Daily Papers

Large Language Models (LLMs) have demonstrated unprecedented capabilities across various natural language processing tasks. Their ability to process and generate viable text and code has made them ubiquitous in many fields, while their deployment as knowledge bases and "reasoning" tools remains an area of ongoing research. In geography, a growing body of literature has been focusing on evaluating LLMs' geographical knowledge and their ability to perform spatial reasoning. However, very little is still known about the internal functioning of these models, especially about how they process geographical information. In this chapter, we establish a novel framework for the study of geospatial mechanistic interpretability - using spatial analysis to reverse engineer how LLMs handle geographical information. Our aim is to advance our understanding of the internal representations that these complex models generate while processing geographical information - what one might call "how LLMs think about geographic information" if such phrasing was not an undue anthropomorphism. We first outline the use of probing in revealing internal structures within LLMs. We then introduce the field of mechanistic interpretability, discussing the superposition hypothesis and the role of sparse autoencoders in disentangling polysemantic internal representations of LLMs into more interpretable, monosemantic features. In our experiments, we use spatial autocorrelation to show how features obtained for placenames display spatial patterns related to their geographic location and can thus be interpreted geospatially, providing insights into how these models process geographical information. We conclude by discussing how our framework can help shape the study and use of foundation models in geography.

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.

Neural networks often pack many unrelated concepts into a single neuron - a puzzling phenomenon known as 'polysemanticity' which makes interpretability much more challenging. This paper provides a toy model where polysemanticity can be fully understood, arising as a result of models storing additional sparse features in "superposition." We demonstrate the existence of a phase change, a surprising connection to the geometry of uniform polytopes, and evidence of a link to adversarial examples. We also discuss potential implications for mechanistic interpretability.

Instruction tuning improves the ability of large language models (LLMs) to follow diverse human instructions, but achieving strong performance on specific target tasks remains challenging. A critical bottleneck is selecting the most relevant data to maximize task-specific performance. Existing data selection approaches include unstable influence-based methods and more stable distribution alignment methods, the latter of which critically rely on the underlying sample representation. In practice, most distribution alignment methods, from shallow features (e.g., BM25) to neural embeddings (e.g., BGE, LLM2Vec), may fail to capture how the model internally processes samples. To bridge this gap, we adopt a model-centric strategy in which each sample is represented by its neuronal activation pattern in the model, directly reflecting internal computation. However, directly using raw neuron activations leads to spurious similarity between unrelated samples due to neuron polysemanticity, where a single neuron may respond to multiple, unrelated concepts. To address this, we employ sparse autoencoders to disentangle polysemantic activations into sparse, monosemantic representations, and introduce a dedicated similarity metric for this space to better identify task-relevant data. Comprehensive experiments across multiple instruction datasets, models, tasks, and selection ratios show that our approach consistently outperforms existing data selection baselines in both stability and task-specific performance.

Understanding the internal computations of large language models (LLMs) is crucial for aligning them with human values and preventing undesirable behaviors like toxic content generation. However, mechanistic interpretability is hindered by polysemanticity -- where individual neurons respond to multiple, unrelated concepts. While Sparse Autoencoders (SAEs) have attempted to disentangle these features through sparse dictionary learning, they have compromised LLM performance due to reliance on post-hoc reconstruction loss. To address this issue, we introduce Mixture of Monosemantic Experts for Transformers (Monet) architecture, which incorporates sparse dictionary learning directly into end-to-end Mixture-of-Experts pretraining. Our novel expert decomposition method enables scaling the expert count to 262,144 per layer while total parameters scale proportionally to the square root of the number of experts. Our analyses demonstrate mutual exclusivity of knowledge across experts and showcase the parametric knowledge encapsulated within individual experts. Moreover, Monet allows knowledge manipulation over domains, languages, and toxicity mitigation without degrading general performance. Our pursuit of transparent LLMs highlights the potential of scaling expert counts to enhance} mechanistic interpretability and directly resect the internal knowledge to fundamentally adjust} model behavior. The source code and pretrained checkpoints are available at https://github.com/dmis-lab/Monet.

The fundamental units of internal representations in large language models (LLMs) remain undefined, limiting further understanding of their mechanisms. Neurons or features are often regarded as such units, yet neurons suffer from polysemy, while features face concerns of unreliable reconstruction and instability. To address this issue, we propose the Atoms Theory, which defines such units as atoms. We introduce the atomic inner product (AIP) to correct representation shifting, formally define atoms, and prove the conditions that atoms satisfy the Restricted Isometry Property (RIP), ensuring stable sparse representations over atom set and linking to compressed sensing. Under stronger conditions, we further establish the uniqueness and exact ell_1 recoverability of the sparse representations, and provide guarantees that single-layer sparse autoencoders (SAEs) with threshold activations can reliably identify the atoms. To validate the Atoms Theory, we train threshold-activated SAEs on Gemma2-2B, Gemma2-9B, and Llama3.1-8B, achieving 99.9% sparse reconstruction across layers on average, and more than 99.8% of atoms satisfy the uniqueness condition, compared to 0.5% for neurons and 68.2% for features, showing that atoms more faithfully capture intrinsic representations of LLMs. Scaling experiments further reveal the link between SAEs size and recovery capacity. Overall, this work systematically introduces and validates Atoms Theory of LLMs, providing a theoretical framework for understanding internal representations and a foundation for mechanistic interpretability. Code available at https://github.com/ChenhuiHu/towards_atoms.

Large language models (LLMs) have demonstrated impressive capabilities in various reasoning tasks, aided by techniques like chain-of-thought (CoT) prompting that elicits verbalized reasoning. However, LLMs often generate text with obvious mistakes and contradictions, raising doubts about their ability to robustly process and utilize generated rationales. In this work, we investigate CoT reasoning in LLMs through the lens of internal representations, focusing on how these representations are influenced by generated rationales. Our preliminary analysis reveals that while generated rationales improve answer accuracy, inconsistencies emerge between the model's internal representations in middle layers and those in final layers, potentially undermining the reliability of their reasoning processes. To address this, we propose internal consistency as a measure of the model's confidence by examining the agreement of latent predictions decoded from intermediate layers. Extensive empirical studies across different models and datasets demonstrate that internal consistency effectively distinguishes between correct and incorrect reasoning paths. Motivated by this, we propose a new approach to calibrate CoT reasoning by up-weighting reasoning paths with high internal consistency, resulting in a significant boost in reasoning performance. Further analysis uncovers distinct patterns in attention and feed-forward modules across layers, providing insights into the emergence of internal inconsistency. In summary, our results demonstrate the potential of using internal representations for self-evaluation of LLMs.

Automated interpretability research aims to identify concepts encoded in neural network features to enhance human understanding of model behavior. Current feature description methods face two critical challenges: limited robustness and the flawed assumption that each neuron encodes only a single concept (monosemanticity), despite growing evidence that neurons are often polysemantic. This assumption restricts the expressiveness of feature descriptions and limits their ability to capture the full range of behaviors encoded in model internals. To address this, we introduce Polysemantic FeatuRe Identification and Scoring Method (PRISM), a novel framework that captures the inherent complexity of neural network features. Unlike prior approaches that assign a single description per feature, PRISM provides more nuanced descriptions for both polysemantic and monosemantic features. We apply PRISM to language models and, through extensive benchmarking against existing methods, demonstrate that our approach produces more accurate and faithful feature descriptions, improving both overall description quality (via a description score) and the ability to capture distinct concepts when polysemanticity is present (via a polysemanticity score).

We investigate feature universality in large language models (LLMs), a research field that aims to understand how different models similarly represent concepts in the latent spaces of their intermediate layers. Demonstrating feature universality allows discoveries about latent representations to generalize across several models. However, comparing features across LLMs is challenging due to polysemanticity, in which individual neurons often correspond to multiple features rather than distinct ones. This makes it difficult to disentangle and match features across different models. To address this issue, we employ a method known as dictionary learning by using sparse autoencoders (SAEs) to transform LLM activations into more interpretable spaces spanned by neurons corresponding to individual features. After matching feature neurons across models via activation correlation, we apply representational space similarity metrics like Singular Value Canonical Correlation Analysis to analyze these SAE features across different LLMs. Our experiments reveal significant similarities in SAE feature spaces across various LLMs, providing new evidence for feature universality.

Large language models (LLMs) are expected to respond accurately but often exhibit deficient reasoning or generate hallucinatory content. To address these, studies prefixed with ``Self-'' such as Self-Consistency, Self-Improve, and Self-Refine have been initiated. They share a commonality: involving LLMs evaluating and updating itself to mitigate the issues. Nonetheless, these efforts lack a unified perspective on summarization, as existing surveys predominantly focus on categorization without examining the motivations behind these works. In this paper, we summarize a theoretical framework, termed Internal Consistency, which offers unified explanations for phenomena such as the lack of reasoning and the presence of hallucinations. Internal Consistency assesses the coherence among LLMs' latent layer, decoding layer, and response layer based on sampling methodologies. Expanding upon the Internal Consistency framework, we introduce a streamlined yet effective theoretical framework capable of mining Internal Consistency, named Self-Feedback. The Self-Feedback framework consists of two modules: Self-Evaluation and Self-Update. This framework has been employed in numerous studies. We systematically classify these studies by tasks and lines of work; summarize relevant evaluation methods and benchmarks; and delve into the concern, ``Does Self-Feedback Really Work?'' We propose several critical viewpoints, including the ``Hourglass Evolution of Internal Consistency'', ``Consistency Is (Almost) Correctness'' hypothesis, and ``The Paradox of Latent and Explicit Reasoning''. Furthermore, we outline promising directions for future research. We have open-sourced the experimental code, reference list, and statistical data, available at https://github.com/IAAR-Shanghai/ICSFSurvey.

Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear representation" actually mean? And, how do we make sense of geometric notions (e.g., cosine similarity or projection) in the representation space? To answer these, we use the language of counterfactuals to give two formalizations of "linear representation", one in the output (word) representation space, and one in the input (sentence) space. We then prove these connect to linear probing and model steering, respectively. To make sense of geometric notions, we use the formalization to identify a particular (non-Euclidean) inner product that respects language structure in a sense we make precise. Using this causal inner product, we show how to unify all notions of linear representation. In particular, this allows the construction of probes and steering vectors using counterfactual pairs. Experiments with LLaMA-2 demonstrate the existence of linear representations of concepts, the connection to interpretation and control, and the fundamental role of the choice of inner product.

Large language models (LLMs) often produce errors, including factual inaccuracies, biases, and reasoning failures, collectively referred to as "hallucinations". Recent studies have demonstrated that LLMs' internal states encode information regarding the truthfulness of their outputs, and that this information can be utilized to detect errors. In this work, we show that the internal representations of LLMs encode much more information about truthfulness than previously recognized. We first discover that the truthfulness information is concentrated in specific tokens, and leveraging this property significantly enhances error detection performance. Yet, we show that such error detectors fail to generalize across datasets, implying that -- contrary to prior claims -- truthfulness encoding is not universal but rather multifaceted. Next, we show that internal representations can also be used for predicting the types of errors the model is likely to make, facilitating the development of tailored mitigation strategies. Lastly, we reveal a discrepancy between LLMs' internal encoding and external behavior: they may encode the correct answer, yet consistently generate an incorrect one. Taken together, these insights deepen our understanding of LLM errors from the model's internal perspective, which can guide future research on enhancing error analysis and mitigation.

Much of the excitement in modern AI is driven by the observation that scaling up existing systems leads to better performance. But does better performance necessarily imply better internal representations? While the representational optimist assumes it must, this position paper challenges that view. We compare neural networks evolved through an open-ended search process to networks trained via conventional stochastic gradient descent (SGD) on the simple task of generating a single image. This minimal setup offers a unique advantage: each hidden neuron's full functional behavior can be easily visualized as an image, thus revealing how the network's output behavior is internally constructed neuron by neuron. The result is striking: while both networks produce the same output behavior, their internal representations differ dramatically. The SGD-trained networks exhibit a form of disorganization that we term fractured entangled representation (FER). Interestingly, the evolved networks largely lack FER, even approaching a unified factored representation (UFR). In large models, FER may be degrading core model capacities like generalization, creativity, and (continual) learning. Therefore, understanding and mitigating FER could be critical to the future of representation learning.

We present a study on how and where personas -- defined by distinct sets of human characteristics, values, and beliefs -- are encoded in the representation space of large language models (LLMs). Using a range of dimension reduction and pattern recognition methods, we first identify the model layers that show the greatest divergence in encoding these representations. We then analyze the activations within a selected layer to examine how specific personas are encoded relative to others, including their shared and distinct embedding spaces. We find that, across multiple pre-trained decoder-only LLMs, the analyzed personas show large differences in representation space only within the final third of the decoder layers. We observe overlapping activations for specific ethical perspectives -- such as moral nihilism and utilitarianism -- suggesting a degree of polysemy. In contrast, political ideologies like conservatism and liberalism appear to be represented in more distinct regions. These findings help to improve our understanding of how LLMs internally represent information and can inform future efforts in refining the modulation of specific human traits in LLM outputs. Warning: This paper includes potentially offensive sample statements.

