Mechanistic Interpretability

Random forests (RFs) predict well but are opaque, whereas single decision trees are interpretable but unstable. Artificial representative trees (ARTs) were developed as interpretable surrogate models for RFs, but their use as standalone prediction models with uncertainty quantification has not been systematically investigated. We combine ARTs with leaf-wise Mondrian conformal predictive systems (CPS), enabling a single tree to provide continuous predictions, prediction intervals, and probabilities of exceeding arbitrary thresholds. We compared ARTs with CPS against decision trees with CPS and separate regression and probability trees across five simulation scenarios, 21 benchmark datasets, and a cross-sectional NHANES example data set. Repeated cross-validation assessed predictive performance, interpretability, and stability. ARTs with CPS yield compact, structurally stable trees with substantially more reproducible split-variable selection than decision trees across benchmark datasets and NHANES. Decision trees showed slightly better predictive performance and narrower prediction intervals, while coverage was broadly comparable. CPS-based trees generally achieved lower and less variable Brier scores than multi-model approaches. Combining ARTs with CPS therefore provides a single, interpretable, and stable model for continuous predictions and calibrated probabilities, balancing predictive performance with reproducibility and transparency in settings where stability and interpretability are essential.

Many real-world decisions require prioritizing high-risk cases, such as clinicians prioritizing high-risk patients before lower-risk ones. Falling rule lists (FRLs), which are ordered if--then rules with monotonically decreasing risks, provide an interpretable framework for such tasks; however, their single-path structure yields a highly restricted model class. We introduce falling trees, a new family of interpretable models that enforces the same monotonic risk constraint while permitting tree-structured branching. We present GRAVITree, a novel dynamic-programming-with-bounds algorithm for learning the Rashomon set of falling trees under depth and branching constraints. Our formulation can interpolate between rule lists and full decision trees, enabling user-desired model expressivity. In a new clinical dataset and in many public classification benchmarks, falling trees match or outperform FRLs and other interpretable baselines, often producing more sparse decisions for high-risk instances. Our results show that falling trees strike a practical balance between interpretability, expressiveness, and risk prioritization for high-stakes settings.

Deploying efficient neural networks is essential in resource-constrained environments, yet compact models often sacrifice interpretability - a critical in safety-critical domains such as autonomous driving and medicine. This study investigates whether Knowledge Distillation transfers the spatial feature attribution of a large teacher network to a compact student. To assess the influence of the KD scheme on interpretability, we distill a ResNet-152 teacher into a ResNet-34 student on ImageNet-1K across five configurations by systematically varying the distillation temperature and soft-label loss weight. Models are evaluated on top-1 accuracy, along with two interpretability metrics: Relevance Mass Accuracy and Relevance Rank Accuracy. These metrics are computed via Grad-CAM heatmaps benchmarked against ground-truth object masks. Our results show that top-1 accuracy ranges from 71.6% to 74.0%. For Grad-CAM, RMA ranges from 7.7% to 9.7% and RRA from 7.3% to 10.1%; for Guided Grad-CAM, RMA ranges from 16.1% to 18.6% and RRA from 15.9% to 21.5%. Interpretability proves far more sensitive to the soft-label weight than to the temperature: keeping the student anchored to hard labels preserves both accuracy and coarse localization, whereas weighting the teacher heavily degrades both. Fine-grained attribution, however, fell below the undistilled baseline in every configuration tested, indicating that logit distillation transmits where a model attends more readily than the pixel-level structure of that attention. We evaluate 12 cross-architecture combinations of convolutional and transformer-based models, revealing that the inheritance of fine-grained spatial reasoning is fundamentally bottlenecked by the student's intrinsic structural biases. To our knowledge, this is the first application of this interpretability-aware evaluation framework - previously used for neural network pruning - to KD.

In this reproducibility study, we investigate the transparency and scrutability of recommender systems enhanced by incorporating generated natural-language user profiles that represent user preferences. The original paper explores the synthesis of user profiles from raw user-generated review text across domains such as movies and accommodations (Amazon Movies & TV, TripAdvisor). Crucially, these natural-language user profiles enable direct user interaction and intervention, allowing users to customize recommendations by correcting misattributed preferences or addressing cold-start settings. We successfully reproduce the core findings of the original study. Additionally, we extend the evaluation by conducting systematic context ablation experiments, multi-seed stability across five distinct random seeds to establish statistical reliability, and a mechanistic interpretability analysis using the nnsight framework to probe internal model representations under counterfactual profile perturbations. Our findings verify the original paper's claim that User Profile Recommendation (UPR) achieves competitive performance under its test-set reranking protocol and makes recommendations more transparent. Perturbing the natural-language profiles does change predictions, but it shifts predicted ratings uniformly across genres with no detectable genre-selective effect, leaving rankings unchanged even under direct activation steering. We trace this back to the rating-regression objective rather than the profile interface, with ranking-objective models clearly exceeding in this task.

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.

How do VLMs map from pixels to semantics? To understand this general question, we focus on a narrow one: studying how VLMs perform optical character recognition (OCR). Across four models, we identify attention heads causally necessary for OCR, and discover that these are in fact general-purpose heads that output interpretable semantic features across all image tokens. For example, pointing these heads at an image token containing the word "bike" causes Qwen3-VL-8B to output "bike," but pointing them at a bird wing causes the model to output the token "feathers." We collapse these heads' attention weights into a single verbalization lens transformation that reveals interpretable semantic features in hidden states across all layers. When combined with projection to vocabulary space, we can obtain interpretable labels starting from layer 0, showing that image representations are in fact aligned with language in early layers. We find that we can also use the inverse of this transformation to edit non-word concepts, e.g., replacing a tractor with a revolver in a naturalistic image, providing causal evidence that this subspace is useful for more than just OCR. Our results are an example of how the study of specific mechanisms can shed light on broader interpretability problems.

