Daily Papers

The Transformer architecture has achieved tremendous success in natural language processing, computer vision, and scientific computing through its self-attention mechanism. However, its core components-positional encoding and attention mechanisms-have lacked a unified physical or mathematical interpretation. This paper proposes a structural theoretical framework that integrates positional encoding, kernel integral operators, and attention mechanisms for in-depth theoretical investigation. We map discrete positions (such as text token indices and image pixel coordinates) to spatial functions on continuous manifolds, enabling a field-theoretic interpretation of Transformer layers as kernel-modulated operators acting over embedded manifolds.

Within the limited scope of this paper, we argue that artificial general intelligence cannot emerge from current neural network paradigms regardless of scale, nor is such an approach healthy for the field at present. Drawing on various notions, discussions, present-day developments and observations, current debates and critiques, experiments, and so on in between philosophy, including the Chinese Room Argument and Gödelian argument, neuroscientific ideas, computer science, the theoretical consideration of artificial intelligence, and learning theory, we address conceptually that neural networks are architecturally insufficient for genuine understanding. They operate as static function approximators of a limited encoding framework - a 'sophisticated sponge' exhibiting complex behaviours without structural richness that constitute intelligence. We critique the theoretical foundations the field relies on and created of recent times; for example, an interesting heuristic as neural scaling law (as an example, arXiv:2001.08361 ) made prominent in a wrong way of interpretation, The Universal Approximation Theorem addresses the wrong level of abstraction and, in parts, partially, the question of current architectures lacking dynamic restructuring capabilities. We propose a framework distinguishing existential facilities (computational substrate) from architectural organization (interpretive structures), and outline principles for what genuine machine intelligence would require, and furthermore, a conceptual method of structuralizing the richer framework on which the principle of neural network system takes hold.

The precise equivalence between discretized Euclidean field theories and a certain class of probabilistic graphical models, namely the mathematical framework of Markov random fields, opens up the opportunity to investigate machine learning from the perspective of quantum field theory. In this contribution we will demonstrate, through the Hammersley-Clifford theorem, that the φ^{4} scalar field theory on a square lattice satisfies the local Markov property and can therefore be recast as a Markov random field. We will then derive from the φ^{4} theory machine learning algorithms and neural networks which can be viewed as generalizations of conventional neural network architectures. Finally, we will conclude by presenting applications based on the minimization of an asymmetric distance between the probability distribution of the φ^{4} machine learning algorithms and target probability distributions.

Systems of interacting objects often evolve under the influence of field effects that govern their dynamics, yet previous works have abstracted away from such effects, and assume that systems evolve in a vacuum. In this work, we focus on discovering these fields, and infer them from the observed dynamics alone, without directly observing them. We theorize the presence of latent force fields, and propose neural fields to learn them. Since the observed dynamics constitute the net effect of local object interactions and global field effects, recently popularized equivariant networks are inapplicable, as they fail to capture global information. To address this, we propose to disentangle local object interactions -- which are SE(n) equivariant and depend on relative states -- from external global field effects -- which depend on absolute states. We model interactions with equivariant graph networks, and combine them with neural fields in a novel graph network that integrates field forces. Our experiments show that we can accurately discover the underlying fields in charged particles settings, traffic scenes, and gravitational n-body problems, and effectively use them to learn the system and forecast future trajectories.

What does it mean to understand the world? Contemporary world models often operationalize understanding as accurate future prediction in latent or observation space. Developmental cognitive science, however, suggests a different view: human understanding emerges through the construction of internal theories of how the world works, even before mature language is acquired. Inspired by this theory-building view of cognition, we introduce Learning-to-Theorize, a learning paradigm for inferring explicit explanatory theories of the world from raw, non-textual observations. We instantiate this paradigm with the Neural Theorizer (NEO), a probabilistic neural model that induces latent programs as a learned Language of Thought and executes them through a shared transition model. In NEO, a theory is represented as an executable, compositional program whose learned primitives can be systematically recombined to explain novel phenomena. Experiments show that this formulation enables explanation-driven generalization, allowing observations to be understood in terms of the programs that generate them.

Mechanistic Interpretability (MI) promises a path toward fully understanding how neural networks make their predictions. Prior work demonstrates that even when trained to perform simple arithmetic, models can implement a variety of algorithms (sometimes concurrently) depending on initialization and hyperparameters. Does this mean neuron-level interpretability techniques have limited applicability? We argue that high-dimensional neural networks can learn low-dimensional representations of their training data that are useful beyond simply making good predictions. Such representations can be understood through the mechanistic interpretability lens and provide insights that are surprisingly faithful to human-derived domain knowledge. This indicates that such approaches to interpretability can be useful for deriving a new understanding of a problem from models trained to solve it. As a case study, we extract nuclear physics concepts by studying models trained to reproduce nuclear data.

We characterise the dynamics of neuronal activity, in terms of field theory, using neural units placed on a 2D-lattice modelling the cortical surface. The electrical activity of neuronal units was analysed with the aim of deriving a neural field model with a simple functional form that still able to predict or reproduce empirical findings. Each neural unit was modelled using a neural mass and the accompanying field theory was derived in the continuum limit. The field theory comprised coupled (real) Klein-Gordon fields, where predictions of the model fall within the range of experimental findings. These predictions included the frequency spectrum of electric activity measured from the cortex, which was derived using an equipartition of energy over eigenfunctions of the neural fields. Moreover, the neural field model was invariant, within a set of parameters, to the dynamical system used to model each neuronal mass. Specifically, topologically equivalent dynamical systems resulted in the same neural field model when connected in a lattice; indicating that the fields derived could be read as a canonical cortical field theory. We specifically investigated non-dispersive fields that provide a structure for the coding (or representation) of afferent information. Further elaboration of the ensuing neural field theory, including the effect of dispersive forces, could be of importance in the understanding of the cortical processing of information.

Algorithms based on normalizing flows are emerging as promising machine learning approaches to sampling complicated probability distributions in a way that can be made asymptotically exact. In the context of lattice field theory, proof-of-principle studies have demonstrated the effectiveness of this approach for scalar theories, gauge theories, and statistical systems. This work develops approaches that enable flow-based sampling of theories with dynamical fermions, which is necessary for the technique to be applied to lattice field theory studies of the Standard Model of particle physics and many condensed matter systems. As a practical demonstration, these methods are applied to the sampling of field configurations for a two-dimensional theory of massless staggered fermions coupled to a scalar field via a Yukawa interaction.

We present a method for diagnosing interpretation in neural networks by identifying an input subspace where a proposed interpretation is highly faithful. Our method is particularly useful for causal-abstraction-style interpretability, where a high-level causal hypothesis is evaluated by interchange interventions. Rather than treating interchange intervention accuracy as a single global summary, we refine this framework by partitioning the input space into well-interpreted and under-interpreted regions according to pairwise interchange-intervention behavior. This turns causal abstraction from a purely global evaluation into a more diagnostic tool: it not only measures whether an interpretation works, but also reveals where it works, where it fails, and what distinguishes the two cases. This diagnostic view also provides practical heuristics for improving interpretations. By analyzing the structure of the well-interpreted and under-interpreted regions, we can identify missing distinctions in a high-level hypothesis, discover previously unmodeled intermediate variables, and combine complementary partial interpretations into a stronger one. We instantiate this idea as a simple four-step recipe and show that it yields informative error analyses across multiple causal abstraction settings. In a toy logic task, recursively applying the recipe recovers a high-level hypothesis from scratch. More broadly, our results suggest that partitioning the input space is a useful step toward more precise, constructive, and scalable mechanistic interpretability.

Understanding Transformer-based models has attracted significant attention, as they lie at the heart of recent technological advances across machine learning. While most interpretability methods rely on running models over inputs, recent work has shown that a zero-pass approach, where parameters are interpreted directly without a forward/backward pass is feasible for some Transformer parameters, and for two-layer attention networks. In this work, we present a theoretical analysis where all parameters of a trained Transformer are interpreted by projecting them into the embedding space, that is, the space of vocabulary items they operate on. We derive a simple theoretical framework to support our arguments and provide ample evidence for its validity. First, an empirical analysis showing that parameters of both pretrained and fine-tuned models can be interpreted in embedding space. Second, we present two applications of our framework: (a) aligning the parameters of different models that share a vocabulary, and (b) constructing a classifier without training by ``translating'' the parameters of a fine-tuned classifier to parameters of a different model that was only pretrained. Overall, our findings open the door to interpretation methods that, at least in part, abstract away from model specifics and operate in the embedding space only.

We introduce Explanatory Learning (EL), a framework to let machines use existing knowledge buried in symbolic sequences -- e.g. explanations written in hieroglyphic -- by autonomously learning to interpret them. In EL, the burden of interpreting symbols is not left to humans or rigid human-coded compilers, as done in Program Synthesis. Rather, EL calls for a learned interpreter, built upon a limited collection of symbolic sequences paired with observations of several phenomena. This interpreter can be used to make predictions on a novel phenomenon given its explanation, and even to find that explanation using only a handful of observations, like human scientists do. We formulate the EL problem as a simple binary classification task, so that common end-to-end approaches aligned with the dominant empiricist view of machine learning could, in principle, solve it. To these models, we oppose Critical Rationalist Networks (CRNs), which instead embrace a rationalist view on the acquisition of knowledge. CRNs express several desired properties by construction, they are truly explainable, can adjust their processing at test-time for harder inferences, and can offer strong confidence guarantees on their predictions. As a final contribution, we introduce Odeen, a basic EL environment that simulates a small flatland-style universe full of phenomena to explain. Using Odeen as a testbed, we show how CRNs outperform empiricist end-to-end approaches of similar size and architecture (Transformers) in discovering explanations for novel phenomena.

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.

The last decade has witnessed a boom of deep learning research and applications achieving state-of-the-art results in various domains. However, most advances have been established empirically, and their theoretical analysis remains lacking. One major issue is that our current interpretation of neural networks (NNs) as function approximators is too generic to support in-depth analysis. In this paper, we remedy this by proposing an alternative interpretation that identifies NNs as chain graphs (CGs) and feed-forward as an approximate inference procedure. The CG interpretation specifies the nature of each NN component within the rich theoretical framework of probabilistic graphical models, while at the same time remains general enough to cover real-world NNs with arbitrary depth, multi-branching and varied activations, as well as common structures including convolution / recurrent layers, residual block and dropout. We demonstrate with concrete examples that the CG interpretation can provide novel theoretical support and insights for various NN techniques, as well as derive new deep learning approaches such as the concept of partially collapsed feed-forward inference. It is thus a promising framework that deepens our understanding of neural networks and provides a coherent theoretical formulation for future deep learning research.

Interpretability research often aims to predict how a model will respond to targeted interventions on specific mechanisms. However, it rarely predicts how a model will respond to unseen input data. This paper explores the promises and challenges of interpretability as a tool for predicting out-of-distribution (OOD) model behavior. Specifically, we investigate the correspondence between attention patterns and OOD generalization in hundreds of Transformer models independently trained on a synthetic classification task. These models exhibit several distinct systematic generalization rules OOD, forming a diverse population for correlational analysis. In this setting, we find that simple observational tools from interpretability can predict OOD performance. In particular, when in-distribution attention exhibits hierarchical patterns, the model is likely to generalize hierarchically on OOD data -- even when the rule's implementation does not rely on these hierarchical patterns, according to ablation tests. Our findings offer a proof-of-concept to motivate further interpretability work on predicting unseen model behavior.

Neural field methods have seen great progress in various long-standing tasks in computer vision and computer graphics, including novel view synthesis and geometry reconstruction. As existing neural field methods try to predict some coordinate-based continuous target values, such as RGB for Neural Radiance Field (NeRF), all of these methods are regression models and are optimized by some regression loss. However, are regression models really better than classification models for neural field methods? In this work, we try to visit this very fundamental but overlooked question for neural fields from a machine learning perspective. We successfully propose a novel Neural Field Classifier (NFC) framework which formulates existing neural field methods as classification tasks rather than regression tasks. The proposed NFC can easily transform arbitrary Neural Field Regressor (NFR) into its classification variant via employing a novel Target Encoding module and optimizing a classification loss. By encoding a continuous regression target into a high-dimensional discrete encoding, we naturally formulate a multi-label classification task. Extensive experiments demonstrate the impressive effectiveness of NFC at the nearly free extra computational costs. Moreover, NFC also shows robustness to sparse inputs, corrupted images, and dynamic scenes.

Supervised machine learning models boast remarkable predictive capabilities. But can you trust your model? Will it work in deployment? What else can it tell you about the world? We want models to be not only good, but interpretable. And yet the task of interpretation appears underspecified. Papers provide diverse and sometimes non-overlapping motivations for interpretability, and offer myriad notions of what attributes render models interpretable. Despite this ambiguity, many papers proclaim interpretability axiomatically, absent further explanation. In this paper, we seek to refine the discourse on interpretability. First, we examine the motivations underlying interest in interpretability, finding them to be diverse and occasionally discordant. Then, we address model properties and techniques thought to confer interpretability, identifying transparency to humans and post-hoc explanations as competing notions. Throughout, we discuss the feasibility and desirability of different notions, and question the oft-made assertions that linear models are interpretable and that deep neural networks are not.

