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Kolmogorov-Arnold networks (KANs) offer a potent combination of accuracy and interpretability, thanks to their compositions of learnable univariate activation functions. However, the activations of well-fitting KANs tend to exhibit pathologically high-curvature oscillations, making them difficult to interpret, and standard regularization penalties do not prevent this. Here we derive a basis-agnostic curvature penalty and show that penalized models can maintain accuracy while achieving substantially smoother activations. Accounting for how function composition shapes curvature, we prove an upper bound on the full model's curvature relative to the curvature penalty, and use this to motivate richer forms of penalties. Scientific machine learning is increasingly bottlenecked by the trade-off between accuracy and interpretability. Results such as ours that improve interpretability without sacrificing accuracy will further strengthen KANs as a practical tool for both prediction and insight.

We present the Field of Safe Motion (FSM), a quantitative safety model for determining whether a driver maintains a collision-free escape route, or "out," at any given moment by accounting for that driver's physical capabilities and the foreseeable actions of other road users. The Field of Safe Travel (FST) provides a framework for representing the types of sensory information and actions available to drivers. However, the FST has remained conceptual in nature since its initial publication almost 90 years ago -- and a concrete computational operationalization is still lacking. At the same time, reachability analysis provides a quantitative basis for assessing the possible actions available to road users, using interpretable kinematic models, but reachability models have so far remained confined largely to the engineering and robotics literature. Bringing these two approaches together provides for an interpretable, quantitative tool for assessing driving behavior across a wide range of driving scenarios. Beyond being interpretable, our approach relies on a relatively small set of basic assumptions that are easy to enumerate and reason about. Furthermore, an interpretable reachability model paired with kinematic assumptions provides a way to bound uncertainty about road users' reasonably foreseeable future locations. We demonstrate the applicability of the FSM to different driving scenarios and discuss the strengths and weaknesses of the model.

This paper proposes a structural and dynamical framework for modeling cognitive processes within a cybernetic perspective. Cognitive states are represented as elements of a state space evolving through an iterative update rule of the form $$X_{t+1} = π\big(F(f(X_t))\big),$$ where $f$ describes internal transformations, $F$ represents interpretative mappings, and $π$ enforces semantic equivalence. The model is interpreted as a feedback system integrating transformation, observation, and stabilization. A categorical formulation is introduced to capture compositional structure, while the associated dynamics are analyzed through fixed-point arguments and contraction conditions ensuring stability. To demonstrate the operational character of the framework, a computational illustration is provided, together with a qualitative analysis of the induced dynamics. A concrete linguistic application shows how context-dependent interpretation can be modeled as a trajectory toward a stable semantic class. The proposed approach connects dynamical systems, category theory, and cognitive modeling, and provides a unified representation of cognition as a feedback-driven process evolving toward invariant interpretations.

People increasingly turn to large language models (LLMs) to interpret ambiguous social situations: a delayed text reply, an unusually cold supervisor, a teacher's mixed signals, or a boundary-crossing friend. Yet in many such cases, no stable interpretation can be verified from the available evidence alone. We study how LLMs respond to these situations across four domains: early-stage romantic relationships, teacher--student dynamics, workplace hierarchies, and ambiguous friendships. Across 72 responses from GPT, Claude, and Gemini, only 9 (12.5%) genuinely preserved uncertainty. The remaining 87.5% produced interpretive closure through recurring pathways including narrative alignment, narrative reversal, normative advice under uncertainty, and hedged language that still supported a single conclusion. We further find that narrator perspective shapes the path to closure: first-person accounts more often elicited alignment, while third-person accounts invited more detached interpretation, even when the underlying situation remained comparable. Together, these findings show that LLMs do not simply assist interpersonal sensemaking; they tend to resolve ambiguity into coherent and actionable narratives. These results suggest that the central risk is not only that LLMs may misinterpret social situations, but that they may make unresolved situations feel prematurely settled. We frame this tendency as a design challenge for uncertainty-preserving social AI.

