starting with the basic architecture study, we find that CNN-2D outperforms other architectures in neural decoding tasks and explore its effectiveness from temporal and spatial perspectives. Building on this, we optimize the architecture from macro- to micro-level, achieving improvements in performance at each step. The exploration process and model validations take over 5,000 experiments spanning three distinct modalities (visual, auditory, and speech), three types of brain signals (EEG, SEEG, and ECoG), and eight diverse decoding tasks. Experimental results indicate that NeuroSketch achieves state-of-the-art (SOTA) performance across all evaluated datasets, positioning it as a powerful tool for neural decoding. Our code and scripts are available at https://github.com/Galaxy-Dawn/NeuroSketch.

Visual neural decoding seeks to reconstruct or infer perceived visual stimuli from brain activity patterns, providing critical insights into human cognition and enabling transformative applications in brain-computer interfaces and artificial intelligence. Current approaches, however, remain constrained by the scarcity of high-quality stimulus-brain response pairs and the inherent semantic mismatch between neural representations and visual content. Inspired by perceptual variability and co-adaptive strategy of the biological systems, we propose a novel self-supervised architecture, named NeuroBridge, which integrates Cognitive Prior Augmentation (CPA) with Shared Semantic Projector (SSP) to promote effective cross-modality alignment. Specifically, CPA simulates perceptual variability by applying asymmetric, modality-specific transformations to both EEG signals and images, enhancing semantic diversity. Unlike previous approaches, SSP establishes a bidirectional alignment process through a co-adaptive strategy, which mutually aligns features from two modalities into a shared semantic space for effective cross-modal learning. NeuroBridge surpasses previous state-of-the-art methods under both intra-subject and inter-subject settings. In the intra-subject scenario, it achieves the improvements of 12.3% in top-1 accuracy and 10.2% in top-5 accuracy, reaching 63.2% and 89.9% respectively on a 200-way zero-shot retrieval task. Extensive experiments demonstrate the effectiveness, robustness, and scalability of the proposed framework for neural visual decoding.

The meaning of a natural language utterance is largely determined from its syntax and words. Additionally, there is evidence that humans process an utterance by separating knowledge about the lexicon from syntax knowledge. Theories from semantics and neuroscience claim that complete word meanings are not encoded in the representation of syntax. In this paper, we propose neural units that can enforce this constraint over an LSTM encoder and decoder. We demonstrate that our model achieves competitive performance across a variety of domains including semantic parsing, syntactic parsing, and English to Mandarin Chinese translation. In these cases, our model outperforms the standard LSTM encoder and decoder architecture on many or all of our metrics. To demonstrate that our model achieves the desired separation between the lexicon and syntax, we analyze its weights and explore its behavior when different neural modules are damaged. When damaged, we find that the model displays the knowledge distortions that aphasics are evidenced to have.

The dominant paradigm for neural text generation is left-to-right decoding from autoregressive language models. Constrained or controllable generation under complex lexical constraints, however, requires foresight to plan ahead feasible future paths. Drawing inspiration from the A* search algorithm, we propose NeuroLogic A*esque, a decoding algorithm that incorporates heuristic estimates of future cost. We develop efficient lookahead heuristics that are efficient for large-scale language models, making our method a drop-in replacement for common techniques such as beam search and top-k sampling. To enable constrained generation, we build on NeuroLogic decoding (Lu et al., 2021), combining its flexibility in incorporating logical constraints with A*esque estimates of future constraint satisfaction. Our approach outperforms competitive baselines on five generation tasks, and achieves new state-of-the-art performance on table-to-text generation, constrained machine translation, and keyword-constrained generation. The improvements are particularly notable on tasks that require complex constraint satisfaction or in few-shot or zero-shot settings. NeuroLogic A*esque illustrates the power of decoding for improving and enabling new capabilities of large-scale language models.

Large Language Models (LLMs) typically have billions of parameters and are thus often difficult to interpret in their operation. Such black-box models can pose a significant risk to safety when trusted to make important decisions. The lack of interpretability of LLMs is more related to their sheer size, rather than the complexity of their individual components. The TARS method for knowledge removal (Davies et al 2024) provides strong evidence for the hypothesis that that linear layer weights which act directly on the residual stream may have high correlation with different concepts encoded in the residual stream. Building upon this, we attempt to decode neuron weights directly into token probabilities through the final projection layer of the model (the LM-head). Firstly, we show that with Llama 3.1 8B we can utilise the LM-head to decode specialised feature neurons that respond strongly to certain concepts, with examples such as "dog" and "California". This is then confirmed by demonstrating that these neurons can be clamped to affect the probability of the concept in the output. This extends to the fine-tuned assistant Llama 3.1 8B instruct model, where we find that over 75% of neurons in the up-projection layers have the same top associated token compared to the pretrained model. Finally, we demonstrate that clamping the "dog" neuron leads the instruct model to always discuss dogs when asked about its favourite animal. Through our method, it is possible to map the entirety of Llama 3.1 8B's up-projection neurons in less than 15 minutes with no parallelization.

Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer language models (LMs) can reason according to logical rules. We ask whether those LMs can deduce theorems in propositional calculus and first-order logic; if their relative success in these problems reflects general logical capabilities; and which layers contribute the most to the task. First, we show for several encoder-only LMs that they can be trained, to a reasonable degree, to determine logical validity on various datasets. Next, by cross-probing fine-tuned models on these datasets, we show that LMs have difficulty in transferring their putative logical reasoning ability, which suggests that they may have learned dataset-specific features, instead of a general capability. Finally, we conduct a layerwise probing experiment, which shows that the hypothesis classification task is mostly solved through higher layers.

Recent research in neural machine translation has largely focused on two aspects; neural network architectures and end-to-end learning algorithms. The problem of decoding, however, has received relatively little attention from the research community. In this paper, we solely focus on the problem of decoding given a trained neural machine translation model. Instead of trying to build a new decoding algorithm for any specific decoding objective, we propose the idea of trainable decoding algorithm in which we train a decoding algorithm to find a translation that maximizes an arbitrary decoding objective. More specifically, we design an actor that observes and manipulates the hidden state of the neural machine translation decoder and propose to train it using a variant of deterministic policy gradient. We extensively evaluate the proposed algorithm using four language pairs and two decoding objectives and show that we can indeed train a trainable greedy decoder that generates a better translation (in terms of a target decoding objective) with minimal computational overhead.

A critical component of a successful language generation pipeline is the decoding algorithm. However, the general principles that should guide the choice of decoding algorithm remain unclear. Previous works only compare decoding algorithms in narrow scenarios and their findings do not generalize across tasks. To better structure the discussion, we introduce a taxonomy that groups decoding strategies based on their implicit assumptions about how well the model's likelihood is aligned with the task-specific notion of utility. We argue that this taxonomy allows a broader view of the decoding problem and can lead to generalizable statements because it is grounded on the interplay between the decoding algorithms and the likelihood-utility misalignment. Specifically, by analyzing the correlation between the likelihood and the utility of predictions across a diverse set of tasks, we provide the first empirical evidence supporting the proposed taxonomy, and a set of principles to structure reasoning when choosing a decoding algorithm. Crucially, our analysis is the first one to relate likelihood-based decoding strategies with strategies that rely on external information such as value-guided methods and prompting, and covers the most diverse set of tasks up-to-date.

Inductive Logic Programming (ILP) learns interpretable logical rules from data. Existing methods are transductive: their learned parameters are bound to specific predicates and require retraining for each new task. We introduce Neural Rule Inducer (NRI), a pretrained model for zero-shot rule induction. Rather than encoding literal identities, NRI represents literals using domain-agnostic statistical properties such as class-conditional rates, entropy, and co-occurrence, which generalize across variable identities and counts without retraining. The model consists of a statistical encoder and a parallel slot-based decoder. Parallel decoding preserves the permutation invariance of logical disjunction; an autoregressive decoder would instead impose an arbitrary clause order. Product T-norm relaxation makes rule execution differentiable, allowing end-to-end training on prediction accuracy alone. We evaluate NRI on rule recovery, robustness to label noise and spurious correlations, and zero-shot transfer to real-world benchmarks, and we believe this work opens up the possibility of foundation models for symbolic reasoning. Code and the reference checkpoint are available at https://github.com/phuayj/neural-rule-inducer.

We create a reusable Transformer, BrainBERT, for intracranial recordings bringing modern representation learning approaches to neuroscience. Much like in NLP and speech recognition, this Transformer enables classifying complex concepts, i.e., decoding neural data, with higher accuracy and with much less data by being pretrained in an unsupervised manner on a large corpus of unannotated neural recordings. Our approach generalizes to new subjects with electrodes in new positions and to unrelated tasks showing that the representations robustly disentangle the neural signal. Just like in NLP where one can study language by investigating what a language model learns, this approach opens the door to investigating the brain by what a model of the brain learns. As a first step along this path, we demonstrate a new analysis of the intrinsic dimensionality of the computations in different areas of the brain. To construct these representations, we combine a technique for producing super-resolution spectrograms of neural data with an approach designed for generating contextual representations of audio by masking. In the future, far more concepts will be decodable from neural recordings by using representation learning, potentially unlocking the brain like language models unlocked language.

The development of artificial intelligence systems with advanced reasoning capabilities represents a persistent and long-standing research question. Traditionally, the primary strategy to address this challenge involved the adoption of symbolic approaches, where knowledge was explicitly represented by means of symbols and explicitly programmed rules. However, with the advent of machine learning, there has been a paradigm shift towards systems that can autonomously learn from data, requiring minimal human guidance. In light of this shift, in latest years, there has been increasing interest and efforts at endowing neural networks with the ability to reason, bridging the gap between data-driven learning and logical reasoning. Within this context, Neural Algorithmic Reasoning (NAR) stands out as a promising research field, aiming to integrate the structured and rule-based reasoning of algorithms with the adaptive learning capabilities of neural networks, typically by tasking neural models to mimic classical algorithms. In this dissertation, we provide theoretical and practical contributions to this area of research. We explore the connections between neural networks and tropical algebra, deriving powerful architectures that are aligned with algorithm execution. Furthermore, we discuss and show the ability of such neural reasoners to learn and manipulate complex algorithmic and combinatorial optimization concepts, such as the principle of strong duality. Finally, in our empirical efforts, we validate the real-world utility of NAR networks across different practical scenarios. This includes tasks as diverse as planning problems, large-scale edge classification tasks and the learning of polynomial-time approximate algorithms for NP-hard combinatorial problems. Through this exploration, we aim to showcase the potential integrating algorithmic reasoning in machine learning models.

Complex logical reasoning tasks require a long sequence of reasoning, which a large language model (LLM) with chain-of-thought prompting still falls short. To alleviate this issue, neurosymbolic approaches incorporate a symbolic solver. Specifically, an LLM only translates a natural language problem into a satisfiability (SAT) problem that consists of first-order logic formulas, and a sound symbolic solver returns a mathematically correct solution. However, we discover that LLMs have difficulties to capture complex logical semantics hidden in the natural language during translation. To resolve this limitation, we propose a Compositional First-Order Logic Translation. An LLM first parses a natural language sentence into newly defined logical dependency structures that consist of an atomic subsentence and its dependents, then sequentially translate the parsed subsentences. Since multiple logical dependency structures and sequential translations are possible for a single sentence, we also introduce two Verification algorithms to ensure more reliable results. We utilize an SAT solver to rigorously compare semantics of generated first-order logic formulas and select the most probable one. We evaluate the proposed method, dubbed CLOVER, on seven logical reasoning benchmarks and show that it outperforms the previous neurosymbolic approaches and achieves new state-of-the-art results.

Decoding language from brain activity is a long-awaited goal in both healthcare and neuroscience. Major milestones have recently been reached thanks to intracranial devices: subject-specific pipelines trained on invasive brain responses to basic language tasks now start to efficiently decode interpretable features (e.g. letters, words, spectrograms). However, scaling this approach to natural speech and non-invasive brain recordings remains a major challenge. Here, we propose a single end-to-end architecture trained with contrastive learning across a large cohort of individuals to predict self-supervised representations of natural speech. We evaluate our model on four public datasets, encompassing 169 volunteers recorded with magneto- or electro-encephalography (M/EEG), while they listened to natural speech. The results show that our model can identify, from 3s of MEG signals, the corresponding speech segment with up to 72.5% top-10 accuracy out of 1,594 distinct segments (and 44% top-1 accuracy), and up to 19.1% out of 2,604 segments for EEG recordings -- hence allowing the decoding of phrases absent from the training set. Model comparison and ablation analyses show that these performances directly benefit from our original design choices, namely the use of (i) a contrastive objective, (ii) pretrained representations of speech and (iii) a common convolutional architecture simultaneously trained across several participants. Together, these results delineate a promising path to decode natural language processing in real time from non-invasive recordings of brain activity.

Most efforts to improve the reasoning capabilities of large language models (LLMs) involve either scaling the number of parameters and the size of training data, or scaling inference computation by letting models generate complex chains of thought. Motivated by interpretability studies showing that the crucial computation required for reasoning tasks is concentrated in a limited range of layers, we introduce Encode-Think-Decode (ETD), a method that enhances the reasoning capabilities of a base model by training it to iterate over a small subset of reasoning-relevant layers during the mid-training stage. ETD amplifies latent reasoning while preserving the original architecture, parameter count, hyperparameters, and training data composition. When iterating on the selected layers at inference time, ETD models yield substantial gains on 17 reasoning benchmarks, including +28.4% relative accuracy improvement on GSM8K and +36% on MATH with the OLMo-2 1B Base model. We also explore an adaptive depth strategy that adjusts the computation per input token. Our results show that recursive latent reasoning offers a simple and effective path to stronger LLM reasoning.