In this study, we investigate whether non-English-centric LLMs, despite their strong performance, `think' in their respective dominant language: more precisely, `think' refers to how the representations of intermediate layers, when un-embedded into the vocabulary space, exhibit higher probabilities for certain dominant languages during generation. We term such languages as internal latent languages. We examine the latent language of three typical categories of models for Japanese processing: Llama2, an English-centric model; Swallow, an English-centric model with continued pre-training in Japanese; and LLM-jp, a model pre-trained on balanced English and Japanese corpora. Our empirical findings reveal that, unlike Llama2 which relies exclusively on English as the internal latent language, Japanese-specific Swallow and LLM-jp employ both Japanese and English, exhibiting dual internal latent languages. For any given target language, the model preferentially activates the latent language most closely related to it. In addition, we explore how intermediate layers respond to questions involving cultural conflicts between latent internal and target output languages. We further explore how the language identity shifts across layers while keeping consistent semantic meaning reflected in the intermediate layer representations. This study deepens the understanding of non-English-centric large language models, highlighting the intricate dynamics of language representation within their intermediate layers.

A new prior is proposed for learning representations of high-level concepts of the kind we manipulate with language. This prior can be combined with other priors in order to help disentangling abstract factors from each other. It is inspired by cognitive neuroscience theories of consciousness, seen as a bottleneck through which just a few elements, after having been selected by attention from a broader pool, are then broadcast and condition further processing, both in perception and decision-making. The set of recently selected elements one becomes aware of is seen as forming a low-dimensional conscious state. This conscious state is combining the few concepts constituting a conscious thought, i.e., what one is immediately conscious of at a particular moment. We claim that this architectural and information-processing constraint corresponds to assumptions about the joint distribution between high-level concepts. To the extent that these assumptions are generally true (and the form of natural language seems consistent with them), they can form a useful prior for representation learning. A low-dimensional thought or conscious state is analogous to a sentence: it involves only a few variables and yet can make a statement with very high probability of being true. This is consistent with a joint distribution (over high-level concepts) which has the form of a sparse factor graph, i.e., where the dependencies captured by each factor of the factor graph involve only very few variables while creating a strong dip in the overall energy function. The consciousness prior also makes it natural to map conscious states to natural language utterances or to express classical AI knowledge in a form similar to facts and rules, albeit capturing uncertainty as well as efficient search mechanisms implemented by attention mechanisms.

Understanding how semantic meaning is encoded in the representation spaces of large language models is a fundamental problem in interpretability. In this paper, we study the two foundational questions in this area. First, how are categorical concepts, such as {'mammal', 'bird', 'reptile', 'fish'}, represented? Second, how are hierarchical relations between concepts encoded? For example, how is the fact that 'dog' is a kind of 'mammal' encoded? We show how to extend the linear representation hypothesis to answer these questions. We find a remarkably simple structure: simple categorical concepts are represented as simplices, hierarchically related concepts are orthogonal in a sense we make precise, and (in consequence) complex concepts are represented as polytopes constructed from direct sums of simplices, reflecting the hierarchical structure. We validate these theoretical results on the Gemma large language model, estimating representations for 957 hierarchically related concepts using data from WordNet.

Despite their vast capabilities, Large Language Models (LLMs) often struggle with generating reliable outputs, frequently producing high-confidence inaccuracies known as hallucinations. Addressing this challenge, our research introduces InternalInspector, a novel framework designed to enhance confidence estimation in LLMs by leveraging contrastive learning on internal states including attention states, feed-forward states, and activation states of all layers. Unlike existing methods that primarily focus on the final activation state, InternalInspector conducts a comprehensive analysis across all internal states of every layer to accurately identify both correct and incorrect prediction processes. By benchmarking InternalInspector against existing confidence estimation methods across various natural language understanding and generation tasks, including factual question answering, commonsense reasoning, and reading comprehension, InternalInspector achieves significantly higher accuracy in aligning the estimated confidence scores with the correctness of the LLM's predictions and lower calibration error. Furthermore, InternalInspector excels at HaluEval, a hallucination detection benchmark, outperforming other internal-based confidence estimation methods in this task.

In this work we present successor heads: attention heads that increment tokens with a natural ordering, such as numbers, months, and days. For example, successor heads increment 'Monday' into 'Tuesday'. We explain the successor head behavior with an approach rooted in mechanistic interpretability, the field that aims to explain how models complete tasks in human-understandable terms. Existing research in this area has found interpretable language model components in small toy models. However, results in toy models have not yet led to insights that explain the internals of frontier models and little is currently understood about the internal operations of large language models. In this paper, we analyze the behavior of successor heads in large language models (LLMs) and find that they implement abstract representations that are common to different architectures. They form in LLMs with as few as 31 million parameters, and at least as many as 12 billion parameters, such as GPT-2, Pythia, and Llama-2. We find a set of 'mod-10 features' that underlie how successor heads increment in LLMs across different architectures and sizes. We perform vector arithmetic with these features to edit head behavior and provide insights into numeric representations within LLMs. Additionally, we study the behavior of successor heads on natural language data, identifying interpretable polysemanticity in a Pythia successor head.

Self-consciousness, the introspection of one's existence and thoughts, represents a high-level cognitive process. As language models advance at an unprecedented pace, a critical question arises: Are these models becoming self-conscious? Drawing upon insights from psychological and neural science, this work presents a practical definition of self-consciousness for language models and refines ten core concepts. Our work pioneers an investigation into self-consciousness in language models by, for the first time, leveraging causal structural games to establish the functional definitions of the ten core concepts. Based on our definitions, we conduct a comprehensive four-stage experiment: quantification (evaluation of ten leading models), representation (visualization of self-consciousness within the models), manipulation (modification of the models' representation), and acquisition (fine-tuning the models on core concepts). Our findings indicate that although models are in the early stages of developing self-consciousness, there is a discernible representation of certain concepts within their internal mechanisms. However, these representations of self-consciousness are hard to manipulate positively at the current stage, yet they can be acquired through targeted fine-tuning. Our datasets and code are at https://github.com/OpenCausaLab/SelfConsciousness.

Understanding the internal representations learned by neural networks is a cornerstone challenge in the science of machine learning. While there have been significant recent strides in some cases towards understanding how neural networks implement specific target functions, this paper explores a complementary question -- why do networks arrive at particular computational strategies? Our inquiry focuses on the algebraic learning tasks of modular addition, sparse parities, and finite group operations. Our primary theoretical findings analytically characterize the features learned by stylized neural networks for these algebraic tasks. Notably, our main technique demonstrates how the principle of margin maximization alone can be used to fully specify the features learned by the network. Specifically, we prove that the trained networks utilize Fourier features to perform modular addition and employ features corresponding to irreducible group-theoretic representations to perform compositions in general groups, aligning closely with the empirical observations of Nanda et al. and Chughtai et al. More generally, we hope our techniques can help to foster a deeper understanding of why neural networks adopt specific computational strategies.

Large Language Models (LLMs) are increasingly expected to navigate the nuances of human emotion. While research confirms that LLMs can simulate emotional intelligence, their internal emotional mechanisms remain largely unexplored. This paper investigates the latent emotional representations within modern LLMs by asking: how, where, and for how long is emotion encoded in their neural architecture? To address this, we introduce a novel, large-scale Reddit corpus of approximately 400,000 utterances, balanced across seven basic emotions through a multi-stage process of classification, rewriting, and synthetic generation. Using this dataset, we employ lightweight "probes" to read out information from the hidden layers of various Qwen3 and LLaMA models without altering their parameters. Our findings reveal that LLMs develop a surprisingly well-defined internal geometry of emotion, which sharpens with model scale and significantly outperforms zero-shot prompting. We demonstrate that this emotional signal is not a final-layer phenomenon but emerges early and peaks mid-network. Furthermore, the internal states are both malleable (they can be influenced by simple system prompts) and persistent, as the initial emotional tone remains detectable for hundreds of subsequent tokens. We contribute our dataset, an open-source probing toolkit, and a detailed map of the emotional landscape within LLMs, offering crucial insights for developing more transparent and aligned AI systems. The code and dataset are open-sourced.

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.

As Large Language Models (LLMs) continue to advance, they exhibit certain cognitive patterns similar to those of humans that are not directly specified in training data. This study investigates this phenomenon by focusing on temporal cognition in LLMs. Leveraging the similarity judgment task, we find that larger models spontaneously establish a subjective temporal reference point and adhere to the Weber-Fechner law, whereby the perceived distance logarithmically compresses as years recede from this reference point. To uncover the mechanisms behind this behavior, we conducted multiple analyses across neuronal, representational, and informational levels. We first identify a set of temporal-preferential neurons and find that this group exhibits minimal activation at the subjective reference point and implements a logarithmic coding scheme convergently found in biological systems. Probing representations of years reveals a hierarchical construction process, where years evolve from basic numerical values in shallow layers to abstract temporal orientation in deep layers. Finally, using pre-trained embedding models, we found that the training corpus itself possesses an inherent, non-linear temporal structure, which provides the raw material for the model's internal construction. In discussion, we propose an experientialist perspective for understanding these findings, where the LLMs' cognition is viewed as a subjective construction of the external world by its internal representational system. This nuanced perspective implies the potential emergence of alien cognitive frameworks that humans cannot intuitively predict, pointing toward a direction for AI alignment that focuses on guiding internal constructions. Our code is available at https://TheOtherMind.github.io.

Recent work has proposed the linear representation hypothesis: that language models perform computation by manipulating one-dimensional representations of concepts ("features") in activation space. In contrast, we explore whether some language model representations may be inherently multi-dimensional. We begin by developing a rigorous definition of irreducible multi-dimensional features based on whether they can be decomposed into either independent or non-co-occurring lower-dimensional features. Motivated by these definitions, we design a scalable method that uses sparse autoencoders to automatically find multi-dimensional features in GPT-2 and Mistral 7B. These auto-discovered features include strikingly interpretable examples, e.g. circular features representing days of the week and months of the year. We identify tasks where these exact circles are used to solve computational problems involving modular arithmetic in days of the week and months of the year. Finally, we provide evidence that these circular features are indeed the fundamental unit of computation in these tasks with intervention experiments on Mistral 7B and Llama 3 8B, and we find further circular representations by breaking down the hidden states for these tasks into interpretable components.

We present a method for extracting monosemantic neurons, defined as latent dimensions that align with coherent and interpretable concepts, from user and item embeddings in recommender systems. Our approach employs a Sparse Autoencoder (SAE) to reveal semantic structure within pretrained representations. In contrast to work on language models, monosemanticity in recommendation must preserve the interactions between separate user and item embeddings. To achieve this, we introduce a prediction aware training objective that backpropagates through a frozen recommender and aligns the learned latent structure with the model's user-item affinity predictions. The resulting neurons capture properties such as genre, popularity, and temporal trends, and support post hoc control operations including targeted filtering and content promotion without modifying the base model. Our method generalizes across different recommendation models and datasets, providing a practical tool for interpretable and controllable personalization. Code and evaluation resources are available at https://github.com/DeltaLabTLV/Monosemanticity4Rec.

Object Hallucination (OH) has been acknowledged as one of the major trustworthy challenges in Large Vision-Language Models (LVLMs). Recent advancements in Large Language Models (LLMs) indicate that internal states, such as hidden states, encode the "overall truthfulness" of generated responses. However, it remains under-explored how internal states in LVLMs function and whether they could serve as "per-token" hallucination indicators, which is essential for mitigating OH. In this paper, we first conduct an in-depth exploration of LVLM internal states in relation to OH issues and discover that (1) LVLM internal states are high-specificity per-token indicators of hallucination behaviors. Moreover, (2) different LVLMs encode universal patterns of hallucinations in common latent subspaces, indicating that there exist "generic truthful directions" shared by various LVLMs. Based on these discoveries, we propose Truthful-Guided Pre-Intervention (TruthPrInt) that first learns the truthful direction of LVLM decoding and then applies truthful-guided inference-time intervention during LVLM decoding. We further propose ComnHallu to enhance both cross-LVLM and cross-data hallucination detection transferability by constructing and aligning hallucination latent subspaces. We evaluate TruthPrInt in extensive experimental settings, including in-domain and out-of-domain scenarios, over popular LVLMs and OH benchmarks. Experimental results indicate that TruthPrInt significantly outperforms state-of-the-art methods. Codes will be available at https://github.com/jinhaoduan/TruthPrInt.

We employ new tools from mechanistic interpretability in order to ask whether the internal structure of large language models (LLMs) shows correspondence to the linguistic structures which underlie the languages on which they are trained. In particular, we ask (1) when two languages employ the same morphosyntactic processes, do LLMs handle them using shared internal circuitry? and (2) when two languages require different morphosyntactic processes, do LLMs handle them using different internal circuitry? Using English and Chinese multilingual and monolingual models, we analyze the internal circuitry involved in two tasks. We find evidence that models employ the same circuit to handle the same syntactic process independently of the language in which it occurs, and that this is the case even for monolingual models trained completely independently. Moreover, we show that multilingual models employ language-specific components (attention heads and feed-forward networks) when needed to handle linguistic processes (e.g., morphological marking) that only exist in some languages. Together, our results provide new insights into how LLMs trade off between exploiting common structures and preserving linguistic differences when tasked with modeling multiple languages simultaneously.