The interpretability of complex machine learning models is of paramount importance, especially in real-world high-stakes domains such as healthcare and finance. However, existing post-hoc interpretability methods suffer from inherent limitations: fragmented analytical processes, inadequate capacity to model nonlinear feature interactions, computational inefficiencies, and over-reliance on specific model architectures. To address these challenges, this paper provides a novel method - Adaptive Derivative-Ordered Random Explanation (ADORE) - that leverages first- and second-order derivatives to accommodate nonlinear model complexities, while enabling effective capture of feature-sample interactions within a unified analytical framework. ADORE integrates global feature importance with local sample contributions, precisely quantifying feature impact by capturing both magnitude and direction, and identifying critical samples influencing model decisions. Furthermore, it achieves computational efficiency through randomized singular value decomposition (SVD) and dynamic sparsity detection, making it scalable to large, high-dimensional datasets. Experiments across three data modalities - tabular, text, and image - demonstrate that ADORE outperforms existing methods such as LIME and SHAP in handling complex interactions and computational efficiency, while providing detailed and reliable explanations. To facilitate adoption and reproducibility, ADORE has been released as an open-source Python package, hosted on GitHub, enabling researchers and practitioners to readily adapt and apply our approach to their specific tasks, models, and datasets.

While Large Language Model (LLM)-based Natural Language Inference (NLI) systems achieve high accuracy, their decision-making processes lack auditable structures. This paper explores whether NLI can be performed using only interpretable, graph-based representations of evidence. We introduce a fully graph-based pipeline where the classifier never directly processes the input text. Instead, sentences are decomposed into atomic propositions, converted into ConceptNet triples via constrained decoding, and represented as three graphs per pair: premise, hypothesis, and a retrieved ConceptNet subgraph. These graphs are then fed into a fine-tuned 0.8-billion-parameter language model. On the SNLI dataset, our pipeline achieves 89.7% accuracy, just 1.9 points below an identically trained text-based model. On ANLI, it matches the published performance of RoBERTa-large on rounds R2 and R3 (48.0% vs. 48.9% and 44.9% vs. 44.4%) but trails by 16 points on R1, resulting in an overall gap of 9 to 14 points compared to its text counterpart. We term this gap the price of interpretability and demonstrate that it stems from representational limitations rather than data constraints. Ablation studies further reveal that graphs and text are complementary: combining both modalities achieves 92.1% accuracy on SNLI.

Classification and regression trees are typically constructed using a greedy splitting rule that maximizes the immediate reduction in prediction error at each node. Although this strategy is computationally efficient, it can miss splits that yield small short-term gains but create substantial downstream improvements after further partitioning. We propose a look-ahead tree-building method that evaluates each candidate split by the prediction error reduction achieved after growing a conventional CART subtree below that split. Because the full look-ahead procedure can be computationally expensive, we also describe a smart look-ahead algorithm that learns downstream split values using node-level features. The proposed framework preserves the interpretability of recursive partitioning while improving split selection in hierarchical or interaction-driven settings. We conduct a simulation study comparing conventional, full look-ahead, and smart look-ahead methods under several settings and apply the proposed methods to analyze two real data examples demonstrating the merit of the new methods.

AI-driven automated decision-making requires both predictive performance and interpretability. Recent advances in interpretable machine learning (IML) provide tools for explaining model predictions, but the technical complexity of these explanations may hinder accessibility to non-experts. To address this challenge, this study integrates data storytelling with IML to enhance the explainability of AI-generated decisions for a broader audience. Following the design science research (DSR) paradigm, this study proposes a formal definition of data storytelling in IML, introduces the DIST Pyramid to align data storytelling with IML, and presents the I-P-O Model to describe their interactions. It further develops an architecture to explain AI decisions through distinct "What-if" and "Why-not" event-generation processes. The architecture also employs data desensitization to protect sensitive input data. To validate the approach, a case study is conducted with the Boston Housing dataset, using SHapley Additive exPlanations (SHAP) values and large language models (LLMs) to generate data stories with And-But-Therefore (ABT) structures. An empirical evaluation shows that 76.4% and 74.3% of respondents rated the "What-if" and "Why-not" data stories as more comprehensible, with significantly higher accessibility scores than traditional SHAP visualizations. The paper concludes with the presentation of a narrative interpretation framework that integrates IML and data storytelling, thereby expanding the research scope as well as the practical applicability of AI decision-making.

Mechanistic interpretability has become the dominant lens for understanding frontier language models, as their inner workings are complex and inherently black boxes. To gain insights into these models, interpretable replacement networks (IRNs) are trained at all layers, exposing interpretable features through sparsely activated neurons. However, the faithfulness of an IRN is usually evaluated only empirically on clean data, and we show that even semantically minor input perturbations flip the dominant IRN features-and thus the human-understandable interpretation-across five open-weight model families (GPT-2 small, Gemma 2 2B, Gemma 3 1B, Llama 3.2 1B, R1-Distill-Qwen 1.5B). We propose the first formal verification framework for the faithfulness of an IRN, where reachability analysis certifies a sound upper bound of the faithfulness gap in adversarial scenarios. Moreover, we show that verification-aware training of IRNs substantially tightens this certified bound, restoring a feature-level interpretation that safety auditors can act on. Together, these results give, to the best of our knowledge, the first formal guarantees for mechanistic interpretability of large language models.