Large Language Models (LLMs) achieve strong performance on natural language tasks but remain unreliable in mathematical reasoning, frequently generating fluent yet logically inconsistent solutions. We present NeuroProlog, a neurosymbolic framework that ensures verifiable reasoning by compiling math word problems into executable Prolog programs with formal verification guarantees. We propose a multi-task Cocktail training strategy that jointly optimizes three synergistic objectives in a unified symbolic representation space: (i) mathematical formula-to-rule translation (KB), (ii) natural language-to-program synthesis (SOLVE), and (iii) program-answer alignment. This joint supervision enables positive transfer, where symbolic grounding in formula translation directly improves compositional reasoning capabilities. At inference, we introduce an execution-guided decoding pipeline with fine-grained error taxonomy that enables iterative program repair and quantifies model self-debugging capacity. Comprehensive evaluation on GSM8K across four model scales (3B--32B parameters) demonstrates consistent improvements: cocktail training achieves significant accuracy gains of +5.23\% (Qwen-32B, p < 0.01), +3.43\% (GPT-OSS-20B, p < 0.01), and +5.54\% (Llama-3B, p < 0.05) over single-task baselines. Systematic error analysis reveals scale-dependent learning dynamics: at 32B scale, cocktail training transforms unfixable type errors (12\% repair rate) into correctable domain errors (96\% repair rate), achieving 92.7\% overall correction; at 8B scale, the same training eliminates syntactic errors but introduces semantic failures, revealing a critical capacity threshold for type-safe symbolic reasoning.

Neurosymbolic (NeSy) frameworks combine neural representations and learning with symbolic representations and reasoning. Combining the reasoning capacities, explainability, and interpretability of symbolic processing with the flexibility and power of neural computing allows us to solve complex problems with more reliability while being data-efficient. However, this recently growing topic poses a challenge to developers with its learning curve, lack of user-friendly tools, libraries, and unifying frameworks. In this paper, we characterize the technical facets of existing NeSy frameworks, such as the symbolic representation language, integration with neural models, and the underlying algorithms. A majority of the NeSy research focuses on algorithms instead of providing generic frameworks for declarative problem specification to leverage problem solving. To highlight the key aspects of Neurosymbolic modeling, we showcase three generic NeSy frameworks - DeepProbLog, Scallop, and DomiKnowS. We identify the challenges within each facet that lay the foundation for identifying the expressivity of each framework in solving a variety of problems. Building on this foundation, we aim to spark transformative action and encourage the community to rethink this problem in novel ways.

The escalating demand for efficient decoding in large language models (LLMs) is particularly critical for reasoning-intensive architectures like OpenAI-o3 and DeepSeek-R1, which depend on extended chain-of-thought reasoning. This study investigates speculative decoding techniques through dense LLM architectures to establish foundational insights for accelerating reasoning tasks. While speculative decoding methods leveraging parallel draft-verification cycles have emerged as promising acceleration techniques, the scaling laws governing decoding efficiency remain under-explored compared to conventional backbone LLMs developed through Pretraining->SFT->RLHF training paradigms. In this work, we discover Log-linear Scaling Laws (Theorem 1.1, 1.2 and 1.3) governing draft model acceptance rate (or decoding speed) across three dimensions: pretraining token volume, draft model capacity, and decoding batch size. Building on these laws, we achieve Scylla, which coordinates multi-dimensional scaling for popular LLMs (Llama2/3, Qwen2.5). Empirical validation shows Scylla achieves 1.5-2.2 higher acceptance rate than EAGLE2 and 0.3 higher than EAGLE3 at temperature T = 0, with peak performance gains on summarization and QA tasks (Figure 2). Industrial inference engine deployments demonstrate 2X decoding throughput improvements over EAGLE2 (Table 5), validating the transformative potential of systematic scaling for efficient LLM inference. Code will be released later.

Large language models (LLMs) have demonstrated impressive capabilities in natural language understanding and generation, but they exhibit problems with logical consistency in the output they generate. How can we harness LLMs' broad-coverage parametric knowledge in formal reasoning despite their inconsistency? We present a method for directly integrating an LLM into the interpretation function of the formal semantics for a paraconsistent logic. We provide experimental evidence for the feasibility of the method by evaluating the function using datasets created from several short-form factuality benchmarks. Unlike prior work, our method offers a theoretical framework for neuro-symbolic reasoning that leverages an LLM's knowledge while preserving the underlying logic's soundness and completeness properties.

Large reasoning models (LRMs) achieve strong reasoning performance by emitting long chains of thought. Yet, these verbose traces slow down inference and often drift into unnecessary detail, known as the overthinking phenomenon. To better understand LRMs' behavior, we systematically analyze the token-level misalignment between reasoning and non-reasoning models. While it is expected that their primary difference lies in the stylistic "thinking cues", LRMs uniquely exhibit two pivotal, previously under-explored phenomena: a Global Misalignment Rebound, where their divergence from non-reasoning models persists or even grows as response length increases, and more critically, a Local Misalignment Diminish, where the misalignment concentrates at the "thinking cues" each sentence starts with but rapidly declines in the remaining of the sentence. Motivated by the Local Misalignment Diminish, we propose FoReaL-Decoding, a collaborative fast-slow thinking decoding method for cost-quality trade-off. In FoReaL-Decoding, a Leading model leads the first few tokens for each sentence, and then a weaker draft model completes the following tokens to the end of each sentence. FoReaL-Decoding adopts a stochastic gate to smoothly interpolate between the small and the large model. On four popular math-reasoning benchmarks (AIME24, GPQA-Diamond, MATH500, AMC23), FoReaL-Decoding reduces theoretical FLOPs by 30 to 50% and trims CoT length by up to 40%, while preserving 86 to 100% of model performance. These results establish FoReaL-Decoding as a simple, plug-and-play route to controllable cost-quality trade-offs in reasoning-centric tasks.

Parallel neurosymbolic architectures have been applied effectively in NLP by distilling knowledge from a logic theory into a deep model.However, prior art faces several limitations including supporting restricted forms of logic theories and relying on the assumption of independence between the logic and the deep network. We present Concordia, a framework overcoming the limitations of prior art. Concordia is agnostic both to the deep network and the logic theory offering support for a wide range of probabilistic theories. Our framework can support supervised training of both components and unsupervised training of the neural component. Concordia has been successfully applied to tasks beyond NLP and data classification, improving the accuracy of state-of-the-art on collective activity detection, entity linking and recommendation tasks.

Finding a code to unravel the population of neural responses that leads to a distinct animal behavior has been a long-standing question in the field of neuroscience. With the recent advances in machine learning, it is shown that the hierarchically Deep Neural Networks (DNNs) perform optimally in decoding unique features out of complex datasets. In this study, we utilize the power of a DNN to explore the computational principles in the mammalian brain by exploiting the Neuropixel data from Allen Brain Institute. We decode the neural responses from mouse visual cortex to predict the presented stimuli to the animal for natural (bear, trees, cheetah, etc.) and artificial (drifted gratings, orientated bars, etc.) classes. Our results indicate that neurons in mouse visual cortex encode the features of natural and artificial objects in a distinct manner, and such neural code is consistent across animals. We investigate this by applying transfer learning to train a DNN on the neural responses of a single animal and test its generalized performance across multiple animals. Within a single animal, DNN is able to decode the neural responses with as much as 100% classification accuracy. Across animals, this accuracy is reduced to 91%. This study demonstrates the potential of utilizing the DNN models as a computational framework to understand the neural coding principles in the mammalian brain.

Large language models (LLMs) currently suffer from parameter entanglement, where general reasoning capabilities (logic) and specific factual knowledge (facts) exist in a superposition state within shared weights. This coupling leads to the "memory wall," where computational capacity is squandered on simulating retrieval, often resulting in hallucinations. In this paper, we propose "digital metabolism," a thermodynamic hypothesis suggesting that targeted forgetting is necessary for distilling a pure neural logic core. To validate this hypothesis, we introduce the Regenerative Logic-Core Protocol (RLCP), a dual-stream training framework that renders specific factual dependencies linearly undecodable via deep-layer gradient reversal. Applying RLCP to Qwen2.5-0.5B, we observe a distinct phase transition: the model achieves near-zero retention of targeted factual associations (Accuracy < 7%) while exhibiting changes consistent with an emergent "structural crystallization" effect. Empirical analysis on GSM8K reveals that the "metabolized" model spontaneously adopts chain-of-thought (CoT) scaffolding, which we interpret as compensating for the loss of direct associative recall (shifting from O(1) recall to O(N) reasoning). While the causal mechanism underlying this behavioral shift requires further investigation, our findings provide a dynamic weight-level counterpart to architectural innovations like DeepSeek's Engram, paving the way for modular "Neural CPU + Symbolic RAM" architectures.

Decoding non-invasive brain recordings is pivotal for advancing our understanding of human cognition but faces challenges due to individual differences and complex neural signal representations. Traditional methods often require customized models and extensive trials, lacking interpretability in visual reconstruction tasks. Our framework integrates 3D brain structures with visual semantics using a Vision Transformer 3D. This unified feature extractor efficiently aligns fMRI features with multiple levels of visual embeddings, eliminating the need for subject-specific models and allowing extraction from single-trial data. The extractor consolidates multi-level visual features into one network, simplifying integration with Large Language Models (LLMs). Additionally, we have enhanced the fMRI dataset with diverse fMRI-image-related textual data to support multimodal large model development. Integrating with LLMs enhances decoding capabilities, enabling tasks such as brain captioning, complex reasoning, concept localization, and visual reconstruction. Our approach demonstrates superior performance across these tasks, precisely identifying language-based concepts within brain signals, enhancing interpretability, and providing deeper insights into neural processes. These advances significantly broaden the applicability of non-invasive brain decoding in neuroscience and human-computer interaction, setting the stage for advanced brain-computer interfaces and cognitive models.

The end-to-end nature of neural machine translation (NMT) removes many ways of manually guiding the translation process that were available in older paradigms. Recent work, however, has introduced a new capability: lexically constrained or guided decoding, a modification to beam search that forces the inclusion of pre-specified words and phrases in the output. However, while theoretically sound, existing approaches have computational complexities that are either linear (Hokamp and Liu, 2017) or exponential (Anderson et al., 2017) in the number of constraints. We present a algorithm for lexically constrained decoding with a complexity of O(1) in the number of constraints. We demonstrate the algorithms remarkable ability to properly place these constraints, and use it to explore the shaky relationship between model and BLEU scores. Our implementation is available as part of Sockeye.

Visual encoding and decoding models act as gateways to understanding the neural mechanisms underlying human visual perception. Typically, visual encoding models that predict brain activity from stimuli and decoding models that reproduce stimuli from brain activity are treated as distinct tasks, requiring separate models and training procedures. This separation is inefficient and fails to model the consistency between encoding and decoding processes. To address this limitation, we propose NeuroFlow, the first unified framework that jointly models visual encoding and decoding from neural activity within a single flow model. NeuroFlow introduces two key components: (1) NeuroVAE is designed as a variational backbone to model neural variability and establish a compact, semantically structured latent space for bidirectional modeling across visual and neural modalities. (2) Cross-modal Flow Matching (XFM) bypasses the typical paradigm of noise-to-data diffusion guided by a specific modality condition, instead learning a reversibly consistent flow model between visual and neural latent distributions. For the first time, visual encoding and decoding are reformulated as a time-dependent, reversible process within a shared latent space for unified modeling. Empirical results demonstrate that NeuroFlow achieves superior overall performance in visual encoding and decoding tasks with higher computational efficiency compared to any isolated methods. We further analyze principal factors that steer the model toward encoding-decoding consistency and, through brain functional analyses, demonstrate that NeuroFlow captures consistent activation patterns underlying neural variability. NeuroFlow marks a major step toward unified visual encoding and decoding from neural activity, providing mechanistic insights that inform future bidirectional visual brain-computer interfaces.

We study the problem of combining neural networks with symbolic reasoning. Recently introduced frameworks for Probabilistic Neurosymbolic Learning (PNL), such as DeepProbLog, perform exponential-time exact inference, limiting the scalability of PNL solutions. We introduce Approximate Neurosymbolic Inference (A-NeSI): a new framework for PNL that uses neural networks for scalable approximate inference. A-NeSI 1) performs approximate inference in polynomial time without changing the semantics of probabilistic logics; 2) is trained using data generated by the background knowledge; 3) can generate symbolic explanations of predictions; and 4) can guarantee the satisfaction of logical constraints at test time, which is vital in safety-critical applications. Our experiments show that A-NeSI is the first end-to-end method to solve three neurosymbolic tasks with exponential combinatorial scaling. Finally, our experiments show that A-NeSI achieves explainability and safety without a penalty in performance.

Brain decoding, a pivotal field in neuroscience, aims to reconstruct stimuli from acquired brain signals, primarily utilizing functional magnetic resonance imaging (fMRI). Currently, brain decoding is confined to a per-subject-per-model paradigm, limiting its applicability to the same individual for whom the decoding model is trained. This constraint stems from three key challenges: 1) the inherent variability in input dimensions across subjects due to differences in brain size; 2) the unique intrinsic neural patterns, influencing how different individuals perceive and process sensory information; 3) limited data availability for new subjects in real-world scenarios hampers the performance of decoding models. In this paper, we present a novel approach, MindBridge, that achieves cross-subject brain decoding by employing only one model. Our proposed framework establishes a generic paradigm capable of addressing these challenges by introducing biological-inspired aggregation function and novel cyclic fMRI reconstruction mechanism for subject-invariant representation learning. Notably, by cycle reconstruction of fMRI, MindBridge can enable novel fMRI synthesis, which also can serve as pseudo data augmentation. Within the framework, we also devise a novel reset-tuning method for adapting a pretrained model to a new subject. Experimental results demonstrate MindBridge's ability to reconstruct images for multiple subjects, which is competitive with dedicated subject-specific models. Furthermore, with limited data for a new subject, we achieve a high level of decoding accuracy, surpassing that of subject-specific models. This advancement in cross-subject brain decoding suggests promising directions for wider applications in neuroscience and indicates potential for more efficient utilization of limited fMRI data in real-world scenarios. Project page: https://littlepure2333.github.io/MindBridge

Speculative decoding is a technique that uses multiple language models to accelerate infer- ence. Previous works have used an experi- mental approach to optimize the throughput of the inference pipeline, which involves LLM training and can be costly. This study of spec- ulative decoding proposes a theory that ana- lytically connects the key hyperparameters of pre-trained LLMs to the throughput efficiency of a downstream SD-based inference system. The theory allows the prediction of throughput- optimal hyperparameters for the components of an inference system before their pre-training.