Recent advances in Large Multimodal Models (LMMs) lead to significant breakthroughs in both academia and industry. One question that arises is how we, as humans, can understand their internal neural representations. This paper takes an initial step towards addressing this question by presenting a versatile framework to identify and interpret the semantics within LMMs. Specifically, 1) we first apply a Sparse Autoencoder(SAE) to disentangle the representations into human understandable features. 2) We then present an automatic interpretation framework to interpreted the open-semantic features learned in SAE by the LMMs themselves. We employ this framework to analyze the LLaVA-NeXT-8B model using the LLaVA-OV-72B model, demonstrating that these features can effectively steer the model's behavior. Our results contribute to a deeper understanding of why LMMs excel in specific tasks, including EQ tests, and illuminate the nature of their mistakes along with potential strategies for their rectification. These findings offer new insights into the internal mechanisms of LMMs and suggest parallels with the cognitive processes of the human brain.

Integrated Information Theory (IIT) provides a quantitative framework for explaining consciousness phenomenon, positing that conscious systems comprise elements integrated through causal properties. We apply IIT 3.0 and 4.0 -- the latest iterations of this framework -- to sequences of Large Language Model (LLM) representations, analyzing data derived from existing Theory of Mind (ToM) test results. Our study systematically investigates whether the differences of ToM test performances, when presented in the LLM representations, can be revealed by IIT estimates, i.e., Phi^{max} (IIT 3.0), Phi (IIT 4.0), Conceptual Information (IIT 3.0), and Phi-structure (IIT 4.0). Furthermore, we compare these metrics with the Span Representations independent of any estimate for consciousness. This additional effort aims to differentiate between potential "consciousness" phenomena and inherent separations within LLM representational space. We conduct comprehensive experiments examining variations across LLM transformer layers and linguistic spans from stimuli. Our results suggest that sequences of contemporary Transformer-based LLM representations lack statistically significant indicators of observed "consciousness" phenomena but exhibit intriguing patterns under spatio-permutational analyses. The Appendix and code are available as Supplementary Materials at: https://doi.org/10.1016/j.nlp.2025.100163.

Large Language Models (LLMs) often generate inconsistent responses when prompted with semantically equivalent paraphrased inputs. Recently, activation steering, a technique that modulates LLMs' behaviours by adjusting their latent representations during inference time, has been explored to improve the semantic consistency of LLMs. However, these methods typically operate at the model component level, such as layer hidden states or attention head outputs. They face a challenge due to the ``polysemanticity issue'', where the model components of LLMs typically encode multiple entangled features, making precise steering difficult. To address this challenge, we drill down to feature-level representations and propose LF-Steering, a novel activation steering approach to precisely identify latent feature representations responsible for semantic inconsistency. More specifically, our method maps the hidden states of the relevant transformer layer into a sparsely activated, high-dimensional feature space based on a sparse autoencoder (SAE), ensuring model steering based on decoupled feature representations with minimal interference. Comprehensive experiments on NLU and NLG datasets demonstrate the effectiveness of our method in enhancing semantic consistency, resulting in significant performance gains for various NLU and NLG tasks.

Implicit neural representations (INR) have gained significant popularity for signal and image representation for many end-tasks, such as superresolution, 3D modeling, and more. Most INR architectures rely on sinusoidal positional encoding, which accounts for high-frequency information in data. However, the finite encoding size restricts the model's representational power. Higher representational power is needed to go from representing a single given image to representing large and diverse datasets. Our approach addresses this gap by representing an image with a polynomial function and eliminates the need for positional encodings. Therefore, to achieve a progressively higher degree of polynomial representation, we use element-wise multiplications between features and affine-transformed coordinate locations after every ReLU layer. The proposed method is evaluated qualitatively and quantitatively on large datasets like ImageNet. The proposed Poly-INR model performs comparably to state-of-the-art generative models without any convolution, normalization, or self-attention layers, and with far fewer trainable parameters. With much fewer training parameters and higher representative power, our approach paves the way for broader adoption of INR models for generative modeling tasks in complex domains. The code is available at https://github.com/Rajhans0/Poly_INR

Neural Module Networks, originally proposed for the task of visual question answering, are a class of neural network architectures that involve human-specified neural modules, each designed for a specific form of reasoning. In current formulations of such networks only the parameters of the neural modules and/or the order of their execution is learned. In this work, we further expand this approach and also learn the underlying internal structure of modules in terms of the ordering and combination of simple and elementary arithmetic operators. Our results show that one is indeed able to simultaneously learn both internal module structure and module sequencing without extra supervisory signals for module execution sequencing. With this approach, we report performance comparable to models using hand-designed modules.

The success of pre-trained contextualized representations has prompted researchers to analyze them for the presence of linguistic information. Indeed, it is natural to assume that these pre-trained representations do encode some level of linguistic knowledge as they have brought about large empirical improvements on a wide variety of NLP tasks, which suggests they are learning true linguistic generalization. In this work, we focus on intrinsic probing, an analysis technique where the goal is not only to identify whether a representation encodes a linguistic attribute but also to pinpoint where this attribute is encoded. We propose a novel latent-variable formulation for constructing intrinsic probes and derive a tractable variational approximation to the log-likelihood. Our results show that our model is versatile and yields tighter mutual information estimates than two intrinsic probes previously proposed in the literature. Finally, we find empirical evidence that pre-trained representations develop a cross-lingually entangled notion of morphosyntax.

There is growing interest in leveraging mechanistic interpretability and controllability to better understand and influence the internal dynamics of large language models (LLMs). However, current methods face fundamental challenges in reliably localizing and manipulating feature representations. Sparse Autoencoders (SAEs) have recently emerged as a promising direction for feature extraction at scale, yet they, too, are limited by incomplete feature isolation and unreliable monosemanticity. To systematically quantify these limitations, we introduce Feature Monosemanticity Score (FMS), a novel metric to quantify feature monosemanticity in latent representation. Building on these insights, we propose Guided Sparse Autoencoders (G-SAE), a method that conditions latent representations on labeled concepts during training. We demonstrate that reliable localization and disentanglement of target concepts within the latent space improve interpretability, detection of behavior, and control. Specifically, our evaluations on toxicity detection, writing style identification, and privacy attribute recognition show that G-SAE not only enhances monosemanticity but also enables more effective and fine-grained steering with less quality degradation. Our findings provide actionable guidelines for measuring and advancing mechanistic interpretability and control of LLMs.

Every day, humans perceive objects and communicate these perceptions through various channels. In this paper, we present a computational model designed to track and simulate the perception of objects, as well as their representations as conveyed in communication. We delineate two fundamental components of our internal representation, termed "observed" and "seen", which we correlate with established concepts in computer vision, namely encoding and decoding. These components are integrated into semiotic networks, which simulate perceptual inference of object perception and human communication. Our model of object perception by a person allows us to define object perception by {\em a network}. We demonstrate this with an example of an image baseline classifier by constructing a new network that includes the baseline classifier and an additional layer. This layer produces the images "perceived" by the entire network, transforming it into a perceptualized image classifier. This facilitates visualization of the acquired network. Within our network, the image representations become more efficient for classification tasks when they are assembled and randomized. In our experiments, the perceptualized network outperformed the baseline classifier on MNIST training databases consisting of a restricted number of images. Our model is not limited to persons and can be applied to any system featuring a loop involving the processing from "internal" to "external" representations.

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".

In "Backprop as functor", the authors show that the fundamental elements of deep learning -- gradient descent and backpropagation -- can be conceptualized as a strong monoidal functor Para(Euc)toLearn from the category of parameterized Euclidean spaces to that of learners, a category developed explicitly to capture parameter update and backpropagation. It was soon realized that there is an isomorphism LearncongPara(Slens), where Slens is the symmetric monoidal category of simple lenses as used in functional programming. In this note, we observe that Slens is a full subcategory of Poly, the category of polynomial functors in one variable, via the functor Amapsto Ay^A. Using the fact that (Poly,otimes) is monoidal closed, we show that a map Ato B in Para(Slens) has a natural interpretation in terms of dynamical systems (more precisely, generalized Moore machines) whose interface is the internal-hom type [Ay^A,By^B]. Finally, we review the fact that the category p-Coalg of dynamical systems on any p in Poly forms a topos, and consider the logical propositions that can be stated in its internal language. We give gradient descent as an example, and we conclude by discussing some directions for future work.

We analyse perception and memory, using mathematical models for knowledge graphs and tensors, to gain insights into the corresponding functionalities of the human mind. Our discussion is based on the concept of propositional sentences consisting of subject-predicate-object (SPO) triples for expressing elementary facts. SPO sentences are the basis for most natural languages but might also be important for explicit perception and declarative memories, as well as intra-brain communication and the ability to argue and reason. A set of SPO sentences can be described as a knowledge graph, which can be transformed into an adjacency tensor. We introduce tensor models, where concepts have dual representations as indices and associated embeddings, two constructs we believe are essential for the understanding of implicit and explicit perception and memory in the brain. We argue that a biological realization of perception and memory imposes constraints on information processing. In particular, we propose that explicit perception and declarative memories require a semantic decoder, which, in a simple realization, is based on four layers: First, a sensory memory layer, as a buffer for sensory input, second, an index layer representing concepts, third, a memoryless representation layer for the broadcasting of information ---the "blackboard", or the "canvas" of the brain--- and fourth, a working memory layer as a processing center and data buffer. We discuss the operations of the four layers and relate them to the global workspace theory. In a Bayesian brain interpretation, semantic memory defines the prior for observable triple statements. We propose that ---in evolution and during development--- semantic memory, episodic memory, and natural language evolved as emergent properties in agents' process to gain a deeper understanding of sensory information.

How do sequence models represent their decision-making process? Prior work suggests that Othello-playing neural network learned nonlinear models of the board state (Li et al., 2023). In this work, we provide evidence of a closely related linear representation of the board. In particular, we show that probing for "my colour" vs. "opponent's colour" may be a simple yet powerful way to interpret the model's internal state. This precise understanding of the internal representations allows us to control the model's behaviour with simple vector arithmetic. Linear representations enable significant interpretability progress, which we demonstrate with further exploration of how the world model is computed.

Large language models (LLMs) have demonstrated enhanced performance through the Thinking then Responding paradigm, where models generate internal thoughts before final responses (aka, System 2 thinking). However, existing research lacks a systematic understanding of the mechanisms underlying how thinking patterns affect performance across model sizes. In this work, we conduct a comprehensive analysis of the impact of various thinking types on model performance and introduce ThinkPatterns-21k, a curated dataset comprising 21k instruction-response pairs (QA) collected from existing instruction-following datasets with five thinking types. For each pair, we augment it with five distinct internal thinking patterns: one unstructured thinking (monologue) and four structured variants (decomposition, self-ask, self-debate and self-critic), while maintaining the same instruction and response. Through extensive evaluation across different model sizes (3B-32B parameters), we have two key findings: (1) smaller models (<30B parameters) can benefit from most of structured thinking patterns, while larger models (32B) with structured thinking like decomposition would degrade performance and (2) unstructured monologue demonstrates broad effectiveness across different model sizes. Finally, we released all of our datasets, checkpoints, training logs of diverse thinking patterns to reproducibility, aiming to facilitate further research in this direction.

How do humans learn language, and can the first language be learned at all? These fundamental questions are still hotly debated. In contemporary linguistics, there are two major schools of thought that give completely opposite answers. According to Chomsky's theory of universal grammar, language cannot be learned because children are not exposed to sufficient data in their linguistic environment. In contrast, usage-based models of language assume a profound relationship between language structure and language use. In particular, contextual mental processing and mental representations are assumed to have the cognitive capacity to capture the complexity of actual language use at all levels. The prime example is syntax, i.e., the rules by which words are assembled into larger units such as sentences. Typically, syntactic rules are expressed as sequences of word classes. However, it remains unclear whether word classes are innate, as implied by universal grammar, or whether they emerge during language acquisition, as suggested by usage-based approaches. Here, we address this issue from a machine learning and natural language processing perspective. In particular, we trained an artificial deep neural network on predicting the next word, provided sequences of consecutive words as input. Subsequently, we analyzed the emerging activation patterns in the hidden layers of the neural network. Strikingly, we find that the internal representations of nine-word input sequences cluster according to the word class of the tenth word to be predicted as output, even though the neural network did not receive any explicit information about syntactic rules or word classes during training. This surprising result suggests, that also in the human brain, abstract representational categories such as word classes may naturally emerge as a consequence of predictive coding and processing during language acquisition.