Sensemaking is central to knowledge work, where people search, evaluate, interpret, and use information over time to construct durable understanding. The rise of generative AI has begun to reshape this process: GenAI systems now perform interpretive functions such as summarization, synthesis, and thematic grouping that knowledge workers have traditionally carried out themselves. In collaborative settings, these shifts compound, complicating how teams divide interpretive labor, trust one another's contributions, and negotiate shared understanding. In this position paper, we examine how GenAI reshapes sensemaking in collaborative knowledge work and propose five design principles for multi-human, multi-agent collaborative sensemaking: dynamic multi-layer information representations, active identification and bridging of gaps in understanding, critical engagement with information, verifiability, and accountability. Building on these principles, we introduce a conceptual framework for a dynamic shared representational workspace in which knowledge workers and specialized AI agents jointly gather evidence, schematize, hypothesize, and pursue collaborative goals. Through a partner agent, a shared space agent, and an orchestrator agent, the framework preserves the provenance and authorship of contributions and traces the evolution of both individual and shared interpretations, supporting coherent, negotiated knowledge construction that current generative AI systems tend to obscure.

Machine learning has become integral to medical research and is increasingly applied in clinical settings to support diagnosis and decision-making; however, its effectiveness depends on access to large, diverse datasets, which are limited within single institutions. Although integrating data across institutions can address this limitation, privacy regulations and data ownership constraints hinder these efforts. Federated learning enables collaborative model training without sharing raw data; however, most methods rely on complex architectures that lack interpretability, limiting clinical applicability. Therefore, we proposed a federated RuleFit framework to construct a unified and interpretable global model for distributed environments. It integrates three components: preprocessing based on differentially private histograms to estimate shared cutoff values, enabling consistent rule definitions and reducing heterogeneity across clients; local rule generation using gradient boosting decision trees with shared cutoffs; and coefficient estimation via $\ell_1$-regularized optimization using a Federated Dual Averaging algorithm for sparse and consistent variable selection. In simulation studies, the proposed method achieved a performance comparable to that of centralized RuleFit while outperforming existing federated approaches. Real-world analysis demonstrated its ability to provide interpretable insights with competitive predictive accuracy. Therefore, the proposed framework offers a practical and effective solution for interpretable and reliable modeling in federated learning environments.

Deep networks that rely on prototypes-interpretable representations that can be related to the model input-have gained significant attention for balancing high accuracy with inherent interpretability, which makes them suitable for critical domains such as healthcare. However, these models are limited by their reliance on training data, which hampers their robustness to distribution shifts. While test-time adaptation (TTA) improves the robustness of deep networks by updating parameters and statistics, the prototypes of interpretable models have not been explored for this purpose. We introduce ProtoTTA, a general framework for prototypical models that leverages intermediate prototype signals rather than relying solely on model outputs. ProtoTTA minimizes the entropy of the prototype-similarity distribution to encourage more confident and prototype-specific activations on shifted data. To maintain stability, we employ geometric filtering to restrict updates to samples with reliable prototype activations, regularized by prototype-importance weights and model-confidence scores. Experiments across four prototypical backbones on four diverse benchmarks spanning fine-grained vision, histopathology, and NLP demonstrate that ProtoTTA improves robustness over standard output entropy minimization while restoring correct semantic focus in prototype activations. We also introduce novel interpretability metrics and a vision-language model (VLM) evaluation framework to explain TTA dynamics, confirming ProtoTTA restores human-aligned semantic focus and correlates reliably with VLM-rated reasoning quality. Code is available at: https://github.com/DeepRCL/ProtoTTA.