We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic processor for objects with properties, relations, logic connectives, and quantifiers. After being trained on small-scale tasks (such as sorting short arrays), NLMs can recover lifted rules, and generalize to large-scale tasks (such as sorting longer arrays). In our experiments, NLMs achieve perfect generalization in a number of tasks, from relational reasoning tasks on the family tree and general graphs, to decision making tasks including sorting arrays, finding shortest paths, and playing the blocks world. Most of these tasks are hard to accomplish for neural networks or inductive logic programming alone.

Predictive coding networks are neuroscience-inspired models with roots in both Bayesian statistics and neuroscience. Training such models, however, is quite inefficient and unstable. In this work, we show how by simply changing the temporal scheduling of the update rule for the synaptic weights leads to an algorithm that is much more efficient and stable than the original one, and has theoretical guarantees in terms of convergence. The proposed algorithm, that we call incremental predictive coding (iPC) is also more biologically plausible than the original one, as it it fully automatic. In an extensive set of experiments, we show that iPC constantly performs better than the original formulation on a large number of benchmarks for image classification, as well as for the training of both conditional and masked language models, in terms of test accuracy, efficiency, and convergence with respect to a large set of hyperparameters.

Despite the tremendous success, existing machine learning models still fall short of human-like systematic generalization -- learning compositional rules from limited data and applying them to unseen combinations in various domains. We propose Neural-Symbolic Recursive Machine (NSR) to tackle this deficiency. The core representation of NSR is a Grounded Symbol System (GSS) with combinatorial syntax and semantics, which entirely emerges from training data. Akin to the neuroscience studies suggesting separate brain systems for perceptual, syntactic, and semantic processing, NSR implements analogous separate modules of neural perception, syntactic parsing, and semantic reasoning, which are jointly learned by a deduction-abduction algorithm. We prove that NSR is expressive enough to model various sequence-to-sequence tasks. Superior systematic generalization is achieved via the inductive biases of equivariance and recursiveness embedded in NSR. In experiments, NSR achieves state-of-the-art performance in three benchmarks from different domains: SCAN for semantic parsing, PCFG for string manipulation, and HINT for arithmetic reasoning. Specifically, NSR achieves 100% generalization accuracy on SCAN and PCFG and outperforms state-of-the-art models on HINT by about 23%. Our NSR demonstrates stronger generalization than pure neural networks due to its symbolic representation and inductive biases. NSR also demonstrates better transferability than existing neural-symbolic approaches due to less domain-specific knowledge required.

Visual decoding from brain signals is a key challenge at the intersection of computer vision and neuroscience, requiring methods that bridge neural representations and computational models of vision. A field-wide goal is to achieve generalizable, cross-subject models. A major obstacle towards this goal is the substantial variability in neural representations across individuals, which has so far required training bespoke models or fine-tuning separately for each subject. To address this challenge, we introduce a meta-optimized approach for semantic visual decoding from fMRI that generalizes to novel subjects without any fine-tuning. By simply conditioning on a small set of image-brain activation examples from the new individual, our model rapidly infers their unique neural encoding patterns to facilitate robust and efficient visual decoding. Our approach is explicitly optimized for in-context learning of the new subject's encoding model and performs decoding by hierarchical inference, inverting the encoder. First, for multiple brain regions, we estimate the per-voxel visual response encoder parameters by constructing a context over multiple stimuli and responses. Second, we construct a context consisting of encoder parameters and response values over multiple voxels to perform aggregated functional inversion. We demonstrate strong cross-subject and cross-scanner generalization across diverse visual backbones without retraining or fine-tuning. Moreover, our approach requires neither anatomical alignment nor stimulus overlap. This work is a critical step towards a generalizable foundation model for non-invasive brain decoding.

Current advances in Artificial Intelligence (AI) and Machine Learning (ML) have achieved unprecedented impact across research communities and industry. Nevertheless, concerns about trust, safety, interpretability and accountability of AI were raised by influential thinkers. Many have identified the need for well-founded knowledge representation and reasoning to be integrated with deep learning and for sound explainability. Neural-symbolic computing has been an active area of research for many years seeking to bring together robust learning in neural networks with reasoning and explainability via symbolic representations for network models. In this paper, we relate recent and early research results in neurosymbolic AI with the objective of identifying the key ingredients of the next wave of AI systems. We focus on research that integrates in a principled way neural network-based learning with symbolic knowledge representation and logical reasoning. The insights provided by 20 years of neural-symbolic computing are shown to shed new light onto the increasingly prominent role of trust, safety, interpretability and accountability of AI. We also identify promising directions and challenges for the next decade of AI research from the perspective of neural-symbolic systems.

Symbolic logical reasoning is a critical yet underexplored capability of large language models (LLMs), providing reliable and verifiable decision-making in high-stakes domains such as mathematical reasoning and legal judgment. In this study, we present a systematic analysis of logical reasoning under controlled increases in logical complexity, and reveal a previously unrecognized phenomenon, which we term Logical Phase Transitions: rather than degrading smoothly, logical reasoning performance remains stable within a regime but collapses abruptly beyond a critical logical depth, mirroring physical phase transitions such as water freezing beyond a critical temperature threshold. Building on this insight, we propose Neuro-Symbolic Curriculum Tuning, a principled framework that adaptively aligns natural language with logical symbols to establish a shared representation, and reshapes training dynamics around phase-transition boundaries to progressively strengthen reasoning at increasing logical depths. Experiments on five benchmarks show that our approach effectively mitigates logical reasoning collapse at high complexity, yielding average accuracy gains of +1.26 in naive prompting and +3.95 in CoT, while improving generalization to unseen logical compositions. Code and data are available at https://github.com/AI4SS/Logical-Phase-Transitions.

Do large language models (LLMs) solve reasoning tasks by learning robust generalizable algorithms, or do they memorize training data? To investigate this question, we use arithmetic reasoning as a representative task. Using causal analysis, we identify a subset of the model (a circuit) that explains most of the model's behavior for basic arithmetic logic and examine its functionality. By zooming in on the level of individual circuit neurons, we discover a sparse set of important neurons that implement simple heuristics. Each heuristic identifies a numerical input pattern and outputs corresponding answers. We hypothesize that the combination of these heuristic neurons is the mechanism used to produce correct arithmetic answers. To test this, we categorize each neuron into several heuristic types-such as neurons that activate when an operand falls within a certain range-and find that the unordered combination of these heuristic types is the mechanism that explains most of the model's accuracy on arithmetic prompts. Finally, we demonstrate that this mechanism appears as the main source of arithmetic accuracy early in training. Overall, our experimental results across several LLMs show that LLMs perform arithmetic using neither robust algorithms nor memorization; rather, they rely on a "bag of heuristics".

Large language models (LLMs) exhibit strong reasoning abilities, often attributed to few-shot or zero-shot chain-of-thought (CoT) prompting. While effective, these methods require labor-intensive prompt engineering, raising the question of whether reasoning can be induced without reliance on explicit prompts. In this work, we unlock the reasoning capabilities of LLMs without explicit prompting. Inspired by zero-shot CoT and CoT-decoding, we propose a novel decoding strategy that systematically nudges LLMs to continue reasoning, thereby preventing immature reasoning processes. Specifically, we monitor the model's generation and inject a designated phrase whenever it is likely to conclude its response prematurely, before completing the reasoning process. Our experimental evaluations on diverse reasoning benchmarks demonstrate that our proposed strategy substantially improves LLM reasoning capabilities, highlighting the potential of decoding-based interventions as an alternative to traditional prompting techniques.

To mitigate the high inference latency stemming from autoregressive decoding in Large Language Models (LLMs), Speculative Decoding has emerged as a novel decoding paradigm for LLM inference. In each decoding step, this method first efficiently drafts several future tokens and then verifies them in parallel. Unlike autoregressive decoding, Speculative Decoding facilitates the simultaneous decoding of multiple tokens per step, thereby accelerating inference. This paper presents a comprehensive overview and analysis of this promising decoding paradigm. We begin by providing a formal definition and formulation of Speculative Decoding. Then, we organize in-depth discussions on its key facets, including current leading techniques, the challenges faced, and potential future directions in this field. We aim for this work to serve as a catalyst for further research on Speculative Decoding, ultimately contributing to more efficient LLM inference.

Natural generation allows Large Language Models (LLMs) to produce free-form responses with rich reasoning, yet the lack of structure makes outputs difficult to verify. Conversely, constrained decoding ensures standardized formats but can inadvertently restrict reasoning capabilities by imposing constraints too early in the generation process. We propose a hybrid approach, namely In-Writing, that combines free-form reasoning and structured generation in a single call. The model first performs unconstrained reasoning and only applies structured decoding after a trigger token is generated, explicitly decoupling reasoning from formatting. We establish that our trigger-token strategies are able to virtually eradicate premature triggering, a failure mode in which constrained decoding interrupts on-going reasoning. Evaluations across diverse datasets covering classification and reasoning tasks demonstrate that our approach outperforms the state-of-the-art by achieving accuracy gains of up to 27% over natural generation. Our code are available at: https://github.com/Nokia-Bell-Labs/InWriting.

Inference-time scaling has emerged as a powerful alternative to parameter scaling for improving language model performance on complex reasoning tasks. While existing methods have shown strong performance gains under fixed compute budgets, there has been little focus on optimally utilizing that budget during inference. In this work, we introduce A*-decoding, a search-based inference-time strategy that builds on the A* search algorithm to optimally utilize a fixed compute budget by prioritizing high-quality reasoning paths during generation. We frame language model decoding as a structured search in a state space of partial solutions, applying the A* transition model to identify promising continuations guided by an external process supervision signal. In our experiments, A*-decoding reaches the performance levels of strong inference scaling baselines like best-of-N and particle filtering while using up to 3x fewer tokens and 30% fewer PRM passes under equivalent compute budgets. On the MATH500 and AIME 2024 benchmarks, A*-decoding enables Llama-3.2-1B-Instruct to match the performance of the 70x larger Llama-3.1-70B-Instruct, and allows Qwen3-1.7B to reach o1-like reasoning accuracy. These results highlight the power of structured search in decoding, offering an alternative to brute-force sampling or scale-driven gains. Our work demonstrates how thoughtful inference-time strategies can enhance reasoning in SLMs, pointing toward future advances in more efficient and scalable language model deployment.

Recent advancements in large language models have showcased their remarkable generalizability across various domains. However, their reasoning abilities still have significant room for improvement, especially when confronted with scenarios requiring multi-step reasoning. Although large language models possess extensive knowledge, their behavior, particularly in terms of reasoning, often fails to effectively utilize this knowledge to establish a coherent thinking paradigm. Generative language models sometimes show hallucinations as their reasoning procedures are unconstrained by logical principles. Aiming to improve the zero-shot chain-of-thought reasoning ability of large language models, we propose Logical Chain-of-Thought (LogiCoT), a neurosymbolic framework that leverages principles from symbolic logic to verify and revise the reasoning processes accordingly. Experimental evaluations conducted on language tasks in diverse domains, including arithmetic, commonsense, symbolic, causal inference, and social problems, demonstrate the efficacy of the enhanced reasoning paradigm by logic.

Identifying what individual neurons encode in higher-order visual cortex is an open problem. Responses resist intuitive parameterization, and the deep-network embeddings used in their place are black boxes. Here, we introduce NEURRATOR, a framework that decodes spiking activity into free-form natural-language narration of the viewed scene at single-neuron resolution. A learned encoder maps spike trains from arbitrary subsets of simultaneously-recorded neurons into the patch-embedding space of a frozen CLIP, from which a multimodal language model and sparse autoencoder generates and validates a description with no language-side training. Applied to Neuropixel recordings of mouse visual cortex during natural-movie viewing, NEURRATOR narrates from thousands of neurons, singular cortical regions, local populations, or from a molecularly-defined cell-types. We use this property to (i) quantify how decoding fidelity scales with population size and cortical region, and (ii) "neurrate", in plain language, what individual neurons and genetically-tagged inhibitory cell-types contribute to visual representation. This recasts cell identity from a classification target into a functional probe of the visual system, providing a new unit of biological insights in neural systems.

Modern neuroprostheses can now restore communication in patients who have lost the ability to speak or move. However, these invasive devices entail risks inherent to neurosurgery. Here, we introduce a non-invasive method to decode the production of sentences from brain activity and demonstrate its efficacy in a cohort of 35 healthy volunteers. For this, we present Brain2Qwerty, a new deep learning architecture trained to decode sentences from either electro- (EEG) or magneto-encephalography (MEG), while participants typed briefly memorized sentences on a QWERTY keyboard. With MEG, Brain2Qwerty reaches, on average, a character-error-rate (CER) of 32% and substantially outperforms EEG (CER: 67%). For the best participants, the model achieves a CER of 19%, and can perfectly decode a variety of sentences outside of the training set. While error analyses suggest that decoding depends on motor processes, the analysis of typographical errors suggests that it also involves higher-level cognitive factors. Overall, these results narrow the gap between invasive and non-invasive methods and thus open the path for developing safe brain-computer interfaces for non-communicating patients.

In the past five years, the use of generative and foundational AI systems has greatly improved the decoding of brain activity. Visual perception, in particular, can now be decoded from functional Magnetic Resonance Imaging (fMRI) with remarkable fidelity. This neuroimaging technique, however, suffers from a limited temporal resolution (approx0.5 Hz) and thus fundamentally constrains its real-time usage. Here, we propose an alternative approach based on magnetoencephalography (MEG), a neuroimaging device capable of measuring brain activity with high temporal resolution (approx5,000 Hz). For this, we develop an MEG decoding model trained with both contrastive and regression objectives and consisting of three modules: i) pretrained embeddings obtained from the image, ii) an MEG module trained end-to-end and iii) a pretrained image generator. Our results are threefold: Firstly, our MEG decoder shows a 7X improvement of image-retrieval over classic linear decoders. Second, late brain responses to images are best decoded with DINOv2, a recent foundational image model. Third, image retrievals and generations both suggest that high-level visual features can be decoded from MEG signals, although the same approach applied to 7T fMRI also recovers better low-level features. Overall, these results, while preliminary, provide an important step towards the decoding -- in real-time -- of the visual processes continuously unfolding within the human brain.