Entrepreneurial cognition is a foundation of entrepreneurship research. Yet the growing involvement of large language models (LLMs) in entrepreneurial work extends the cognition question beyond human actors to systems whose internal representations remain largely unexplored. We introduce artificial entrepreneurial cognition, the functional organisation of entrepreneurship-relevant representations and computations inside artificial intelligence (AI) systems. We bring mechanistic interpretability into entrepreneurship research through representation engineering. Focusing on opportunity recognition (OR), we construct 636 matched OR-present and OR-absent scenario pairs and recover an OR direction in Llama 3.1 8B-Instruct. Rather than infer the construct from outputs, we intervene directly on this direction, steering the model up and down along what we call the opportunity recognition dial, and its opportunity judgments shift with it. To our knowledge, this is the first causal intervention on an internal representation of an entrepreneurship construct inside an LLM. Held-out tests, lexical and topical controls, behavioural ablation, and geometric comparisons show that the direction is recoverable, consequential, and distinct from the opportunity evaluation and exploitation directions, although steering it also shifts judgments about these neighbouring stages. Recovery, signed steering, and geometric separation hold across four additional LLMs spanning different scales and families. These results give the contested distinction between opportunity recognition and evaluation a concrete representational form inside AI systems. More broadly, they establish internal representations as a new object of entrepreneurship inquiry and show how entrepreneurship theory can guide their identification, causal manipulation, and interpretation.

Reinforcement learning (RL) is widely utilized in large language model training to improve targeted capabilities, yet how RL reshapes a model remains poorly understood. Prior attempts to explain how RL works largely offer behavioral perspectives, leaving open what RL gives a model at the representation level: can RL create genuinely novel features, and which existing features does it enhance or suppress? Recent developments in mechanistic interpretability suggest sparse autoencoders (SAEs) as a promising lens to decompose internal activations into human-interpretable features; however, they cannot be directly applied to tracking change across training. In this work, we introduce Fixed-SAE Track, a framework that trains one shared SAE per considered layer on activations pooled across the base model and all RL checkpoints, holding every feature direction fixed so that representation shifts are rigorously defined through the activations of interpretable SAE latents, including the detection of emerging novel features. Validated across multiple datasets and RL algorithms, we find that RL-induced drift is small, gradual, concept specific, and concentrated in late layers, mainly enhancing the sampling rates of a small set of ladder tokens, formatting scaffolding such as step breaks and answer delimiters, rather than reshaping problem content. Steering these features into the base model recovers around 80% of RL's performance gain, suggesting that RL primarily elicits capabilities the model already possesses, much as steering does. We further design a synthetic benchmark with features known by construction to test whether RL can instill genuinely novel features. We believe Fixed-SAE Track provides a principled approach to tracking representation shifts and offers representational evidence for understanding how reinforcement learning changes the inner representation of LLMs.

Data attribution seeks to quantify how individual training examples shape a model's predictions and underpins problems including data valuation, machine unlearning, and model interpretability. Despite having a long line of work, computationally scalable methods often struggle to predict the effect of removing training data in neural networks due to their non-convex nature. To overcome this challenge, metagradient-based methods such as MAGIC (Ilyas and Engstrom, 2025) differentiate each prediction through the entire training run and compute its exact influence with respect to the training data, but require a separate run for every prediction. To reduce this cost, we cast budgeted attribution as estimating a large influence matrix from a small number of measurements. We show that the measurements most appropriate for recovering this matrix differ from those best suited for attribution itself. We then present two algorithms, MAGE and SPELL, suited for reconstruction and attribution respectively, that run on existing metagradient machinery at no extra cost. Empirical studies demonstrate strong performance over existing baselines across training scales and measurement budgets.

Fine-grained control of language model behaviors (e.g., steering) is among the more actionable outcomes of interpretability research. For binary concepts such as refusal, a single direction in activation space often suffices for steering. However, many concepts are not binary: Animals and Countries contain many subcategories, each with multiple instances. For these concepts, the search space over possible representation geometries is far larger than for binary concepts; it is thus not clear what geometries are most appropriate, nor what methods are most effective at recovering them. In this work, we introduce MAxBench, a geometry-agnostic evaluation framework for multinomial concept representations based on sampling from the recovered concept representation. We use MAxBench to compare 10 localization methods (covering 5 geometry types) across 6 concepts and 4 models. Using this framework, we find that (i) affine subspaces steer more reliably and have greater recall than rank-one or linear subspaces; (ii) much of this advantage is due to better non-zero offsets rather than the choice of bases; (iii) manifold steering is competitive with the best methods when applicable; and (iv) no method consistently outperforms prompting, in alignment with prior findings on binary concepts. These findings underscore the importance of expanding the scope of interpretability research and meta-evaluation to concepts with more varied structure.

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.

Evaluating the quality of explanations produced by explainable AI (XAI) methods remains challenging because existing approaches often rely on subjective human judgment, limiting reproducibility, scalability, and comparability between studies. We examine whether LLMs can serve as a reproducible and scalable mechanism to make comparative assessments of the quality of XAI explanations. We introduce XAI-Arena, an LLM-as-a-judge framework for scalable, reproducible, multidimensional, and stakeholder-sensitive evaluation of XAI explanation quality. XAI-Arena then allows us to compare XAI explanations along various dimensions, namely, perceived simplicity, clarity, task adequacy, trust calibration, actionability, transparency, faithfulness, and overall interpretability. We then benchmark XAI explanation methods across various datasets, machine learning models, and stakeholder personas. Human validation shows a strong positive association between LLM-generated and human ratings (Spearman's rho=.693, p<.001). Together, LLM-based evaluations can capture systematic differences in XAI explanation quality and provide a scalable and reproducible framework for comparative assessment of XAI explanations.