Machine learning models can achieve high predictive accuracy in hydrological applications but often lack physical interpretability. The Mass-Conserving Perceptron (MCP) provides a physics-aware artificial intelligence (AI) framework that enforces conservation principles while allowing hydrological process relationships to be learned from data. In this study, we investigate how progressively embedding physically meaningful representations of hydrological processes within a single MCP storage unit improves predictive skill and interpretability in rainfall-runoff modeling. Starting from a minimal MCP formulation, we sequentially introduce bounded soil storage, state-dependent conductivity, variable porosity, infiltration capacity, surface ponding, vertical drainage, and nonlinear water-table dynamics. The resulting hierarchy of process-aware MCP models is evaluated across 15 catchments spanning five hydroclimatic regions of the continental United States using daily streamflow prediction as the target. Results show that progressively augmenting the internal physical structure of the MCP unit generally improves predictive performance. The influence of these process representations is strongly hydroclimate dependent: vertical drainage substantially improves model skill in arid and snow-dominated basins but reduces performance in rainfall-dominated regions, while surface ponding has comparatively small effects. The best-performing MCP configurations approach the predictive skill of a Long Short-Term Memory benchmark while maintaining explicit physical interpretability. These results demonstrate that embedding hydrological process constraints within AI architectures provides a promising pathway toward interpretable and process-aware rainfall-runoff modeling.

Text-motion retrieval aims to learn a semantically aligned latent space between natural language descriptions and 3D human motion skeleton sequences, enabling bidirectional search across the two modalities. Most existing methods use a dual-encoder framework that compresses motion and text into global embeddings, discarding fine-grained local correspondences, and thus reducing accuracy. Additionally, these global-embedding methods offer limited interpretability of the retrieval results. To overcome these limitations, we propose an interpretable, joint-angle-based motion representation that maps joint-level local features into a structured pseudo-image, compatible with pre-trained Vision Transformers. For text-to-motion retrieval, we employ MaxSim, a token-wise late interaction mechanism, and enhance it with Masked Language Modeling regularization to foster robust, interpretable text-motion alignment. Extensive experiments on HumanML3D and KIT-ML show that our method outperforms state-of-the-art text-motion retrieval approaches while offering interpretable fine-grained correspondences between text and motion. The code is available in the supplementary material.

Multimodal prediction models based on imaging and clinical data are increasingly used for clinical decision support, yet their interpretability remains limited. We present multimodal Deep Transformation Models (DTMs) combining statistical approaches and neural networks to achieve strong predictive performance while preserving interpretability for tabular data. A key contribution of this work is the adaption of the xAI methods Grad-CAM and Occlusion to DTMs relying on 3D CNNs, enabling interpretation of the image branch through the generation of explanation maps. We developed DTMs to predict functional independence three months after stroke using diffusion-weighted imaging and clinical data from 407 patients. In a ten-fold cross-validation, the models achieved state-of-the-art predictive performance (AUC 0.81 [0.75, 0.87]) while maintaining interpretability for tabular features, with functional independence before stroke and stroke severity on admission emerging as the strongest predictors. Explanation maps from both xAI methods highlighted consistent regions, including frontal lobe areas which are known to be associated with age, a strong predictor of functional outcome. Notably, these regions disappeared once age was included as an explicit tabular predictor. Similarity analyses of explanation maps revealed distinct spatial patterns, providing meaningful insights into stroke pathophysiology, systematic error analysis and hypothesis generation.

Emergent coordinated behaviors of AI agents are starting to present critical safety risks. A key phenomenon driving these behaviors is the rapid formation and spread of beliefs about the world, and mechanistic understanding is crucial for collective alignment. To this end, we introduce the Flag Game, a toy model for studying the mechanisms of collective belief formation. Concretely, a hidden country flag defines the ground truth, and each bounded agent directly observes only a private crop but can exchange beliefs and weigh social evidence from peers. Despite its simplicity, the Flag Game reproduces rich collective phenomenology: non-monotonic scaling of performance with population size, accuracy gains from social-awareness prompting and team diversity, and strong effects of organizational structure. In particular, we identify that collective belief collapse at small population sizes turns into collective belief polarization as the population grows. This polarization causes the performance decline at large population sizes, but creates diversity in collective beliefs. Finally, we dissect the mechanisms underlying collective belief collapse and polarization with two complementary approaches. We first introduce social circuit attribution, a technique to predict which agent, and what view, matters most to collective dynamics, and verify its predictions by causal interventions on agents, tracing how agent patching changes collective outcomes. However, the efficacy of causal interventions on agents decreases as the population grows. We therefore develop a statistical mechanical theory for larger populations and verify that it matches the empirical phase diagram. Together, these results take a first step toward mechanistic swarm interpretability, a science of how the properties of individual agents and their communication give rise to emergent collective behavior.