Recent advances in Reasoning LLMs (e.g., DeepSeek-R1 and OpenAI-o1) have showcased impressive reasoning capabilities via reinforcement learning. However, extending these capabilities to Multimodal LLMs (MLLMs) is hampered by the prohibitive costs of retraining and the scarcity of high-quality, verifiable multimodal reasoning datasets. This paper introduces FRANK Model, a training-FRee ANd r1-liKe MLLM that imbues off-the-shelf MLLMs with reasoning and reflection abilities, without any gradient updates or extra supervision. Our key insight is to decouple perception and reasoning across MLLM decoder layers. Specifically, we observe that compared to the deeper decoder layers, the shallow decoder layers allocate more attention to visual tokens, while the deeper decoder layers concentrate on textual semantics. This observation motivates a hierarchical weight merging approach that combines a visual-pretrained MLLM with a reasoning-specialized LLM. To this end, we propose a layer-wise, Taylor-derived closed-form fusion mechanism that integrates reasoning capacity into deep decoder layers while preserving visual grounding in shallow decoder layers. Extensive experiments on challenging multimodal reasoning benchmarks demonstrate the effectiveness of our approach. On the MMMU benchmark, our model FRANK-38B achieves an accuracy of 69.2, outperforming the strongest baseline InternVL2.5-38B by +5.3, and even surpasses the proprietary GPT-4o model. Our project homepage is at: http://iip.whu.edu.cn/frank/index.html

Hierarchical classification offers an approach to incorporate the concept of mistake severity by leveraging a structured, labeled hierarchy. However, decoding in such settings frequently relies on heuristic decision rules, which may not align with task-specific evaluation metrics. In this work, we propose a framework for the optimal decoding of an output probability distribution with respect to a target metric. We derive optimal decision rules for increasingly complex prediction settings, providing universal algorithms when candidates are limited to the set of nodes. In the most general case of predicting a subset of nodes, we focus on rules dedicated to the hierarchical hF_{beta} scores, tailored to hierarchical settings. To demonstrate the practical utility of our approach, we conduct extensive empirical evaluations, showcasing the superiority of our proposed optimal strategies, particularly in underdetermined scenarios. These results highlight the potential of our methods to enhance the performance and reliability of hierarchical classifiers in real-world applications. The code is available at https://github.com/RomanPlaud/hierarchical_decision_rules

The "Reversal Curse" refers to the scenario where auto-regressive decoder large language models (LLMs), such as ChatGPT, trained on "A is B" fail to learn "B is A", demonstrating a basic failure of logical deduction. This raises a red flag in the use of GPT models for certain general tasks such as constructing knowledge graphs, considering their adherence to this symmetric principle. In our study, we examined a bidirectional LLM, BERT, and found that it is immune to the reversal curse. Driven by ongoing efforts to construct biomedical knowledge graphs with LLMs, we also embarked on evaluating more complex but essential deductive reasoning capabilities. This process included first training encoder and decoder language models to master the intersection (cap) and union (cup) operations on two sets and then moving on to assess their capability to infer different combinations of union (cup) and intersection (cap) operations on three newly created sets. The findings showed that while both encoder and decoder language models, trained for tasks involving two sets (union/intersection), were proficient in such scenarios, they encountered difficulties when dealing with operations that included three sets (various combinations of union and intersection). Our research highlights the distinct characteristics of encoder and decoder models in simple and complex logical reasoning. In practice, the choice between BERT and GPT should be guided by the specific requirements and nature of the task at hand, leveraging their respective strengths in bidirectional context comprehension and sequence prediction.

For half a century, artificial intelligence research has attempted to reproduce the human qualities of abstraction and reasoning - creating computer systems that can learn new concepts from a minimal set of examples, in settings where humans find this easy. While specific neural networks are able to solve an impressive range of problems, broad generalisation to situations outside their training data has proved elusive.In this work, we look at several novel approaches for solving the Abstraction & Reasoning Corpus (ARC), a dataset of abstract visual reasoning tasks introduced to test algorithms on broad generalization. Despite three international competitions with $100,000 in prizes, the best algorithms still fail to solve a majority of ARC tasks and rely on complex hand-crafted rules, without using machine learning at all. We revisit whether recent advances in neural networks allow progress on this task. First, we adapt the DreamCoder neurosymbolic reasoning solver to ARC. DreamCoder automatically writes programs in a bespoke domain-specific language to perform reasoning, using a neural network to mimic human intuition. We present the Perceptual Abstraction and Reasoning Language (PeARL) language, which allows DreamCoder to solve ARC tasks, and propose a new recognition model that allows us to significantly improve on the previous best implementation.We also propose a new encoding and augmentation scheme that allows large language models (LLMs) to solve ARC tasks, and find that the largest models can solve some ARC tasks. LLMs are able to solve a different group of problems to state-of-the-art solvers, and provide an interesting way to complement other approaches. We perform an ensemble analysis, combining models to achieve better results than any system alone. Finally, we publish the arckit Python library to make future research on ARC easier.

Recent advances in reasoning models have demonstrated significant improvements in accuracy, particularly for complex tasks such as mathematical reasoning, by employing detailed and comprehensive reasoning processes. However, generating these lengthy reasoning sequences is computationally expensive and time-consuming. To address this inefficiency, we leverage the inherent parallelizability of certain tasks to accelerate the reasoning process. Specifically, when multiple parallel reasoning branches exist, we decode multiple tokens per step using a specialized attention mask, processing them within a single sequence, avoiding additional memory usage. Experimental results show that our method achieves over 100% speedup in decoding time while maintaining the answer quality.

Rule-based models are attractive for various tasks because they inherently lead to interpretable and explainable decisions and can easily incorporate prior knowledge. However, such systems are difficult to apply to problems involving natural language, due to its linguistic variability. In contrast, neural models can cope very well with ambiguity by learning distributed representations of words and their composition from data, but lead to models that are difficult to interpret. In this paper, we describe a model combining neural networks with logic programming in a novel manner for solving multi-hop reasoning tasks over natural language. Specifically, we propose to use a Prolog prover which we extend to utilize a similarity function over pretrained sentence encoders. We fine-tune the representations for the similarity function via backpropagation. This leads to a system that can apply rule-based reasoning to natural language, and induce domain-specific rules from training data. We evaluate the proposed system on two different question answering tasks, showing that it outperforms two baselines -- BIDAF (Seo et al., 2016a) and FAST QA (Weissenborn et al., 2017b) on a subset of the WikiHop corpus and achieves competitive results on the MedHop data set (Welbl et al., 2017).

Recently, Large Reasoning Models (LRMs) have demonstrated remarkable capabilities in code reasoning by scaling up the length of Chain-of-Thought (CoT). However, excessively long reasoning traces introduce substantial challenges in terms of training cost, inference latency, and deployment feasibility. While various CoT compression approaches have emerged to address this challenge, they face inherent trade-offs: token-level methods often disrupt syntactic and logical coherence, while step-level methods based on perplexity fail to reliably capture the logically critical reasoning steps. In this paper, we propose ASAP (Anchor-guided, Surprisal-based Pruning), a novel coarse-to-fine framework for CoT compression. ASAP first performs anchor-guided pruning to preserve the core reasoning structure, which efficiently reduces the search space for subsequent processing. It then enables a logic-aware pruning by selecting logically essential reasoning steps based on a novel first-token surprisal metric. Finally, ASAP teaches models to autonomously generate and leverage these concise CoTs at inference time, enabling efficient reasoning in coding tasks. Experiments show that ASAP achieves state-of-the-art accuracy across multiple code generation benchmarks while substantially reducing training and inference costs. On the challenging LiveCodeBench v4_v5 benchmark, our approach reduces token generation by 23.5% and inference latency by 43.5% compared to the strongest baseline, while achieving a competitive accuracy of 36.19% in Pass@1. Our results highlight a promising direction for building powerful and efficient LRMs.

Every day, the human brain processes an immense volume of visual information, relying on intricate neural mechanisms to perceive and interpret these stimuli. Recent breakthroughs in functional magnetic resonance imaging (fMRI) have enabled scientists to extract visual information from human brain activity patterns. In this study, we present an innovative method for decoding brain activity into meaningful images and captions, with a specific focus on brain captioning due to its enhanced flexibility as compared to brain decoding into images. Our approach takes advantage of cutting-edge image captioning models and incorporates a unique image reconstruction pipeline that utilizes latent diffusion models and depth estimation. We utilized the Natural Scenes Dataset, a comprehensive fMRI dataset from eight subjects who viewed images from the COCO dataset. We employed the Generative Image-to-text Transformer (GIT) as our backbone for captioning and propose a new image reconstruction pipeline based on latent diffusion models. The method involves training regularized linear regression models between brain activity and extracted features. Additionally, we incorporated depth maps from the ControlNet model to further guide the reconstruction process. We evaluate our methods using quantitative metrics for both generated captions and images. Our brain captioning approach outperforms existing methods, while our image reconstruction pipeline generates plausible images with improved spatial relationships. In conclusion, we demonstrate significant progress in brain decoding, showcasing the enormous potential of integrating vision and language to better understand human cognition. Our approach provides a flexible platform for future research, with potential applications in various fields, including neural art, style transfer, and portable devices.

Interpreting the information encoded in model weights remains a fundamental challenge in mechanistic interpretability. In this work, we introduce ROTATE (Rotation-Optimized Token Alignment in weighT spacE), a data-free method requiring no forward passes that disentangles MLP neurons directly in weight space. Our approach relies on a key statistical observation: neurons that encode coherent, monosemantic concepts exhibit high kurtosis when projected onto the model's vocabulary. By optimizing rotations of neuron weights to maximize their vocabulary-space kurtosis, our method recovers sparse, interpretable directions which we name vocabulary channels. Experiments on Llama-3.1-8B-Instruct and Gemma-2-2B-it demonstrate that ROTATE consistently recovers vocabulary channels that are faithful to the neuron's behavior. ablating individual channels selectively disables corresponding input activations or the promotion of specific concepts. Moreover, aggregating channel-level descriptions yields comprehensive neuron descriptions that outperform optimized activation-based baselines by 2-3x in head-to-head comparisons. By providing a data-free decomposition of neuron weights, ROTATE offers a scalable, fine-grained building block for interpreting LMs.

Recent studies have revealed a number of pathologies of neural machine translation (NMT) systems. Hypotheses explaining these mostly suggest there is something fundamentally wrong with NMT as a model or its training algorithm, maximum likelihood estimation (MLE). Most of this evidence was gathered using maximum a posteriori (MAP) decoding, a decision rule aimed at identifying the highest-scoring translation, i.e. the mode. We argue that the evidence corroborates the inadequacy of MAP decoding more than casts doubt on the model and its training algorithm. In this work, we show that translation distributions do reproduce various statistics of the data well, but that beam search strays from such statistics. We show that some of the known pathologies and biases of NMT are due to MAP decoding and not to NMT's statistical assumptions nor MLE. In particular, we show that the most likely translations under the model accumulate so little probability mass that the mode can be considered essentially arbitrary. We therefore advocate for the use of decision rules that take into account the translation distribution holistically. We show that an approximation to minimum Bayes risk decoding gives competitive results confirming that NMT models do capture important aspects of translation well in expectation.

We introduce Reward-Guided Speculative Decoding (RSD), a novel framework aimed at improving the efficiency of inference in large language models (LLMs). RSD synergistically combines a lightweight draft model with a more powerful target model, incorporating a controlled bias to prioritize high-reward outputs, in contrast to existing speculative decoding methods that enforce strict unbiasedness. RSD employs a process reward model to evaluate intermediate decoding steps and dynamically decide whether to invoke the target model, optimizing the trade-off between computational cost and output quality. We theoretically demonstrate that a threshold-based mixture strategy achieves an optimal balance between resource utilization and performance. Extensive evaluations on challenging reasoning benchmarks, including Olympiad-level tasks, show that RSD delivers significant efficiency gains against decoding with the target model only (up to 4.4x fewer FLOPs), while achieving significant better accuracy than parallel decoding method on average (up to +3.5). These results highlight RSD as a robust and cost-effective approach for deploying LLMs in resource-intensive scenarios.

We present a new large-scale electroencephalography (EEG) dataset as part of the THINGS initiative, comprising over 1.6 million visual stimulus trials collected from 20 participants, and totaling more than twice the size of the most popular current benchmark dataset, THINGS-EEG2. Crucially, our data was recorded using a 32-channel consumer-grade wet electrode system costing ~$2.2k, around 27x cheaper than research-grade EEG systems typically used in cognitive neuroscience labs. Our work is one of the first open-source, large-scale EEG resource designed to closely reflect the quality of hardware that is practical to deploy in real-world, downstream applications of brain-computer interfaces (BCIs). We aim to explore the specific question of whether deep neural network-based BCI research and semantic decoding methods can be effectively conducted with such affordable systems, filling an important gap in current literature that is extremely relevant for future research. In our analysis, we not only demonstrate that decoding of high-level semantic information from EEG of visualized images is possible at consumer-grade hardware, but also that our data can facilitate effective EEG-to-Image reconstruction even despite significantly lower signal-to-noise ratios. In addition to traditional benchmarks, we also conduct analyses of EEG-to-Image models that demonstrate log-linear decoding performance with increasing data volume on our data, and discuss the trade-offs between hardware cost, signal fidelity, and the scale of data collection efforts in increasing the size and utility of currently available datasets. Our contributions aim to pave the way for large-scale, cost-effective EEG research with widely accessible equipment, and position our dataset as a unique resource for the democratization and development of effective deep neural models of visual cognition.