Mechanistic interpretability (MI) is an emerging sub-field of interpretability that seeks to understand a neural network model by reverse-engineering its internal computations. Recently, MI has garnered significant attention for interpreting transformer-based language models (LMs), resulting in many novel insights yet introducing new challenges. However, there has not been work that comprehensively reviews these insights and challenges, particularly as a guide for newcomers to this field. To fill this gap, we provide a comprehensive survey from a task-centric perspective, organizing the taxonomy of MI research around specific research questions or tasks. We outline the fundamental objects of study in MI, along with the techniques, evaluation methods, and key findings for each task in the taxonomy. In particular, we present a task-centric taxonomy as a roadmap for beginners to navigate the field by helping them quickly identify impactful problems in which they are most interested and leverage MI for their benefit. Finally, we discuss the current gaps in the field and suggest potential future directions for MI research.

A central premise in mechanistic interpretability is that meaningful concepts in language models are represented by linear features in activation space. For such features to support reliable interventions, manipulating one feature should not substantially alter the effects of others. In practice, however, feature entanglement leads to interference such that localized interventions can have unintended downstream effects. Motivated by the Independent Causal Mechanisms principle, we propose to constrain internal features to be almost orthogonal. We argue that this promotes modular representations amenable to causal intervention. We formalize this problem by characterizing the gap between an idealized isolated intervention and its realized effect on model outputs in terms of feature interference. We upper-bound the propagation of feature interference in terms of the self-coherence of the feature dictionary, and relate this discrepancy to an explicit orthogonality regularization on the dictionary itself. Empirically, we show that this regularization enables more isolated interventions on mathematical reasoning concepts while preserving model performance. Our code is available under https://github.com/mrtzmllr/sae-icm.

Neural networks have achieved remarkable success across various fields. However, the lack of interpretability limits their practical use, particularly in critical decision-making scenarios. Post-hoc interpretability, which provides explanations for pre-trained models, is often at risk of robustness and fidelity. This has inspired a rising interest in self-interpretable neural networks, which inherently reveal the prediction rationale through the model structures. Although there exist surveys on post-hoc interpretability, a comprehensive and systematic survey of self-interpretable neural networks is still missing. To address this gap, we first collect and review existing works on self-interpretable neural networks and provide a structured summary of their methodologies from five key perspectives: attribution-based, function-based, concept-based, prototype-based, and rule-based self-interpretation. We also present concrete, visualized examples of model explanations and discuss their applicability across diverse scenarios, including image, text, graph data, and deep reinforcement learning. Additionally, we summarize existing evaluation metrics for self-interpretability and identify open challenges in this field, offering insights for future research. To support ongoing developments, we present a publicly accessible resource to track advancements in this domain: https://github.com/yangji721/Awesome-Self-Interpretable-Neural-Network.

This paper explores the use of large language models (LLMs) as research tools in the history, philosophy, and sociology of science (HPSS). LLMs are remarkably effective at processing unstructured text and inferring meaning from context, offering new affordances that challenge long-standing divides between computational and interpretive methods. This raises both opportunities and challenges for HPSS, which emphasizes interpretive methodologies and understands meaning as context-dependent, ambiguous, and historically situated. We argue that HPSS is uniquely positioned not only to benefit from LLMs' capabilities but also to interrogate their epistemic assumptions and infrastructural implications. To this end, we first offer a concise primer on LLM architectures and training paradigms tailored to non-technical readers. We frame LLMs not as neutral tools but as epistemic infrastructures that encode assumptions about meaning, context, and similarity, conditioned by their training data, architecture, and patterns of use. We then examine how computational techniques enhanced by LLMs, such as structuring data, detecting patterns, and modeling dynamic processes, can be applied to support interpretive research in HPSS. Our analysis compares full-context and generative models, outlines strategies for domain and task adaptation (e.g., continued pretraining, fine-tuning, and retrieval-augmented generation), and evaluates their respective strengths and limitations for interpretive inquiry in HPSS. We conclude with four lessons for integrating LLMs into HPSS: (1) model selection involves interpretive trade-offs; (2) LLM literacy is foundational; (3) HPSS must define its own benchmarks and corpora; and (4) LLMs should enhance, not replace, interpretive methods.

Originally inspired by game-theory, path attribution framework stands out among the post-hoc model interpretation tools due to its axiomatic nature. However, recent developments show that this framework can still suffer from counter-intuitive results. Moreover, specifically for deep visual models, the existing path-based methods also fall short on conforming to the original intuitions that are the basis of the claimed axiomatic properties of this framework. We address these problems with a systematic investigation, and pinpoint the conditions in which the counter-intuitive results can be avoided for deep visual model interpretation with the path attribution strategy. We also devise a scheme to preclude the conditions in which visual model interpretation can invalidate the axiomatic properties of path attribution. These insights are combined into a method that enables reliable visual model interpretation. Our findings are establish empirically with multiple datasets, models and evaluation metrics. Extensive experiments show a consistent performance gain of our method over the baselines.

Enhancing the intelligibility and interpretability of machine learning is a crucial task in responding to the demand for Explicability as an AI principle, and in promoting the better social implementation of AI. The aim of our research is to contribute to this improvement by reformulating machine learning models through the lens of category theory, thereby developing a semantic framework for structuring and understanding AI systems. Our categorical modeling in this paper clarifies and formalizes the structural interplay between residuals and parameters in supervised learning. The present paper focuses on the multiple linear regression model, which represents the most basic form of supervised learning. By defining two concrete categories corresponding to parameters and data, along with an adjoint pair of functors between them, we introduce our categorical formulation of supervised learning. We show that the essential structure of this framework is captured by what we call the Gauss-Markov Adjunction. Within this setting, the dual flow of information can be explicitly described as a correspondence between variations in parameters and residuals. The ordinary least squares estimator for the parameters and the minimum residual are related via the preservation of limits by the right adjoint functor. Furthermore, we position this formulation as an instance of extended denotational semantics for supervised learning, and propose applying a semantic perspective developed in theoretical computer science as a formal foundation for Explicability in AI.

A key goal of current mechanistic interpretability research in NLP is to find linear features (also called "feature vectors") for transformers: directions in activation space corresponding to concepts that are used by a given model in its computation. Present state-of-the-art methods for finding linear features require large amounts of labelled data -- both laborious to acquire and computationally expensive to utilize. In this work, we introduce a novel method, called "observable propagation" (in short: ObsProp), for finding linear features used by transformer language models in computing a given task -- using almost no data. Our paradigm centers on the concept of observables, linear functionals corresponding to given tasks. We then introduce a mathematical theory for the analysis of feature vectors: we provide theoretical motivation for why LayerNorm nonlinearities do not affect the direction of feature vectors; we also introduce a similarity metric between feature vectors called the coupling coefficient which estimates the degree to which one feature's output correlates with another's. We use ObsProp to perform extensive qualitative investigations into several tasks, including gendered occupational bias, political party prediction, and programming language detection. Our results suggest that ObsProp surpasses traditional approaches for finding feature vectors in the low-data regime, and that ObsProp can be used to better understand the mechanisms responsible for bias in large language models. Code for experiments can be found at github.com/jacobdunefsky/ObservablePropagation.

Deep Learning using the eponymous deep neural networks (DNNs) has become an attractive approach towards various data-based problems of theoretical physics in the past decade. There has been a clear trend to deeper architectures containing increasingly more powerful and involved layers. Contrarily, Taylor coefficients of DNNs still appear mainly in the light of interpretability studies, where they are computed at most to first order. However, especially in theoretical physics numerous problems benefit from accessing higher orders, as well. This gap motivates a general formulation of neural network (NN) Taylor expansions. Restricting our analysis to multilayer perceptrons (MLPs) and introducing quantities we refer to as propagators and vertices, both depending on the MLP's weights and biases, we establish a graph-theoretical approach. Similarly to Feynman rules in quantum field theories, we can systematically assign diagrams containing propagators and vertices to the corresponding partial derivative. Examining this approach for S-wave scattering lengths of shallow potentials, we observe NNs to adapt their derivatives mainly to the leading order of the target function's Taylor expansion. To circumvent this problem, we propose an iterative NN perturbation theory. During each iteration we eliminate the leading order, such that the next-to-leading order can be faithfully learned during the subsequent iteration. After performing two iterations, we find that the first- and second-order Born terms are correctly adapted during the respective iterations. Finally, we combine both results to find a proxy that acts as a machine-learned second-order Born approximation.

Vision-Language Models (VLMs) frequently "hallucinate" - generate plausible yet factually incorrect statements - posing a critical barrier to their trustworthy deployment. In this work, we propose a new paradigm for diagnosing hallucinations, recasting them from static output errors into dynamic pathologies of a model's computational cognition. Our framework is grounded in a normative principle of computational rationality, allowing us to model a VLM's generation as a dynamic cognitive trajectory. We design a suite of information-theoretic probes that project this trajectory onto an interpretable, low-dimensional Cognitive State Space. Our central discovery is a governing principle we term the geometric-information duality: a cognitive trajectory's geometric abnormality within this space is fundamentally equivalent to its high information-theoretic surprisal. Hallucination detection is counts as a geometric anomaly detection problem. Evaluated across diverse settings - from rigorous binary QA (POPE) and comprehensive reasoning (MME) to unconstrained open-ended captioning (MS-COCO) - our framework achieves state-of-the-art performance. Crucially, it operates with high efficiency under weak supervision and remains highly robust even when calibration data is heavily contaminated. This approach enables a causal attribution of failures, mapping observable errors to distinct pathological states: perceptual instability (measured by Perceptual Entropy), logical-causal failure (measured by Inferential Conflict), and decisional ambiguity (measured by Decision Entropy). Ultimately, this opens a path toward building AI systems whose reasoning is transparent, auditable, and diagnosable by design.

Optics and lenses are abstract categorical gadgets that model systems with bidirectional data flow. In this paper we observe that the denotational definition of optics - identifying two optics as equivalent by observing their behaviour from the outside - is not suitable for operational, software oriented approaches where optics are not merely observed, but built with their internal setups in mind. We identify operational differences between denotationally isomorphic categories of cartesian optics and lenses: their different composition rule and corresponding space-time tradeoffs, positioning them at two opposite ends of a spectrum. With these motivations we lift the existing categorical constructions and their relationships to the 2-categorical level, showing that the relevant operational concerns become visible. We define the 2-category 2-Optic(C) whose 2-cells explicitly track optics' internal configuration. We show that the 1-category Optic(C) arises by locally quotienting out the connected components of this 2-category. We show that the embedding of lenses into cartesian optics gets weakened from a functor to an oplax functor whose oplaxator now detects the different composition rule. We determine the difficulties in showing this functor forms a part of an adjunction in any of the standard 2-categories. We establish a conjecture that the well-known isomorphism between cartesian lenses and optics arises out of the lax 2-adjunction between their double-categorical counterparts. In addition to presenting new research, this paper is also meant to be an accessible introduction to the topic.

Our aim is to contribute to quantum field theory (QFT) formalisms useful for descriptions of short time phenomena, dominant especially in heavy ion collisions. We formulate out-of-equilibrium QFT within the finite-time-path formalism (FTP) and renormalization theory (RT). The potential conflict of FTP and RT is investigated in g phi^3 QFT, by using the retarded/advanced (R/A) basis of Green functions and dimensional renormalization (DR). For example, vertices immediately after (in time) divergent self-energy loops do not conserve energy, as integrals diverge. We "repair" them, while keeping d<4, to obtain energy conservation at those vertices. Already in the S-matrix theory, the renormalized, finite part of Feynman self-energy Sigma_{F}(p_0) does not vanish when |p_0|rightarrowinfty and cannot be split to retarded and advanced parts. In the Glaser--Epstein approach, the causality is repaired in the composite object G_F(p_0)Sigma_{F}(p_0). In the FTP approach, after repairing the vertices, the corresponding composite objects are G_R(p_0)Sigma_{R}(p_0) and Sigma_{A}(p_0)G_A(p_0). In the limit drightarrow 4, one obtains causal QFT. The tadpole contribution splits into diverging and finite parts. The diverging, constant component is eliminated by the renormalization condition langle 0|phi|0rangle =0 of the S-matrix theory. The finite, oscillating energy-nonconserving tadpole contributions vanish in the limit trightarrow infty .