In Decentralized Multi-Agent Reinforcement Learning (MARL), the development of Emergent Communication has long been constrained by the ``Joint Exploration Dilemma'', leading agents to fall into a ``Communication Vacuum Equilibrium'' . Traditional methods address this by introducing inductive biases to facilitate communication emergence . This study fundamentally questions whether such artificial inductive biases are, in fact, over-engineering. Through experiments with the ``AI Mother Tongue'' (AIM) framework, based on a Vector Quantized Variational Autoencoder (VQ-VAE), we demonstrate that when agents possess an endogenous symbol system, their neural representations naturally exhibit spontaneous semantic compression and Nash equilibrium-driven semantic convergence, achieving effective symbolic communication without external inductive biases. This aligns with recent neuroscience findings suggesting that the human brain does not directly use human language for internal thought , and resonates with research on ``soft thinking'' capabilities in Large Language Models (LLMs) . Compared to traditional explicit communication methods, AIM demonstrates stronger generality and efficiency. The interpretable analysis toolkit developed in this study confirms that symbol usage exhibits a significant power-law distribution, leading to three major theoretical insights: the ``Neural Communication Hypothesis'', the ``Tool-First Principle'', and the ``Semantic Interpretability Paradigm''. Future research will explore the integration of Hierarchical Quantized Variational Autoencoders (HQ-VAE) to enhance AIM's complex expressive capabilities and investigate the potential for ``Reinforcement Learning (RL) Low-Level Pre-training''. This discovery offers new avenues for bridging symbolism and connectionism.

Modelling compositionality has been a longstanding area of research in the field of vector space semantics. The categorical approach to compositionality maps grammar onto vector spaces in a principled way, but comes under fire for requiring the formation of very high-dimensional matrices and tensors, and therefore being computationally infeasible. In this paper I show how a linear simplification of recursive neural tensor network models can be mapped directly onto the categorical approach, giving a way of computing the required matrices and tensors. This mapping suggests a number of lines of research for both categorical compositional vector space models of meaning and for recursive neural network models of compositionality.

Several studies have explored the mechanisms of large language models (LLMs) in coding tasks, but most have focused on programming languages (PLs) in a monolingual setting. In this paper, we investigate the relationship between multiple PLs and English in the concept space of LLMs. We perform a few-shot translation task on 21 PL pairs using two Llama-based models. By decoding the embeddings of intermediate layers during this task, we observe that the concept space is closer to English (including PL keywords) and assigns high probabilities to English tokens in the second half of the intermediate layers. We analyze neuron activations for 11 PLs and English, finding that while language-specific neurons are primarily concentrated in the bottom layers, those exclusive to each PL tend to appear in the top layers. For PLs that are highly aligned with multiple other PLs, identifying language-specific neurons is not feasible. These PLs also tend to have a larger keyword set than other PLs and are closer to the model's concept space regardless of the input/output PL in the translation task. Our findings provide insights into how LLMs internally represent PLs, revealing structural patterns in the model's concept space. Code is available at https://github.com/cisnlp/code-specific-neurons.

We report the presence of a simple neural mechanism that represents an input-output function as a vector within autoregressive transformer language models (LMs). Using causal mediation analysis on a diverse range of in-context-learning (ICL) tasks, we find that a small number attention heads transport a compact representation of the demonstrated task, which we call a function vector (FV). FVs are robust to changes in context, i.e., they trigger execution of the task on inputs such as zero-shot and natural text settings that do not resemble the ICL contexts from which they are collected. We test FVs across a range of tasks, models, and layers and find strong causal effects across settings in middle layers. We investigate the internal structure of FVs and find while that they often contain information that encodes the output space of the function, this information alone is not sufficient to reconstruct an FV. Finally, we test semantic vector composition in FVs, and find that to some extent they can be summed to create vectors that trigger new complex tasks. Taken together, our findings suggest that LLMs contain internal abstractions of general-purpose functions that can be invoked in a variety of contexts.

Compositionality, the notion that the meaning of an expression is constructed from the meaning of its parts and syntactic rules, permits the infinite productivity of human language. For the first time, artificial language models (LMs) are able to match human performance in a number of compositional generalization tasks. However, much remains to be understood about the representational mechanisms underlying these abilities. We take a high-level geometric approach to this problem by relating the degree of compositionality in a dataset to the intrinsic dimensionality of its representations under an LM, a measure of feature complexity. We find not only that the degree of dataset compositionality is reflected in representations' intrinsic dimensionality, but that the relationship between compositionality and geometric complexity arises due to learned linguistic features over training. Finally, our analyses reveal a striking contrast between linear and nonlinear dimensionality, showing that they respectively encode formal and semantic aspects of linguistic composition.

Chain-of-thought (CoT) reasoning has enabled transformer-based language models to excel at complex mathematics and multi-step planning. However, in standard decoder-only architectures, these reasoning steps are externalized in natural language, improving interpretability at the cost of efficiency. To capture reasoning that is not easily represented in words, many works have explored recurrent architectures that aim to internalize reasoning in latent space, potentially supporting latent CoT. In this paper, we investigate whether such reasoning structures emerge in Huginn-3.5B, a depth-recurrent Transformer that reuses layers at inference time without increasing parameter count. We examine the model's internal behavior on arithmetic tasks using a suite of probing techniques including the Logit Lens and Coda Lens. Our findings reveal limited evidence of interpretable latent CoT by tracking rank trajectories of final and intermediate result tokens. Furthermore, we uncover significant probing inconsistencies across recurrent blocks, where the interpretability of hidden states depends heavily on both the layer index and the decoding method. Finally, we empirically show that increasing recurrence depth yields only marginal gains and falls well short of models that explicitly externalize reasoning steps. The code is available at https://github.com/wenquanlu/huginn-latent-cot.

We introduce a new type of deep contextualized word representation that models both (1) complex characteristics of word use (e.g., syntax and semantics), and (2) how these uses vary across linguistic contexts (i.e., to model polysemy). Our word vectors are learned functions of the internal states of a deep bidirectional language model (biLM), which is pre-trained on a large text corpus. We show that these representations can be easily added to existing models and significantly improve the state of the art across six challenging NLP problems, including question answering, textual entailment and sentiment analysis. We also present an analysis showing that exposing the deep internals of the pre-trained network is crucial, allowing downstream models to mix different types of semi-supervision signals.

Large language models (LLMs) have multilingual capabilities and can solve tasks across various languages. However, we show that current LLMs make key decisions in a representation space closest to English, regardless of their input and output languages. Exploring the internal representations with a logit lens for sentences in French, German, Dutch, and Mandarin, we show that the LLM first emits representations close to English for semantically-loaded words before translating them into the target language. We further show that activation steering in these LLMs is more effective when the steering vectors are computed in English rather than in the language of the inputs and outputs. This suggests that multilingual LLMs perform key reasoning steps in a representation that is heavily shaped by English in a way that is not transparent to system users.

We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints which models must satisfy and specifying their implementations. Focusing on building a such a bridge, we propose to apply category theory -- precisely, the universal algebra of monads valued in a 2-category of parametric maps -- as a single theory elegantly subsuming both of these flavours of neural network design. To defend our position, we show how this theory recovers constraints induced by geometric deep learning, as well as implementations of many architectures drawn from the diverse landscape of neural networks, such as RNNs. We also illustrate how the theory naturally encodes many standard constructs in computer science and automata theory.

We introduce a novel framework that utilizes the internal weight activations of modern Large Language Models (LLMs) to construct a metric space of languages. Unlike traditional approaches based on hand-crafted linguistic features, our method automatically derives high-dimensional vector representations by computing weight importance scores via an adapted pruning algorithm. Our approach captures intrinsic language characteristics that reflect linguistic phenomena. We validate our approach across diverse datasets and multilingual LLMs, covering 106 languages. The results align well with established linguistic families while also revealing unexpected inter-language connections that may indicate historical contact or language evolution. The source code, computed language latent vectors, and visualization tool are made publicly available at https://github.com/mshamrai/deep-language-geometry.

Instruction-following is crucial for building AI agents with large language models (LLMs), as these models must adhere strictly to user-provided constraints and guidelines. However, LLMs often fail to follow even simple and clear instructions. To improve instruction-following behavior and prevent undesirable outputs, a deeper understanding of how LLMs' internal states relate to these outcomes is required. Our analysis of LLM internal states reveal a dimension in the input embedding space linked to successful instruction-following. We demonstrate that modifying representations along this dimension improves instruction-following success rates compared to random changes, without compromising response quality. Further investigation reveals that this dimension is more closely related to the phrasing of prompts rather than the inherent difficulty of the task or instructions. This discovery also suggests explanations for why LLMs sometimes fail to follow clear instructions and why prompt engineering is often effective, even when the content remains largely unchanged. This work provides insight into the internal workings of LLMs' instruction-following, paving the way for reliable LLM agents.

We provide a construction for categorical representation learning and introduce the foundations of "categorifier". The central theme in representation learning is the idea of everything to vector. Every object in a dataset S can be represented as a vector in R^n by an encoding map E: Obj(S)toR^n. More importantly, every morphism can be represented as a matrix E: Hom(S)toR^{n}_{n}. The encoding map E is generally modeled by a deep neural network. The goal of representation learning is to design appropriate tasks on the dataset to train the encoding map (assuming that an encoding is optimal if it universally optimizes the performance on various tasks). However, the latter is still a set-theoretic approach. The goal of the current article is to promote the representation learning to a new level via a category-theoretic approach. As a proof of concept, we provide an example of a text translator equipped with our technology, showing that our categorical learning model outperforms the current deep learning models by 17 times. The content of the current article is part of the recent US patent proposal (patent application number: 63110906).

We investigate compositional structures in data embeddings from pre-trained vision-language models (VLMs). Traditionally, compositionality has been associated with algebraic operations on embeddings of words from a pre-existing vocabulary. In contrast, we seek to approximate representations from an encoder as combinations of a smaller set of vectors in the embedding space. These vectors can be seen as "ideal words" for generating concepts directly within the embedding space of the model. We first present a framework for understanding compositional structures from a geometric perspective. We then explain what these compositional structures entail probabilistically in the case of VLM embeddings, providing intuitions for why they arise in practice. Finally, we empirically explore these structures in CLIP's embeddings and we evaluate their usefulness for solving different vision-language tasks such as classification, debiasing, and retrieval. Our results show that simple linear algebraic operations on embedding vectors can be used as compositional and interpretable methods for regulating the behavior of VLMs.

Scientific studies of consciousness rely on objects whose existence is assumed to be independent of any consciousness. On the contrary, we assume consciousness to be fundamental, and that one of the main features of consciousness is characterized as being other-dependent. We set up a framework which naturally subsumes this feature by defining a compact closed category where morphisms represent conscious processes. These morphisms are a composition of a set of generators, each being specified by their relations with other generators, and therefore co-dependent. The framework is general enough and fits well into a compositional model of consciousness. Interestingly, we also show how our proposal may become a step towards avoiding the hard problem of consciousness, and thereby address the combination problem of conscious experiences.

We investigate the internal representations of vision-and-language models (VLMs) and how they encode task representations. We consider tasks specified through examples or instructions, using either text or image inputs. Surprisingly, we find that conceptually similar tasks are mapped to similar task vector representations, regardless of how they are specified. Our findings suggest that to output answers, tokens in VLMs undergo three distinct phases: input, task, and answer, a process which is consistent across different modalities and specifications. The task vectors we identify in VLMs are general enough to be derived in one modality (e.g., text) and transferred to another (e.g., image). Additionally, we find that ensembling exemplar and instruction based task vectors produce better task representations. Taken together, these insights shed light on the underlying mechanisms of VLMs, particularly their ability to represent tasks in a shared manner across different modalities and task specifications. Project page: https://task-vectors-are-cross-modal.github.io.

Natural language is composed of words, but modern large language models (LLMs) process sub-words as input. A natural question raised by this discrepancy is whether LLMs encode words internally, and if so how. We present evidence that LLMs engage in an intrinsic detokenization process, where sub-word sequences are combined into coherent whole-word representations at their last token. Our experiments show that this process primarily takes place within the early and middle layers of the model. We further demonstrate its robustness to arbitrary splits (e.g., "cats" to "ca" and "ts"), typos, and importantly-to out-of-vocabulary words: when feeding the last token internal representations of such words to the model as input, it can "understand" them as the complete word despite never seeing such representations as input during training. Our findings suggest that LLMs maintain a latent vocabulary beyond the tokenizer's scope. These insights provide a practical, finetuning-free application for expanding the vocabulary of pre-trained models. By enabling the addition of new vocabulary words, we reduce input length and inference iterations, which reduces both space and model latency, with little to no loss in model accuracy.