Quite surprisingly, exact maximum a posteriori (MAP) decoding of neural language generators frequently leads to low-quality results. Rather, most state-of-the-art results on language generation tasks are attained using beam search despite its overwhelmingly high search error rate. This implies that the MAP objective alone does not express the properties we desire in text, which merits the question: if beam search is the answer, what was the question? We frame beam search as the exact solution to a different decoding objective in order to gain insights into why high probability under a model alone may not indicate adequacy. We find that beam search enforces uniform information density in text, a property motivated by cognitive science. We suggest a set of decoding objectives that explicitly enforce this property and find that exact decoding with these objectives alleviates the problems encountered when decoding poorly calibrated language generation models. Additionally, we analyze the text produced using various decoding strategies and see that, in our neural machine translation experiments, the extent to which this property is adhered to strongly correlates with BLEU.

Decoding approaches are widely used in neuroscience and machine learning to compare stimulus representations across neural systems, such as different brain regions, organisms, and deep learning models. Popular methods include decoding (perceptual) manifolds and alignment metrics such as Representational Similarity Analysis (RSA) and Dynamic Similarity Analysis (DSA), where similarity in decoding representations is interpreted as evidence for similar computation. This paper demonstrates a fundamental weakness behind this approach: it is misleading to assume that representational geometry is representative of a neuronal population as a whole, when such representations may actually be shaped by a very small subset of neurons. We show that the complementary encoding paradigm addresses this issue directly: it characterizes how neurons are organized globally in terms of their responses to a set of data, providing insight into how the decoding representation is implemented by neurons within a population. We demonstrate across experiments in biological systems and deep learning models that (i) surprisingly, similar decoding behavior and high representational alignment can arise from small, non-representative subpopulations of neurons; and critically, (ii) alignment metrics are insensitive to encoding manifold topology (how function is distributed across neurons), despite this being a key signature of differentiation across biological systems. A controlled MNIST experiment provides causal evidence: decoding metrics remain unchanged even when encoding topology is causally manipulated via the training loss. Overall, similarity in decoding behavior, as measured by classic alignment metrics, does not imply similarity in function or computation, motivating the use of encoding manifolds as a complementary tool for comparing neural systems.

Language models have achieved impressive results in natural language processing tasks, but their ability to perform symbolic operations and arithmetic operations, remains limited, which attribute to their learn the rules implicitly from data. We explore how to incorporate compiled neural networks (CoNNs) which weight is specially designed, into the architecture of language models to enable the language model trained by gradient to obtain fully rule comprehension ability. The incorporation of compiled neural networks offers a promising direction for improving the performance of language models on compound tasks, particularly in areas that require a deeper comprehension of abstract rules beyond recognizing patterns in training data. Our method, which call "Neural Comprehension", helps language models achieve absolute accuracy in symbolic operations, thereby enhancing their ability for rule reasoning, symbolic reasoning, and arithmetic reasoning. Our code is publicly available at: https://github.com/WENGSYX/Neural-Comprehension.

Implementing Boolean functions with circuits consisting of logic gates is fundamental in digital computer design. However, the implemented circuit must be exactly equivalent, which hinders generative neural approaches on this task due to their occasionally wrong predictions. In this study, we introduce a generative neural model, the "Circuit Transformer", which eliminates such wrong predictions and produces logic circuits strictly equivalent to given Boolean functions. The main idea is a carefully designed decoding mechanism that builds a circuit step-by-step by generating tokens, which has beneficial "cutoff properties" that block a candidate token once it invalidate equivalence. In such a way, the proposed model works similar to typical LLMs while logical equivalence is strictly preserved. A Markov decision process formulation is also proposed for optimizing certain objectives of circuits. Experimentally, we trained an 88-million-parameter Circuit Transformer to generate equivalent yet more compact forms of input circuits, outperforming existing neural approaches on both synthetic and real world benchmarks, without any violation of equivalence constraints.

While interpretability research has shed light on some internal algorithms utilized by transformer-based LLMs, reasoning in natural language, with its deep contextuality and ambiguity, defies easy categorization. As a result, formulating clear and motivating questions for circuit analysis that rely on well-defined in-domain and out-of-domain examples required for causal interventions is challenging. Although significant work has investigated circuits for specific tasks, such as indirect object identification (IOI), deciphering natural language reasoning through circuits remains difficult due to its inherent complexity. In this work, we take initial steps to characterize causal reasoning in LLMs by analyzing clear-cut cause-and-effect sentences like "I opened an umbrella because it started raining," where causal interventions may be possible through carefully crafted scenarios using GPT-2 small. Our findings indicate that causal syntax is localized within the first 2-3 layers, while certain heads in later layers exhibit heightened sensitivity to nonsensical variations of causal sentences. This suggests that models may infer reasoning by (1) detecting syntactic cues and (2) isolating distinct heads in the final layers that focus on semantic relationships.

We propose a fully spectral, neuro\-symbolic reasoning architecture that leverages Graph Signal Processing (GSP) as the primary computational backbone for integrating symbolic logic and neural inference. Unlike conventional reasoning models that treat spectral graph methods as peripheral components, our approach formulates the entire reasoning pipeline in the graph spectral domain. Logical entities and relationships are encoded as graph signals, processed via learnable spectral filters that control multi-scale information propagation, and mapped into symbolic predicates for rule-based inference. We present a complete mathematical framework for spectral reasoning, including graph Fourier transforms, band-selective attention, and spectral rule grounding. Experiments on benchmark reasoning datasets (ProofWriter, EntailmentBank, bAbI, CLUTRR, and ARC-Challenge) demonstrate improvements in logical consistency, interpretability, and computational efficiency over state\-of\-the\-art neuro\-symbolic models. Our results suggest that GSP provides a mathematically grounded and computationally efficient substrate for robust and interpretable reasoning systems.

Harnessing the statistical power of neural networks to perform language understanding and symbolic reasoning is difficult, when it requires executing efficient discrete operations against a large knowledge-base. In this work, we introduce a Neural Symbolic Machine, which contains (a) a neural "programmer", i.e., a sequence-to-sequence model that maps language utterances to programs and utilizes a key-variable memory to handle compositionality (b) a symbolic "computer", i.e., a Lisp interpreter that performs program execution, and helps find good programs by pruning the search space. We apply REINFORCE to directly optimize the task reward of this structured prediction problem. To train with weak supervision and improve the stability of REINFORCE, we augment it with an iterative maximum-likelihood training process. NSM outperforms the state-of-the-art on the WebQuestionsSP dataset when trained from question-answer pairs only, without requiring any feature engineering or domain-specific knowledge.

Attempts to render deep learning models interpretable, data-efficient, and robust have seen some success through hybridisation with rule-based systems, for example, in Neural Theorem Provers (NTPs). These neuro-symbolic models can induce interpretable rules and learn representations from data via back-propagation, while providing logical explanations for their predictions. However, they are restricted by their computational complexity, as they need to consider all possible proof paths for explaining a goal, thus rendering them unfit for large-scale applications. We present Conditional Theorem Provers (CTPs), an extension to NTPs that learns an optimal rule selection strategy via gradient-based optimisation. We show that CTPs are scalable and yield state-of-the-art results on the CLUTRR dataset, which tests systematic generalisation of neural models by learning to reason over smaller graphs and evaluating on larger ones. Finally, CTPs show better link prediction results on standard benchmarks in comparison with other neural-symbolic models, while being explainable. All source code and datasets are available online, at https://github.com/uclnlp/ctp.

Natural language is an appealing medium for explaining how large language models process and store information, but evaluating the faithfulness of such explanations is challenging. To help address this, we develop two modes of evaluation for natural language explanations that claim individual neurons represent a concept in a text input. In the observational mode, we evaluate claims that a neuron a activates on all and only input strings that refer to a concept picked out by the proposed explanation E. In the intervention mode, we construe E as a claim that the neuron a is a causal mediator of the concept denoted by E. We apply our framework to the GPT-4-generated explanations of GPT-2 XL neurons of Bills et al. (2023) and show that even the most confident explanations have high error rates and little to no causal efficacy. We close the paper by critically assessing whether natural language is a good choice for explanations and whether neurons are the best level of analysis.

We present a framework where neural models develop an AI Mother Tongue, a native symbolic language that simultaneously supports intuitive reasoning, compositional symbol chains, and inherent interpretability. Unlike post-hoc explanation methods, our approach embeds reasoning directly into the model's representations: symbols capture meaningful semantic patterns, chains trace decision paths, and gated induction mechanisms guide selective focus, yielding transparent yet flexible reasoning. We introduce complementary training objectives to enhance symbol purity and decision sparsity, and employ a sequential specialization strategy to first build broad symbolic competence and then refine intuitive judgments. Experiments on AI tasks demonstrate competitive accuracy alongside verifiable reasoning traces, showing that AI Mother Tongue can serve as a unified mechanism for interpretability, intuition, and symbolic reasoning in neural models.

Recent advancements in multimodal large reasoning models (MLRMs) have significantly improved performance in visual question answering. However, we observe that transition words (e.g., because, however, and wait) are closely associated with hallucinations and tend to exhibit high-entropy states. We argue that adequate contextual reasoning information can be directly extracted from the token probability distribution. Inspired by superposed representation theory, we propose leveraging latent superposed reasoning to integrate multiple candidate semantics and maintain latent reasoning trajectories. The hypothesis is that reliance on discrete textual inputs may drive the model toward sequential explicit reasoning, underutilizing dense contextual cues during high-entropy reasoning stages. Therefore, we propose constructing rich semantic representations from the token probability distributions to enhance in-context reasoning. With this goal, we present Latent Entropy-Aware Decoding (LEAD), an efficient plug-and-play decoding strategy that leverages semantic context to achieve reliable reasoning. The heart of our method lies in entropy-aware reasoning mode switching. The model employs probability-weighted continuous embeddings under high-entropy states and transitions back to discrete token embeddings as entropy decreases. Moreover, we propose a prior-guided visual anchor injection strategy that encourages the model to focus on visual information. Extensive experiments show that LEAD effectively mitigates hallucinations across various MLRMs on multiple benchmarks.

Multilingual reasoning remains a significant challenge for large language models (LLMs), with performance disproportionately favoring high-resource languages. Drawing inspiration from cognitive neuroscience, which suggests that human reasoning functions largely independently of language processing, we hypothesize that LLMs similarly encode reasoning and language as separable components that can be disentangled to enhance multilingual reasoning. To evaluate this, we perform a causal intervention by ablating language-specific representations at inference time. Experiments on 10 open-weight LLMs spanning 11 typologically diverse languages show that this language-specific ablation consistently boosts multilingual reasoning performance. Layer-wise analyses further confirm that language and reasoning representations can be effectively disentangled throughout the model, yielding improved multilingual reasoning capabilities, while preserving top-layer language features remains essential for maintaining linguistic fidelity. Compared to post-training methods such as supervised fine-tuning or reinforcement learning, our training-free language-reasoning disentanglement achieves comparable or superior results with minimal computational overhead. These findings shed light on the internal mechanisms underlying multilingual reasoning in LLMs and suggest a lightweight and interpretable strategy for improving cross-lingual generalization.

The brain understands the external world through an internal model that generates predictions and refines them based on prediction errors. A complete prediction specifies what will happen, when it will happen, and with what probability, which we refer to as a "prediction object". Existing models typically capture only what and when, omit probabilities, and rely on biologically-implausible algorithms. Here we show that a single population of spiking neurons can jointly encode the prediction object through a biologically grounded learning mechanism. We implement a heterogeneous Izhikevich spiking reservoir with readouts trained by an error-modulated, attention-gated three-factor Hebbian rule and test it on a novel paradigm that controls both the timing and probability of upcoming stimuli. By integrating real-time learning of "when" with offline consolidation of "what", the model encodes the complete prediction object, firing at the correct times with magnitudes proportional to the probabilities. Critically, it rapidly adapts to changes in both stimulus timing and probability, an ability that global least-squares methods such as FORCE lack without explicit resets. During learning, the model self-organizes its readout weights into near-orthogonal subspaces for "what" and "when," showing that multiplexed encoding arises naturally from generic recurrent dynamics under local, error-gated modulation. These results challenge the view that "what" and "when" predictions require separate modules, suggesting instead that mixed selectivity within shared populations supports flexible predictive cognition. The model also predicts phase-specific neuromodulation and overlapping neural subspaces, offering a parsimonious alternative to hierarchical predictive-coding accounts.

We investigate a relatively under-explored class of hybrid neurosymbolic models that integrate symbolic learning with neural reasoning to construct data generators meeting formal correctness criteria. In Symbolic Neural Generators (SNGs), symbolic learners examine logical specifications of feasible data from a small set of instances -- sometimes just one. Each specification in turn constrains the conditional information supplied to a neural-based generator, which rejects any instance violating the symbolic specification. Like other neurosymbolic approaches, SNG exploits the complementary strengths of symbolic and neural methods. The outcome of an SNG is a pair (H, X), where H is a symbolic description of feasible instances constructed from data, and X a set of generated new instances that satisfy the description. We introduce a semantics for such systems, based on the construction of appropriate base and fibre partially-ordered sets combined into an overall partial order. We implement an SNG combining a restricted form of Inductive Logic Programming (ILP) with a large language model (LLM) and evaluate it on early-stage drug design. Our main interest is the description and the set of potential inhibitor molecules generated by the SNG. On benchmark problems -- where drug targets are well understood -- SNG performance is statistically comparable to state-of-the-art methods. On exploratory problems with poorly understood targets, generated molecules exhibit binding affinities on par with leading clinical candidates. Experts further find the symbolic specifications useful as preliminary filters, with several generated molecules identified as viable for synthesis and wet-lab testing.

Test-time scaling has enabled Large Language Models (LLMs) to tackle complex reasoning, yet the limitations of current Chain-of-Thought (CoT) evaluation obscures whether performance gains stem from genuine reasoning or mere verbosity. To address this, (1) we propose a novel neuro-symbolic framework for the non-intrusive, comprehensive process-centric evaluation of reasoning. (2) Through this lens, we identify four distinct behavioral prototypes and diagnose the failure modes. (3) We examine the impact of inference mode, training strategy, and model scale. Our analysis reveals that extended token generation is not a prerequisite for deep reasoning. Furthermore, we reveal critical constraints: mixing long and short CoT data in training risks in premature saturation and collapse, while distillation into smaller models captures behavioral length but fails to replicate logical efficacy due to intrinsic capacity limits.