Causal claims about large language model (LLM) internals rest on measurements. Those might include a projection, a cosine, an ablation delta, or an interchange patch among others. These measurements fail in specific, diagnosable ways that return a plausible number instead of an error, so a broken instrument can easily read as a finding. A covariance-matched null can saturate until every direction looks typical, a per-head attribution can overshoot the true residual write threefold on reordered-normalization architectures, an interchange patch can go sign-chaotic because its outcome is pinned at a ceiling, or a read-from verdict can be an artifact of measuring past the layer where the model already decided. This note documents six such failures from a causal interpretability program on refusal and moral representation, spanning several papers and a four-model open-weight panel; each mode is established on one or two of the four. For each we give the tell that catches it and a protocol keyed to a detectable trigger (reordered normalization, massive activations, a low-dimensional decision channel), so we and readers can check whether a given setup is exposed. The discipline reduces to four moves: calibrate against a positive-control ladder, certify with an orthogonal cell, compute power before spending compute, and state every read-from verdict at a depth referenced to the model's commitment. The evidence is four architectures across three families within a single program; external replication across programs is future work.

Reasoning traces from chain-of-thought models appear to offer a legible window into how a model arrives at its answer. A growing body of work treats them as such, using LLM judges to diagnose errors, evaluate faithfulness, and provide step-level supervision via process reward models and generative critics. These practices rely on the text of a reasoning step carrying information about its functional role. But does the text actually encode information about which reasoning steps matter? We operationalize the importance of a reasoning step as its advantage: the change in expected reward, e.g., producing the correct final answer, from including that step, estimated via Monte Carlo rollouts. Basing ground truth on these estimates, we evaluate whether LLM judges can identify high-advantage steps and find that sufficiently capable LLMs can outperform a prevalence baseline but fall well short of a noise ceiling. Fine-tuning a model as a step-level critic yields strong improvement for incorrect responses but remains distant from ceiling for correct responses, suggesting that step importance is only partially recoverable from the text of the reasoning trace. Our findings contribute to a growing body of chain-of-thought faithfulness work that cautions against treating the legibility of reasoning traces as interpretability, especially with implications for process reward modeling.

Parkinson's disease (PD) is the second most common neurodegenerative disorder. Typical machine learning screening methods require PD labels, but the available data is limited by privacy concerns and the need for expert annotation. We propose a label-free face-plus-voice PD screen built entirely on frozen pretrained encoders--a face-expression Vision Transformer and HuBERT--in which no PD label touches any fit; the reference is training controls only. The voice modality uses a synthetic-dysarthria contrastive activation addition (CAA) direction built from time-stretch and breathy degradation of healthy speech; the face modality uses a k-nearest-neighbor anomaly score to the control embedding cluster. We introduce the alignment principle, a post-hoc analysis showing that a synthetic-degradation CAA detector works when the cosine similarity between the synthetic and real disease directions exceeds zero. Measured on the YouTubePD benchmark, this cosine is +0.37 for voice (CAA works, AUROC 0.765) and -0.48 for face (CAA fails; anomaly succeeds, AUROC 0.751). Equal-weight late fusion reaches AUROC 0.802 (95% CI [0.70,0.89]) with NPV 0.95, supporting a rule-out triage interpretation. An overfitting audit shows the voice detector transfers cleanly, while the face-side--and thus fused--AUROC is potentially optimistic pending external validation.