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

We investigate the generalization capabilities of small language models under two popular adaptation paradigms: few-shot prompting and supervised fine-tuning. While prompting is often favored for its parameter efficiency and flexibility, it remains unclear how robust this approach is in low-resource settings and under distributional shifts. This paper presents a comparative study of prompting and fine-tuning across task formats, prompt styles, and model scales, with a focus on their behavior in both in-distribution and out-of-distribution (OOD) settings. Beyond accuracy, we analyze the internal representations learned by each approach to assess the stability and abstraction of task-specific features. Our findings highlight critical differences in how small models internalize and generalize knowledge under different adaptation strategies. This work offers practical guidance for model selection in low-data regimes and contributes empirical insight into the ongoing debate over prompting versus fine-tuning. Code for the experiments is available at the following

Coecke, Sadrzadeh, and Clark (arXiv:1003.4394v1 [cs.CL]) developed a compositional model of meaning for distributional semantics, in which each word in a sentence has a meaning vector and the distributional meaning of the sentence is a function of the tensor products of the word vectors. Abstractly speaking, this function is the morphism corresponding to the grammatical structure of the sentence in the category of finite dimensional vector spaces. In this paper, we provide a concrete method for implementing this linear meaning map, by constructing a corpus-based vector space for the type of sentence. Our construction method is based on structured vector spaces whereby meaning vectors of all sentences, regardless of their grammatical structure, live in the same vector space. Our proposed sentence space is the tensor product of two noun spaces, in which the basis vectors are pairs of words each augmented with a grammatical role. This enables us to compare meanings of sentences by simply taking the inner product of their vectors.

Recent works have demonstrated reasonable success of representation learning in hypercomplex space. Specifically, "fully-connected layers with Quaternions" (4D hypercomplex numbers), which replace real-valued matrix multiplications in fully-connected layers with Hamilton products of Quaternions, both enjoy parameter savings with only 1/4 learnable parameters and achieve comparable performance in various applications. However, one key caveat is that hypercomplex space only exists at very few predefined dimensions (4D, 8D, and 16D). This restricts the flexibility of models that leverage hypercomplex multiplications. To this end, we propose parameterizing hypercomplex multiplications, allowing models to learn multiplication rules from data regardless of whether such rules are predefined. As a result, our method not only subsumes the Hamilton product, but also learns to operate on any arbitrary nD hypercomplex space, providing more architectural flexibility using arbitrarily 1/n learnable parameters compared with the fully-connected layer counterpart. Experiments of applications to the LSTM and Transformer models on natural language inference, machine translation, text style transfer, and subject verb agreement demonstrate architectural flexibility and effectiveness of the proposed approach.

Large Language Models (LLMs) are prone to hallucination, the generation of plausible yet factually incorrect statements. This work investigates the intrinsic, architectural origins of this failure mode through three primary contributions.First, to enable the reliable tracing of internal semantic failures, we propose Distributional Semantics Tracing (DST), a unified framework that integrates established interpretability techniques to produce a causal map of a model's reasoning, treating meaning as a function of context (distributional semantics). Second, we pinpoint the model's layer at which a hallucination becomes inevitable, identifying a specific commitment layer where a model's internal representations irreversibly diverge from factuality. Third, we identify the underlying mechanism for these failures. We observe a conflict between distinct computational pathways, which we interpret using the lens of dual-process theory: a fast, heuristic associative pathway (akin to System 1) and a slow, deliberate contextual pathway (akin to System 2), leading to predictable failure modes such as Reasoning Shortcut Hijacks. Our framework's ability to quantify the coherence of the contextual pathway reveals a strong negative correlation (rho = -0.863) with hallucination rates, implying that these failures are predictable consequences of internal semantic weakness. The result is a mechanistic account of how, when, and why hallucinations occur within the Transformer architecture.

Despite rapid adoption and deployment of large language models (LLMs), the internal computations of these models remain opaque and poorly understood. In this work, we seek to understand how high-level human-interpretable features are represented within the internal neuron activations of LLMs. We train k-sparse linear classifiers (probes) on these internal activations to predict the presence of features in the input; by varying the value of k we study the sparsity of learned representations and how this varies with model scale. With k=1, we localize individual neurons which are highly relevant for a particular feature, and perform a number of case studies to illustrate general properties of LLMs. In particular, we show that early layers make use of sparse combinations of neurons to represent many features in superposition, that middle layers have seemingly dedicated neurons to represent higher-level contextual features, and that increasing scale causes representational sparsity to increase on average, but there are multiple types of scaling dynamics. In all, we probe for over 100 unique features comprising 10 different categories in 7 different models spanning 70 million to 6.9 billion parameters.

Large language models follow a lineage of many NLP applications that were directly inspired by distributional semantics, but do not seem to be closely related to it anymore. In this paper, we propose to employ the distributional theory of meaning once again. Using Independent Component Analysis to overcome some of its challenging aspects, we show that large language models represent semantic features in their hidden states.

Sparse Autoencoders (SAEs) have recently been shown to enhance interpretability and steerability in Large Language Models (LLMs). In this work, we extend the application of SAEs to Vision-Language Models (VLMs), such as CLIP, and introduce a comprehensive framework for evaluating monosemanticity in vision representations. Our experimental results reveal that SAEs trained on VLMs significantly enhance the monosemanticity of individual neurons while also exhibiting hierarchical representations that align well with expert-defined structures (e.g., iNaturalist taxonomy). Most notably, we demonstrate that applying SAEs to intervene on a CLIP vision encoder, directly steer output from multimodal LLMs (e.g., LLaVA) without any modifications to the underlying model. These findings emphasize the practicality and efficacy of SAEs as an unsupervised approach for enhancing both the interpretability and control of VLMs.

It has been observed that representations learned by distinct neural networks conceal structural similarities when the models are trained under similar inductive biases. From a geometric perspective, identifying the classes of transformations and the related invariances that connect these representations is fundamental to unlocking applications, such as merging, stitching, and reusing different neural modules. However, estimating task-specific transformations a priori can be challenging and expensive due to several factors (e.g., weights initialization, training hyperparameters, or data modality). To this end, we introduce a versatile method to directly incorporate a set of invariances into the representations, constructing a product space of invariant components on top of the latent representations without requiring prior knowledge about the optimal invariance to infuse. We validate our solution on classification and reconstruction tasks, observing consistent latent similarity and downstream performance improvements in a zero-shot stitching setting. The experimental analysis comprises three modalities (vision, text, and graphs), twelve pretrained foundational models, nine benchmarks, and several architectures trained from scratch.

The Linear Representation Hypothesis (LRH) states that neural networks learn to encode concepts as directions in activation space, and a strong version of the LRH states that models learn only such encodings. In this paper, we present a counterexample to this strong LRH: when trained to repeat an input token sequence, gated recurrent neural networks (RNNs) learn to represent the token at each position with a particular order of magnitude, rather than a direction. These representations have layered features that are impossible to locate in distinct linear subspaces. To show this, we train interventions to predict and manipulate tokens by learning the scaling factor corresponding to each sequence position. These interventions indicate that the smallest RNNs find only this magnitude-based solution, while larger RNNs have linear representations. These findings strongly indicate that interpretability research should not be confined by the LRH.

We investigate the internal representations of vision-language models (VLMs) to address hallucinations, a persistent challenge despite advances in model size and training. We project VLMs' internal image representations to their language vocabulary and observe more confident output probabilities on real objects than hallucinated objects. We additionally use these output probabilities to spatially localize real objects. Building on this approach, we introduce a knowledge erasure algorithm that removes hallucinations by linearly orthogonalizing image features with respect to hallucinated object features. We show that targeted edits to a model's latent representations can reduce hallucinations by up to 25.7% on the COCO2014 dataset while preserving performance. Our findings demonstrate how a deeper understanding of VLMs' latent representations can enhance reliability and enable novel capabilities, such as zero-shot segmentation.

Motivated by the hypothesis that neural network representations encode abstract, interpretable features as linearly accessible, approximately orthogonal directions, sparse autoencoders (SAEs) have become a popular tool in interpretability. However, recent work has demonstrated phenomenology of model representations that lies outside the scope of this hypothesis, showing signatures of hierarchical, nonlinear, and multi-dimensional features. This raises the question: do SAEs represent features that possess structure at odds with their motivating hypothesis? If not, does avoiding this mismatch help identify said features and gain further insights into neural network representations? To answer these questions, we take a construction-based approach and re-contextualize the popular matching pursuits (MP) algorithm from sparse coding to design MP-SAE -- an SAE that unrolls its encoder into a sequence of residual-guided steps, allowing it to capture hierarchical and nonlinearly accessible features. Comparing this architecture with existing SAEs on a mixture of synthetic and natural data settings, we show: (i) hierarchical concepts induce conditionally orthogonal features, which existing SAEs are unable to faithfully capture, and (ii) the nonlinear encoding step of MP-SAE recovers highly meaningful features, helping us unravel shared structure in the seemingly dichotomous representation spaces of different modalities in a vision-language model, hence demonstrating the assumption that useful features are solely linearly accessible is insufficient. We also show that the sequential encoder principle of MP-SAE affords an additional benefit of adaptive sparsity at inference time, which may be of independent interest. Overall, we argue our results provide credence to the idea that interpretability should begin with the phenomenology of representations, with methods emerging from assumptions that fit it.

We frame the problem of unifying representations in neural models as one of sparse model recovery and introduce a framework that extends sparse autoencoders (SAEs) to lifted spaces and infinite-dimensional function spaces, enabling mechanistic interpretability of large neural operators (NO). While the Platonic Representation Hypothesis suggests that neural networks converge to similar representations across architectures, the representational properties of neural operators remain underexplored despite their growing importance in scientific computing. We compare the inference and training dynamics of SAEs, lifted-SAE, and SAE neural operators. We highlight how lifting and operator modules introduce beneficial inductive biases, enabling faster recovery, improved recovery of smooth concepts, and robust inference across varying resolutions, a property unique to neural operators.

As Large Language Models become more ubiquitous across domains, it becomes important to examine their inherent limitations critically. This work argues that hallucinations in language models are not just occasional errors but an inevitable feature of these systems. We demonstrate that hallucinations stem from the fundamental mathematical and logical structure of LLMs. It is, therefore, impossible to eliminate them through architectural improvements, dataset enhancements, or fact-checking mechanisms. Our analysis draws on computational theory and Godel's First Incompleteness Theorem, which references the undecidability of problems like the Halting, Emptiness, and Acceptance Problems. We demonstrate that every stage of the LLM process-from training data compilation to fact retrieval, intent classification, and text generation-will have a non-zero probability of producing hallucinations. This work introduces the concept of Structural Hallucination as an intrinsic nature of these systems. By establishing the mathematical certainty of hallucinations, we challenge the prevailing notion that they can be fully mitigated.

Despite superior reasoning prowess demonstrated by Large Language Models (LLMs) with Chain-of-Thought (CoT) prompting, a lack of understanding prevails around the internal mechanisms of the models that facilitate CoT generation. This work investigates the neural sub-structures within LLMs that manifest CoT reasoning from a mechanistic point of view. From an analysis of LLaMA-2 7B applied to multistep reasoning over fictional ontologies, we demonstrate that LLMs deploy multiple parallel pathways of answer generation for step-by-step reasoning. These parallel pathways provide sequential answers from the input question context as well as the generated CoT. We observe a striking functional rift in the middle layers of the LLM. Token representations in the initial half remain strongly biased towards the pretraining prior, with the in-context taking over abruptly in the later half. This internal phase shift manifests in different functional components: attention heads that write the answer token predominantly appear in the later half, attention heads that move information along ontological relationships appear exclusively in the initial half, and so on. To the best of our knowledge, this is the first attempt towards mechanistic investigation of CoT reasoning in LLMs.

Large language models (LLMs) can sometimes report the strategies they actually use to solve tasks, but they can also fail to do so. This suggests some degree of metacognition -- the capacity to monitor one's own cognitive processes for subsequent reporting and self-control. Metacognitive abilities enhance AI capabilities but raise safety concerns, as models might obscure their internal processes to evade neural-activation-based oversight mechanisms designed to detect harmful behaviors. Given society's increased reliance on these models, it is critical that we understand the limits of their metacognitive abilities, particularly their ability to monitor their internal activations. To address this, we introduce a neuroscience-inspired neurofeedback paradigm designed to quantify the ability of LLMs to explicitly report and control their activation patterns. By presenting models with sentence-label pairs where labels correspond to sentence-elicited internal activations along specific directions in the neural representation space, we demonstrate that LLMs can learn to report and control these activations. The performance varies with several factors: the number of example pairs provided, the semantic interpretability of the target neural direction, and the variance explained by that direction. These results reveal a "metacognitive space" with dimensionality much lower than the model's neural space, suggesting LLMs can monitor only a subset of their neural mechanisms. Our findings provide empirical evidence quantifying metacognitive capabilities in LLMs, with significant implications for AI safety.

Distributional word representation methods exploit word co-occurrences to build compact vector encodings of words. While these representations enjoy widespread use in modern natural language processing, it is unclear whether they accurately encode all necessary facets of conceptual meaning. In this paper, we evaluate how well these representations can predict perceptual and conceptual features of concrete concepts, drawing on two semantic norm datasets sourced from human participants. We find that several standard word representations fail to encode many salient perceptual features of concepts, and show that these deficits correlate with word-word similarity prediction errors. Our analyses provide motivation for grounded and embodied language learning approaches, which may help to remedy these deficits.