We demonstrate that Contrastive Decoding -- a simple, computationally light, and training-free text generation method proposed by Li et al 2022 -- achieves large out-of-the-box improvements over greedy decoding on a variety of reasoning tasks. Originally shown to improve the perceived quality of long-form text generation, Contrastive Decoding searches for strings that maximize a weighted difference in likelihood between strong and weak models. We show that Contrastive Decoding leads LLaMA-65B to outperform LLaMA 2, GPT-3.5 and PaLM 2-L on the HellaSwag commonsense reasoning benchmark, and to outperform LLaMA 2, GPT-3.5 and PaLM-540B on the GSM8K math word reasoning benchmark, in addition to improvements on a collection of other tasks. Analysis suggests that Contrastive Decoding improves over existing methods by preventing some abstract reasoning errors, as well as by avoiding simpler modes such as copying sections of the input during chain-of-thought. Overall, Contrastive Decoding outperforms nucleus sampling for long-form generation and greedy decoding for reasoning tasks, making it a powerful general purpose method for generating text from language models.

The integration of symbolic computing with neural networks has intrigued researchers since the first theorizations of Artificial intelligence (AI). The ability of Neuro-Symbolic (NeSy) methods to infer or exploit behavioral schema has been widely considered as one of the possible proxies for human-level intelligence. However, the limited semantic generalizability and the challenges in declining complex domains with pre-defined patterns and rules hinder their practical implementation in real-world scenarios. The unprecedented results achieved by connectionist systems since the last AI breakthrough in 2017 have raised questions about the competitiveness of NeSy solutions, with particular emphasis on the Natural Language Processing and Computer Vision fields. This survey examines task-specific advancements in the NeSy domain to explore how incorporating symbolic systems can enhance explainability and reasoning capabilities. Our findings are meant to serve as a resource for researchers exploring explainable NeSy methodologies for real-life tasks and applications. Reproducibility details and in-depth comments on each surveyed research work are made available at https://github.com/disi-unibo-nlp/task-oriented-neuro-symbolic.git.

One of the roadblocks to a better understanding of neural networks' internals is polysemanticity, where neurons appear to activate in multiple, semantically distinct contexts. Polysemanticity prevents us from identifying concise, human-understandable explanations for what neural networks are doing internally. One hypothesised cause of polysemanticity is superposition, where neural networks represent more features than they have neurons by assigning features to an overcomplete set of directions in activation space, rather than to individual neurons. Here, we attempt to identify those directions, using sparse autoencoders to reconstruct the internal activations of a language model. These autoencoders learn sets of sparsely activating features that are more interpretable and monosemantic than directions identified by alternative approaches, where interpretability is measured by automated methods. Ablating these features enables precise model editing, for example, by removing capabilities such as pronoun prediction, while disrupting model behaviour less than prior techniques. This work indicates that it is possible to resolve superposition in language models using a scalable, unsupervised method. Our method may serve as a foundation for future mechanistic interpretability work, which we hope will enable greater model transparency and steerability.

Pretrained generative models have opened new frontiers in brain decoding by enabling the synthesis of realistic texts and images from non-invasive brain recordings. However, the reliability of such outputs remains questionable--whether they truly reflect semantic activation in the brain, or are merely hallucinated by the powerful generative models. In this paper, we focus on EEG-to-text decoding and address its hallucination issue through the lens of posterior collapse. Acknowledging the underlying mismatch in information capacity between EEG and text, we reframe the decoding task as semantic summarization of core meanings rather than previously verbatim reconstruction of stimulus texts. To this end, we propose the Generative Language Inspection Model (GLIM), which emphasizes learning informative and interpretable EEG representations to improve semantic grounding under heterogeneous and small-scale data conditions. Experiments on the public ZuCo dataset demonstrate that GLIM consistently generates fluent, EEG-grounded sentences without teacher forcing. Moreover, it supports more robust evaluation beyond text similarity, through EEG-text retrieval and zero-shot semantic classification across sentiment categories, relation types, and corpus topics. Together, our architecture and evaluation protocols lay the foundation for reliable and scalable benchmarking in generative brain decoding.

Understanding what individual neurons encode is a core question in neuroscience. In primary visual cortex (V1), mathematical models (e.g., Gabor functions) capture neural selectivity, but no comparable framework exists for higher areas. We show that natural language can fill this role: across macaque V1 and V4, the selectivity of most neurons is captured by concise, verifiable semantic descriptions. Using digital twins of V1 and V4, we develop a closed-loop framework that translates each neuron's high- and low-activating images into dense captions, generates a semantic hypothesis and synthesized images, and verifies the hypothesis in silico. Descriptions range from oriented edges and spatial frequency in V1 to conjunctions of form, color, and texture in V4. In V4, images generated from activating and suppressing hypotheses drove 96.1% of neurons above the 95th and 97.6% below the 5th percentile of natural-image responses, respectively (vs. ~10% for random images); V1 activation results matched V4, while V1 suppression was less describable in language. Representational similarity analysis reveals partial alignment between neural activity, vision embeddings, and language embeddings, with vision most aligned to neural activity; alignment lost in the text bottleneck is recovered when hypotheses are rendered back into images, showing that linguistic compression is lossy yet semantically faithful. Together, these results show that combining generative models with neural digital twins enables interpretable, testable descriptions of neural function at scale, toward agentic scientific discovery.

Decoding methods play an indispensable role in converting language models from next-token predictors into practical task solvers. Prior research on decoding methods, primarily focusing on task-specific models, may not extend to the current era of general-purpose large language models (LLMs). Moreover, the recent influx of decoding strategies has further complicated this landscape. This paper provides a comprehensive and multifaceted analysis of various decoding methods within the context of LLMs, evaluating their performance, robustness to hyperparameter changes, and decoding speeds across a wide range of tasks, models, and deployment environments. Our findings reveal that decoding method performance is notably task-dependent and influenced by factors such as alignment, model size, and quantization. Intriguingly, sensitivity analysis exposes that certain methods achieve superior performance at the cost of extensive hyperparameter tuning, highlighting the trade-off between attaining optimal results and the practicality of implementation in varying contexts.

Modeling the interplay between external stimuli and internal neural representations is a pivotal research area for Brain-Computer Interfaces (BCIs). A major limitation of prior work is the prevailing paradigm of specialized, single-task models, which curtails versatility and neglects inter-task synergies. To address this, we propose Mind-Omni, the first versatile framework that unifies seven distinct encoding and decoding tasks through a discrete diffusion paradigm. At its core is a novel Brain Tokenizer that transforms heterogeneous, continuous brain signals into standardized, discrete tokens. This enables direct, token-level interactions for mutual understanding and generation between any two or more modalities within a shared semantic space. To unlock advanced reasoning capabilities, we further curate a specialized Brain Question Answering (BQA) instruction-tuning dataset. Our model not only establishes a new state-of-the-art among multi-task unified frameworks but also provides strong evidence for multi-task synergy. By demonstrating performance competitive with, and at times superior to, larger specialized models, our work offers a powerful new paradigm for neural modeling and paves the way for foundation models of neural activity. The code is publicly available at https://github.com/ReedOnePeck/Mind-Omni.

Large language models (LLMs) exhibit impressive capabilities but struggle with reasoning errors due to hallucinations and flawed logic. To investigate their internal representations of reasoning, we introduce ArrangementPuzzle, a novel puzzle dataset with structured solutions and automated stepwise correctness verification. We trained a classifier model on LLM activations on this dataset and found that it achieved over 80% accuracy in predicting reasoning correctness, implying that LLMs internally distinguish between correct and incorrect reasoning steps, with the strongest representations in middle-late Transformer layers. Further analysis reveals that LLMs encode abstract reasoning concepts within the middle activation layers of the transformer architecture, distinguishing logical from semantic equivalence. These findings provide insights into LLM reasoning mechanisms and contribute to improving AI reliability and interpretability, thereby offering the possibility to manipulate and refine LLM reasoning.

Speculative decoding (SD) is a widely adopted approach for accelerating inference in large language models (LLMs), particularly when the draft and target models are well aligned. However, state-of-the-art SD methods typically rely on tightly coupled, self-attention-based Transformer decoders, often augmented with auxiliary pooling or fusion layers. This coupling makes them increasingly complex and harder to generalize across different models. We present Budget EAGLE (Beagle), the first, to our knowledge, cross-attention-based Transformer decoder SD model that achieves performance on par with leading self-attention SD models (EAGLE-v2) while eliminating the need for pooling or auxiliary components, simplifying the architecture, improving training efficiency, and maintaining stable memory usage during training-time simulation. To enable effective training of this novel architecture, we propose Two-Stage Block-Attention Training, a new method that achieves training stability and convergence efficiency in block-level attention scenarios. Extensive experiments across multiple LLMs and datasets show that Beagle achieves competitive inference speedups and higher training efficiency than EAGLE-v2, offering a strong alternative for architectures in speculative decoding.

Recent advances such as OpenAI-o1 and DeepSeek R1 have demonstrated the potential of Reinforcement Learning (RL) to enhance reasoning abilities in Large Language Models (LLMs). While open-source replication efforts have primarily focused on mathematical and coding domains, methods and resources for developing general reasoning capabilities remain underexplored. This gap is partly due to the challenge of collecting diverse and verifiable reasoning data suitable for RL. We hypothesize that logical reasoning is critical for developing general reasoning capabilities, as logic forms a fundamental building block of reasoning. In this work, we present SynLogic, a data synthesis framework and dataset that generates diverse logical reasoning data at scale, encompassing 35 diverse logical reasoning tasks. The SynLogic approach enables controlled synthesis of data with adjustable difficulty and quantity. Importantly, all examples can be verified by simple rules, making them ideally suited for RL with verifiable rewards. In our experiments, we validate the effectiveness of RL training on the SynLogic dataset based on 7B and 32B models. SynLogic leads to state-of-the-art logical reasoning performance among open-source datasets, surpassing DeepSeek-R1-Distill-Qwen-32B by 6 points on BBEH. Furthermore, mixing SynLogic data with mathematical and coding tasks improves the training efficiency of these domains and significantly enhances reasoning generalization. Notably, our mixed training model outperforms DeepSeek-R1-Zero-Qwen-32B across multiple benchmarks. These findings position SynLogic as a valuable resource for advancing the broader reasoning capabilities of LLMs. We open-source both the data synthesis pipeline and the SynLogic dataset at https://github.com/MiniMax-AI/SynLogic.

Large Language Models (LLMs) still struggle with multi-step logical reasoning. Existing approaches either purely refine the reasoning chain in natural language form or attach a symbolic solver as an external module. In this work, we instead ask whether LLMs contain a shared internal logical subspace that simultaneously aligns natural-language and symbolic-language views of the reasoning process. Our hypothesis is that this logical subspace captures logical reasoning capabilities in LLMs that are shared across views while remaining independent of surface forms. To verify this, we employ Canonical Correlation Analysis on the paired residual activations from natural-language and symbolic-language reasoning chains, learning a low-dimensional subspace with maximum cross-view correlation. Furthermore, we design a training-free approach that steers LLMs reasoning chain along this logical subspace, thereby leveraging the complementary reasoning signals from both views. Experiments on four logical reasoning benchmarks demonstrate the effectiveness of our approach, improving accuracy by up to 11 percentage points and generalizing well on out-of-domain problems.

Transferring reasoning capabilities from larger language models to smaller ones through supervised fine-tuning often fails counterintuitively, with performance degrading despite access to high-quality teacher demonstrations. We identify that this failure stems from distributional misalignment: reasoning traces from larger models contain tokens that are low probability under the student's distribution, exceeding the internal representation capacity of smaller architectures and creating learning barriers rather than helpful guidance. We propose Reverse Speculative Decoding (RSD), a mechanism for generating student-friendly reasoning traces in which the teacher model proposes candidate tokens but the student model determines acceptance based on its own probability distributions, filtering low probability tokens. When applied to Qwen3-0.6B, direct distillation of s1K-1.1 reasoning trace data degrades average performance across major reasoning benchmarks by 20.5\%, while the same model trained on RSD-generated reasoning traces achieves meaningful improvements of 4.9\%. Our analysis reveals that low probability tokens constitute the critical bottleneck in reasoning ability transfer. However, cross-model experiments demonstrate that RSD traces are model-specific rather than universally applicable, indicating that distributional alignment must be tailored for each student architecture's unique internal representation.

We interpret the function of individual neurons in CLIP by automatically describing them using text. Analyzing the direct effects (i.e. the flow from a neuron through the residual stream to the output) or the indirect effects (overall contribution) fails to capture the neurons' function in CLIP. Therefore, we present the "second-order lens", analyzing the effect flowing from a neuron through the later attention heads, directly to the output. We find that these effects are highly selective: for each neuron, the effect is significant for <2% of the images. Moreover, each effect can be approximated by a single direction in the text-image space of CLIP. We describe neurons by decomposing these directions into sparse sets of text representations. The sets reveal polysemantic behavior - each neuron corresponds to multiple, often unrelated, concepts (e.g. ships and cars). Exploiting this neuron polysemy, we mass-produce "semantic" adversarial examples by generating images with concepts spuriously correlated to the incorrect class. Additionally, we use the second-order effects for zero-shot segmentation and attribute discovery in images. Our results indicate that a scalable understanding of neurons can be used for model deception and for introducing new model capabilities.

Attending to what is relevant is fundamental to both the mammalian brain and modern machine learning models such as Transformers. Yet, determining relevance remains a core challenge, traditionally offloaded to learning algorithms like backpropagation. Inspired by recent cellular neurobiological evidence linking neocortical pyramidal cells to distinct mental states, this work shows how models (e.g., Transformers) can emulate high-level perceptual processing and awake thought (imagination) states to pre-select relevant information before applying attention. Triadic neuronal-level modulation loops among questions (Q), clues (keys, K), and hypotheses (values, V) enable diverse, deep, parallel reasoning chains at the representation level and allow a rapid shift from initial biases to refined understanding. This leads to orders-of-magnitude faster learning with significantly reduced computational demand (e.g., fewer heads, layers, and tokens), at an approximate cost of O(N), where N is the number of input tokens. Results span reinforcement learning (e.g., CarRacing in a high-dimensional visual setup), computer vision, and natural language question answering.