At Noora Health, our nurses answer more than 50,000 medical queries per month on our WhatsApp-based service that provides caregivers with on-demand support. Their most time-critical task is emergency triage: deciding which queries need immediate in-person attention. To support them, we built a system that uses a large language model (LLM) to classify whether a message is an emergency and provide a rationale for interpretability. But the system was opaque: analyzing mistakes meant reading reasoning chains for each message, which is infeasible at our scale. Prompt changes meant re-running a full evaluation to prevent regressions, which was both costly and operationally challenging. Clinicians follow a decision tree to make this call, but it was never documented or passed to the model, which relied on a flat list of danger signs. To address these issues, we decomposed triage into two steps: an LLM extracts canonical symptoms and patient context from the query using a clinician-authored vocabulary, and a deterministic rule engine captures the scenarios that indicate an emergency. We show that the new system raised recall from 0.565 to 0.810 and F1 from 0.606 to 0.702, with structured rules driving most of the accuracy gains while the decomposition provides auditability: clinical experts can inspect each stage of the new system to see whether the query was mistranslated, symptoms were incorrectly extracted, patient context was wrongly inferred, or the necessary rules were missing. They can add new rules independently without causing regressions and avoid running costly evaluations. Since deployment, the new system has triaged 152,421 patient queries and flagged 28,535 (18.7%) as emergencies. The over-escalation rate has been 17.8%, without any increase in missed emergencies. Clinicians have also added 48 new rules since deployment, evidence of the faster correction loop we set out to build.

Blood-brain barrier (BBB) permeability is a critical determinant in the development of central nervous system therapeutics because it directly influences the ability of drug candidates to reach their target sites within the brain. In this study, an explainable machine learning framework was developed to predict BBB permeability using molecular descriptors generated from the MoleculeNet BBBP dataset with the RDKit cheminformatics toolkit. Fifteen physicochemical descriptors extracted from 2,039 compounds were used to train four supervised machine learning algorithms, including Logistic Regression, Support Vector Machine (SVM), Random Forest, and Extreme Gradient Boosting (XGBoost). Hyperparameter optimization was performed using GridSearchCV, while model interpretability was investigated using SHapley Additive exPlanations (SHAP). Among the evaluated models, the optimized XGBoost classifier achieved the best predictive performance, with an accuracy of 88.97%, a precision of 88.92%, a recall of 97.76%, an F1-score of 93.13%, and a ROC-AUC of 0.9282. Stratified five-fold cross-validation further demonstrated the robustness of the proposed model, yielding a mean ROC-AUC of 0.8982 +/- 0.0130. Feature importance and SHAP analyses consistently identified TPSA, HBD, and LogP as the most influential molecular descriptors governing BBB permeability prediction. Overall, the proposed framework provides an accurate, interpretable, and computationally efficient approach for BBB permeability prediction and may serve as a valuable tool for the early-stage screening of CNS drug candidates.

Reasoning representations are increasingly used as explanations for large language model outputs. Yet they are typically evaluated with model-centric criteria, such as answer accuracy and faithfulness, leaving it unclear whether they help people evaluate model responses. In this work, we study reasoning representations as human-facing interfaces rather than proxies for model reasoning ability. We conduct a controlled human study of six reasoning formats across tasks of varying complexity, supported by a web-based framework that randomizes task domains, problem instances, and representation order. The study collects fine-grained judgments of structural understanding, error detection and localization, and trust calibration. Our study shows a mismatch between perceived preference and support for human evaluation. Participants prefer planning- and decomposition-based representations, but simpler chain-of-thought traces better support verification, trust, and interpretability. Preferred representations also introduce calibration risks, with more false alarms on correct traces and high trust despite low willingness to verify.

Industrial fraud detection often relies on costly expert-crafted features that overlook graph-structured relational signals, while GNNs often do not meet the interpretability and deployment requirements of financial risk control. We propose GraphFAS (Graph Feature Automated Selection), a distributed feature selection procedure based on Boruta that bridges this gap through: (1) a non-parametric graph feature generation module that constructs explicit, interpretable structural features via multi-hop subgraph extraction and multi-scale aggregation without learned parameters; and (2) an automated distributed feature selection algorithm extending Boruta with median-based aggregation across partitions to robustly identify informative features at scale with minimal domain expertise. Compared with end-to-end GNN pipelines, GraphFAS decouples feature aggregation from model training, enabling direct integration with tabular models and direct compatibility with TreeSHAPbased explanations. Deployed in Alipay, GraphFAS delivers orderof-magnitude improvements in engineering efficiency while showing strong performance against expert-driven and graph-learning baselines on large-scale graphs.

Recent methods in language model interpretability employ techniques such as sparse autoencoders to decompose residual stream contributions into linear, semantically meaningful features. Such methods are commonly interpreted as identifying features that persist in the residual stream and that subsequent layers build upon. We challenge this view by identifying the Transformer Layer Correction Mechanism (TLCM), wherein adjacent transformer layers systematically counteract portions of each other's contributions. TLCM appears in 5 out of 7 major open-source model families and activates across nearly all tokens in diverse texts. We show that TLCM emerges during pretraining, operates most strongly on contextually dependent tokens, and adaptively calibrates its correction strength based on the preceding layer's output. Using the layer Jacobian, we further show that TLCM selectively corrects specific subspaces while reinforcing others, which we interpret through a ``propose-and-reject'' framework in which layers propose candidate features and subsequent layers selectively remove inappropriate ones. This dynamic suggests that the residual stream at any layer contains transient proposals alongside persistent features, helping explain why SAE feature descriptions often have low specificity, why effective model steering requires extreme feature amplification, and why transcoders hold a theoretical advantage over SAEs.

Associative Recall (AR) is the cognitive ability to learn and retrieve links between items in memory. In NLP, AR is used as a benchmark for evaluating the in-context memory capacity of architectures such as Mamba, and has been found to strongly correlate with language modeling performance. This paper explores AR from the perspective of mechanistic interpretability, aiming to reverse-engineer the exact internal algorithm used by Mamba to perform recall. Our key insight is that Mamba performs recall by implicitly learning linear hash functions, and we identify the low-level circuit that enables this behavior. Building on these findings and inspired by theoretical tools in similarity-preserving hashing, such as the Johnson-Lindenstrauss lemma, we develop a theoretical framework for analyzing AR, which we term Recall Scaling Laws. Given the vocabulary size and the number of facts in context, this framework allows us to (1) predict the embedding and state dimensions required for Mamba to achieve perfect recall, (2) predict recall success probability given the model dimensions, and (3) analyze multi-layer models and multi-head SSM patterns. Empirical results show that our theoretical findings are accurate and predictive, offering insights into how AR capacity scales with vocabulary, state, embedding size, and architecture.