Large Language Models (LLMs) have demonstrated pronounced ideological leanings, yet the stability and depth of these positions remain poorly understood. Surface-level responses can often be manipulated through simple prompt engineering, calling into question whether they reflect a coherent underlying ideology. This paper investigates the concept of "ideological depth" in LLMs, defined as the robustness and complexity of their internal political representations. We employ a dual approach: first, we measure the "steerability" of two well-known open-source LLMs using instruction prompting and activation steering. We find that while some models can easily switch between liberal and conservative viewpoints, others exhibit resistance or an increased rate of refusal, suggesting a more entrenched ideological structure. Second, we probe the internal mechanisms of these models using Sparse Autoencoders (SAEs). Preliminary analysis reveals that models with lower steerability possess more distinct and abstract ideological features. Our evaluations reveal that one model can contain 7.3x more political features than another model of similar size. This allows targeted ablation of a core political feature in an ideologically "deep" model, leading to consistent, logical shifts in its reasoning across related topics, whereas the same intervention in a "shallow" model results in an increase in refusal outputs. Our findings suggest that ideological depth is a quantifiable property of LLMs and that steerability serves as a valuable window into their latent political architecture.

We study how rich visual semantic information is represented within various layers and denoising timesteps of different diffusion architectures. We uncover monosemantic interpretable features by leveraging k-sparse autoencoders (k-SAE). We substantiate our mechanistic interpretations via transfer learning using light-weight classifiers on off-the-shelf diffusion models' features. On 4 datasets, we demonstrate the effectiveness of diffusion features for representation learning. We provide in-depth analysis of how different diffusion architectures, pre-training datasets, and language model conditioning impacts visual representation granularity, inductive biases, and transfer learning capabilities. Our work is a critical step towards deepening interpretability of black-box diffusion models. Code and visualizations available at: https://github.com/revelio-diffusion/revelio

Modelling compositional meaning for sentences using empirical distributional methods has been a challenge for computational linguists. We implement the abstract categorical model of Coecke et al. (arXiv:1003.4394v1 [cs.CL]) using data from the BNC and evaluate it. The implementation is based on unsupervised learning of matrices for relational words and applying them to the vectors of their arguments. The evaluation is based on the word disambiguation task developed by Mitchell and Lapata (2008) for intransitive sentences, and on a similar new experiment designed for transitive sentences. Our model matches the results of its competitors in the first experiment, and betters them in the second. The general improvement in results with increase in syntactic complexity showcases the compositional power of our model.

In this work, we present a naive initialization scheme for word vectors based on a dense, independent co-occurrence model and provide preliminary results that suggest it is competitive and warrants further investigation. Specifically, we demonstrate through information-theoretic minimum description length (MDL) probing that our model, EigenNoise, can approach the performance of empirically trained GloVe despite the lack of any pre-training data (in the case of EigenNoise). We present these preliminary results with interest to set the stage for further investigations into how this competitive initialization works without pre-training data, as well as to invite the exploration of more intelligent initialization schemes informed by the theory of harmonic linguistic structure. Our application of this theory likewise contributes a novel (and effective) interpretation of recent discoveries which have elucidated the underlying distributional information that linguistic representations capture from data and contrast distributions.

Neural networks transform high-dimensional data into compact, structured representations, often modeled as elements of a lower dimensional latent space. In this paper, we present an alternative interpretation of neural models as dynamical systems acting on the latent manifold. Specifically, we show that autoencoder models implicitly define a latent vector field on the manifold, derived by iteratively applying the encoding-decoding map, without any additional training. We observe that standard training procedures introduce inductive biases that lead to the emergence of attractor points within this vector field. Drawing on this insight, we propose to leverage the vector field as a representation for the network, providing a novel tool to analyze the properties of the model and the data. This representation enables to: (i) analyze the generalization and memorization regimes of neural models, even throughout training; (ii) extract prior knowledge encoded in the network's parameters from the attractors, without requiring any input data; (iii) identify out-of-distribution samples from their trajectories in the vector field. We further validate our approach on vision foundation models, showcasing the applicability and effectiveness of our method in real-world scenarios.

We propose to extract meaning representations from autoregressive language models by considering the distribution of all possible trajectories extending an input text. This strategy is prompt-free, does not require fine-tuning, and is applicable to any pre-trained autoregressive model. Moreover, unlike vector-based representations, distribution-based representations can also model asymmetric relations (e.g., direction of logical entailment, hypernym/hyponym relations) by using algebraic operations between likelihood functions. These ideas are grounded in distributional perspectives on semantics and are connected to standard constructions in automata theory, but to our knowledge they have not been applied to modern language models. We empirically show that the representations obtained from large models align well with human annotations, outperform other zero-shot and prompt-free methods on semantic similarity tasks, and can be used to solve more complex entailment and containment tasks that standard embeddings cannot handle. Finally, we extend our method to represent data from different modalities (e.g., image and text) using multimodal autoregressive models. Our code is available at: https://github.com/tianyu139/meaning-as-trajectories

Neurons in large language models often exhibit polysemanticity, simultaneously encoding multiple unrelated concepts and obscuring interpretability. Instead of relying on post-hoc methods, we present MoE-X, a Mixture-of-Experts (MoE) language model designed to be intrinsically interpretable. Our approach is motivated by the observation that, in language models, wider networks with sparse activations are more likely to capture interpretable factors. However, directly training such large sparse networks is computationally prohibitive. MoE architectures offer a scalable alternative by activating only a subset of experts for any given input, inherently aligning with interpretability objectives. In MoE-X, we establish this connection by rewriting the MoE layer as an equivalent sparse, large MLP. This approach enables efficient scaling of the hidden size while maintaining sparsity. To further enhance interpretability, we enforce sparse activation within each expert and redesign the routing mechanism to prioritize experts with the highest activation sparsity. These designs ensure that only the most salient features are routed and processed by the experts. We evaluate MoE-X on chess and natural language tasks, showing that it achieves performance comparable to dense models while significantly improving interpretability. MoE-X achieves a perplexity better than GPT-2, with interpretability surpassing even sparse autoencoder (SAE)-based approaches.

We investigate the construction of latent spaces through self-supervised learning to support semantically meaningful operations. Analogous to operational amplifiers, these "operational latent spaces" (OpLaS) not only demonstrate semantic structure such as clustering but also support common transformational operations with inherent semantic meaning. Some operational latent spaces are found to have arisen "unintentionally" in the progress toward some (other) self-supervised learning objective, in which unintended but still useful properties are discovered among the relationships of points in the space. Other spaces may be constructed "intentionally" by developers stipulating certain kinds of clustering or transformations intended to produce the desired structure. We focus on the intentional creation of operational latent spaces via self-supervised learning, including the introduction of rotation operators via a novel "FiLMR" layer, which can be used to enable ring-like symmetries found in some musical constructions.

While the problem of hallucinations in neural machine translation has long been recognized, so far the progress on its alleviation is very little. Indeed, recently it turned out that without artificially encouraging models to hallucinate, previously existing methods fall short and even the standard sequence log-probability is more informative. It means that characteristics internal to the model can give much more information than we expect, and before using external models and measures, we first need to ask: how far can we go if we use nothing but the translation model itself ? We propose to use a method that evaluates the percentage of the source contribution to a generated translation. Intuitively, hallucinations are translations "detached" from the source, hence they can be identified by low source contribution. This method improves detection accuracy for the most severe hallucinations by a factor of 2 and is able to alleviate hallucinations at test time on par with the previous best approach that relies on external models. Next, if we move away from internal model characteristics and allow external tools, we show that using sentence similarity from cross-lingual embeddings further improves these results.

Representations are at the core of all deep reinforcement learning (RL) methods for both Markov decision processes (MDPs) and partially observable Markov decision processes (POMDPs). Many representation learning methods and theoretical frameworks have been developed to understand what constitutes an effective representation. However, the relationships between these methods and the shared properties among them remain unclear. In this paper, we show that many of these seemingly distinct methods and frameworks for state and history abstractions are, in fact, based on a common idea of self-predictive abstraction. Furthermore, we provide theoretical insights into the widely adopted objectives and optimization, such as the stop-gradient technique, in learning self-predictive representations. These findings together yield a minimalist algorithm to learn self-predictive representations for states and histories. We validate our theories by applying our algorithm to standard MDPs, MDPs with distractors, and POMDPs with sparse rewards. These findings culminate in a set of preliminary guidelines for RL practitioners.

The Backpropagation algorithm, widely used to train neural networks, has often been criticised for its lack of biological realism. In an attempt to find a more biologically plausible alternative, and avoid to back-propagate gradients in favour of using local learning rules, the recently introduced Forward-Forward algorithm replaces the traditional forward and backward passes of Backpropagation with two forward passes. In this work, we show that internal representations obtained with the Forward-Forward algorithm organize into robust, category-specific ensembles, composed by an extremely low number of active units (high sparsity). This is remarkably similar to what is observed in cortical representations during sensory processing. While not found in models trained with standard Backpropagation, sparsity emerges also in networks optimized by Backpropagation, on the same training objective of Forward-Forward. These results suggest that the learning procedure proposed by Forward-Forward may be superior to Backpropagation in modelling learning in the cortex, even when a backward pass is used.

We study the challenge of achieving theoretically grounded feature recovery using Sparse Autoencoders (SAEs) for the interpretation of Large Language Models. Existing SAE training algorithms often lack rigorous mathematical guarantees and suffer from practical limitations such as hyperparameter sensitivity and instability. To address these issues, we first propose a novel statistical framework for the feature recovery problem, which includes a new notion of feature identifiability by modeling polysemantic features as sparse mixtures of underlying monosemantic concepts. Building on this framework, we introduce a new SAE training algorithm based on ``bias adaptation'', a technique that adaptively adjusts neural network bias parameters to ensure appropriate activation sparsity. We theoretically prove that this algorithm correctly recovers all monosemantic features when input data is sampled from our proposed statistical model. Furthermore, we develop an improved empirical variant, Group Bias Adaptation (GBA), and demonstrate its superior performance against benchmark methods when applied to LLMs with up to 1.5 billion parameters. This work represents a foundational step in demystifying SAE training by providing the first SAE algorithm with theoretical recovery guarantees, thereby advancing the development of more transparent and trustworthy AI systems through enhanced mechanistic interpretability.

Current vision systems typically assign fixed-length representations to images, regardless of the information content. This contrasts with human intelligence - and even large language models - which allocate varying representational capacities based on entropy, context and familiarity. Inspired by this, we propose an approach to learn variable-length token representations for 2D images. Our encoder-decoder architecture recursively processes 2D image tokens, distilling them into 1D latent tokens over multiple iterations of recurrent rollouts. Each iteration refines the 2D tokens, updates the existing 1D latent tokens, and adaptively increases representational capacity by adding new tokens. This enables compression of images into a variable number of tokens, ranging from 32 to 256. We validate our tokenizer using reconstruction loss and FID metrics, demonstrating that token count aligns with image entropy, familiarity and downstream task requirements. Recurrent token processing with increasing representational capacity in each iteration shows signs of token specialization, revealing potential for object / part discovery.

Representation learning, and interpreting learned representations, are key areas of focus in machine learning and neuroscience. Both fields generally use representations as a means to understand or improve a system's computations. In this work, however, we explore surprising dissociations between representation and computation that may pose challenges for such efforts. We create datasets in which we attempt to match the computational role that different features play, while manipulating other properties of the features or the data. We train various deep learning architectures to compute these multiple abstract features about their inputs. We find that their learned feature representations are systematically biased towards representing some features more strongly than others, depending upon extraneous properties such as feature complexity, the order in which features are learned, and the distribution of features over the inputs. For example, features that are simpler to compute or learned first tend to be represented more strongly and densely than features that are more complex or learned later, even if all features are learned equally well. We also explore how these biases are affected by architectures, optimizers, and training regimes (e.g., in transformers, features decoded earlier in the output sequence also tend to be represented more strongly). Our results help to characterize the inductive biases of gradient-based representation learning. These results also highlight a key challenge for interpretability - or for comparing the representations of models and brains - disentangling extraneous biases from the computationally important aspects of a system's internal representations.

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

Sparse autoencoders (SAEs) have gained a lot of attention as a promising tool to improve the interpretability of large language models (LLMs) by mapping the complex superposition of polysemantic neurons into monosemantic features and composing a sparse dictionary of words. However, traditional performance metrics like Mean Squared Error and L0 sparsity ignore the evaluation of the semantic representational power of SAEs -- whether they can acquire interpretable monosemantic features while preserving the semantic relationship of words. For instance, it is not obvious whether a learned sparse feature could distinguish different meanings in one word. In this paper, we propose a suite of evaluations for SAEs to analyze the quality of monosemantic features by focusing on polysemous words. Our findings reveal that SAEs developed to improve the MSE-L0 Pareto frontier may confuse interpretability, which does not necessarily enhance the extraction of monosemantic features. The analysis of SAEs with polysemous words can also figure out the internal mechanism of LLMs; deeper layers and the Attention module contribute to distinguishing polysemy in a word. Our semantics focused evaluation offers new insights into the polysemy and the existing SAE objective and contributes to the development of more practical SAEs.