Decoding imagined speech from non-invasive brain recordings is challenging because imagined datasets are scarce and difficult to align temporally across subjects and sessions In this work, we propose a new approach to the decoding of imagined speech that leverages the richer and more reliably labeled recordings during listening to speech. We collected paired listened and imagined MEG recordings to rhythmic melodic and spoken stimuli from trained musicians. Using trained musicians helped improve temporal alignment across conditions. We then developed a three-stage decoding pipeline that revealed consistent and meaningful relationships between neural activity evoked by imagining and listening to the same stimuli. First, we trained six linear and neural models to map imagined MEG responses to listened responses. We evaluated these models against a null baseline from unseen subjects to validate that the predicted-listening responses preserve stimulus-specific information. In the second stage, we trained a contrastive word decoder exclusively on the listened MEG responses, and evaluated it using four embedding strategies including semantic, acoustic, and phonetic representations. In the third stage, we process the imagined MEG responses from held-out subjects through the mapping pipeline to compute the corresponding listening responses that are then decoded by the listened decoder. Using rank-based analysis, we show that the imagined words are decodable significantly above chance. We shall report here the results of a proof-of-concept implementation to decode imagined speech, where all evaluations are performed on held-out subjects. We also demonstrate that performance improves with training data size, suggesting that this approach is scalable and can directly be made applicable to realistic brain-computer interface scenarios.

Speech brain-computer interfaces aim to decipher what a person is trying to say from neural activity alone, restoring communication to people with paralysis who have lost the ability to speak intelligibly. The Brain-to-Text Benchmark '24 and associated competition was created to foster the advancement of decoding algorithms that convert neural activity to text. Here, we summarize the lessons learned from the competition ending on June 1, 2024 (the top 4 entrants also presented their experiences in a recorded webinar). The largest improvements in accuracy were achieved using an ensembling approach, where the output of multiple independent decoders was merged using a fine-tuned large language model (an approach used by all 3 top entrants). Performance gains were also found by improving how the baseline recurrent neural network (RNN) model was trained, including by optimizing learning rate scheduling and by using a diphone training objective. Improving upon the model architecture itself proved more difficult, however, with attempts to use deep state space models or transformers not yet appearing to offer a benefit over the RNN baseline. The benchmark will remain open indefinitely to support further work towards increasing the accuracy of brain-to-text algorithms.

Reasoning models excel by generating long chain-of-thoughts, but decoding the resulting thousands of tokens is slow. Token-level speculative decoding (SD) helps, but its benefit is capped, because the chance that an entire gamma-token guess is correct falls exponentially as gamma grows. This means allocating more compute for longer token drafts faces an algorithmic ceiling -- making the speedup modest and hardware-agnostic. We raise this ceiling with Lookahead Reasoning, which exploits a second, step-level layer of parallelism. Our key insight is that reasoning models generate step-by-step, and each step needs only to be semantically correct, not exact token matching. In Lookahead Reasoning, a lightweight draft model proposes several future steps; the target model expands each proposal in one batched pass, and a verifier keeps semantically correct steps while letting the target regenerate any that fail. Token-level SD still operates within each reasoning step, so the two layers of parallelism multiply. We show Lookahead Reasoning lifts the peak speedup of SD both theoretically and empirically. Across GSM8K, AIME, and other benchmarks, Lookahead Reasoning improves the speedup of SD from 1.4x to 2.1x while preserving answer quality, and its speedup scales better with additional GPU throughput. Our code is available at https://github.com/hao-ai-lab/LookaheadReasoning

Speculative Decoding is a widely used technique to speed up inference for Large Language Models (LLMs) without sacrificing quality. When performing inference, speculative decoding uses a smaller draft model to generate speculative tokens and then uses the target LLM to verify those draft tokens. The speedup provided by speculative decoding heavily depends on the choice of the draft model. In this work, we perform a detailed study comprising over 350 experiments with LLaMA-65B and OPT-66B using speculative decoding and delineate the factors that affect the performance gain provided by speculative decoding. Our experiments indicate that the performance of speculative decoding depends heavily on the latency of the draft model, and the draft model's capability in language modeling does not correlate strongly with its performance in speculative decoding. Based on these insights we explore a new design space for draft models and design hardware-efficient draft models for speculative decoding. Our newly designed draft model for LLaMA-65B can provide 60% higher throughput than existing draft models and can generalize further to the LLaMA-2 model family and supervised fine-tuned models.

Large language models have demonstrated exceptional capability in natural language understanding and generation. However, their generation speed is limited by the inherently sequential nature of their decoding process, posing challenges for real-time applications. This paper introduces Lexical Unit Decoding (LUD), a novel decoding methodology implemented in a data-driven manner, accelerating the decoding process without sacrificing output quality. The core of our approach is the observation that a pre-trained language model can confidently predict multiple contiguous tokens, forming the basis for a lexical unit, in which these contiguous tokens could be decoded in parallel. Extensive experiments validate that our method substantially reduces decoding time while maintaining generation quality, i.e., 33\% speed up on natural language generation with no quality loss, and 30\% speed up on code generation with a negligible quality loss of 3\%. Distinctively, LUD requires no auxiliary models and does not require changes to existing architectures. It can also be integrated with other decoding acceleration methods, thus achieving an even more pronounced inference efficiency boost. We posit that the foundational principles of LUD could define a new decoding paradigm for future language models, enhancing their applicability for a broader spectrum of applications. All codes are be publicly available at https://github.com/tjunlp-lab/Lexical-Unit-Decoding-LUD-. Keywords: Parallel Decoding, Lexical Unit Decoding, Large Language Model

In this technical note, we study the problem of inverse permutation learning in decoder-only transformers. Given a permutation and a string to which that permutation has been applied, the model is tasked with producing the original (``canonical'') string. We argue that this task models a natural robustness property across a variety of reasoning tasks, including long-context retrieval, multiple choice QA and in-context learning. Our primary contribution is an impossibility result: we show that an arbitrary depth, decoder-only transformer cannot learn this task. This result concerns the expressive capacity of decoder-only transformer models and is agnostic to training dynamics or sample complexity. We give a pair of alternative constructions under which inverse permutation learning is feasible. The first of these highlights the fundamental role of the causal attention mask, and reveals a gap between the expressivity of encoder-decoder transformers and the more popular decoder-only architecture. The latter result is more surprising: we show that simply padding the input with ``scratch tokens" yields a construction under which inverse permutation learning is possible. We conjecture that this may suggest an alternative mechanism by which chain-of-thought prompting or, more generally, intermediate ``thinking'' tokens can enable reasoning in large language models, even when these tokens encode no meaningful semantic information (e.g., the results of intermediate computations).

Diagrams matter. Unfortunately, the deep learning community has no standard method for diagramming architectures. The current combination of linear algebra notation and ad-hoc diagrams fails to offer the necessary precision to understand architectures in all their detail. However, this detail is critical for faithful implementation, mathematical analysis, further innovation, and ethical assurances. I present neural circuit diagrams, a graphical language tailored to the needs of communicating deep learning architectures. Neural circuit diagrams naturally keep track of the changing arrangement of data, precisely show how operations are broadcast over axes, and display the critical parallel behavior of linear operations. A lingering issue with existing diagramming methods is the inability to simultaneously express the detail of axes and the free arrangement of data, which neural circuit diagrams solve. Their compositional structure is analogous to code, creating a close correspondence between diagrams and implementation. In this work, I introduce neural circuit diagrams for an audience of machine learning researchers. After introducing neural circuit diagrams, I cover a host of architectures to show their utility and breed familiarity. This includes the transformer architecture, convolution (and its difficult-to-explain extensions), residual networks, the U-Net, and the vision transformer. I include a Jupyter notebook that provides evidence for the close correspondence between diagrams and code. Finally, I examine backpropagation using neural circuit diagrams. I show their utility in providing mathematical insight and analyzing algorithms' time and space complexities.

Large language models (LLMs) generalize smoothly across continuous semantic spaces, yet strict logical reasoning demands the formation of discrete decision boundaries. Prevailing theories relying on linear isometric projections fail to resolve this fundamental tension. In this work, we argue that task context operates as a non-isometric dynamical operator that enforces a necessary "topological distortion." By applying Gram-Schmidt decomposition to residual-stream activations , we reveal a dual-modulation mechanism driving this process: a class-agnostic topological preservation that anchors global structure to prevent semantic collapse, and a specific algebraic divergence that directionally tears apart cross-class concepts to forge logical boundaries. We validate this geometric evolution across a gradient of tasks, from simple mapping to complex primality testing. Crucially, targeted specific vector ablation establishes a strict causal binding between this topology and model function: algebraically erasing the divergence component collapses parity classification accuracy from 100% to chance levels (38.57%). Furthermore, we uncover a three-phase layer-wise geometric dynamic and demonstrate that under social pressure prompts, models fail to generate sufficient divergence. This results in a "manifold entanglement" that geometrically explains sycophancy and hallucination. Ultimately, our findings revise the linear-isometric presumption, demonstrating that the emergence of discrete logic in LLMs is purchased at an irreducible cost of topological deformation.

With the growing accessibility and wide adoption of large language models, concerns about their safety and alignment with human values have become paramount. In this paper, we identify a concerning phenomenon: Reasoning-Induced Misalignment (RIM), in which misalignment emerges when reasoning capabilities strengthened-particularly when specific types of reasoning patterns are introduced during inference or training. Beyond reporting this vulnerability, we provide the first mechanistic account of its origins. Through representation analysis, we discover that specific attention heads facilitate refusal by reducing their attention to CoT tokens, a mechanism that modulates the model's rationalization process during inference. During training, we find significantly higher activation entanglement between reasoning and safety in safety-critical neurons than in control neurons, particularly after fine-tuning with those identified reasoning patterns. This entanglement strongly correlates with catastrophic forgetting, providing a neuron-level explanation for RIM.

Computationally intensive decoding procedures--including search, reranking, and self-critique--can improve the quality of language model (LM) outputs in problems spanning code generation, numerical reasoning, and dialog. Existing work typically applies the same decoding procedure for every input to an LM. But not all inputs require the same amount of computation to process. Can we allocate decoding computation adaptively, using more resources to answer questions whose answers will be harder to compute? We present an approach that predicts the distribution of rewards given an input and computation budget, then allocates additional computation to inputs for which it is predicted to be most useful. We apply this approach in two decoding procedures: first, an adaptive best-of-k procedure that dynamically selects the number of samples to generate as input to a reranker; second, a routing procedure that dynamically responds to a query using a decoding procedure that is expensive but accurate, or one that is cheaper but less capable. Across a suite of programming, mathematics, and dialog tasks, we show that accurate computation-allocation procedures can be learned, and reduce computation by up to 50% at no cost to response quality, or improve quality by up to 10% at a fixed computational budget.

Recent breakthroughs in large language models (LLMs) have led to notable successes in complex reasoning tasks, such as mathematical problem solving. A common strategy for improving performance is parallel thinking, in which multiple reasoning traces are generated and the final prediction is made using aggregation schemes like majority voting or best-of-N decoding. However, two key challenges persist. First, multi-sample decoding incurs substantial inference latency, especially for long-form outputs. Second, effective mechanisms for reliably assessing the correctness of individual reasoning traces are still limited. To address these challenges, we introduce One-Token Verification (OTV), a computational method that estimates reasoning correctness in a single forward pass during generation. OTV is activated by a learnable token and integrated into the LLM via low-rank adaptation to probe internal reasoning signals through the key-value cache, supporting token-level correctness estimation at any stage of generation without disrupting primary reasoning. Experiments on mathematical reasoning benchmarks demonstrate that OTV consistently surpasses existing verifiers. Additionally, OTV reduces token usage by up to 90% through correctness-guided early termination, prioritizing shorter, more reliable solutions.

Neural-symbolic methods have demonstrated efficiency in enhancing the reasoning abilities of large language models (LLMs). However, existing methods mainly rely on syntactically mapping natural languages to complete formal languages like Python and SQL. Those methods require that reasoning tasks be convertible into programs, which cater to the computer execution mindset and deviate from human reasoning habits. To broaden symbolic methods' applicability and adaptability in the real world, we propose the Meta-Reasoning from a linguistic perspective. This method empowers LLMs to deconstruct reasoning-independent semantic information into generic symbolic representations, thereby efficiently capturing more generalized reasoning knowledge. We conduct extensive experiments on more than ten datasets encompassing conventional reasoning tasks like arithmetic, symbolic, and logical reasoning, and the more complex interactive reasoning tasks like theory-of-mind reasoning. Experimental results demonstrate that Meta-Reasoning significantly enhances in-context reasoning accuracy, learning efficiency, out-of-domain generalization, and output stability compared to the Chain-of-Thought technique. Code and data are publicly available at https://github.com/Alsace08/Meta-Reasoning.

Decoding and expressing brain activity in a comprehensible form is a challenging frontier in AI. This paper presents Thought2Text, which uses instruction-tuned Large Language Models (LLMs) fine-tuned with EEG data to achieve this goal. The approach involves three stages: (1) training an EEG encoder for visual feature extraction, (2) fine-tuning LLMs on image and text data, enabling multimodal description generation, and (3) further fine-tuning on EEG embeddings to generate text directly from EEG during inference. Experiments on a public EEG dataset collected for six subjects with image stimuli and text captions demonstrate the efficacy of multimodal LLMs (LLaMA-v3, Mistral-v0.3, Qwen2.5), validated using traditional language generation evaluation metrics, as well as fluency and adequacy measures. This approach marks a significant advancement towards portable, low-cost "thoughts-to-text" technology with potential applications in both neuroscience and natural language processing.