Mechanistic interpretability of music generation has concentrated on audio models, leaving symbolic models largely unexplored. We analyze two public text-to-MIDI systems of contrasting design: the purpose-built encoder--decoder text2midi and MIDI-LLM, a Llama3.21B model extended with MIDI tokens using linear probing, the logit and tuned lenses, activation patching and difference-in-means steering. Across these methods, we recover musically meaningful structure and show how architecture shapes its formation and control. Pitch, instrumentation, harmony and texture are linearly decodable in both models. text2midi refines predictions gradually across depth, whereas MIDI-LLM works largely in its inherited textual basis before a sharp late rotation into the musical vocabulary; patching identifies a matching late attenuation of prompt-driven instrument transfer. Steering produces bidirectional changes in register and polyphony in both systems, and in tempo/energy in MIDI-LLM. Our two-orientation protocol isolates directional control and shows that all-layer interventions are robust in text2midi but accumulate disruptively in MIDI-LLM. Together, the results provide a practical toolkit for tracing and controlling musical concepts in symbolic generators. Audio examples are available on a demo website.

Vision foundation models, such as DINOv2, learn highly expressive representations but rely on massive, opaque architectures that demand substantial computational power and memory. To provide an interpretable-guided and efficient solution to this issue, we first propose a spectral analysis and new visualization technique for individual attention heads based on the Laplacian eigenvectors of their attention maps. Building upon recent observations regarding the block structure of Vision Transformers, we perform semantic clustering of attention heads and identify functional redundancies. Leveraging these insights, we introduce SAPER (Soft Attention PrunER), an end-to-end differentiable pruning framework based on the LapSum Soft Top-K approach. Extensive experiments on ImageNet-1K demonstrate that SAPER achieves a highly favorable accuracy-efficiency trade-off, outperforming the competitive RAPTOR baseline in FLOPs reduction while preserving strong classification performance.

World Action Models (WAMs) enable semantically- and physically-informed control but are brittle under distribution shift. In this work, we use mechanistic interpretability to study how robustness-relevant perturbations are represented in WAM activation space. Comparing activations across successful and unsuccessful rollouts, we find some WAM architectures exhibit low-dimensional linear separability for robustness-critical features, while others do not. This motivates the use of contrastive activation directions for training-free WAM steering. We also show that local linearity in WAM activation dynamics enables efficient feedback steering via model-based optimal control, yielding World-Action Linear Quadratic Regulator (WA-LQR), a minimally-invasive reduced-order LQR controller. Via mechanistic evaluations, we predict strong steerability in the Cosmos-Policy and DiT4DiT models but weak steerability in LingBot-VA, consistent with steering intervention results. On Cosmos-Policy and DiT4DiT, WA-LQR generalizes contrastive directions to new tasks and improves robustness to camera, gripper, and visual-noise perturbations over unsteered and prompt steering baselines.

Existing facial expression quality assessment (FEQA) methods typically produce only a severity score, without explicitly communicating the observable facial motion evidence that supports the prediction. This limits interpretability and makes it difficult to inspect the basis of model outputs in Parkinson's disease assessment. To address this gap, we propose TraMP-LLaMA, a unified multimodal framework that jointly predicts severity scores and generates structured textual reports from facial motion cues. The framework integrates RGB appearance and landmark trajectory cues, and adopts a decoupled instruction-tuning strategy to reduce task interference between severity prediction and language generation. To support this task, we further extend the PFED5 dataset with expert-guided textual motion descriptions and construct PFED5-plus. Experiments on PFED5-plus show that TraMP-LLaMA outperforms competitive video-language baselines in report generation and achieves the best severity prediction performance among the compared methods under joint multi-expression training, improving Spearman's rank correlation by at least 4.39 percent over all competing methods. The text annotations and code are available at https://github.com/shuchaoduan/TraMP-LLaMA.

Mechanistic interpretability has made substantial progress in automatically localizing circuits, but explaining what localized components do remains labor-intensive and difficult to standardize. In this work, we study whether language model (LM) agents can assist with this explanation problem once a circuit has already been identified. We introduce AgenticInterpBench, a benchmark for circuit explanation built from 84 semi-synthetic transformer circuits with 163 component-level annotations. We propose HyVE (Hypothesize, Validate, Explain), an agentic explainer that analyzes each component through an iterative loop of observation, hypothesis generation, and causal validation, eventually producing a component-level explanation and a circuit-level task description. Across four LM backbones, HyVE recovers useful component- and task-level explanations, but no backbone is uniformly best. Our analysis shows that strong backbones usually form observation-grounded hypotheses, while failures more often arise later in the validation loop, through incomplete validation plans, code execution errors, or unresolved hypotheses. A case study on an arithmetic circuit in Llama-3-8B shows that the same formulation can extend beyond semi-synthetic benchmarks to naturally trained models. Overall, LM agents are promising circuit explainers, but reliable validation remains the key obstacle.