Hallucinations in large language models are a widespread problem, yet the mechanisms behind whether models will hallucinate are poorly understood, limiting our ability to solve this problem. Using sparse autoencoders as an interpretability tool, we discover that a key part of these mechanisms is entity recognition, where the model detects if an entity is one it can recall facts about. Sparse autoencoders uncover meaningful directions in the representation space, these detect whether the model recognizes an entity, e.g. detecting it doesn't know about an athlete or a movie. This suggests that models can have self-knowledge: internal representations about their own capabilities. These directions are causally relevant: capable of steering the model to refuse to answer questions about known entities, or to hallucinate attributes of unknown entities when it would otherwise refuse. We demonstrate that despite the sparse autoencoders being trained on the base model, these directions have a causal effect on the chat model's refusal behavior, suggesting that chat finetuning has repurposed this existing mechanism. Furthermore, we provide an initial exploration into the mechanistic role of these directions in the model, finding that they disrupt the attention of downstream heads that typically move entity attributes to the final token.

Recently proposed self-supervised learning approaches have been successful for pre-training speech representation models. The utility of these learned representations has been observed empirically, but not much has been studied about the type or extent of information encoded in the pre-trained representations themselves. Developing such insights can help understand the capabilities and limits of these models and enable the research community to more efficiently develop their usage for downstream applications. In this work, we begin to fill this gap by examining one recent and successful pre-trained model (wav2vec 2.0), via its intermediate representation vectors, using a suite of analysis tools. We use the metrics of canonical correlation, mutual information, and performance on simple downstream tasks with non-parametric probes, in order to (i) query for acoustic and linguistic information content, (ii) characterize the evolution of information across model layers, and (iii) understand how fine-tuning the model for automatic speech recognition (ASR) affects these observations. Our findings motivate modifying the fine-tuning protocol for ASR, which produces improved word error rates in a low-resource setting.

Decomposing model activations into interpretable components is a key open problem in mechanistic interpretability. Sparse autoencoders (SAEs) are a popular method for decomposing the internal activations of trained transformers into sparse, interpretable features, and have been applied to MLP layers and the residual stream. In this work we train SAEs on attention layer outputs and show that also here SAEs find a sparse, interpretable decomposition. We demonstrate this on transformers from several model families and up to 2B parameters. We perform a qualitative study of the features computed by attention layers, and find multiple families: long-range context, short-range context and induction features. We qualitatively study the role of every head in GPT-2 Small, and estimate that at least 90% of the heads are polysemantic, i.e. have multiple unrelated roles. Further, we show that Sparse Autoencoders are a useful tool that enable researchers to explain model behavior in greater detail than prior work. For example, we explore the mystery of why models have so many seemingly redundant induction heads, use SAEs to motivate the hypothesis that some are long-prefix whereas others are short-prefix, and confirm this with more rigorous analysis. We use our SAEs to analyze the computation performed by the Indirect Object Identification circuit (Wang et al.), validating that the SAEs find causally meaningful intermediate variables, and deepening our understanding of the semantics of the circuit. We open-source the trained SAEs and a tool for exploring arbitrary prompts through the lens of Attention Output SAEs.

Do LLMs genuinely incorporate external definitions, or do they primarily rely on their parametric knowledge? To address these questions, we conduct controlled experiments across multiple explanation benchmark datasets (general and domain-specific) and label definition conditions, including expert-curated, LLM-generated, perturbed, and swapped definitions. Our results reveal that while explicit label definitions can enhance accuracy and explainability, their integration into an LLM's task-solving processes is neither guaranteed nor consistent, suggesting reliance on internalized representations in many cases. Models often default to their internal representations, particularly in general tasks, whereas domain-specific tasks benefit more from explicit definitions. These findings underscore the need for a deeper understanding of how LLMs process external knowledge alongside their pre-existing capabilities.

Recent progress has been made towards learning invariant or equivariant representations with self-supervised learning. While invariant methods are evaluated on large scale datasets, equivariant ones are evaluated in smaller, more controlled, settings. We aim at bridging the gap between the two in order to learn more diverse representations that are suitable for a wide range of tasks. We start by introducing a dataset called 3DIEBench, consisting of renderings from 3D models over 55 classes and more than 2.5 million images where we have full control on the transformations applied to the objects. We further introduce a predictor architecture based on hypernetworks to learn equivariant representations with no possible collapse to invariance. We introduce SIE (Split Invariant-Equivariant) which combines the hypernetwork-based predictor with representations split in two parts, one invariant, the other equivariant, to learn richer representations. We demonstrate significant performance gains over existing methods on equivariance related tasks from both a qualitative and quantitative point of view. We further analyze our introduced predictor and show how it steers the learned latent space. We hope that both our introduced dataset and approach will enable learning richer representations without supervision in more complex scenarios. Code and data are available at https://github.com/facebookresearch/SIE.

Vision encoders are increasingly used in modern applications, from vision-only models to multimodal systems such as vision-language models. Despite their remarkable success, it remains unclear how these architectures represent features internally. Here, we propose a novel approach for interpreting vision features via image reconstruction. We compare two related model families, SigLIP and SigLIP2, which differ only in their training objective, and show that encoders pre-trained on image-based tasks retain significantly more image information than those trained on non-image tasks such as contrastive learning. We further apply our method to a range of vision encoders, ranking them by the informativeness of their feature representations. Finally, we demonstrate that manipulating the feature space yields predictable changes in reconstructed images, revealing that orthogonal rotations (rather than spatial transformations) control color encoding. Our approach can be applied to any vision encoder, shedding light on the inner structure of its feature space. The code and model weights to reproduce the experiments are available in GitHub.

Linear sequences of words are implicitly represented in our brains by hierarchical structures that organize the composition of words in sentences. Linguists formalize different frameworks to model this hierarchy; two of the most common syntactic frameworks are Constituency and Dependency. Constituency represents sentences as nested groups of phrases, while dependency represents a sentence by assigning relations between its words. Recently, the pursuit of intelligent machines has produced Language Models (LMs) capable of solving many language tasks with a human-level performance. Many studies now question whether LMs implicitly represent syntactic hierarchies. This thesis focuses on producing constituency and dependency structures from LMs in an unsupervised setting. I review the critical methods in this field and highlight a line of work that utilizes a numerical representation for binary constituency trees (Syntactic Distance). I present a detailed study on StructFormer (SF) (Shen et al., 2021), which retrofits a transformer encoder architecture with a parser network to produce constituency and dependency structures. I present six experiments to analyze and address this field's challenges; experiments include investigating the effect of repositioning the parser network within the SF architecture, evaluating subword-based induced trees, and benchmarking the models developed in the thesis experiments on linguistic tasks. Models benchmarking is performed by participating in the BabyLM challenge, published at CoNLL 2023 (Momen et al., 2023). The results of this thesis encourage further development in the direction of retrofitting transformer-based models to induce syntactic structures, supported by the acceptable performance of SF in different experimental settings and the observed limitations that require innovative solutions to advance the state of syntactic structure induction.

The objective of pre-trained language models is to learn contextual representations of textual data. Pre-trained language models have become mainstream in natural language processing and code modeling. Using probes, a technique to study the linguistic properties of hidden vector spaces, previous works have shown that these pre-trained language models encode simple linguistic properties in their hidden representations. However, none of the previous work assessed whether these models encode the whole grammatical structure of a programming language. In this paper, we prove the existence of a syntactic subspace, lying in the hidden representations of pre-trained language models, which contain the syntactic information of the programming language. We show that this subspace can be extracted from the models' representations and define a novel probing method, the AST-Probe, that enables recovering the whole abstract syntax tree (AST) of an input code snippet. In our experimentations, we show that this syntactic subspace exists in five state-of-the-art pre-trained language models. In addition, we highlight that the middle layers of the models are the ones that encode most of the AST information. Finally, we estimate the optimal size of this syntactic subspace and show that its dimension is substantially lower than those of the models' representation spaces. This suggests that pre-trained language models use a small part of their representation spaces to encode syntactic information of the programming languages.

Many recent studies have found evidence for emergent reasoning capabilities in large language models (LLMs), but debate persists concerning the robustness of these capabilities, and the extent to which they depend on structured reasoning mechanisms. To shed light on these issues, we study the internal mechanisms that support abstract reasoning in LLMs. We identify an emergent symbolic architecture that implements abstract reasoning via a series of three computations. In early layers, symbol abstraction heads convert input tokens to abstract variables based on the relations between those tokens. In intermediate layers, symbolic induction heads perform sequence induction over these abstract variables. Finally, in later layers, retrieval heads predict the next token by retrieving the value associated with the predicted abstract variable. These results point toward a resolution of the longstanding debate between symbolic and neural network approaches, suggesting that emergent reasoning in neural networks depends on the emergence of symbolic mechanisms.

One of the primary driving forces contributing to the superior performance of Large Language Models (LLMs) is the extensive availability of human-annotated natural language data, which is used for alignment fine-tuning. This inspired researchers to investigate self-training methods to mitigate the extensive reliance on human annotations. However, the current success of self-training has been primarily observed in natural language scenarios, rather than in the increasingly important neural-symbolic scenarios. To this end, we propose an environment-guided neural-symbolic self-training framework named ENVISIONS. It aims to overcome two main challenges: (1) the scarcity of symbolic data, and (2) the limited proficiency of LLMs in processing symbolic language. Extensive evaluations conducted on three distinct domains demonstrate the effectiveness of our approach. Additionally, we have conducted a comprehensive analysis to uncover the factors contributing to ENVISIONS's success, thereby offering valuable insights for future research in this area. Code will be available at https://github.com/xufangzhi/ENVISIONS.

Transformer models underpin many recent advances in practical machine learning applications, yet understanding their internal behavior continues to elude researchers. Given the size and complexity of these models, forming a comprehensive picture of their inner workings remains a significant challenge. To this end, we set out to understand small transformer models in a more tractable setting: that of solving mazes. In this work, we focus on the abstractions formed by these models and find evidence for the consistent emergence of structured internal representations of maze topology and valid paths. We demonstrate this by showing that the residual stream of only a single token can be linearly decoded to faithfully reconstruct the entire maze. We also find that the learned embeddings of individual tokens have spatial structure. Furthermore, we take steps towards deciphering the circuity of path-following by identifying attention heads (dubbed adjacency heads), which are implicated in finding valid subsequent tokens.

Set representation has become ubiquitous in deep learning for modeling the inductive bias of neural networks that are insensitive to the input order. DeepSets is the most widely used neural network architecture for set representation. It involves embedding each set element into a latent space with dimension L, followed by a sum pooling to obtain a whole-set embedding, and finally mapping the whole-set embedding to the output. In this work, we investigate the impact of the dimension L on the expressive power of DeepSets. Previous analyses either oversimplified high-dimensional features to be one-dimensional features or were limited to analytic activations, thereby diverging from practical use or resulting in L that grows exponentially with the set size N and feature dimension D. To investigate the minimal value of L that achieves sufficient expressive power, we present two set-element embedding layers: (a) linear + power activation (LP) and (b) linear + exponential activations (LE). We demonstrate that L being poly(N, D) is sufficient for set representation using both embedding layers. We also provide a lower bound of L for the LP embedding layer. Furthermore, we extend our results to permutation-equivariant set functions and the complex field.

We study how large language models (LLMs) ``think'' through their representation space. We propose a novel geometric framework that models an LLM's reasoning as flows -- embedding trajectories evolving where logic goes. We disentangle logical structure from semantics by employing the same natural deduction propositions with varied semantic carriers, allowing us to test whether LLMs internalize logic beyond surface form. This perspective connects reasoning with geometric quantities such as position, velocity, and curvature, enabling formal analysis in representation and concept spaces. Our theory establishes: (1) LLM reasoning corresponds to smooth flows in representation space, and (2) logical statements act as local controllers of these flows' velocities. Using learned representation proxies, we design controlled experiments to visualize and quantify reasoning flows, providing empirical validation of our theoretical framework. Our work serves as both a conceptual foundation and practical tools for studying reasoning phenomenon, offering a new lens for interpretability and formal analysis of LLMs' behavior.

Language models show a surprising range of capabilities, but the source of their apparent competence is unclear. Do these networks just memorize a collection of surface statistics, or do they rely on internal representations of the process that generates the sequences they see? We investigate this question by applying a variant of the GPT model to the task of predicting legal moves in a simple board game, Othello. Although the network has no a priori knowledge of the game or its rules, we uncover evidence of an emergent nonlinear internal representation of the board state. Interventional experiments indicate this representation can be used to control the output of the network and create "latent saliency maps" that can help explain predictions in human terms.