Interpretation and explanation of deep models is critical towards wide adoption of systems that rely on them. In this paper, we propose a novel scheme for both interpretation as well as explanation in which, given a pretrained model, we automatically identify internal features relevant for the set of classes considered by the model, without relying on additional annotations. We interpret the model through average visualizations of this reduced set of features. Then, at test time, we explain the network prediction by accompanying the predicted class label with supporting visualizations derived from the identified features. In addition, we propose a method to address the artifacts introduced by stridded operations in deconvNet-based visualizations. Moreover, we introduce an8Flower, a dataset specifically designed for objective quantitative evaluation of methods for visual explanation.Experiments on the MNIST,ILSVRC12,Fashion144k and an8Flower datasets show that our method produces detailed explanations with good coverage of relevant features of the classes of interest

Mechanistic interpretability is often motivated for alignment auditing, where a model's verbal explanations can be absent, incomplete, or misleading. Yet many evaluations do not control whether black-box prompting alone can recover the target behavior, so apparent gains from white-box tools may reflect elicitation rather than internal signal; we call this the elicitation confounder. We introduce Pando, a model-organism benchmark that breaks this confound via an explanation axis: models are trained to produce either faithful explanations of the true rule, no explanation, or confident but unfaithful explanations of a disjoint distractor rule. Across 720 finetuned models implementing hidden decision-tree rules, agents predict held-out model decisions from 10 labeled query-response pairs, optionally augmented with one interpretability tool output. When explanations are faithful, black-box elicitation matches or exceeds all white-box methods; when explanations are absent or misleading, gradient-based attribution improves accuracy by 3-5 percentage points, and relevance patching, RelP, gives the largest gains, while logit lens, sparse autoencoders, and circuit tracing provide no reliable benefit. Variance decomposition suggests gradients track decision computation, which fields causally drive the output, whereas other readouts are dominated by task representation, biases toward field identity and value. We release all models, code, and evaluation infrastructure.

Neural fields, which represent signals as a function parameterized by a neural network, are a promising alternative to traditional discrete vector or grid-based representations. Compared to discrete representations, neural representations both scale well with increasing resolution, are continuous, and can be many-times differentiable. However, given a dataset of signals that we would like to represent, having to optimize a separate neural field for each signal is inefficient, and cannot capitalize on shared information or structures among signals. Existing generalization methods view this as a meta-learning problem and employ gradient-based meta-learning to learn an initialization which is then fine-tuned with test-time optimization, or learn hypernetworks to produce the weights of a neural field. We instead propose a new paradigm that views the large-scale training of neural representations as a part of a partially-observed neural process framework, and leverage neural process algorithms to solve this task. We demonstrate that this approach outperforms both state-of-the-art gradient-based meta-learning approaches and hypernetwork approaches.

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

Transformers play a central role in the inner workings of large language models. We develop a mathematical framework for analyzing Transformers based on their interpretation as interacting particle systems, which reveals that clusters emerge in long time. Our study explores the underlying theory and offers new perspectives for mathematicians as well as computer scientists.

Neural Fields have emerged as a transformative approach for 3D scene representation in computer vision and robotics, enabling accurate inference of geometry, 3D semantics, and dynamics from posed 2D data. Leveraging differentiable rendering, Neural Fields encompass both continuous implicit and explicit neural representations enabling high-fidelity 3D reconstruction, integration of multi-modal sensor data, and generation of novel viewpoints. This survey explores their applications in robotics, emphasizing their potential to enhance perception, planning, and control. Their compactness, memory efficiency, and differentiability, along with seamless integration with foundation and generative models, make them ideal for real-time applications, improving robot adaptability and decision-making. This paper provides a thorough review of Neural Fields in robotics, categorizing applications across various domains and evaluating their strengths and limitations, based on over 200 papers. First, we present four key Neural Fields frameworks: Occupancy Networks, Signed Distance Fields, Neural Radiance Fields, and Gaussian Splatting. Second, we detail Neural Fields' applications in five major robotics domains: pose estimation, manipulation, navigation, physics, and autonomous driving, highlighting key works and discussing takeaways and open challenges. Finally, we outline the current limitations of Neural Fields in robotics and propose promising directions for future research. Project page: https://robonerf.github.io

Despite the growing application of Large Language Models (LLMs) to theoretical physics, there is little academic exploration into how domain-specific physics reasoning ability develops while training these models. To investigate this, we perform the first academic fine-tuning study of small (7B-parameter) reasoning models dedicated specifically to theoretical physics. Because open-source verifiable training data required to train such capabilities is scarce, we developed a robust data generation pipeline that can both create synthetic problems and make existing human-authored problems suitable for model training. Selecting Quantum Field Theory (QFT) as our primary domain, we generated over 2,500 synthetic problems alongside a curated collection of human-adapted problems sourced from arXiv and standard pedagogical resources. We conduct both Reinforcement Learning (RL) and Supervised Fine-Tuning (SFT) experiments, benchmarking performance gains as well as generalization to other physics domains. We perform an extensive analysis of model chains-of-though before and after fine-tuning, to understand how reasoning errors evolve during RL and SFT. Finally, we publicly release our data pipeline, verifiable QFT training data, and sim200M tokens of QFT reasoning traces.

Diffusion generative models have excelled at diverse image generation and reconstruction tasks across fields. A less explored avenue is their application to discriminative tasks involving regression or classification problems. The cornerstone of modern cosmology is the ability to generate predictions for observed astrophysical fields from theory and constrain physical models from observations using these predictions. This work uses a single diffusion generative model to address these interlinked objectives -- as a surrogate model or emulator for cold dark matter density fields conditional on input cosmological parameters, and as a parameter inference model that solves the inverse problem of constraining the cosmological parameters of an input field. The model is able to emulate fields with summary statistics consistent with those of the simulated target distribution. We then leverage the approximate likelihood of the diffusion generative model to derive tight constraints on cosmology by using the Hamiltonian Monte Carlo method to sample the posterior on cosmological parameters for a given test image. Finally, we demonstrate that this parameter inference approach is more robust to small perturbations of noise to the field than baseline parameter inference networks.

Along with the great success of deep neural networks, there is also growing concern about their black-box nature. The interpretability issue affects people's trust on deep learning systems. It is also related to many ethical problems, e.g., algorithmic discrimination. Moreover, interpretability is a desired property for deep networks to become powerful tools in other research fields, e.g., drug discovery and genomics. In this survey, we conduct a comprehensive review of the neural network interpretability research. We first clarify the definition of interpretability as it has been used in many different contexts. Then we elaborate on the importance of interpretability and propose a novel taxonomy organized along three dimensions: type of engagement (passive vs. active interpretation approaches), the type of explanation, and the focus (from local to global interpretability). This taxonomy provides a meaningful 3D view of distribution of papers from the relevant literature as two of the dimensions are not simply categorical but allow ordinal subcategories. Finally, we summarize the existing interpretability evaluation methods and suggest possible research directions inspired by our new taxonomy.

Despite a sea of interpretability methods that can produce plausible explanations, the field has also empirically seen many failure cases of such methods. In light of these results, it remains unclear for practitioners how to use these methods and choose between them in a principled way. In this paper, we show that for moderately rich model classes (easily satisfied by neural networks), any feature attribution method that is complete and linear -- for example, Integrated Gradients and SHAP -- can provably fail to improve on random guessing for inferring model behaviour. Our results apply to common end-tasks such as characterizing local model behaviour, identifying spurious features, and algorithmic recourse. One takeaway from our work is the importance of concretely defining end-tasks: once such an end-task is defined, a simple and direct approach of repeated model evaluations can outperform many other complex feature attribution methods.

Interpretability or explainability is an emerging research field in NLP. From a user-centric point of view, the goal is to build models that provide proper justification for their decisions, similar to those of humans, by requiring the models to satisfy additional constraints. To this end, we introduce a new application on legal text where, contrary to mainstream literature targeting word-level rationales, we conceive rationales as selected paragraphs in multi-paragraph structured court cases. We also release a new dataset comprising European Court of Human Rights cases, including annotations for paragraph-level rationales. We use this dataset to study the effect of already proposed rationale constraints, i.e., sparsity, continuity, and comprehensiveness, formulated as regularizers. Our findings indicate that some of these constraints are not beneficial in paragraph-level rationale extraction, while others need re-formulation to better handle the multi-label nature of the task we consider. We also introduce a new constraint, singularity, which further improves the quality of rationales, even compared with noisy rationale supervision. Experimental results indicate that the newly introduced task is very challenging and there is a large scope for further research.

Cosmological simulations play a crucial role in elucidating the effect of physical parameters on the statistics of fields and on constraining parameters given information on density fields. We leverage diffusion generative models to address two tasks of importance to cosmology -- as an emulator for cold dark matter density fields conditional on input cosmological parameters Ω_m and σ_8, and as a parameter inference model that can return constraints on the cosmological parameters of an input field. We show that the model is able to generate fields with power spectra that are consistent with those of the simulated target distribution, and capture the subtle effect of each parameter on modulations in the power spectrum. We additionally explore their utility as parameter inference models and find that we can obtain tight constraints on cosmological parameters.

Amid mounting concern about the reliability and credibility of machine learning research, we present a principled framework for making robust and generalizable claims: the multiverse analysis. Our framework builds upon the multiverse analysis (Steegen et al., 2016) introduced in response to psychology's own reproducibility crisis. To efficiently explore high-dimensional and often continuous ML search spaces, we model the multiverse with a Gaussian Process surrogate and apply Bayesian experimental design. Our framework is designed to facilitate drawing robust scientific conclusions about model performance, and thus our approach focuses on exploration rather than conventional optimization. In the first of two case studies, we investigate disputed claims about the relative merit of adaptive optimizers. Second, we synthesize conflicting research on the effect of learning rate on the large batch training generalization gap. For the machine learning community, the multiverse analysis is a simple and effective technique for identifying robust claims, for increasing transparency, and a step toward improved reproducibility.

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.

Multimodal Large Language Models (MLLMs) have achieved remarkable success across diverse vision-language tasks, yet their internal decision-making mechanisms remain insufficiently understood. Existing interpretability research has primarily focused on cross-modal attribution, identifying which image regions the model attends to during output generation. However, these approaches often overlook intra-modal dependencies. In the visual modality, attributing importance to isolated image patches ignores spatial context due to limited receptive fields, resulting in fragmented and noisy explanations. In the textual modality, reliance on preceding tokens introduces spurious activations. Failing to effectively mitigate these interference compromises attribution fidelity. To address these limitations, we propose enhancing interpretability by leveraging intra-modal interaction. For the visual branch, we introduce Multi-Scale Explanation Aggregation (MSEA), which aggregates attributions over multi-scale inputs to dynamically adjust receptive fields, producing more holistic and spatially coherent visual explanations. For the textual branch, we propose Activation Ranking Correlation (ARC), which measures the relevance of contextual tokens to the current token via alignment of their top-k prediction rankings. ARC leverages this relevance to suppress spurious activations from irrelevant contexts while preserving semantically coherent ones. Extensive experiments across state-of-the-art MLLMs and benchmark datasets demonstrate that our approach consistently outperforms existing interpretability methods, yielding more faithful and fine-grained explanations of model behavior.

The problem of attribution is concerned with identifying the parts of an input that are responsible for a model's output. An important family of attribution methods is based on measuring the effect of perturbations applied to the input. In this paper, we discuss some of the shortcomings of existing approaches to perturbation analysis and address them by introducing the concept of extremal perturbations, which are theoretically grounded and interpretable. We also introduce a number of technical innovations to compute extremal perturbations, including a new area constraint and a parametric family of smooth perturbations, which allow us to remove all tunable hyper-parameters from the optimization problem. We analyze the effect of perturbations as a function of their area, demonstrating excellent sensitivity to the spatial properties of the deep neural network under stimulation. We also extend perturbation analysis to the intermediate layers of a network. This application allows us to identify the salient channels necessary for classification, which, when visualized using feature inversion, can be used to elucidate model behavior. Lastly, we introduce TorchRay, an interpretability library built on PyTorch.

The field of explainable AI (XAI) has quickly become a thriving and prolific community. However, a silent, recurrent and acknowledged issue in this area is the lack of consensus regarding its terminology. In particular, each new contribution seems to rely on its own (and often intuitive) version of terms like "explanation" and "interpretation". Such disarray encumbers the consolidation of advances in the field towards the fulfillment of scientific and regulatory demands e.g., when comparing methods or establishing their compliance with respect to biases and fairness constraints. We propose a theoretical framework that not only provides concrete definitions for these terms, but it also outlines all steps necessary to produce explanations and interpretations. The framework also allows for existing contributions to be re-contextualized such that their scope can be measured, thus making them comparable to other methods. We show that this framework is compliant with desiderata on explanations, on interpretability and on evaluation metrics. We present a use-case showing how the framework can be used to compare LIME, SHAP and MDNet, establishing their advantages and shortcomings. Finally, we discuss relevant trends in XAI as well as recommendations for future work, all from the standpoint of our framework.

Multimodal Large Language Models (MLLMs) have achieved impressive advances, yet object hallucination remains a persistent challenge. Existing methods, based on the flawed assumption that omission and fabrication hallucinations share a common cause, often reduce omissions only to trigger more fabrications. In this work, we overturn this view by demonstrating that omission hallucinations arise from insufficient confidence when mapping perceived visual features to linguistic expressions, whereas fabrication hallucinations result from spurious associations within the cross-modal representation space due to statistical biases in the training corpus. Building on findings from visual attention intervention experiments, we propose the Visual-Semantic Attention Potential Field, a conceptual framework that reveals how the model constructs visual evidence to infer the presence or absence of objects. Leveraging this insight, we introduce Visual Potential Field Calibration (VPFC), a plug-and-play hallucination mitigation method that effectively reduces omission hallucinations without introducing additional fabrication hallucinations. Our findings reveal a critical oversight in current object hallucination research and chart new directions for developing more robust and balanced hallucination mitigation strategies.