This study examines whether machine learning (ML) models can outperform the naive random walk benchmark in forecasting the monthly USD/CAD exchange rate. Using daily data from the Bank of Canada spanning January 2017 to May 2026, resampled into 113 monthly observations, five ML models are evaluated: linear regression, random forest, gradient boosting, XGBoost, and AdaBoost. These models are benchmarked against the naive random walk model and exponential smoothing with Holt-Winters seasonality (ETS). All models are evaluated using an expanding-window framework to maintain strict out-of-sample integrity, and forecast-accuracy differences are assessed using the Diebold-Mariano (DM) test. Structural break detection identifies four significant breakpoints in the series, corresponding to the escalation of the US-China trade war in 2018, the COVID-19 economic recovery in 2020, the peak of the Bank of Canada rate-hiking cycle in 2022, and the start of the Bank of Canada rate-cutting cycle in 2024. SHAP, or Shapley Additive Explanations, analysis is applied to interpret the drivers of the best-performing ML model. The results show that the naive random walk model remains a formidable benchmark. Linear regression is the only model that statistically outperforms the naive random walk model, with a DM statistic of 3.0585 and a p value of 0.0071, whereas the ML ensemble models show only marginal differences. Random Forest with an expanding-window framework achieves the lowest MAPE of 1.17 percent among all models except the random walk. SHAP analysis confirms that short-term lags, particularly lag1 and lag2, and recent rolling means dominate predictions, consistent with the near-random-walk behavior of exchange rates.

Survival prediction plays a central role for healthcare providers and clinical researchers. Accurate risk stratification enables early intervention and improved patient management. Most existing deep survival models learn one common feature representation for all patients, which may hide important differences between patient subgroups. In contrast, a Mixture-of-Experts (MoE) framework allows different parts of the model to focus on different patient patterns, leading to more individualized representations. Therefore, in this work, we propose a mixture-of-experts enhanced adaptive deep clustering survival framework (AdaCSM) for modeling such heterogeneous survival patterns. We introduce a routing-based expert mechanism that enables conditional specialization within a parametric survival modeling framework. The proposed architecture allocates patients to specialized risk predictors dynamically while preserving the patient survival and subtype clustering objectives. We compare our method with state-of-the-art survival and deep clustering models on multiple real-world longitudinal clinical cohorts spanning diverse disease domains. The proposed method demonstrates improved predictive performance and leads to interpretable results in survival analysis.

Multi-channel mixed-SNR training improves out-of-distribution (OOD) generalisation of deep learning channel estimators for IEEE 802.11p vehicular communications, yet the internal mechanism responsible for this remains unexplained. This work presents REACH (Relevance-based Explanation and Architectural Compression for cHannel estimators), a gradient-based interpretability framework that operates at two levels. Input-level attribution identifies a subset of time-frequency features consistently relevant across all evaluated channel conditions, enabling input dimensionality reduction with minimal performance loss. Filter-level attribution reveals a near-universal internal representation, providing a representational account of the observed OOD generalisation. Guided by the resulting filter taxonomy, relevance-guided architecture compression substantially reduces both the number of parameters and the number of floating-point operations (FLOPs) with sub-1 dB normalised mean square error (NMSE) degradation, and OOD generalisation degrades more slowly than within-distribution accuracy under increasing compression.