We observe a phenomenon that current algorithmic research in the field of explainable artificial intelligence primarily pursues better performance on several proxy metrics. On the one hand, these proxy metrics themselves are more or less flawed and cannot properly measure the quality of methods. On the other hand, metric-oriented research approaches often lead to the neglect of the rationality and interpretability of the methods themselves. Explainable artificial intelligence is abbreviated as XAI. The metric-driven research paradigm has resulted in a lack of interpretability of the relevant XAI methods themselves. Accordingly, there is a need for interpretability research on XAI methods, which can be playfully referred to as XXAI. This paper is one of our works on XXAI. This paper takes Generic Attention-model Explainability (GAE), a widely influential model interpretation method , or rather, XAI method that represents an important technical route, as the research object, and explores the real working mechanism and flaws of this method as well as the technical route it represents. Based on the conclusions of this study, it may be necessary to re-examine or verify GAE-related methods and their domain applications. We argue that GAE is an interpretation method that focuses on the attention process. After pointing out the working mechanism and flaws of GAE, we propose Cumulative Asset Holdings (CAH), a more reasonable Transformer interpretation method integrating both process-based and feature-based ideas from an economic zero-sum games perspective. In addition, it is worth noting that our method is applicable to models with special tokens, where existing methods may suffer from limitations. The model simplification research method and the analysis of additive operations adopted in this study may provide inspiration for other research works in XAI.

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.

Unsupervised anomaly detection scores each point of an unlabelled, contaminated sample in a single pass, and increasingly must also explain why a point is flagged. Yet the dominant detectors give a score with no account of which features drive it, and explanations are bolted on post-hoc with SHAP or LIME, which re-query the detector thousands of times per point and only approximate it. We introduce WAND, an unsupervised tabular anomaly detector that is explainable by design. WAND organises its computation around directions on the unit sphere, scoring each point by how far its projection escapes a sub-Gaussian extreme-value baseline. The originality of our approach is that the witness directions that flag a point, being vectors in feature space, are its explanation, a per-feature attribution obtained at no cost over scoring and, since the score is differentiable, recoverable by gradients. Scoring is linear in the sample size, and a probe-efficiency bound guarantees every anomaly a witness, hence an explanation. Across 47 ADBench datasets WAND attains the best mean Friedman rank at ROC-AUC parity with 16 unsupervised baselines, so the gain is interpretability at no accuracy cost; its native explanations are more accurate and faithful than post-hoc SHAP/LIME and ECOD at a fraction of the query cost. WAND is thus a practical, interpretable solution for explainable anomaly detection.

Most prior works focused on conflicts between an LLM's internal parametric knowledge and externally provided context. In contrast, we investigate how LLMs handle conflicts that arise within contextual knowledge itself. We introduce a taxonomy of six types of contextual conflicts (factual, inferential, temporal, granularity, perspective, and ambiguity) and contribute a comprehensive dataset ContextConflict for this setting. The dataset contains 5,781 samples, covers both reasoning and summarization tasks, and includes both explicit contradictions and implicit conflicts that require multi-step reasoning. Experiments on nine LLMs show that current models still fall short in resolving contextual knowledge conflicts. We further provide mechanistic interpretability insights into how LLMs process such conflicts, revealing their latent awareness of conflicts and the representational geometry underlying conflict processing. In addition, our analysis uncovers a consistent model bias towards earlier evidence, and this positional preference serves as a key obstacle to effective conflict resolution. Motivated by these findings, we further propose a simple training-free, label-free steering method that steers activations to encourage a more comprehensive incorporation of evidences for better conflict resolution. On our dataset, the method consistently improves accuracy on reasoning tasks and generates higher-quality, more balanced summaries for summarization tasks.

Mechanistic interpretability is increasingly used to guide interventions such as activation steering, circuit removal, and safety monitoring. Yet an internal estimate that is accurate on average can still choose a poor action. We present ObserverBench, a benchmark framework for testing whether an internal estimator---an observer---is adequate for the intervention, control, or safety task it directs. Each task fixes the model, information boundary, allowed actions, decision rule, held-out cases, and loss. The benchmark reports estimation accuracy separately from the loss caused by the chosen action. Theory and experiments show why both are needed. In closed-loop control, observer errors matter at the starting point and along directions the allowed intervention can reach. On circuit-intervention tasks in GPT-2-small and Qwen2.5-7B, pairwise observers predict unseen effects more accurately without always choosing better actions; observers trained on action loss choose lower-loss actions. In safety triage, a score that perfectly separates violations can allocate a fixed intervention budget poorly when violations have different costs. Across Qwen2.5-7B, Gemma-2-9B-it, and prospectively frozen Qwen3.5-9B APPS tasks, AUROC can rank monitors differently from deployment loss, and the best information source changes across models. Sparse SAE readouts also trail their layer-matched dense controls on the reported Qwen panels, under disclosed activation-density or checkpoint mismatches. ObserverBench provides fixed task contracts, runnable baselines, and table-based submissions for evaluating interpretability methods through the actions they enable.