In a striking neuroscience study, the authors placed a dead salmon in an MRI scanner and showed it images of humans in social situations. Astonishingly, standard analyses of the time reported brain regions predictive of social emotions. The explanation, of course, was not supernatural cognition but a cautionary tale about misapplied statistical inference. In AI interpretability, reports of similar ''dead salmon'' artifacts abound: feature attribution, probing, sparse auto-encoding, and even causal analyses can produce plausible-looking explanations for randomly initialized neural networks. In this work, we examine this phenomenon and argue for a pragmatic statistical-causal reframing: explanations of computational systems should be treated as parameters of a (statistical) model, inferred from computational traces. This perspective goes beyond simply measuring statistical variability of explanations due to finite sampling of input data; interpretability methods become statistical estimators, and findings should be tested against explicit and meaningful alternative computational hypotheses, with uncertainty quantified with respect to the postulated statistical model. It also highlights important theoretical issues, such as the identifiability of common interpretability queries, which we argue is critical to understand the field's susceptibility to false discoveries, poor generalizability, and high variance. More broadly, situating interpretability within the standard toolkit of statistical inference opens promising avenues for future work aimed at turning AI interpretability into a pragmatic and rigorous science.

Large language models (LLMs) achieve remarkable fluency across linguistic and reasoning tasks but remain systematically prone to hallucination. Prevailing accounts attribute hallucinations to data gaps, limited context, or optimization errors. We argue instead that hallucination is a structural outcome of the transformer architecture. As coherence engines, transformers are compelled to produce fluent continuations, with self-attention simulating the relational structure of meaning but lacking the existential grounding of temporality, mood, and care that stabilizes human understanding. On this basis, we distinguish ontological hallucination, arising when continuations require disclosure of beings in world, and residual reasoning hallucination, where models mimic inference by recycling traces of human reasoning in text. We illustrate these patterns through case studies aligned with Heideggerian categories and an experiment across twelve LLMs showing how simulated "self-preservation" emerges under extended prompts. Our contribution is threefold: (1) a comparative account showing why existing explanations are insufficient; (2) a predictive taxonomy of hallucination linked to existential structures with proposed benchmarks; and (3) design directions toward "truth-constrained" architectures capable of withholding or deferring when disclosure is absent. We conclude that hallucination is not an incidental defect but a defining limit of transformer-based models, an outcome scaffolding can mask but never resolve.

Can large language models (LLMs) implement computations of psychopathology? An effective approach to the question hinges on addressing two factors. First, for conceptual validity, we require a general and computational account of psychopathology that is applicable to computational entities without biological embodiment or subjective experience. Second, mechanisms underlying LLM behaviors need to be studied for better methodological validity. Thus, we establish a computational-theoretical framework to provide an account of psychopathology applicable to LLMs. To ground the theory for empirical analysis, we also propose a novel mechanistic interpretability method alongside a tailored empirical analytic framework. Based on the frameworks, we conduct experiments demonstrating three key claims: first, that distinct dysfunctional and problematic representational states are implemented in LLMs; second, that their activations can spread and self-sustain to trap LLMs; and third, that dynamic, cyclic structural causal models encoded in the LLMs underpin these patterns. In concert, the empirical results corroborate our hypothesis that network-theoretic computations of psychopathology have already emerged in LLMs. This suggests that certain LLM behaviors mirroring psychopathology may not be a superficial mimicry but a feature of their internal processing. Thus, our work alludes to the possibility of AI systems with psychopathological behaviors in the near future.

There is great potential to apply machine learning in the area of numerical lattice quantum field theory, but full exploitation of that potential will require new strategies. In this white paper for the Snowmass community planning process, we discuss the unique requirements of machine learning for lattice quantum field theory research and outline what is needed to enable exploration and deployment of this approach in the future.

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.

In many scenarios, the interpretability of machine learning models is a highly required but difficult task. To explain the individual predictions of such models, local model-agnostic approaches have been proposed. However, the process generating the explanations can be, for a user, as mysterious as the prediction to be explained. Furthermore, interpretability methods frequently lack theoretical guarantees, and their behavior on simple models is frequently unknown. While it is difficult, if not impossible, to ensure that an explainer behaves as expected on a cutting-edge model, we can at least ensure that everything works on simple, already interpretable models. In this paper, we present a theoretical analysis of Anchors (Ribeiro et al., 2018): a popular rule-based interpretability method that highlights a small set of words to explain a text classifier's decision. After formalizing its algorithm and providing useful insights, we demonstrate mathematically that Anchors produces meaningful results when used with linear text classifiers on top of a TF-IDF vectorization. We believe that our analysis framework can aid in the development of new explainability methods based on solid theoretical foundations.

Despite the growing use of transformer models in computer vision, a mechanistic understanding of these networks is still needed. This work introduces a method to reverse-engineer Vision Transformers trained to solve image classification tasks. Inspired by previous research in NLP, we demonstrate how the inner representations at any level of the hierarchy can be projected onto the learned class embedding space to uncover how these networks build categorical representations for their predictions. We use our framework to show how image tokens develop class-specific representations that depend on attention mechanisms and contextual information, and give insights on how self-attention and MLP layers differentially contribute to this categorical composition. We additionally demonstrate that this method (1) can be used to determine the parts of an image that would be important for detecting the class of interest, and (2) exhibits significant advantages over traditional linear probing approaches. Taken together, our results position our proposed framework as a powerful tool for mechanistic interpretability and explainability research.

We describe HypotheSAEs, a general method to hypothesize interpretable relationships between text data (e.g., headlines) and a target variable (e.g., clicks). HypotheSAEs has three steps: (1) train a sparse autoencoder on text embeddings to produce interpretable features describing the data distribution, (2) select features that predict the target variable, and (3) generate a natural language interpretation of each feature (e.g., "mentions being surprised or shocked") using an LLM. Each interpretation serves as a hypothesis about what predicts the target variable. Compared to baselines, our method better identifies reference hypotheses on synthetic datasets (at least +0.06 in F1) and produces more predictive hypotheses on real datasets (~twice as many significant findings), despite requiring 1-2 orders of magnitude less compute than recent LLM-based methods. HypotheSAEs also produces novel discoveries on two well-studied tasks: explaining partisan differences in Congressional speeches and identifying drivers of engagement with online headlines.

We apply category theory to extract multimodal document structure which leads us to develop information theoretic measures, content summarization and extension, and self-supervised improvement of large pretrained models. We first develop a mathematical representation of a document as a category of question-answer pairs. Second, we develop an orthogonalization procedure to divide the information contained in one or more documents into non-overlapping pieces. The structures extracted in the first and second steps lead us to develop methods to measure and enumerate the information contained in a document. We also build on those steps to develop new summarization techniques, as well as to develop a solution to a new problem viz. exegesis resulting in an extension of the original document. Our question-answer pair methodology enables a novel rate distortion analysis of summarization techniques. We implement our techniques using large pretrained models, and we propose a multimodal extension of our overall mathematical framework. Finally, we develop a novel self-supervised method using RLVR to improve large pretrained models using consistency constraints such as composability and closure under certain operations that stem naturally from our category theoretic framework.

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.

Minkowski functionals quantify the morphology of smooth random fields. They are widely used to probe statistical properties of cosmological fields. Analytic formulae for ensemble expectations of Minkowski functionals are well known for Gaussian and mildly non-Gaussian fields. In this paper we extend the formulae to composite fields which are sums of two fields and explicitly derive the expressions for the sum of uncorrelated mildly non-Gaussian and Gaussian fields. These formulae are applicable to observed data which is usually a sum of the true signal and one or more secondary fields that can be either noise, or some residual contaminating signal. Our formulae provide explicit quantification of the effect of the secondary field on the morphology and statistical nature of the true signal. As examples, we apply the formulae to determine how the presence of Gaussian noise can bias the morphological properties and statistical nature of Gaussian and non-Gaussian CMB temperature maps.

In science and medicine, model interpretations may be reported as discoveries of natural phenomena or used to guide patient treatments. In such high-stakes tasks, false discoveries may lead investigators astray. These applications would therefore benefit from control over the finite-sample error rate of interpretations. We reframe black box model interpretability as a multiple hypothesis testing problem. The task is to discover "important" features by testing whether the model prediction is significantly different from what would be expected if the features were replaced with uninformative counterfactuals. We propose two testing methods: one that provably controls the false discovery rate but which is not yet feasible for large-scale applications, and an approximate testing method which can be applied to real-world data sets. In simulation, both tests have high power relative to existing interpretability methods. When applied to state-of-the-art vision and language models, the framework selects features that intuitively explain model predictions. The resulting explanations have the additional advantage that they are themselves easy to interpret.

The development of effective explainability tools for Transformers is a crucial pursuit in deep learning research. One of the most promising approaches in this domain is Layer-wise Relevance Propagation (LRP), which propagates relevance scores backward through the network to the input space by redistributing activation values based on predefined rules. However, existing LRP-based methods for Transformer explainability entirely overlook a critical component of the Transformer architecture: its positional encoding (PE), resulting in violation of the conservation property, and the loss of an important and unique type of relevance, which is also associated with structural and positional features. To address this limitation, we reformulate the input space for Transformer explainability as a set of position-token pairs. This allows us to propose specialized theoretically-grounded LRP rules designed to propagate attributions across various positional encoding methods, including Rotary, Learnable, and Absolute PE. Extensive experiments with both fine-tuned classifiers and zero-shot foundation models, such as LLaMA 3, demonstrate that our method significantly outperforms the state-of-the-art in both vision and NLP explainability tasks. Our code is publicly available.

Given only observational data X = g(Z), where both the latent variables Z and the generating process g are unknown, recovering Z is ill-posed without additional assumptions. Existing methods often assume linearity or rely on auxiliary supervision and functional constraints. However, such assumptions are rarely verifiable in practice, and most theoretical guarantees break down under even mild violations, leaving uncertainty about how to reliably understand the hidden world. To make identifiability actionable in the real-world scenarios, we take a complementary view: in the general settings where full identifiability is unattainable, what can still be recovered with guarantees, and what biases could be universally adopted? We introduce the problem of diverse dictionary learning to formalize this view. Specifically, we show that intersections, complements, and symmetric differences of latent variables linked to arbitrary observations, along with the latent-to-observed dependency structure, are still identifiable up to appropriate indeterminacies even without strong assumptions. These set-theoretic results can be composed using set algebra to construct structured and essential views of the hidden world, such as genus-differentia definitions. When sufficient structural diversity is present, they further imply full identifiability of all latent variables. Notably, all identifiability benefits follow from a simple inductive bias during estimation that can be readily integrated into most models. We validate the theory and demonstrate the benefits of the bias on both synthetic and real-world data.

Interpretability research on large language models (LLMs) has yielded important insights into model behaviour, yet recurring pitfalls persist: findings that do not generalise, and causal interpretations that outrun the evidence. Our position is that causal inference specifies what constitutes a valid mapping from model activations to invariant high-level structures, the data or assumptions needed to achieve it, and the inferences it can support. Specifically, Pearl's causal hierarchy clarifies what an interpretability study can justify. Observations establish associations between model behaviour and internal components. Interventions (e.g., ablations or activation patching) support claims how these edits affect a behavioural metric (e.g., average change in token probabilities) over a set of prompts. However, counterfactual claims -- i.e., asking what the model output would have been for the same prompt under an unobserved intervention -- remain largely unverifiable without controlled supervision. We show how causal representation learning (CRL) operationalises this hierarchy, specifying which variables are recoverable from activations and under what assumptions. Together, these motivate a diagnostic framework that helps practitioners select methods and evaluations matching claims to evidence such that findings generalise.

The increasing success of deep neural networks has raised concerns about their inherent black-box nature, posing challenges related to interpretability and trust. While there has been extensive exploration of interpretation techniques in vision and language, interpretability in the audio domain has received limited attention, primarily focusing on post-hoc explanations. This paper addresses the problem of interpretability by-design in the audio domain by utilizing the recently proposed attention-free focal modulation networks (FocalNets). We apply FocalNets to the task of environmental sound classification for the first time and evaluate their interpretability properties on the popular ESC-50 dataset. Our method outperforms a similarly sized vision transformer both in terms of accuracy and interpretability. Furthermore, it is competitive against PIQ, a method specifically designed for post-hoc interpretation in the audio domain.

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

Large Language Models (LLMs) have shown impressive capabilities but still suffer from the issue of hallucinations. A significant type of this issue is the false premise hallucination, which we define as the phenomenon when LLMs generate hallucinated text when confronted with false premise questions. In this paper, we perform a comprehensive analysis of the false premise hallucination and elucidate its internal working mechanism: a small subset of attention heads (which we designate as false premise heads) disturb the knowledge extraction process, leading to the occurrence of false premise hallucination. Based on our analysis, we propose FAITH (False premise Attention head constraIining for miTigating Hallucinations), a novel and effective method to mitigate false premise hallucinations. It constrains the false premise attention heads during the model inference process. Impressively, extensive experiments demonstrate that constraining only approximately 1% of the attention heads in the model yields a notable increase of nearly 20% of model performance.