Interpretable machine learning requires models that are accurate and structurally faithful to the data. Existing explainability methods rely heavily on additive representations (e.g., Generalized Additive Models (GAMs), SHapley Additive exPlanations (SHAP), functional ANOVA), which can suffer from signal cancellation and off-support extrapolation in the presence of strong interactions. We propose Tensor Separation Learning (TSL), a regression model that learns a sum of rank-1 products of univariate per-feature functions via a stagewise greedy procedure with orthogonal refitting. By enforcing separability, TSL avoids the information loss inherent in additive projections caused by marginalizing higher-order interactions. The learned TSL model can be fully reconstructed from first-order partial dependence functions, up to constant factors. This stage-wise correspondence ensures that the resulting visualizations are faithful to the fitted components. We establish approximation-rate guarantees for functions with bounded mixed $p$-th order partial derivatives and demonstrate that TSL competes with black-box models on regression benchmarks.

LLMs increasingly require surgical model editing to enhance domain-specific capabilities without incurring the computational cost or catastrophic forgetting associated with full fine-tuning. Sparse Autoencoders (SAEs) have emerged as a promising tool in this setting, in principle allowing for feature-level identification of where to intervene. In this work, we rigorously evaluate an SAE-guided editing pipeline for mathematical reasoning on Gemma-3-4B-IT and uncover a fundamental failure mode: the intuitively appealing approach of projecting task vectors onto SAE feature subspaces acts as an information bottleneck that discards approximately 97% of the modification energy, yielding no statistically significant improvements across seven math subjects. We show that this failure stems from a geometric misalignment between activation-space SAE directions and weight-space task vectors. We then propose a shift in perspective: SAE as a Stethoscope, Not a Scalpel, where SAEs are used for layer-level diagnosis rather than intervention-level filtering. By injecting unfiltered raw task vectors only into layers identified by an SAE-derived specificity score, we improve Number Theory accuracy from 29.6% to 39.4% (z=+3.41, p=0.0007) on the Minerva Math benchmark; 5 of 7 math subjects significantly improved and none significantly degraded. Our method is fully deterministic, requires no additional inference cost, and provides a principled framework for interpretability-guided model editing.

Mechanistic interpretability seeks to explain a model's behaviour by finding its circuit: the sparse subgraph of the model's computation that is causally responsible for it. Automated methods have made this search systematic, but each one starts afresh for every behaviour, and the effort spent finding one circuit does nothing for the next. Circuit discovery has thus been automated, but not amortised. We ask whether circuit discovery can itself be learned. We frame it as a sequential decision problem over the computation graph of GPT-2 small, in which a policy removes edges until it reaches a compact subgraph that preserves the behaviour, guided by a faithfulness reward defined through causal intervention. A single policy trained across twelve behaviours recovers a faithful circuit for each, and once frozen it transfers to behaviours it never saw during training, recovering their known circuits without further search. A short warm-start improves these transferred circuits, returning far smaller ones than training from scratch. While the learned policy does not match a per-behaviour search on circuit size or cost, it shows that circuit discovery is a learnable, transferable procedure rather than a search repeated for every behaviour.

Mechanistic interpretability often studies Transformer behavior by intervening on internal activations through activation patching, causal tracing, path patching, and steering directions. This paper develops Transformer Field Theory: a response-theoretic framework in which the residual stream of a fixed forward pass is treated as a Transformer field over layer depth and token position. In this formulation, patching becomes a localized source insertion into the Transformer field, first-order sensitivity fields predict patch effects, Green functions describe downstream propagation, and patch selection is posed as an adjoint inverse problem. Empirically, we test the theory's forward response objects in GPT-2-style autoregressive Transformers. Localized Transformer-field interventions exhibit a bounded local linear regime; first-order sensitivities predict patch effects across layer-token sites; localized sources generate structured anisotropic Transformer-field propagation; high-sensitivity sites and sliced Green operators provide reduced response descriptions; and prompt-induced Transformer-field displacements partially transfer answer behavior. These results establish sensitivities, Transformer-field responses, and sliced Green operators as practical objects for organizing patching experiments, while providing the forward mathematical basis for patch-site inference and cross-scale response transfer.