Large language models (LLMs) have shown extraordinary performance in various language tasks, but high computational requirements hinder their widespread deployment. Speculative decoding, which uses amateur models to predict the generation of expert models, has been proposed as a way to accelerate LLM inference. However, speculative decoding focuses on acceleration instead of making the best use of the token distribution from amateur models. We proposed Speculative Contrastive Decoding (SCD), an accelerated decoding method leveraging the natural contrast between expert and amateur models in speculative decoding. Comprehensive evaluations on four benchmarks show that SCD can achieve similar acceleration factors as speculative decoding while further improving the generation quality as the contrastive decoding. The analysis of token probabilities further demonstrates the compatibility between speculative and contrastive decoding. Overall, SCD provides an effective approach to enhance the decoding quality of LLMs while saving computational resources.

We present SEED (Semantic Evaluation for Visual Brain Decoding), a novel metric for evaluating the semantic decoding performance of visual brain decoding models. It integrates three complementary metrics, each capturing a different aspect of semantic similarity between images inspired by neuroscientific findings. Using carefully crowd-sourced human evaluation data, we demonstrate that SEED achieves the highest alignment with human evaluation, outperforming other widely used metrics. Through the evaluation of existing visual brain decoding models with SEED, we further reveal that crucial information is often lost in translation, even in the state-of-the-art models that achieve near-perfect scores on existing metrics. This finding highlights the limitations of current evaluation practices and provides guidance for future improvements in decoding models. Finally, to facilitate further research, we open-source the human evaluation data, encouraging the development of more advanced evaluation methods for brain decoding. Our code and the human evaluation data are available at https://github.com/Concarne2/SEED.

Large language models (LLMs) suffer from low efficiency as the mismatch between the requirement of auto-regressive decoding and the design of most contemporary GPUs. Specifically, billions to trillions of parameters must be loaded to the GPU cache through its limited memory bandwidth for computation, but only a small batch of tokens is actually computed. Consequently, the GPU spends most of its time on memory transfer instead of computation. Recently, parallel decoding, a type of speculative decoding algorithms, is becoming more popular and has demonstrated impressive efficiency improvement in generation. It introduces extra decoding heads to large models, enabling them to predict multiple subsequent tokens simultaneously and verify these candidate continuations in a single decoding step. However, this approach deviates from the training objective of next token prediction used during pre-training, resulting in a low hit rate for candidate tokens. In this paper, we propose a new speculative decoding algorithm, Clover, which integrates sequential knowledge into the parallel decoding process. This enhancement improves the hit rate of speculators and thus boosts the overall efficiency. Clover transmits the sequential knowledge from pre-speculated tokens via the Regressive Connection, then employs an Attention Decoder to integrate these speculated tokens. Additionally, Clover incorporates an Augmenting Block that modifies the hidden states to better align with the purpose of speculative generation rather than next token prediction. The experiment results demonstrate that Clover outperforms the baseline by up to 91% on Baichuan-Small and 146% on Baichuan-Large, respectively, and exceeds the performance of the previously top-performing method, Medusa, by up to 37% on Baichuan-Small and 57% on Baichuan-Large, respectively.

Autoregressive generation in large language models (LLMs) conventionally decodes from the final layer, assuming that deeper representations yield more reliable next-token predictions. We revisit this assumption by revealing a recurring Guess-Refine-Perturb dynamic: early layers form coarse guesses, intermediate layers refine reasoning-relevant semantics, and final layers can perturb these refined predictions toward generic or alignment-preferred tokens. We introduce Confident Decoding, a training-free decoding strategy that dynamically selects the most reliable near-final layer through entropy-guided conservative backward search. We further provide a theoretical formulation of layer selection as an optimal stopping problem, showing that under bounded projection noise and dominant late-stage alignment perturbation, our search rule filters perturbation while bounding the loss relative to the oracle refinement layer. Experiments across dense and Mixture-of-Experts LLMs demonstrate consistent gains on challenging reasoning benchmarks, including GPQA-Diamond, Omni-MATH, and HLE, with zero memory overhead and less than 2% latency increase. These results suggest dynamically bypassing final-layer perturbations can unlock stronger reasoning behavior from aligned LLMs.

Inference-time optimization scales computation to derive deliberate reasoning steps for effective performance. While previous search-based strategies address the short-sightedness of auto-regressive generation, the vast search space leads to excessive exploration and insufficient exploitation. To strike an efficient balance to derive the optimal step, we frame the decoding strategy as foresight sampling, leveraging simulated future steps to obtain globally optimal step estimation. Built on it, we propose a novel decoding strategy, named phi-Decoding. To provide a precise and expressive estimation of step value, phi-Decoding approximates two distributions via foresight and clustering. Sampling from the joint distribution, the optimal steps can be selected for exploitation. To support adaptive computation allocation, we propose in-width and in-depth pruning strategies, featuring a light-weight solution to achieve inference efficiency. Extensive experiments across seven benchmarks show phi-Decoding outperforms strong baselines in both performance and efficiency. Additional analysis demonstrates its generalization across various LLMs and scalability across a wide range of computing budgets. The code will be released at https://github.com/xufangzhi/phi-Decoding, and the open-source PyPI package is coming soon.

Understanding how Large Language Models (LLMs) perform logical reasoning internally remains a fundamental challenge. While prior mechanistic studies focus on identifying taskspecific circuits, they leave open the question of what computational strategies LLMs employ for propositional reasoning. We address this gap through comprehensive analysis of Qwen3 (8B and 14B) on PropLogic-MI, a controlled dataset spanning 11 propositional logic rule categories across one-hop and two-hop reasoning. Rather than asking ''which components are necessary,'' we ask ''how does the model organize computation?'' Our analysis reveals a coherent computational architecture comprising four interlocking mechanisms: Staged Computation (layer-wise processing phases), Information Transmission (information flow aggregation at boundary tokens), Fact Retrospection (persistent re-access of source facts), and Specialized Attention Heads (functionally distinct head types). These mechanisms generalize across model scales, rule types, and reasoning depths, providing mechanistic evidence that LLMs employ structured computational strategies for logical reasoning.

Large Language Models (LLMs) exhibit a troubling duality, capable of both remarkable generalization and brittle, verbatim memorization of their training data. This unpredictability undermines their reliability in high-stakes applications. In this work, we propose a unified framework to understand, identify, and control these distinct reasoning modes. First, we introduce a theoretical model based on the Information Bottleneck (IB) principle, formalizing generalization as the learning of a compressed, task-relevant representation and memorization as a failure to compress. Building on this theory, we develop Dynamic Mode Steering (DMS), a novel inference-time algorithm which comprises two components: (1) a lightweight, causally-grounded linear probe that identifies the model's instantaneous reliance on memorization, and (2) a dynamic activation steering mechanism that nudges the model's computation towards pre-identified generalization circuits. We frame DMS as a form of adaptive, self-contrastive decoding. Experiments on reasoning and faithfulness tasks demonstrate that DMS significantly improves logical consistency and factual accuracy, thereby offering a principled approach to enhancing LLM reliability.

Interpreting the internal activations of neural networks can produce more faithful explanations of their behavior, but is difficult due to the complex structure of activation space. Existing approaches to scalable interpretability use hand-designed agents that make and test hypotheses about how internal activations relate to external behavior. We propose to instead turn this task into an end-to-end training objective, by training interpretability assistants to accurately predict model behavior from activations through a communication bottleneck. Specifically, an encoder compresses activations to a sparse list of concepts, and a decoder reads this list and answers a natural language question about the model. We show how to pretrain this assistant on large unstructured data, then finetune it to answer questions. The resulting architecture, which we call a Predictive Concept Decoder, enjoys favorable scaling properties: the auto-interp score of the bottleneck concepts improves with data, as does the performance on downstream applications. Specifically, PCDs can detect jailbreaks, secret hints, and implanted latent concepts, and are able to accurately surface latent user attributes.

Code generation, symbolic math reasoning, and other tasks require LLMs to produce outputs that are both syntactically and semantically correct. Constrained LLM generation is a promising direction to enforce adherence to formal grammar, but prior works have empirically observed that strict enforcement of formal constraints often diminishes the reasoning capabilities of LLMs. In this work, we first provide a theoretical explanation for why constraining LLM outputs to very restrictive grammars that only allow syntactically valid final answers reduces the reasoning capabilities of the model. Second, we demonstrate that by augmenting the output grammar with carefully designed additional rules, it is always possible to preserve the reasoning capabilities of the LLM while ensuring syntactic and semantic correctness in its outputs. Building on these theoretical insights, we propose a reasoning-augmented constrained decoding algorithm, CRANE, which effectively balances the correctness of constrained generation with the flexibility of unconstrained generation. Experiments on multiple open-source LLMs and benchmarks show that CRANE significantly outperforms both state-of-the-art constrained decoding strategies and standard unconstrained decoding, showing up to 10% points accuracy improvement over baselines on challenging symbolic reasoning benchmarks GSM-symbolic and FOLIO.

A central goal for mechanistic interpretability has been to identify the right units of analysis in large language models (LLMs) that causally explain their outputs. While early work focused on individual neurons, evidence that neurons often encode multiple concepts has motivated a shift toward analyzing directions in activation space. A key question is how to find directions that capture interpretable features in an unsupervised manner. Current methods rely on dictionary learning with sparse autoencoders (SAEs), commonly trained over residual stream activations to learn directions from scratch. However, SAEs often struggle in causal evaluations and lack intrinsic interpretability, as their learning is not explicitly tied to the computations of the model. Here, we tackle these limitations by directly decomposing MLP activations with semi-nonnegative matrix factorization (SNMF), such that the learned features are (a) sparse linear combinations of co-activated neurons, and (b) mapped to their activating inputs, making them directly interpretable. Experiments on Llama 3.1, Gemma 2 and GPT-2 show that SNMF derived features outperform SAEs and a strong supervised baseline (difference-in-means) on causal steering, while aligning with human-interpretable concepts. Further analysis reveals that specific neuron combinations are reused across semantically-related features, exposing a hierarchical structure in the MLP's activation space. Together, these results position SNMF as a simple and effective tool for identifying interpretable features and dissecting concept representations in LLMs.

Advances in hardware and language model architecture have spurred a revolution in natural language generation. However, autoregressive models compute probability distributions over next-token choices, and sampling from these distributions, known as decoding, has received significantly less attention than other design choices. Existing decoding strategies are largely based on heuristics, resulting in methods that are hard to apply or improve in a principled manner. We develop the theory of decoding strategies for language models by expressing popular decoding algorithms as equilibrium states in the language of ergodic theory and stating the functions they optimize. Using this, we analyze the effect of the local normalization step of top-k, nucleus, and temperature sampling, used to make probabilities sum to one. We argue that local normalization distortion is a fundamental defect of decoding strategies and quantify the size of this distortion and its effect on mathematical proxies for the quality and diversity of generated text. Contrary to the prevailing explanation, we argue that the major cause of the under-performance of top-k sampling relative to nucleus sampling is local normalization distortion. This yields conclusions for the future design of decoding algorithms and the detection of machine-generated text.

Toward combining inductive reasoning with perception abilities, we develop techniques for neurosymbolic program synthesis where perceptual input is first parsed by neural nets into a low-dimensional interpretable representation, which is then processed by a synthesized program. We explore several techniques for relaxing the problem and jointly learning all modules end-to-end with gradient descent: multitask learning; amortized inference; overparameterization; and a differentiable strategy for penalizing lengthy programs. Collectedly this toolbox improves the stability of gradient-guided program search, and suggests ways of learning both how to perceive input as discrete abstractions, and how to symbolically process those abstractions as programs.

Understanding how the brain represents visual information is a fundamental challenge in neuroscience and artificial intelligence. While AI-driven decoding of neural data has provided insights into the human visual system, integrating multimodal neuroimaging signals, such as EEG, MEG, and fMRI, remains a critical hurdle due to their inherent spatiotemporal misalignment. Current approaches often analyze these modalities in isolation, limiting a holistic view of neural representation. In this study, we introduce BrainFLORA, a unified framework for integrating cross-modal neuroimaging data to construct a shared neural representation. Our approach leverages multimodal large language models (MLLMs) augmented with modality-specific adapters and task decoders, achieving state-of-the-art performance in joint-subject visual retrieval task and has the potential to extend multitasking. Combining neuroimaging analysis methods, we further reveal how visual concept representations align across neural modalities and with real world object perception. We demonstrate that the brain's structured visual concept representations exhibit an implicit mapping to physical-world stimuli, bridging neuroscience and machine learning from different modalities of neural imaging. Beyond methodological advancements, BrainFLORA offers novel implications for cognitive neuroscience and brain-computer interfaces (BCIs). Our code is available at https://github.com/ncclab-sustech/BrainFLORA.

Ever since neural models were adopted in data-to-text language generation, they have invariably been reliant on extrinsic components to improve their semantic accuracy, because the models normally do not exhibit the ability to generate text that reliably mentions all of the information provided in the input. In this paper, we propose a novel decoding method that extracts interpretable information from encoder-decoder models' cross-attention, and uses it to infer which attributes are mentioned in the generated text, which is subsequently used to rescore beam hypotheses. Using this decoding method with T5 and BART, we show on three datasets its ability to dramatically reduce semantic errors in the generated outputs, while maintaining their state-of-the-art quality.

Recent work suggests that large language models (LLMs) encode factuality signals in their internal representations, such as hidden states, attention weights, or token probabilities, implying that LLMs may "know what they don't know". However, LLMs can also produce factual errors by relying on shortcuts or spurious associations. These error are driven by the same training objective that encourage correct predictions, raising the question of whether internal computations can reliably distinguish between factual and hallucinated outputs. In this work, we conduct a mechanistic analysis of how LLMs internally process factual queries by comparing two types of hallucinations based on their reliance on subject information. We find that when hallucinations are associated with subject knowledge, LLMs employ the same internal recall process as for correct responses, leading to overlapping and indistinguishable hidden-state geometries. In contrast, hallucinations detached from subject knowledge produce distinct, clustered representations that make them detectable. These findings reveal a fundamental limitation: LLMs do not encode truthfulness in their internal states but only patterns of knowledge recall, demonstrating that "LLMs don't really know what they don't know".