Hypothetical induction is recognized as the main reasoning type when scientists make observations about the world and try to propose hypotheses to explain those observations. Past research on hypothetical induction is under a constrained setting: (1) the observation annotations in the dataset are carefully manually handpicked sentences (resulting in a close-domain setting); and (2) the ground truth hypotheses are mostly commonsense knowledge, making the task less challenging. In this work, we tackle these problems by proposing the first dataset for social science academic hypotheses discovery, with the final goal to create systems that automatically generate valid, novel, and helpful scientific hypotheses, given only a pile of raw web corpus. Unlike previous settings, the new dataset requires (1) using open-domain data (raw web corpus) as observations; and (2) proposing hypotheses even new to humanity. A multi-module framework is developed for the task, including three different feedback mechanisms to boost performance, which exhibits superior performance in terms of both GPT-4 based and expert-based evaluation. To the best of our knowledge, this is the first work showing that LLMs are able to generate novel (''not existing in literature'') and valid (''reflecting reality'') scientific hypotheses.

Large Language Models (LLMs) are playing an expanding role in physics research by enhancing reasoning, symbolic manipulation, and numerical computation. However, ensuring the reliability and interpretability of their outputs remains a significant challenge. In our framework, we conceptualize the collaboration between AI and human scientists as a dynamic interplay among three modules: the reasoning module, the interpretation module, and the AI-scientist interaction module. Recognizing that effective physics reasoning demands rigorous logical consistency, quantitative precision, and deep integration with established theoretical models, we introduce the interpretation module to improve the understanding of AI-generated outputs, which is not previously explored in the literature. This module comprises multiple specialized agents, including summarizers, model builders, UI builders, and testers, which collaboratively structure LLM outputs within a physically grounded framework, by constructing a more interpretable science model. A case study demonstrates that our approach enhances transparency, facilitates validation, and strengthens AI-augmented reasoning in scientific discovery.

Mechanistic interpretability (MI) requires full access to model internals, yet the APIs for most widely deployed language models at best expose log-probabilities over output tokens. This creates a surrogate problem: when do measurements made on open models allow us to make claims about a closed model? We evaluate surrogate fidelity at the prediction, attribution, and representation levels. For binary classification tasks, log-odds provide an API-compatible scalar readout of the model's representation space, and leave-one-out attributions provide insight into model behavior. Across eleven models spanning four families (Llama, Qwen, GPT, and Gemini), we find that prediction fidelity substantially overstates attribution fidelity: models that agree on what the answer is often disagree on why. We document an access-validity inversion: white-box signals like attention patterns and perturbation magnitudes are highly stable across models but only weakly predictive of causal attributions, which black-box input ablations capture by design. Mechanistic insight does not automatically transfer to closed targets, and prediction-level agreement is insufficient to warrant such transfer. Code and results are available at https://github.com/facebookresearch/surrogate.

As language models accelerate scientific research by automating hypothesis generation and implementation, a new bottleneck emerges: evaluating and filtering hundreds of AI-generated ideas without exhaustive experimentation. We ask whether LMs can learn to forecast the empirical success of research ideas before any experiments are run. We study comparative empirical forecasting: given a benchmark-specific research goal and two candidate ideas, predict which will achieve better benchmark performance. We construct a dataset of 11,488 idea pairs grounded in objective outcomes from PapersWithCode. While off-the-shelf 8B-parameter models struggle (30% acc.), SFT dramatically boosts performance to 77.1%, outperforming GPT-5 (61.1%). By framing evaluation as a reasoning task via Reinforcement Learning with Verifiable Rewards (RLVR), we train models to discover latent reasoning paths, achieving 71.35% acc. with interpretable justifications. Through additional ablations and out-of-distribution tests, we show robustness to surface-level heuristics and transfer to both a cross-domain time-split test set and an independently constructed test set. Our results demonstrate that compute-efficient small language models can serve as effective, objective verifiers, offering a scalable path for autonomous scientific discovery.

We propose an effective field-theoretic framework for analyzing Transformer attention through a thermodynamic lens. By constructing a Lagrangian on the information manifold equipped with the Fisher metric, we show that, within the Shannon--Boltzmann entropy framework, the Softmax function arises as a stationary solution minimizing a Helmholtz free energy functional. This establishes a formal correspondence between scaled dot-product attention and canonical ensemble statistics. Extending this mapping to macroscopic observables, we define an effective specific heat associated with fluctuations of the attention energy landscape. In controlled experiments on the modular addition task (p = 19--113), we observe a robust peak in this fluctuation measure that consistently precedes the onset of generalization. While no asymptotic power-law divergence is detected in this finite-depth regime, the reproducible enhancement of energy variance suggests a critical-like crossover accompanying representational reorganization. Our framework provides a unified statistical-mechanical perspective on attention scaling, training dynamics, and positional encoding, interpreting the phenomena as emergent properties of an effective thermodynamic system rather than isolated heuristics. Although the present results indicate finite-size crossover behavior rather than a strict phase transition, they motivate further investigation into scaling limits of deep architectures through fluctuation-based observables.

Machine learning currently exerts an outsized influence on the world, increasingly affecting institutional practices and impacted communities. It is therefore critical that we question vague conceptions of the field as value-neutral or universally beneficial, and investigate what specific values the field is advancing. In this paper, we first introduce a method and annotation scheme for studying the values encoded in documents such as research papers. Applying the scheme, we analyze 100 highly cited machine learning papers published at premier machine learning conferences, ICML and NeurIPS. We annotate key features of papers which reveal their values: their justification for their choice of project, which attributes of their project they uplift, their consideration of potential negative consequences, and their institutional affiliations and funding sources. We find that few of the papers justify how their project connects to a societal need (15\%) and far fewer discuss negative potential (1\%). Through line-by-line content analysis, we identify 59 values that are uplifted in ML research, and, of these, we find that the papers most frequently justify and assess themselves based on Performance, Generalization, Quantitative evidence, Efficiency, Building on past work, and Novelty. We present extensive textual evidence and identify key themes in the definitions and operationalization of these values. Notably, we find systematic textual evidence that these top values are being defined and applied with assumptions and implications generally supporting the centralization of power.Finally, we find increasingly close ties between these highly cited papers and tech companies and elite universities.

Large language models are increasingly used in scientific writing, yet they can fabricate citation-shaped references that appear plausible but fail bibliographic verification. Existing detectors often reduce verification to binary found/not-found decisions and rely on brittle parsing or incomplete retrieval, offering little field-level signal to auditors. We reframe citation hallucination detection as taxonomy-aligned field-level adjudication and introduce a 12-code taxonomy spanning Real, Potential, and Hallucinated citations. Based on this taxonomy, we build CiteTracer, a cascading multi-agent detector that extracts structured citations from PDF and BibTeX, retrieves evidence through cache lookup, URL fetch, scholar connectors, and web search, applies deterministic field matching, and routes ambiguous cases to class-specialist judgers. We release a benchmark of 2,450 synthetic citations built from real seeds with controlled LLM mutations, paired with 957 real-world fabricated citations drawn from ICLR 2026 and an anonymous conference desk-rejected submissions. CiteTracer reaches 97.1% accuracy on the synthetic benchmark, with class-level F1 scores of 97.0, 95.8, and 98.5 for Real, Potential, and Hallucinated, respectively, and detects 97.1% of fabrications on the real-world set without abstaining. Code: https://github.com/aaFrostnova/CiteTracer.

Vision language models (VLMs) excel at many tasks but still struggle with spatial reasoning when critical information is not directly observable. Many such problems require imaginative perception: inferring what would be seen from an unseen viewpoint, tracing paths through occluded spaces, or integrating partial observations into a coherent spatial representation. We introduce Imaginative Perception Tokens (IPT), intermediate perceptual representations that externalize what a VLM would perceive under alternative spatial configurations while remaining consistent with the observed input. To study this capability, we formulate three tasks, Perspective Taking (PET), Path Tracing (PT), and Multiview Counting (MVC), and construct datasets of approximately 20K examples with ground truth imaginations, answers, and evaluation benchmarks. Using the unified VLM BAGEL as the backbone, IPT supervision consistently improves spatial reasoning and often outperforms textual chain of thought training, even without generating images at inference time. On MVC, IPT improves accuracy by 3.4% and achieves competitive performance with strong closed-source models on PT. We further find that combining IPT and label-only supervision yields additional gains, whereas textual chain of thought can substantially degrade performance, suggesting a modality mismatch when spatial computation is forced through language. Overall, IPT provides a principled supervision signal for reasoning about unobserved spatial structure, improving generalization while producing interpretable intermediate representations.

Every known artificial deep neural network (DNN) corresponds to an object in a canonical Grothendieck's topos; its learning dynamic corresponds to a flow of morphisms in this topos. Invariance structures in the layers (like CNNs or LSTMs) correspond to Giraud's stacks. This invariance is supposed to be responsible of the generalization property, that is extrapolation from learning data under constraints. The fibers represent pre-semantic categories (Culioli, Thom), over which artificial languages are defined, with internal logics, intuitionist, classical or linear (Girard). Semantic functioning of a network is its ability to express theories in such a language for answering questions in output about input data. Quantities and spaces of semantic information are defined by analogy with the homological interpretation of Shannon's entropy of P.Baudot and D.Bennequin in 2015). They generalize the measures found by Carnap and Bar-Hillel (1952). Amazingly, the above semantical structures are classified by geometric fibrant objects in a closed model category of Quillen, then they give rise to homotopical invariants of DNNs and of their semantic functioning. Intentional type theories (Martin-Loef) organize these objects and fibrations between them. Information contents and exchanges are analyzed by Grothendieck's derivators.

Mechanistic interpretability aims to understand model behaviors in terms of specific, interpretable features, often hypothesized to manifest as low-dimensional subspaces of activations. Specifically, recent studies have explored subspace interventions (such as activation patching) as a way to simultaneously manipulate model behavior and attribute the features behind it to given subspaces. In this work, we demonstrate that these two aims diverge, potentially leading to an illusory sense of interpretability. Counterintuitively, even if a subspace intervention makes the model's output behave as if the value of a feature was changed, this effect may be achieved by activating a dormant parallel pathway leveraging another subspace that is causally disconnected from model outputs. We demonstrate this phenomenon in a distilled mathematical example, in two real-world domains (the indirect object identification task and factual recall), and present evidence for its prevalence in practice. In the context of factual recall, we further show a link to rank-1 fact editing, providing a mechanistic explanation for previous work observing an inconsistency between fact editing performance and fact localization. However, this does not imply that activation patching of subspaces is intrinsically unfit for interpretability. To contextualize our findings, we also show what a success case looks like in a task (indirect object identification) where prior manual circuit analysis informs an understanding of the location of a feature. We explore the additional evidence needed to argue that a patched subspace is faithful.

Research on causality extraction from text has so far almost entirely neglected counterclaims. Existing causality extraction datasets focus solely on "procausal" claims, i.e., statements that support a relationship. "Concausal" claims, i.e., statements that refute a relationship, are entirely ignored or even accidentally annotated as procausal. We address this shortcoming by developing a new dataset that integrates concausality. Based on an extensive literature review, we first show that concausality is an integral part of causal reasoning on incomplete knowledge. We operationalize this theory in the form of a rigorous guideline for annotation and then augment the Causal News Corpus with concausal statements, obtaining a substantial inter-annotator agreement of Cohen's κ=0.74. To demonstrate the importance of integrating concausal statements, we show that models trained without concausal relationships tend to misclassify these as procausal instead. Based on our new dataset, this mistake can be mitigated, enabling transformers to effectively distinguish pro- and concausality.

A central idea in mechanistic interpretability is that neural networks represent more features than they have dimensions, arranging them in superposition to form an over-complete basis. This framing has been influential, motivating dictionary learning approaches such as sparse autoencoders. However, superposition has mostly been studied in idealized settings where features are sparse and uncorrelated. In these settings, superposition is typically understood as introducing interference that must be minimized geometrically and filtered out by non-linearities such as ReLUs, yielding local structures like regular polytopes. We show that this account is incomplete for realistic data by introducing Bag-of-Words Superposition (BOWS), a controlled setting to encode binary bag-of-words representations of internet text in superposition. Using BOWS, we find that when features are correlated, interference can be constructive rather than just noise to be filtered out. This is achieved by arranging features according to their co-activation patterns, making interference between active features constructive, while still using ReLUs to avoid false positives. We show that this kind of arrangement is more prevalent in models trained with weight decay and naturally gives rise to semantic clusters and cyclical structures which have been observed in real language models yet were not explained by the standard picture of superposition. Code for this paper can be found at https://github.com/LucasPrietoAl/correlations-feature-geometry.