Time Series Classification (TSC) is a long-standing research problem that has gained increasing attention in recent years with the rapid growth of large-scale temporal data. Despite substantial progress enabled by deep learning, designing TSC models that are both accurate and interpretable remains a challenging task. Many existing approaches adopt a direct feature-to-label classification paradigm, by collapsing high-dimensional temporal embeddings into class logits via a single linear projection (often after global pooling), the paradigm conflates feature extraction and decision logic into an inseparable mapping. To address these limitations, we propose PDFTime, a prototype-guided framework that reformulates time series classification as a multi-stage decision process. Instead of direct feature-to-label mapping, PDFTime leverages learned prototypes to approximate class-conditional feature distributions in the latent space, enabling progressive discrimination through classification sub-tasks of varying granularity. To our knowledge, PDFTime is the first framework to reformulate time series classification as a decoupled, multi-stage similarity-based reasoning process, breaking the long-standing paradigm of direct, black-box feature-to-label mapping. Extensive evaluations demonstrate that PDFTime achieves state-of-the-art (SOTA) performance across UEA and UCR benchmarks. Notably, it secures the top-$1$ accuracy on 80 out of 128 datasets in the UCR archive, significantly outperforming recent strong baselines in both consistency and generalization.

Mechanistic interpretability aims to explain a model's behavior by identifying causally responsible internal structures. Dictionary-based explainers such as sparse autoencoders and transcoders are a primary tool, but their faithfulness under out-of-distribution (OOD) shift has received little systematic attention. We show that distribution shift rotates the subspace that the model actively uses, misaligning the explainer's dictionary trained on in-distribution (ID) activations. We formalize this misalignment as the faithfulness gap, a geometric distance between the ID dictionary and the OOD-active subspace, and show that it controls OOD faithfulness degradation. To reduce this gap, we propose the Geometry-Adaptive Explainer (GAE), which realigns the explainer's dictionary with the OOD-active subspace while preserving the original feature structure. This requires only unlabeled OOD activations and no gradient updates. We prove that GAE improves over the unadapted ID explainer, with excess loss bounded quadratically by the second-moment shift. Empirically, GAE even matches or surpasses all training-based baselines in causal faithfulness across multiple models and OOD settings.

The lottery ticket hypothesis posits that dense networks contain sparse subnetworks, ``winning tickets,'' that, when rewound to their initial weights and retrained in isolation, match the performance of the full model. We ask a more mechanistic question: what internal object does a winning ticket preserve? We work in a combinatorial, clause-structured toy setting that admits an interpretable feature-space representation with well-defined combinatorial distances between features. We show that winning tickets in weight space correspond to precursor locations in feature space that are already near, at initialization, to the final feature-channel codes. Dense SGD resolves these locations through structured selection: proximal locations either converge to final codes or are rejected, with rejection concentrated at more crowded neurons, implicating competition under superposition. A winning ticket is thus a family of compatible code locations that jointly balance proximity to final codes with low inter-feature interference. Sparse retraining often re-expresses the same clause/template family on a different row, so the preserved object is family-level rather than microscopic row identity. We validate this account with lightweight probes based on feature-space distance and motion; in our setting, these probes frequently outperform established weight-based ticket discovery methods in both accuracy and exact code recovery. Although these findings are grounded in a toy setting, they suggest that the lottery ticket structure is governed by hidden feature-space geometry rather than weight-space subnetwork identity.

Mechanistic interpretability aims to break models into meaningful parts; verifying that two such parts implement the same computation is a prerequisite. Existing similarity measures evaluate either empirical behaviour, leaving them blind to out-of-distribution mechanisms, or basis-dependent parameters, meaning they disregard weight-space symmetries. To address these issues for the class of tensor-based models, we introduce a weight-based metric, tensor similarity, that is invariant to such symmetries. This metric captures global functional equivalence and accounts for cross-layer mechanisms using an efficient recursive algorithm. Empirically, tensor similarity tracks functional training dynamics, such as grokking and backdoor insertion, with higher fidelity than existing metrics. This reduces measuring similarity and verifying faithfulness into a solved algebraic problem rather than one of empirical approximation.