Reliable disaster damage assessment requires models that provide both accurate predictions and transparent explanations. However, existing multimodal approaches are limited by scarce annotated data and insufficient evaluation of reasoning quality. This study proposes a two-stage training framework that integrates Supervised Fine-Tuning (SFT) and Direct Preference Optimization (DPO) within a unified data construction pipeline. From a single Human-in-the-Loop (HITL) annotation workflow, two complementary datasets are derived, namely ReasoningSet, which contains validated rationales for SFT, and PreferenceSet, which comprises paired rationales for DPO-based alignment. The framework evaluates both classification performance and explanation quality using automatic metrics, model-based scoring, and human ranking. Experimental results show that SFT improves accuracy from 73.64% to 78.29% and increases Macro-F1 by 29% compared to the baseline, while explanation quality improves by approximately 25%. Subsequent DPO alignment further enhances interpretability on the PreferenceSet. Cross-model validation on InternVL-3-8B and LLaVA-1.5-7B demonstrates the robustness and generalizability of the approach. The proposed framework improves detection of underrepresented mild damage cases, reduces high-risk misclassifications, and strengthens alignment between model reasoning and human judgment. Overall, it provides a reproducible pathway to develop reliable multimodal systems that deliver auditable, actionable disaster insights for emergency management.

Large Language Models (LLMs) have demonstrated remarkable performance across diverse tasks, from text summarization to question answering. Despite these capabilities, their black-box nature obscures internal decision-making processes. Mechanistic interpretability (MI) aims to address this by reverse-engineering neural networks into human-understandable algorithms. Current MI approaches for LLMs typically follow a two-stage paradigm: first identifying important components (circuit discovery), where components are typically individual nodes such as an attention head or feedforward neuron, and second determining the role they play in a certain task (functional interpretation). However, this sequential approach overlooks a fundamental insight: a component's importance and its functional role are inherently codependent. Unifying these stages presents two key challenges: (1) functional roles are often tied to specific nodes or components, limiting generalization, and (2) their identification relies on subjective interpretation rather than quantifiable metrics. To address these challenges, we propose S^3martCirc (Self-supervised Smart Circuit Discovery), a unified framework that simultaneously discovers circuits and interprets functionality. S^3martCirc abstracts node behavior into two general computational roles that generalize across tasks and defines a quantitative metric for assigning them, enabling importance and functional role to be discovered jointly rather than in sequence. Extensive experiments show that our framework outperforms existing methods in circuit discovery.

This paper presents Murano, an open source framework for designing, running, and reproducing mechanistic interpretability studies of large language models, intended for researchers across disciplines. These studies often combine loading, recording, attribution, intervention, and evaluation, while existing libraries tend to focus on different parts of this workflow. As a result, researchers using several libraries may need to adapt outputs from one for use by another. To bridge this gap, Murano represents operations from these five areas as composable steps. Steps exchange named result artifacts and declare the inputs they require and the outputs they produce. A pipeline executes its steps in the order supplied, and Murano uses canonical addresses when component identities pass between operations. Murano builds on existing interpretability and machine learning libraries. We demonstrate Murano through two reproductions of established interpretability studies and one illustrative sparse autoencoder case study.

Large language models are trained to follow instructions while refusing harmful requests. Jailbreaks exploit this balance to elicit content a model would ordinarily reject. Roleplay jailbreaks are especially concerning: the harmful request can remain visible inside a roleplay wrapper made of a persona, scenario, and task, yet the model may comply. We use mechanistic interpretability to determine how this context reverses refusal and which elements contribute to the reversal. Across two benchmarks, three model families, and four authored wrappers, we compare matched harmful and benign requests with and without this wrapper. We trace hidden-state contrasts from the request to the final prompt state, isolate wrapper operations through controlled counterfactuals, intervene on their activation directions in held-out evaluation requests, and decompose effective directions geometrically. Our analysis yields three findings. (1) Successful attacks retain the measured harmful-versus-benign distinction at the request, while its refusal-associated expression weakens where the answer begins, a pattern we call safety-relay attenuation. (2) Constructing the complete roleplay around the request and framing it within the scenario contribute causally: removing the associated activation changes restores refusal. (3) These effects largely share internal structure, and most repair is reproduced by components aligned with the model's ordinary refusal of harmful requests without roleplay; scenario framing retains a smaller, model-dependent component. Together, these findings explain how roleplay can produce compliance despite retained evidence of harm and identify a concrete target for future safeguards: maintaining the connection from harm recognition to refusal.

Large language models (LLMs) are built from structured high-dimensional objects such as token representations, weights, adaptation updates, caches, and activations, whose multilinear structure is underexploited by the conventional matrix-centric view. Tensor decompositions and tensor networks provide a principled algebraic language for this structure, yet the literature often treats them as isolated compression mechanisms. This survey organizes tensor methods for LLMs through two complementary views: a seven-stage lifecycle taxonomy covering tokenization, embeddings, pre-training, adaptation, compression, inference, and interpretability, and a component view covering embeddings, attention, and feed-forward networks. We provide unified notation and theoretical foundations, analyze tensorization strategies for individual Transformer components, and compare methods at each lifecycle stage while making differences in evaluation protocols and model scales explicit. We further connect tensor methods to neighboring efficiency techniques and probabilistic tensor networks. Finally, we synthesize open challenges and introduce $ρ_{\rm gap}$, a metric for the compression-realization gap between theoretical memory reduction and measured system-level speedup. By treating tensorization as a common structural principle, the survey provides a structured entry point to tensorized language models and clarifies when parameter savings can plausibly translate into memory efficiency, computational efficiency, or interpretability. The GitHub page dedicated to this paper is accessible at \href{https://github.com/ma-tt-a/awesome-tensor-methods-for-llms}{this https URL}.

Discovering stable neuron behavior across entire domains remains a challenge in mechanistic interpretability. Existing methods often rely on instance-level point estimates or computationally expensive procedures, which either obscure population-level variability or limit scalable domain-wide analysis. We present RACE (Residual Alignment for Consistency Estimation), a forward-pass statistical framework that evaluates the domain-wide functional consistency of Transformer neurons. Compared with gradient-based point estimates, RACE produces neuron rankings that yield more domain-specific effects under perturbation. Token-distribution shifts support the connection between the selected neurons and the target domain, while scoring requires roughly one-hundredth of the computational overhead of the gradient-based methods. Code is available at https://github.com/Nexround/RACE.