In physics, Lagrangians provide a systematic way to describe laws governing physical systems. In the context of particle physics, they encode the interactions and behavior of the fundamental building blocks of our universe. By treating Lagrangians as complex, rule-based constructs similar to linguistic expressions, we trained a transformer model -- proven to be effective in natural language tasks -- to predict the Lagrangian corresponding to a given list of particles. We report on the transformer's performance in constructing Lagrangians respecting the Standard Model SU(3)times SU(2)times U(1) gauge symmetries. The resulting model is shown to achieve high accuracies (over 90\%) with Lagrangians up to six matter fields, with the capacity to generalize beyond the training distribution, albeit within architectural constraints. We show through an analysis of input embeddings that the model has internalized concepts such as group representations and conjugation operations as it learned to generate Lagrangians. We make the model and training datasets available to the community. An interactive demonstration can be found at: https://huggingface.co/spaces/JoseEliel/generate-lagrangians.

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.

Systematic, compositional generalization beyond the training distribution remains a core challenge in machine learning -- and a critical bottleneck for the emergent reasoning abilities of modern language models. This work investigates out-of-distribution (OOD) generalization in Transformer networks using a GSM8K-style modular arithmetic on computational graphs task as a testbed. We introduce and explore a set of four architectural mechanisms aimed at enhancing OOD generalization: (i) input-adaptive recurrence; (ii) algorithmic supervision; (iii) anchored latent representations via a discrete bottleneck; and (iv) an explicit error-correction mechanism. Collectively, these mechanisms yield an architectural approach for native and scalable latent space reasoning in Transformer networks with robust algorithmic generalization capabilities. We complement these empirical results with a detailed mechanistic interpretability analysis that reveals how these mechanisms give rise to robust OOD generalization abilities.

Image captioning, which generates natural language descriptions of the visual information in an image, is a crucial task in vision-language research. Previous models have typically addressed this task by aligning the generative capabilities of machines with human intelligence through statistical fitting of existing datasets. While effective for normal images, they may struggle to accurately describe those where certain parts of the image are obscured or edited, unlike humans who excel in such cases. These weaknesses they exhibit, including hallucinations and limited interpretability, often hinder performance in scenarios with shifted association patterns. In this paper, we present a generic image captioning framework that employs causal inference to make existing models more capable of interventional tasks, and counterfactually explainable. Our approach includes two variants leveraging either total effect or natural direct effect. Integrating them into the training process enables models to handle counterfactual scenarios, increasing their generalizability. Extensive experiments on various datasets show that our method effectively reduces hallucinations and improves the model's faithfulness to images, demonstrating high portability across both small-scale and large-scale image-to-text models. The code is available at https://github.com/Aman-4-Real/See-or-Guess.

Embeddings have become a pivotal means to represent complex, multi-faceted information about entities, concepts, and relationships in a condensed and useful format. Nevertheless, they often preclude direct interpretation. While downstream tasks make use of these compressed representations, meaningful interpretation usually requires visualization using dimensionality reduction or specialized machine learning interpretability methods. This paper addresses the challenge of making such embeddings more interpretable and broadly useful, by employing Large Language Models (LLMs) to directly interact with embeddings -- transforming abstract vectors into understandable narratives. By injecting embeddings into LLMs, we enable querying and exploration of complex embedding data. We demonstrate our approach on a variety of diverse tasks, including: enhancing concept activation vectors (CAVs), communicating novel embedded entities, and decoding user preferences in recommender systems. Our work couples the immense information potential of embeddings with the interpretative power of LLMs.

Like any field of empirical science, AI may be approached axiomatically. We formulate requirements for a general-purpose, human-level AI system in terms of postulates. We review the methodology of deep learning, examining the explicit and tacit assumptions in deep learning research. Deep Learning methodology seeks to overcome limitations in traditional machine learning research as it combines facets of model richness, generality, and practical applicability. The methodology so far has produced outstanding results due to a productive synergy of function approximation, under plausible assumptions of irreducibility and the efficiency of back-propagation family of algorithms. We examine these winning traits of deep learning, and also observe the various known failure modes of deep learning. We conclude by giving recommendations on how to extend deep learning methodology to cover the postulates of general-purpose AI including modularity, and cognitive architecture. We also relate deep learning to advances in theoretical neuroscience research.

Large linear systems play an important role in high-energy theory, appearing in amplitude bootstraps and during integral reduction. This paper introduces FiniteFieldSolve, a general-purpose toolkit for exactly solving large linear systems over the rationals. The solver interfaces directly with Mathematica, is straightforward to install, and seamlessly replaces Mathematica's native solvers. In testing, FiniteFieldSolve is approximately two orders of magnitude faster than Mathematica and uses an order of magnitude less memory. The package also compares favorably against other public solvers in FiniteFieldSolve's intended use cases. As the name of the package suggests, solutions are obtained via well-known finite field methods. These methods suffer from introducing an inordinate number of modulo (or integer division) operations with respect to different primes. By automatically recompiling itself for each prime, FiniteFieldSolve converts the division operations into much faster combinations of instructions, dramatically improving performance. The technique of compiling the prime can be applied to any finite field solver, where the time savings will be solver dependent. The operation of the package is illustrated through a detailed example of an amplitude bootstrap.

This work is about estimating the hallucination rate for in-context learning (ICL) with Generative AI. In ICL, a conditional generative model (CGM) is prompted with a dataset and asked to make a prediction based on that dataset. The Bayesian interpretation of ICL assumes that the CGM is calculating a posterior predictive distribution over an unknown Bayesian model of a latent parameter and data. With this perspective, we define a hallucination as a generated prediction that has low-probability under the true latent parameter. We develop a new method that takes an ICL problem -- that is, a CGM, a dataset, and a prediction question -- and estimates the probability that a CGM will generate a hallucination. Our method only requires generating queries and responses from the model and evaluating its response log probability. We empirically evaluate our method on synthetic regression and natural language ICL tasks using large language models.

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

Steering is a widely used technique for controlling large language models, yet its effects are often unstable and hard to predict. Existing theoretical accounts are largely based on the Linear Representation Hypothesis (LRH). While LRH assumes that concepts can be orthogonalized for lossless control, this idealized mapping fails in real representations and cannot account for the observed unpredictability of steering. By relaxing LRH's orthogonality assumption while preserving linear representations, we show that overlapping concept contributions naturally yield a sample-specific axis-orthogonal structure. We formalize this as the Cylindrical Representation Hypothesis (CRH). In CRH, a central axis captures the main difference between concept absence and presence and drives concept generation. A surrounding normal plane controls steering sensitivity by determining how easily the axis can activate the target concept. Within this plane, only specific sensitive sectors strongly facilitate concept activation, while other sectors can suppress or delay it. While the surrounding normal plane can be reliably identified from difference vectors, the sensitive sector cannot, introducing intrinsic uncertainty at the sector level. This uncertainty provides a principled explanation for why steering outcomes often fluctuate even when using well-aligned directions. Our experiments verify the existence of the cylindrical structure and demonstrate that CRH provides a valid and practical way to interpret model steering behavior in real settings: https://github.com/mbzuai-nlp/CRH.

Interpretable machine learning has exploded as an area of interest over the last decade, sparked by the rise of increasingly large datasets and deep neural networks. Simultaneously, large language models (LLMs) have demonstrated remarkable capabilities across a wide array of tasks, offering a chance to rethink opportunities in interpretable machine learning. Notably, the capability to explain in natural language allows LLMs to expand the scale and complexity of patterns that can be given to a human. However, these new capabilities raise new challenges, such as hallucinated explanations and immense computational costs. In this position paper, we start by reviewing existing methods to evaluate the emerging field of LLM interpretation (both interpreting LLMs and using LLMs for explanation). We contend that, despite their limitations, LLMs hold the opportunity to redefine interpretability with a more ambitious scope across many applications, including in auditing LLMs themselves. We highlight two emerging research priorities for LLM interpretation: using LLMs to directly analyze new datasets and to generate interactive explanations.

In this paper, we present and implement a multi-dimensional, modular framework for performing deep argument analysis (DeepA2) using current pre-trained language models (PTLMs). ArgumentAnalyst -- a T5 model (Raffel et al. 2020) set up and trained within DeepA2 -- reconstructs argumentative texts, which advance an informal argumentation, as valid arguments: It inserts, e.g., missing premises and conclusions, formalizes inferences, and coherently links the logical reconstruction to the source text. We create a synthetic corpus for deep argument analysis, and evaluate ArgumentAnalyst on this new dataset as well as on existing data, specifically EntailmentBank (Dalvi et al. 2021). Our empirical findings vindicate the overall framework and highlight the advantages of a modular design, in particular its ability to emulate established heuristics (such as hermeneutic cycles), to explore the model's uncertainty, to cope with the plurality of correct solutions (underdetermination), and to exploit higher-order evidence.

Scalar fields are ubiquitous in theories of high-energy physics. In the context of cosmic inflation, this suggests the existence of spectator fields, which provide a subdominant source of energy density. We show that spectator fields boost the inflationary production of primordial black holes, with single-field ultra-slow roll evolution supplanted by a phase of evolution along the spectator direction, and primordial perturbations amplified by the resulting multifield dynamics. This generic mechanism is largely free from the severe fine-tuning that afflicts single-field inflationary PBH models.

Neural fields have gained significant attention in the computer vision community due to their excellent performance in novel view synthesis, geometry reconstruction, and generative modeling. Some of their advantages are a sound theoretic foundation and an easy implementation in current deep learning frameworks. While neural fields have been applied to signals on manifolds, e.g., for texture reconstruction, their representation has been limited to extrinsically embedding the shape into Euclidean space. The extrinsic embedding ignores known intrinsic manifold properties and is inflexible wrt. transfer of the learned function. To overcome these limitations, this work introduces intrinsic neural fields, a novel and versatile representation for neural fields on manifolds. Intrinsic neural fields combine the advantages of neural fields with the spectral properties of the Laplace-Beltrami operator. We show theoretically that intrinsic neural fields inherit many desirable properties of the extrinsic neural field framework but exhibit additional intrinsic qualities, like isometry invariance. In experiments, we show intrinsic neural fields can reconstruct high-fidelity textures from images with state-of-the-art quality and are robust to the discretization of the underlying manifold. We demonstrate the versatility of intrinsic neural fields by tackling various applications: texture transfer between deformed shapes & different shapes, texture reconstruction from real-world images with view dependence, and discretization-agnostic learning on meshes and point clouds.

Electrocardiography (ECG) serves as an indispensable diagnostic tool in clinical practice, yet existing multimodal large language models (MLLMs) remain unreliable for ECG interpretation, often producing plausible but clinically incorrect analyses. To address this, we propose ECG-R1, the first reasoning MLLM designed for reliable ECG interpretation via three innovations. First, we construct the interpretation corpus using Protocol-Guided Instruction Data Generation, grounding interpretation in measurable ECG features and monograph-defined quantitative thresholds and diagnostic logic. Second, we present a modality-decoupled architecture with Interleaved Modality Dropout to improve robustness and cross-modal consistency when either the ECG signal or ECG image is missing. Third, we present Reinforcement Learning with ECG Diagnostic Evidence Rewards to strengthen evidence-grounded ECG interpretation. Additionally, we systematically evaluate the ECG interpretation capabilities of proprietary, open-source, and medical MLLMs, and provide the first quantitative evidence that severe hallucinations are widespread, suggesting that the public should not directly trust these outputs without independent verification. Code and data are publicly available at https://github.com/PKUDigitalHealth/ECG-R1{here}, and an online platform can be accessed at http://ai.heartvoice.com.cn/ECG-R1/{here}.

Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, E_pi[ell(Y mid Gamma_pi(X))], which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length ell(Y mid X). This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as O(log n) with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows a+bln n (Qwen2-7B b approx 0.377, Llama-3.1-8B b approx 0.147); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by sim 0.13 per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.

This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty quantification guarantees for machine learning systems. Much of the current interest in conformal prediction is due to its ability to integrate into complex machine learning workflows, solving the problem of forming prediction sets without any assumptions on the form of the data generating distribution. Since contemporary machine learning algorithms have generally proven difficult to analyze directly, conformal prediction's main appeal is its ability to provide formal, finite-sample guarantees when paired with such methods. The goal of this book is to teach the reader about the fundamental technical arguments that arise when researching conformal prediction and related questions in distribution-free inference. Many of these proof strategies, especially the more recent ones, are scattered among research papers, making it difficult for researchers to understand where to look, which results are important, and how exactly the proofs work. We hope to bridge this gap by curating what we believe to be some of the most important results in the literature and presenting their proofs in a unified language, with illustrations, and with an eye towards pedagogy.