While numerous works have assessed the generative performance of language models (LMs) on tasks requiring Theory of Mind reasoning, research into the models' internal representation of mental states remains limited. Recent work has used probing to demonstrate that LMs can represent beliefs of themselves and others. However, these claims are accompanied by limited evaluation, making it difficult to assess how mental state representations are affected by model design and training choices. We report an extensive benchmark with various LM types with different model sizes, fine-tuning approaches, and prompt designs to study the robustness of mental state representations and memorisation issues within the probes. Our results show that the quality of models' internal representations of the beliefs of others increases with model size and, more crucially, with fine-tuning. We are the first to study how prompt variations impact probing performance on theory of mind tasks. We demonstrate that models' representations are sensitive to prompt variations, even when such variations should be beneficial. Finally, we complement previous activation editing experiments on Theory of Mind tasks and show that it is possible to improve models' reasoning performance by steering their activations without the need to train any probe.

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.

People can categorize the same entity at multiple taxonomic levels, such as basic (bear), superordinate (animal), and subordinate (grizzly bear). While prior research has focused on basic-level categories, this study is the first attempt to examine the organization of categories by analyzing exemplars produced at the subordinate level. We present a new Italian psycholinguistic dataset of human-generated exemplars for 187 concrete words. We then use these data to evaluate whether textual and vision LLMs produce meaningful exemplars that align with human category organization across three key tasks: exemplar generation, category induction, and typicality judgment. Our findings show a low alignment between humans and LLMs, consistent with previous studies. However, their performance varies notably across different semantic domains. Ultimately, this study highlights both the promises and the constraints of using AI-generated exemplars to support psychological and linguistic research.

According to Algorithmic Information Theory (AIT) -- Intelligent representations compress data into the shortest possible program that can reconstruct its content, exhibiting low Kolmogorov Complexity (KC). In contrast, most visual representation learning systems use fixed-length representations for all inputs, ignoring variations in complexity or familiarity. Recent adaptive tokenization methods address this by allocating variable-length representations but typically require test-time search over multiple encodings to find the most predictive one. Inspired by Kolmogorov Complexity principles, we propose a single-pass adaptive tokenizer, KARL, which predicts the appropriate number of tokens for an image in a single forward pass, halting once its approximate KC is reached. The token count serves as a proxy for the minimum description length. KARL's training procedure closely resembles the Upside-Down Reinforcement Learning paradigm, as it learns to conditionally predict token halting based on a desired reconstruction quality. KARL matches the performance of recent adaptive tokenizers while operating in a single pass. We present scaling laws for KARL, analyzing the role of encoder/decoder size, continuous vs. discrete tokenization and more. Additionally, we offer a conceptual study drawing an analogy between Adaptive Image Tokenization and Algorithmic Information Theory, examining the predicted image complexity (KC) across axes such as structure vs. noise and in- vs. out-of-distribution familiarity -- revealing alignment with human intuition.

Autoregressive language models (LMs) generate one token at a time, yet human reasoning operates over higher-level abstractions - sentences, propositions, and concepts. This contrast raises a central question- Can LMs likewise learn to reason over structured semantic units rather than raw token sequences? In this work, we investigate whether pretrained LMs can be lifted into such abstract reasoning spaces by building on their learned representations. We present a framework that adapts a pretrained token-level LM to operate in sentence space by autoregressively predicting continuous embeddings of next sentences. We explore two embedding paradigms inspired by classical representation learning: 1) semantic embeddings, learned via autoencoding to preserve surface meaning; and 2) contextual embeddings, trained via next-sentence prediction to encode anticipatory structure. We evaluate both under two inference regimes: Discretized, which decodes each predicted embedding into text before re-encoding; and Continuous, which reasons entirely in embedding space for improved efficiency. Across four domains - mathematics, logic, commonsense, and planning - contextual embeddings under continuous inference show competitive performance with Chain-of-Thought (CoT) while reducing inference-time FLOPs on average by half. We also present early signs of scalability and modular adaptation. Finally, to visualize latent trajectories, we introduce SentenceLens, a diagnostic tool that decodes intermediate model states into interpretable sentences. Together, our results indicate that pretrained LMs can effectively transition to abstract, structured reasoning within latent embedding spaces.

Large multimodal models (LMMs) combine unimodal encoders and large language models (LLMs) to perform multimodal tasks. Despite recent advancements towards the interpretability of these models, understanding internal representations of LMMs remains largely a mystery. In this paper, we present a novel framework for the interpretation of LMMs. We propose a dictionary learning based approach, applied to the representation of tokens. The elements of the learned dictionary correspond to our proposed concepts. We show that these concepts are well semantically grounded in both vision and text. Thus we refer to these as ``multi-modal concepts''. We qualitatively and quantitatively evaluate the results of the learnt concepts. We show that the extracted multimodal concepts are useful to interpret representations of test samples. Finally, we evaluate the disentanglement between different concepts and the quality of grounding concepts visually and textually. Our code is publicly available at https://github.com/mshukor/xl-vlms

In many computer vision applications, images are acquired with arbitrary or random rotations and translations, and in such setups, it is desirable to obtain semantic representations disentangled from the image orientation. Examples of such applications include semiconductor wafer defect inspection, plankton microscope images, and inference on single-particle cryo-electron microscopy (cryo-EM) micro-graphs. In this work, we propose Invariant Representation Learning with Implicit Neural Representation (IRL-INR), which uses an implicit neural representation (INR) with a hypernetwork to obtain semantic representations disentangled from the orientation of the image. We show that IRL-INR can effectively learn disentangled semantic representations on more complex images compared to those considered in prior works and show that these semantic representations synergize well with SCAN to produce state-of-the-art unsupervised clustering results.

We introduce the first metric for evaluating disentanglement at individual hierarchy levels of a structured latent representation. Applied to object-centric generative models, this offers a systematic, unified approach to evaluating (i) object separation between latent slots (ii) disentanglement of object properties inside individual slots (iii) disentanglement of intrinsic and extrinsic object properties. We theoretically show that for structured representations, our framework gives stronger guarantees of selecting a good model than previous disentanglement metrics. Experimentally, we demonstrate that viewing object compositionality as a disentanglement problem addresses several issues with prior visual metrics of object separation. As a core technical component, we present the first representation probing algorithm handling slot permutation invariance.

This thesis introduces quantum natural language processing (QNLP) models based on a simple yet powerful analogy between computational linguistics and quantum mechanics: grammar as entanglement. The grammatical structure of text and sentences connects the meaning of words in the same way that entanglement structure connects the states of quantum systems. Category theory allows to make this language-to-qubit analogy formal: it is a monoidal functor from grammar to vector spaces. We turn this abstract analogy into a concrete algorithm that translates the grammatical structure onto the architecture of parameterised quantum circuits. We then use a hybrid classical-quantum algorithm to train the model so that evaluating the circuits computes the meaning of sentences in data-driven tasks. The implementation of QNLP models motivated the development of DisCoPy (Distributional Compositional Python), the toolkit for applied category theory of which the first chapter gives a comprehensive overview. String diagrams are the core data structure of DisCoPy, they allow to reason about computation at a high level of abstraction. We show how they can encode both grammatical structures and quantum circuits, but also logical formulae, neural networks or arbitrary Python code. Monoidal functors allow to translate these abstract diagrams into concrete computation, interfacing with optimised task-specific libraries. The second chapter uses DisCopy to implement QNLP models as parameterised functors from grammar to quantum circuits. It gives a first proof-of-concept for the more general concept of functorial learning: generalising machine learning from functions to functors by learning from diagram-like data. In order to learn optimal functor parameters via gradient descent, we introduce the notion of diagrammatic differentiation: a graphical calculus for computing the gradients of parameterised diagrams.

Universality is a key hypothesis in mechanistic interpretability -- that different models learn similar features and circuits when trained on similar tasks. In this work, we study the universality hypothesis by examining how small neural networks learn to implement group composition. We present a novel algorithm by which neural networks may implement composition for any finite group via mathematical representation theory. We then show that networks consistently learn this algorithm by reverse engineering model logits and weights, and confirm our understanding using ablations. By studying networks of differing architectures trained on various groups, we find mixed evidence for universality: using our algorithm, we can completely characterize the family of circuits and features that networks learn on this task, but for a given network the precise circuits learned -- as well as the order they develop -- are arbitrary.

We ask whether multilingual language models trained on unbalanced, English-dominated corpora use English as an internal pivot language -- a question of key importance for understanding how language models function and the origins of linguistic bias. Focusing on the Llama-2 family of transformer models, our study uses carefully constructed non-English prompts with a unique correct single-token continuation. From layer to layer, transformers gradually map an input embedding of the final prompt token to an output embedding from which next-token probabilities are computed. Tracking intermediate embeddings through their high-dimensional space reveals three distinct phases, whereby intermediate embeddings (1) start far away from output token embeddings; (2) already allow for decoding a semantically correct next token in the middle layers, but give higher probability to its version in English than in the input language; (3) finally move into an input-language-specific region of the embedding space. We cast these results into a conceptual model where the three phases operate in "input space", "concept space", and "output space", respectively. Crucially, our evidence suggests that the abstract "concept space" lies closer to English than to other languages, which may have important consequences regarding the biases held by multilingual language models.

This paper proposes a novel framework for understanding large language models (LLMs) by reconceptualizing them as semiotic machines rather than as imitations of human cognition. Drawing from structuralist and post-structuralist theories of language-specifically the works of Ferdinand de Saussure and Jacques Derrida-I argue that LLMs should be understood as models of language itself, aligning with Derrida's concept of 'writing' (l'ecriture). The paper is structured into three parts. First, I lay the theoretical groundwork by explaining how the word2vec embedding algorithm operates within Saussure's framework of language as a relational system of signs. Second, I apply Derrida's critique of Saussure to position 'writing' as the object modeled by LLMs, offering a view of the machine's 'mind' as a statistical approximation of sign behavior. Finally, the third section addresses how modern LLMs reflect post-structuralist notions of unfixed meaning, arguing that the "next token generation" mechanism effectively captures the dynamic nature of meaning. By reconceptualizing LLMs as semiotic machines rather than cognitive models, this framework provides an alternative lens through which to assess the strengths and limitations of LLMs, offering new avenues for future research.

Modern language models can process inputs across diverse languages and modalities. We hypothesize that models acquire this capability through learning a shared representation space across heterogeneous data types (e.g., different languages and modalities), which places semantically similar inputs near one another, even if they are from different modalities/languages. We term this the semantic hub hypothesis, following the hub-and-spoke model from neuroscience (Patterson et al., 2007) which posits that semantic knowledge in the human brain is organized through a transmodal semantic "hub" which integrates information from various modality-specific "spokes" regions. We first show that model representations for semantically equivalent inputs in different languages are similar in the intermediate layers, and that this space can be interpreted using the model's dominant pretraining language via the logit lens. This tendency extends to other data types, including arithmetic expressions, code, and visual/audio inputs. Interventions in the shared representation space in one data type also predictably affect model outputs in other data types, suggesting that this shared representations space is not simply a vestigial byproduct of large-scale training on broad data, but something that is actively utilized by the model during input processing.

Large Language Models (LLMs) have demonstrated strong generalization across a wide range of tasks. Reasoning with LLMs is central to solving multi-step problems and complex decision-making. To support efficient reasoning, recent studies have shifted attention from explicit chain-of-thought prompting toward implicit reasoning, where reasoning occurs silently via latent structures without emitting intermediate textual steps. Implicit reasoning brings advantages such as lower generation cost, faster inference, and better alignment with internal computation. Although prior surveys have discussed latent representations in the context of reasoning, a dedicated and mechanism-level examination of how reasoning unfolds internally within LLMs remains absent. This survey fills that gap by introducing a taxonomy centered on execution paradigms, shifting the focus from representational forms to computational strategies. We organize existing methods into three execution paradigms based on \textit{how and where internal computation unfolds}: latent optimization, signal-guided control, and layer-recurrent execution. We also review structural, behavioral and representation-based evidence that supports the presence of implicit reasoning in LLMs. We further provide a structured overview of the evaluation metrics and benchmarks used in existing works to assess the effectiveness and reliability of implicit reasoning. We maintain a continuously updated project at: https://github.com/digailab/awesome-llm-implicit-reasoning.

Large Language Models (LLMs) display striking surface fluency yet systematically fail at tasks requiring symbolic reasoning, arithmetic accuracy, and logical consistency. This paper offers a structural diagnosis of such failures, revealing a persistent gap between comprehension and competence. Through controlled experiments and architectural analysis, we demonstrate that LLMs often articulate correct principles without reliably applying them--a failure rooted not in knowledge access, but in computational execution. We term this phenomenon the computational split-brain syndrome, where instruction and action pathways are geometrically and functionally dissociated. This core limitation recurs across domains, from mathematical operations to relational inferences, and explains why model behavior remains brittle even under idealized prompting. We argue that LLMs function as powerful pattern completion engines, but lack the architectural scaffolding for principled, compositional reasoning. Our findings delineate the boundary of current LLM capabilities and motivate future models with metacognitive control, principle lifting, and structurally grounded execution. This diagnosis also clarifies why mechanistic interpretability findings may reflect training-specific pattern coordination rather than universal computational principles, and why the geometric separation between instruction and execution pathways suggests limitations in neural introspection and mechanistic analysis.