Tabular-to-image methods have emerged as novel approaches to leverage the high predictive performance of convolutional neural networks and vision transformers. They convert tabular data into image representations, mapping each feature at a fixed pixel location derived from a dimensionality-reduction method (e.g., t-SNE, UMAP, PCA). However, they encode only the marginal value of each feature and discard information about feature relationships. We propose TabSOM, a tabular-to-image encoding built on the Self-Organizing Map (SOM), which provides: (i) a spatial layout in which every input feature occupies a fixed canvas position derived from its component plane via collision-free Hungarian assignment; and (ii) a graph that captures pairwise feature relationships derived from the SOM component planes. The resulting image stacks two multi-scale node channels: one encodes feature values at fixed scales, while the other encodes pairwise feature interactions as spatial connections between related features. Two SOM-derived interpretability approaches are introduced: a prototype-inspired partial dependence plot and a class--separation importance score. Benchmarked against twelve existing tabular-to-image methods across public binary-classification datasets, TabSOM ranks first or second on every dataset and achieves the lowest variance of any method evaluated. Interpretability obtained with TabSOM was validated against Random Forest, XGBoost, and SHAP, the class-separation score shows reasonable agreement with established baselines on the top-ranked features while capturing complementary structural information from input data. These results demonstrate that TabSOM provides an effective and interpretable approach for applying deep learning architectures to tabular data, bridging the performance--interpretability gap in this domain.

Vision-language-action models (VLAs) are moving rapidly towards deployment as general-purpose manipulation policies, but we currently lack basic tools for understanding what these models represent internally or for monitoring them at runtime. Leveraging ideas from mechanistic interpretability, we probe the residual stream of $π_{0.5}$ and find that task progress, the normalized time remaining in a trajectory, is linearly readable from the activations. We find that this signal is present in the pretrained PaliGemma backbone prior to training on any robot-specific data. A single linear probe generalizes to unseen tasks and varies under language counterfactuals when trained on multi-prompt data, but does not enable meaningful steering of the policy. These properties make the signal directly useful for instrumenting deployed VLAs. We use the probe as a simple label-free OOD detector, which detects stalled task progress, and find it competitive with state-of-the-art methods. Our results suggest that VLAs have rich, linearly readable internal representations of semantic quantities like task progress, and that learning to read these signals offers a lightweight, interpretable path toward monitoring deployed visuomotor policies.

Mechanistic interpretability of large language models lacks spatially resolved, falsifiable tools for testing whether internal components are specialized for distinct cognitive operations. We adapt subtraction analysis, the standard framework of human neuroimaging, from biological brains to perturbed transformers, and apply the same logic to both substrates in parallel. Building on the Brain-LLM Unified Model (BLUM), which showed that layer-perturbed LLaVA-1.6-Vicuna-13B error profiles match the lesion patterns of aphasic patients, we develop PRISM (Perturbation-based Regional Interpretability through Subtraction Mapping). PRISM maps the seven clinical Philadelphia Naming Test categories, subtracts error classes pairwise, and treats each perturbation seed as a subject in a group analysis with threshold-free cluster enhancement along the layer axis. We run a structurally matched analysis on 213 chronic post-stroke aphasia patients using correlation-difference lesion-symptom mapping, and replicate both sides on held-out splits. The designs match in subject dimension (seeds, patients), spatial dimension (layers, atlas-parcellated cortex) and thresholding, but the contrast operator differs: a within-subject error-proportion difference for the LLM, a between-subject correlation difference for the cortex. Both substrates recover a robust phonemic-favoring dissociation, a deep layer cluster and a frontal-perisylvian cortical cluster, both replicating; the semantic-favoring direction is a consistently signed but non-significant trend on both. PRISM thus gives a falsifiable, spatially resolved test of functional-specialization claims in transformer language models. A confirmatory ROI-level intervention (PRISM Stage 3) licensing the strongest causal-mechanism claim is left to subsequent work.

AI models have achieved remarkable success across diverse domains, yet the mechanisms underlying their capabilities and the risks they may pose remain poorly understood. As AI development becomes faster and increasingly automated, mechanistic exploration remains largely manual, widening the gap between what models can do and our ability to understand and control them. To bridge this gap, we introduce Mechanist, an agentic system that uses AI as a scientific instrument for the autonomous discovery of mechanisms underlying AI intelligence. To support autonomous mechanistic discovery, we construct an interpretability-focused knowledge graph of approximately 13,000 papers and integrate it with a multidisciplinary database of 43 million papers spanning 26 fields. We further curate a library of 32 foundational methods for mechanism analysis, causal intervention, and validation. Compared with Claude Code and existing AI-scientist systems, Mechanist generates more valuable mechanism hypotheses and executes experiments more reliably. Mechanist also demonstrates a progression from discovering model behaviors to explaining and controlling AI models. Specifically, Mechanist first uncovers a counterintuitive safety risk in scientific laboratories, showing that unsafe traits can transfer across modalities through apparently safe training data. Mechanist then develops a mechanism theory of belief, revealing how models represent world knowledge, form beliefs, infer the beliefs of others, and how these mechanisms emerge during pretraining. Finally, Mechanist translates these mechanistic insights into practical interventions that improve model performance across diverse scenarios and steer scientific foundation models toward generating DNA sequences with specified properties.