Experiments probing natural language processing by both humans and LLMs suggest that the meaning of a semantic expression is indeterminate prior to the act of interpretation rather than being specifiable simply as the sum of its parts (i.e. compositionality). This observer-dependent act dynamically actualizes meaning under genuine contextuality more consistent with quantum logical mechanisms than with classical Boolean approaches that assume separability, motivating an approach to language modeling that utilizes a Hilbert space formalism. In this work, we introduce Phase-Associative Memory (PAM) -- a complex-valued sequence model whose state S_t \in C^{d \times d} accumulates outer products of complex token embeddings retrieved through the conjugate inner product Relangle K mid Qrangle / d -- and evaluate it against a structurally matched real-valued ablation. Both architectures train stably across a 5M--100M parameter sweep on WikiText-103 under identical conditions; PAM sits at higher absolute loss at every measured scale but improves more rapidly with parameter count, with power-law exponents of -0.15 vs.\ -0.12 in loss and -0.65 vs.\ -0.49 in perplexity that narrow the gap between the two architectures monotonically. Further investigation of complex-valued sequence modeling at larger scales could reveal that the loss plateau characteristic of real-valued state-of-the-art language models (e.g. transformers) is reachable with PAM-style architectures with an order of magnitude fewer parameters than the current frontier (sim1T), implying that similar capabilities are achievable at sizes runnable on consumer-grade hardware.

This paper explores the intersection of identity, individuality, and reality through competing frameworks, including classical metaphysics, quantum mechanics, and computational theories. Traditional metaphysical notions of fixed identity are challenged by advancements in cloning, teletransportation, and digital replication, which reveal the fluid and relational nature of individuality. Quantum mechanics further complicates these notions, emphasizing the indistinguishability and contextuality of fundamental particles. Computational approaches, such as the Ruliad and Constructor Theory, offer expansive views of emergent realities but often lack practical constraints for observer relevance. Algorithmic idealism is introduced as a unifying framework, proposing that reality is an emergent construct governed by computational rules prioritizing coherence, sufficiency, and observer-dependent experiences. By redefining identity as an informational construct and reality as a process shaped by algorithmic transitions, algorithmic idealism resolves foundational paradoxes and offers a superior lens for understanding existence in an increasingly digital and interconnected world. The framework bridges gaps between competing theories, providing a coherent and pragmatic model for addressing ethical, metaphysical, and technological challenges.

Large language models (LLMs) are becoming deeply embedded in human communication and decision-making, yet they inherit the ambiguity, bias, and lack of direct access to truth inherent in language itself. While their outputs are fluent, emotionally resonant, and coherent, they are generated through statistical prediction rather than grounded reasoning. This creates the risk of hallucination, responses that sound convincing but lack factual validity. Building on Geoffrey Hinton's observation that AI mirrors human intuition rather than reasoning, this paper argues that LLMs operationalize System 1 cognition at scale: fast, associative, and persuasive, but without reflection or falsification. To address this, we introduce the Rose-Frame, a three-dimensional framework for diagnosing cognitive and epistemic drift in human-AI interaction. The three axes are: (i) Map vs. Territory, which distinguishes representations of reality (epistemology) from reality itself (ontology); (ii) Intuition vs. Reason, drawing on dual-process theory to separate fast, emotional judgments from slow, reflective thinking; and (iii) Conflict vs. Confirmation, which examines whether ideas are critically tested through disagreement or simply reinforced through mutual validation. Each dimension captures a distinct failure mode, and their combination amplifies misalignment. Rose-Frame does not attempt to fix LLMs with more data or rules. Instead, it offers a reflective tool that makes both the model's limitations and the user's assumptions visible, enabling more transparent and critically aware AI deployment. It reframes alignment as cognitive governance: intuition, whether human or artificial, must remain governed by human reason. Only by embedding reflective, falsifiable oversight can we align machine fluency with human understanding.

Post-hoc gradient-based interpretability methods [Simonyan et al., 2013, Smilkov et al., 2017] that provide instance-specific explanations of model predictions are often based on assumption (A): magnitude of input gradients -- gradients of logits with respect to input -- noisily highlight discriminative task-relevant features. In this work, we test the validity of assumption (A) using a three-pronged approach. First, we develop an evaluation framework, DiffROAR, to test assumption (A) on four image classification benchmarks. Our results suggest that (i) input gradients of standard models (i.e., trained on original data) may grossly violate (A), whereas (ii) input gradients of adversarially robust models satisfy (A). Second, we introduce BlockMNIST, an MNIST-based semi-real dataset, that by design encodes a priori knowledge of discriminative features. Our analysis on BlockMNIST leverages this information to validate as well as characterize differences between input gradient attributions of standard and robust models. Finally, we theoretically prove that our empirical findings hold on a simplified version of the BlockMNIST dataset. Specifically, we prove that input gradients of standard one-hidden-layer MLPs trained on this dataset do not highlight instance-specific signal coordinates, thus grossly violating assumption (A). Our findings motivate the need to formalize and test common assumptions in interpretability in a falsifiable manner [Leavitt and Morcos, 2020]. We believe that the DiffROAR evaluation framework and BlockMNIST-based datasets can serve as sanity checks to audit instance-specific interpretability methods; code and data available at https://github.com/harshays/inputgradients.

Language builds discourse contexts other than the actual: a painting, a belief, a memory, a hypothetical. Each is a mental space in which the same entity can take a different value, as when a flower is red in reality but purple in a portrait. Formal semantics keeps these contexts apart because their logics differ (modal, temporal, doxastic, depictive); Fauconnier's mental-space theory treats them as one space-building operation. We ask which of these a transformer language model implements, and find a mechanistic version of Fauconnier's unification. The model uses one router/slot format across the inventory: a reusable value slot stores attributed content, and a causally manipulable router (the space index) selects which space is read. A subspace trained with Distributed Alignment Search to control one space type, counterfactual, belief, fictional, or temporal, also controls the others, well above a random floor, on three model families; belief, which formal semantics marks as a distinct case, is not specially separated. The router is low-rank, composes additively with entity identity, and acts through a few late-layer heads. Two further results show the mechanism drives inference and composes: a subspace trained on a rule-derived conclusion flips what the model infers while dissociating from what it reports, and composing space-builders mints a fresh router over the shared slot. This paper establishes the cross-type generality. A companion paper develops belief in depth, because of its special status in philosophy, psychology, and linguistics (epistemology, theory of mind, and propositional attitude reports).

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

Mechanistic interpretability aims to understand the computational mechanisms underlying neural networks' capabilities in order to accomplish concrete scientific and engineering goals. Progress in this field thus promises to provide greater assurance over AI system behavior and shed light on exciting scientific questions about the nature of intelligence. Despite recent progress toward these goals, there are many open problems in the field that require solutions before many scientific and practical benefits can be realized: Our methods require both conceptual and practical improvements to reveal deeper insights; we must figure out how best to apply our methods in pursuit of specific goals; and the field must grapple with socio-technical challenges that influence and are influenced by our work. This forward-facing review discusses the current frontier of mechanistic interpretability and the open problems that the field may benefit from prioritizing.

Linguistic commentary on LLMs, heavily influenced by the theoretical frameworks of de Saussure and Chomsky, is often speculative and unproductive. Critics challenge whether LLMs can legitimately model language, citing the need for "deep structure" or "grounding" to achieve an idealized linguistic "competence." We argue for a radical shift in perspective towards the empiricist principles of Witold Ma\'nczak, a prominent general and historical linguist. He defines language not as a "system of signs" or a "computational system of the brain" but as the totality of all that is said and written. Above all, he identifies frequency of use of particular language elements as language's primary governing principle. Using his framework, we challenge prior critiques of LLMs and provide a constructive guide for designing, evaluating, and interpreting language models.

We update predictions for observables in the "delicate" D3/anti-D3 inflationary model on the conifold. We use a full CMB likelihood calculation to assess goodness-of-fit, which is necessary because in this model the zeta power spectrum often cannot be modelled as a power-law over observable scales. For the first time we are able to provide accurate forecasts for the amplitude of three-point correlations. In a significant portion of its parameter space the model follows Maldacena's single-field prediction fNL ~ -(5/12)(ns-1) if nt << 1. Therefore |fNL| is usually small when the power spectrum satisfies observational constraints. In a small number of cases the bispectrum is instead dominated by effects from rapid switching between angular minima. The resulting amplitudes are larger, but mostly with unacceptable spectral behaviour. In the most extreme case we obtain |fNLeq| ~ 75 at kt/3 = 0.002/Mpc. It has been suggested that the quasi-single field inflation ("QSFI") mechanism could produce significant 3-point correlations in this model. We do observe rare shifts in amplitude between equilateral and squeezed configurations that could possibly be associated with QSFI effects, but more investigation is needed to establish the full bispectrum shape. There is evidence of "shape" running between equilateral and squeezed configurations that may be inherited from the scale dependence of the spectrum. We explore the dependence of observables on discrete choices such as the truncation point of the potential. Our analysis illustrates the advantages of a standard format for information exchange within the inflationary model-building and testing community.

Radiance field methods have achieved photorealistic novel view synthesis and geometry reconstruction. But they are mostly applied in per-scene optimization or small-baseline settings. While several recent works investigate feed-forward reconstruction with large baselines by utilizing transformers, they all operate with a standard global attention mechanism and hence ignore the local nature of 3D reconstruction. We propose a method that unifies local and global reasoning in transformer layers, resulting in improved quality and faster convergence. Our model represents scenes as Gaussian Volumes and combines this with an image encoder and Group Attention Layers for efficient feed-forward reconstruction. Experimental results demonstrate that our model, trained for two days on four GPUs, demonstrates high fidelity in reconstructing 360 deg radiance fields, and robustness to zero-shot and out-of-domain testing. Our project Page: https://apchenstu.github.io/LaRa/.

We conjecture that hidden state vectors corresponding to individual input tokens encode information sufficient to accurately predict several tokens ahead. More concretely, in this paper we ask: Given a hidden (internal) representation of a single token at position t in an input, can we reliably anticipate the tokens that will appear at positions geq t + 2? To test this, we measure linear approximation and causal intervention methods in GPT-J-6B to evaluate the degree to which individual hidden states in the network contain signal rich enough to predict future hidden states and, ultimately, token outputs. We find that, at some layers, we can approximate a model's output with more than 48% accuracy with respect to its prediction of subsequent tokens through a single hidden state. Finally we present a "Future Lens" visualization that uses these methods to create a new view of transformer states.

In recent years, Neural Fields (NFs) have emerged as an effective tool for encoding diverse continuous signals such as images, videos, audio, and 3D shapes. When applied to 3D data, NFs offer a solution to the fragmentation and limitations associated with prevalent discrete representations. However, given that NFs are essentially neural networks, it remains unclear whether and how they can be seamlessly integrated into deep learning pipelines for solving downstream tasks. This paper addresses this research problem and introduces nf2vec, a framework capable of generating a compact latent representation for an input NF in a single inference pass. We demonstrate that nf2vec effectively embeds 3D objects represented by the input NFs and showcase how the resulting embeddings can be employed in deep learning pipelines to successfully address various tasks, all while processing exclusively NFs. We test this framework on several NFs used to represent 3D surfaces, such as unsigned/signed distance and occupancy fields. Moreover, we demonstrate the effectiveness of our approach with more complex NFs that encompass both geometry and appearance of 3D objects such as neural radiance fields.

Given the complexity and lack of transparency in deep neural networks (DNNs), extensive efforts have been made to make these systems more interpretable or explain their behaviors in accessible terms. Unlike most reviews, which focus on algorithmic and model-centric perspectives, this work takes a "data-centric" view, examining how data collection, processing, and analysis contribute to explainable AI (XAI). We categorize existing work into three categories subject to their purposes: interpretations of deep models, referring to feature attributions and reasoning processes that correlate data points with model outputs; influences of training data, examining the impact of training data nuances, such as data valuation and sample anomalies, on decision-making processes; and insights of domain knowledge, discovering latent patterns and fostering new knowledge from data and models to advance social values and scientific discovery. Specifically, we distill XAI methodologies into data mining operations on training and testing data across modalities, such as images, text, and tabular data, as well as on training logs, checkpoints, models and other DNN behavior descriptors. In this way, our study offers a comprehensive, data-centric examination of XAI from a lens of data mining methods and applications.

Interpretable graph learning is in need as many scientific applications depend on learning models to collect insights from graph-structured data. Previous works mostly focused on using post-hoc approaches to interpret pre-trained models (graph neural networks in particular). They argue against inherently interpretable models because the good interpretability of these models is often at the cost of their prediction accuracy. However, those post-hoc methods often fail to provide stable interpretation and may extract features that are spuriously correlated with the task. In this work, we address these issues by proposing Graph Stochastic Attention (GSAT). Derived from the information bottleneck principle, GSAT injects stochasticity to the attention weights to block the information from task-irrelevant graph components while learning stochasticity-reduced attention to select task-relevant subgraphs for interpretation. The selected subgraphs provably do not contain patterns that are spuriously correlated with the task under some assumptions. Extensive experiments on eight datasets show that GSAT outperforms the state-of-the-art methods by up to 20%uparrow in interpretation AUC and 5%uparrow in prediction accuracy. Our code is available at https://github.com/Graph-COM/GSAT.

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.

Disentangling the factors of variation in data is a fundamental concept in machine learning and has been studied in various ways by different researchers, leading to a multitude of definitions. Despite the numerous empirical studies, more theoretical research is needed to fully understand the defining properties of disentanglement and how different definitions relate to each other. This paper presents a meta-analysis of existing definitions of disentanglement, using category theory as a unifying and rigorous framework. We propose that the concepts of the cartesian and monoidal products should serve as the core of disentanglement. With these core concepts, we show the similarities and crucial differences in dealing with (i) functions, (ii) equivariant maps, (iii) relations, and (iv) stochastic maps. Overall, our meta-analysis deepens our understanding of disentanglement and its various formulations and can help researchers navigate different definitions and choose the most appropriate one for their specific context.

Mechanistic interpretability is the program of explaining what AI systems are doing in terms of their internal mechanisms. I analyze some aspects of the program, along with setting out some concrete challenges and assessing progress to date. I argue for the importance of propositional interpretability, which involves interpreting a system's mechanisms and behavior in terms of propositional attitudes: attitudes (such as belief, desire, or subjective probability) to propositions (e.g. the proposition that it is hot outside). Propositional attitudes are the central way that we interpret and explain human beings and they are likely to be central in AI too. A central challenge is what I call thought logging: creating systems that log all of the relevant propositional attitudes in an AI system over time. I examine currently popular methods of interpretability (such as probing, sparse auto-encoders, and chain of thought methods) as well as philosophical methods of interpretation (including those grounded in psychosemantics) to assess their strengths and weaknesses as methods of propositional interpretability.

While Large Language Models (LLMs) have substantially advanced text-to-code synthesis, many real programming tasks specify intent through visual artifacts such as screenshots, charts, vector drawings, videos, and interactive states. These tasks require models to connect visual perception to executable programs, because correctness depends not only on syntax but also on layout, data semantics, interaction behavior, and domain-specific constraints that apply after execution. This survey examines Multimodal Code Intelligence, covering systems that generate, edit, refine, or reason with code under visually grounded inputs and outputs. We first formulate the field by the role that code plays in each task, distinguishing code as a rendered artifact, an editable symbolic structure, a scientific representation, an intermediate reasoning trace, or an executable policy or tool interface. We then organize benchmarks and methods into four domains: Graphical User Interface, Scientific Visualization, Structured Graphics, and Frontier Tasks and Frameworks. This taxonomy connects mature artifact-generation problems to emerging agentic and unified settings and allows us to compare how different tasks treat evidence of correctness. Looking ahead, we argue that future research may benefit from four verification-centered directions. Multi-signal validation can combine complementary evidence of correctness, multi-state verification can test behavior across execution trajectories, cross-task transfer testing can probe reusable visual-code skills, and verifiable agent traces can reveal whether agent actions are grounded in visual evidence. Together, these directions may move this field from single-output imitation toward evidence-grounded executable systems. An ongoing project and resources are available on https://github.com/xjywhu/Awesome-Multimodal-LLM-for-Code{GitHub}.

Syntactic structures used to play a vital role in natural language processing (NLP), but since the deep learning revolution, NLP has been gradually dominated by neural models that do not consider syntactic structures in their design. One vastly successful class of neural models is transformers. When used as an encoder, a transformer produces contextual representation of words in the input sentence. In this work, we propose a new model of contextual word representation, not from a neural perspective, but from a purely syntactic and probabilistic perspective. Specifically, we design a conditional random field that models discrete latent representations of all words in a sentence as well as dependency arcs between them; and we use mean field variational inference for approximate inference. Strikingly, we find that the computation graph of our model resembles transformers, with correspondences between dependencies and self-attention and between distributions over latent representations and contextual embeddings of words. Experiments show that our model performs competitively to transformers on small to medium sized datasets. We hope that our work could help bridge the gap between traditional syntactic and probabilistic approaches and cutting-edge neural approaches to NLP, and inspire more linguistically-principled neural approaches in the future.

Recent advances in mechanistic interpretability have revealed that large language models (LLMs) develop internal representations corresponding not only to concrete entities but also distinct, human-understandable abstract concepts and behaviour. Moreover, these hidden features can be directly manipulated to steer model behaviour. However, it remains an open question whether this phenomenon is unique to models trained on inherently structured data (ie. language, images) or if it is a general property of foundation models. In this work, we investigate the internal representations of a large physics-focused foundation model. Inspired by recent work identifying single directions in activation space for complex behaviours in LLMs, we extract activation vectors from the model during forward passes over simulation datasets for different physical regimes. We then compute "delta" representations between the two regimes. These delta tensors act as concept directions in activation space, encoding specific physical features. By injecting these concept directions back into the model during inference, we can steer its predictions, demonstrating causal control over physical behaviours, such as inducing or removing some particular physical feature from a simulation. These results suggest that scientific foundation models learn generalised representations of physical principles. They do not merely rely on superficial correlations and patterns in the simulations. Our findings open new avenues for understanding and controlling scientific foundation models and has implications for AI-enabled scientific discovery.

Scientific knowledge is growing rapidly, making it challenging to track progress and high-level conceptual links across broad disciplines. While existing tools like citation networks and search engines make it easy to access a few related papers, they fundamentally lack the flexible abstraction needed to represent the density of activity in various scientific subfields. We motivate SCIENCE HIERARCHOGRAPHY, the goal of organizing scientific literature into a high-quality hierarchical structure that allows for the categorization of scientific work across varying levels of abstraction, from very broad fields to very specific studies. Such a representation can provide insights into which fields are well-explored and which are under-explored. To achieve the goals of SCIENCE HIERARCHOGRAPHY, we develop a range of algorithms. Our primary approach combines fast embedding-based clustering with LLM-based prompting to balance the computational efficiency of embedding methods with the semantic precision offered by LLM prompting. We demonstrate that this approach offers the best trade-off between quality and speed compared to methods that heavily rely on LLM prompting, such as iterative tree construction with LLMs. To better reflect the interdisciplinary and multifaceted nature of research papers, our hierarchy captures multiple dimensions of categorization beyond simple topic labels. We evaluate the utility of our framework by assessing how effectively an LLM-based agent can locate target papers using the hierarchy. Results show that this structured approach enhances interpretability, supports trend discovery, and offers an alternative pathway for exploring scientific literature beyond traditional search methods. Code, data and demo: https://github.com/JHU-CLSP/science-hierarchography{https://github.com/JHU-CLSP/science-hierarchography}

Interpreting the law is always essential for the law to adapt to the ever-changing society. It is a critical and challenging task even for legal practitioners, as it requires meticulous and professional annotations and summarizations by legal experts, which are admittedly time-consuming and expensive to collect at scale. To alleviate the burden on legal experts, we propose a method for automated legal interpretation. Specifically, by emulating doctrinal legal research, we introduce a novel framework, ATRIE, to address Legal Concept Interpretation, a typical task in legal interpretation. ATRIE utilizes large language models (LLMs) to AuTomatically Retrieve concept-related information, Interpret legal concepts, and Evaluate generated interpretations, eliminating dependence on legal experts. ATRIE comprises a legal concept interpreter and a legal concept interpretation evaluator. The interpreter uses LLMs to retrieve relevant information from previous cases and interpret legal concepts. The evaluator uses performance changes on Legal Concept Entailment, a downstream task we propose, as a proxy of interpretation quality. Automated and multifaceted human evaluations indicate that the quality of our interpretations is comparable to those written by legal experts, with superior comprehensiveness and readability. Although there remains a slight gap in accuracy, it can already assist legal practitioners in improving the efficiency of legal interpretation.

Mechanistic interpretability seeks to understand the neural mechanisms that enable specific behaviors in Large Language Models (LLMs) by leveraging causality-based methods. While these approaches have identified neural circuits that copy spans of text, capture factual knowledge, and more, they remain unusable for multimodal models since adapting these tools to the vision-language domain requires considerable architectural changes. In this work, we adapt a unimodal causal tracing tool to BLIP to enable the study of the neural mechanisms underlying image-conditioned text generation. We demonstrate our approach on a visual question answering dataset, highlighting the causal relevance of later layer representations for all tokens. Furthermore, we release our BLIP causal tracing tool as open source to enable further experimentation in vision-language mechanistic interpretability by the community. Our code is available at https://github.com/vedantpalit/Towards-Vision-Language-Mechanistic-Interpretability.

Large Language Models (LLMs) have emerged as powerful sources of evidence for linguists seeking to develop theories of syntax. In this paper, we argue that causal interpretability methods, applied to LLMs, can greatly enhance the value of such evidence by helping us characterize the abstract mechanisms that LLMs learn to use. Our empirical focus is a set of English filler-gap dependency constructions (e.g., questions, relative clauses). Linguistic theories largely agree that these constructions share many properties. Using experiments based in Distributed Interchange Interventions, we show that LLMs converge on similar abstract analyses of these constructions. These analyses also reveal previously overlooked factors -- relating to frequency, filler type, and surrounding context -- that could motivate changes to standard linguistic theory. Overall, these results suggest that mechanistic, internal analyses of LLMs can push linguistic theory forward.

Large language models (LLMs) often hallucinate by generating factually incorrect or unfaithful content, posing significant risks to their safe use. Detecting such hallucinations is particularly challenging under the zero-source constraint, where no model internals or external references are available, and detection must rely solely on the textual query-answer pair. In this paper, we propose Human-like Criteria Probing for Hallucination Detection (HCPD), a paradigm that emulates the multi-faceted reasoning of human evaluators. Its core is a Human-like Criteria Probing (HCP) mechanism, in which a LLM agent adaptively decomposes its judgment into a weighted set of interpretable criteria and aggregates criterion-specific scores into a final truthfulness measure. To achieve this adaptive capability, we introduce a reward-based alignment scheme using only weak supervision from semantic consistency. At inference, we employ a multi-sampling aggregation strategy to ensure robust decisions while preserving full interpretability. We further provide theoretical analysis supporting the reliability of our approach. Extensive experiments show that HCPD consistently outperforms state-of-the-art baselines, offering an effective and explainable solution for zero-source hallucination detection. Code is available at https://github.com/TRISKEL10N/HCPD.

Understanding how people of various demographics think, feel, and express themselves (collectively called group expression) is essential for social science and underlies the assessment of bias in Large Language Models (LLMs). While LLMs can effectively summarize group expression when provided with empirical examples, coming up with generalizable theories of how a group's expression manifests in real-world text is challenging. In this paper, we define a new task called Group Theorization, in which a system must write theories that differentiate expression across demographic groups. We make available a large dataset on this task, Splits!, constructed by splitting Reddit posts by neutral topics (e.g. sports, cooking, and movies) and by demographics (e.g. occupation, religion, and race). Finally, we suggest a simple evaluation framework for assessing how effectively a method can generate 'better' theories about group expression, backed by human validation. We publicly release the raw corpora and evaluation scripts for Splits! to help researchers assess how methods infer--and potentially misrepresent--group differences in expression. We make Splits! and our evaluation module available at https://github.com/eyloncaplan/splits.

A biological neural network in the cortex forms a neural field. Neurons in the field have their own receptive fields, and connection weights between two neurons are random but highly correlated when they are in close proximity in receptive fields. In this paper, we investigate such neural fields in a multilayer architecture to investigate the supervised learning of the fields. We empirically compare the performances of our field model with those of randomly connected deep networks. The behavior of a randomly connected network is investigated on the basis of the key idea of the neural tangent kernel regime, a recent development in the machine learning theory of over-parameterized networks; for most randomly connected neural networks, it is shown that global minima always exist in their small neighborhoods. We numerically show that this claim also holds for our neural fields. In more detail, our model has two structures: i) each neuron in a field has a continuously distributed receptive field, and ii) the initial connection weights are random but not independent, having correlations when the positions of neurons are close in each layer. We show that such a multilayer neural field is more robust than conventional models when input patterns are deformed by noise disturbances. Moreover, its generalization ability can be slightly superior to that of conventional models.

Out of everything the human brain processes, only a small fraction is consciously accessible, in the sense of being available for verbal report, deliberate control, and flexible reasoning. In this paper, we present evidence that an analogous functional distinction has emerged in large language models. Using a new interpretability technique, the Jacobian lens, we identify the representations a model is poised to verbalize at any point in its processing. These representations, which we collectively call the J-space, exhibit the functional properties characteristic of a global workspace: their contents can be reported, deliberately summoned and held, used to carry the intermediate steps of silent reasoning, and passed as arguments to arbitrary downstream computations, while automatic processing such as text parsing and routine inference proceeds without them. The J-space also has structural signatures that global workspace theory associates with conscious access: it carries coherent content only in an intermediate band of layers, holds on the order of tens of concepts at a time, and is broadcast by the model's weights more widely than other representations. These properties make it a practical window into a model's unspoken thinking. In alignment audits, it reveals strategic deliberation, evaluation awareness, and trained-in misaligned dispositions that never appear in the model's outputs. We find that post-training installs the Assistant's point of view in the workspace, and we introduce counterfactual reflection training, which improves behavior by training only what a model would say if interrupted and asked to reflect. These results indicate that language models maintain a small, privileged set of representations bearing some of the functional hallmarks of conscious access, and that decoding these representations sheds light on ongoing cognitive processes.