The adaptive neuro-fuzzy inference system (ANFIS) is an interpretable reasoning framework capable of generating explicit IF-THEN fuzzy rules, making it suitable for tasks requiring transparent reasoning. However, existing ANFIS models generally construct rule antecedents and perform inference in Euclidean space, limiting their representational capacity and predictive performance. To address this issue, we propose Hyperbolic ANFIS (HyperANFIS), a hyperbolic extension of ANFIS. HyperANFIS preserves the fuzzy semantics and core architecture of conventional ANFIS while performing rule-prototype learning, rule activation, and consequent aggregation in hyperbolic space. It also retains the ability to generate interpretable IF-THEN rules. By exploiting the representational properties of hyperbolic geometry, HyperANFIS strengthens the fuzzy inference process, thereby improving predictive accuracy, inter-rule collaboration, and the credibility of its interpretable rules. Experimental results show that HyperANFIS consistently outperforms the standard ANFIS baseline and various ANFIS variants across all datasets, while also generating higher-quality fuzzy rules.

The Workshop on Trustworthy Natural Language Processing (TrustNLP), co-located with major ACL conferences since 2021, has grown from 8 proceedings papers to 41 over six editions, documenting a field-wide transition from post-hoc interpretability of static models to mechanistic understanding and proactive control of generative systems. We synthesize insights from all 144 proceedings papers, classifying them along six trust dimensions grounded in established frameworks (TrustLLM, DecodingTrust). We observe co-occurrences with capability emergence. The release of the first high-impact chat models activated all trust dimensions simultaneously, while subsequent model generations shifted focus toward truthfulness and safety alignment. Analysis from the classification study reveals that truthfulness is the fastest-growing dimension (absent in 2021-2022, comprising 37% of papers by 2025-2026), fairness remains the most consistent theme, and explainability exhibits a U-shaped trajectory; declining as post-hoc methods lost relevance but resurging in 2026 through mechanistic interpretability. A cross-venue comparison with ACL, NAACL, EACL, and EMNLP (~2K papers) in the same period shows that TrustNLP's topical distribution closely follows the field average. We identify four structural insights and conclude with actionable directions for the research community.

Sparse autoencoders (SAEs) have helped uncover mechanistic explanations for LLM behaviours such as reasoning, jailbreaking etc., via understanding the corresponding task-relevant and causally effective features. To evaluate such mechanistic explanations, downstream studies must distinguish surface lexical features from genuinely high-level ones. However, neither an autointerp-based semantic description nor causal steering utility fully resolves the abstraction level of a feature. To this end, we introduce \emph{Feature Nonlocality} (FNL), defined as the entropy of the normalized per-position influence on an SAE feature's activation. We report that FNL correlates with existing LLM-based proxy metrics of feature semantic abstractness, and successfully distinguishes context-dependent reasoning features from token-driven ones, correctly assigning the higher FNL to the contextual feature in $73$--$84\%$ of randomly drawn pairs that consist of one contextual and one token-level feature. We demonstrate two downstream applications. We audit SAE-based features used for jailbreak mitigation and find surprisingly that most effective features are positional features with low FNL rather than genuinely recognizing harmful intents. We report that steering high-FNL features in DeepSeek-R1-Distill-Llama-8B improves MATH-500 accuracy by $4.6$ points over the unsteered model and outperforms steering low-FNL features, though the gains are model-specific. We conclude that FNL provides an LLM-independent, label-free, correlational witness of the abstraction level of an SAE feature, with applications in evaluating mechanistic explanations as well as selecting features for downstream interventions.

Machine learning-based Intrusion Detection Systems (IDS) have demonstrated superior performance in securing Unmanned Aerial Vehicle (UAV) networks. However, the 'black-box' nature of these models, combined with the high dimensionality of multimodal cyber-physical data, poses significant interpretability challenges. Static visualization dashboards may struggle to present complex relationships among multimodal cyber-physical features in a form that is easy for operators to inspect and interpret. To address this, we propose a Conversational XAI interface powered by Large Language Models (LLM) to facilitate on-demand investigation. In a controlled experiment with participants, we systematically evaluated the impact of this conversational interface versus a traditional XAI Dashboard on operator understanding, trust, and reliance during post-incident auditing tasks. Our results suggest that the conversational interface was perceived as more useful than the dashboard, potentially because it helped participants access and synthesize relevant information more easily. However, this benefit was accompanied by a lower level of appropriate self-reliance, indicating a potential risk of over-reliance. One possible interpretation is that the natural-language responses made the AI advice easier to accept, which may have reduced participants' tendency to verify the underlying evidence when the IDS was incorrect. These findings point to a potential trade-off in human-AI collaboration for UAV intrusion auditing: interaction mechanisms that improve perceived usability may also increase the risk of inappropriate reliance. We conclude by discussing design implications for future XAI systems that balance seamless interaction with cognitive forcing functions to foster appropriate reliance.

Mechanistic interpretability explains models by identifying circuits inside them, but has no way to tell whether a circuit is a property of the model or an artifact of the method that found it. Sparse autoencoders illustrate the problem: different seeds and widths recover materially different features from the same activations, and no theory says whether that variability is incidental or structural. We put dictionary learning for interpretability on an identifiability footing. Treating the forward pass as a controlled dynamical system with depth as time and lifting it with the Koopman operator yields a finite linear realisation whose \emph{spectrum} is a coordinate-free property of the model. We prove the spectrum is recoverable from $M$ calibration samples at rate $M^{-1/2}$ up to permutation - to our knowledge the first identifiability theorem for a mechanistic-interpretability primitive, with a matching minimax lower bound, a median-of-means variant for heavy-tailed activations, and a dissociation theorem: whenever the realisation is non-normal, the directions carrying activation variance and the directions carrying information across depth cannot coincide. The identifiable object and the legible object are not the same object. On GPT-2 small, Gemma-2-2B and Qwen3-8B-Base the spectrum converges everywhere and attains the predicted exponent on Qwen3-8B-Base ($0.506 \pm 0.031$); shortfalls collapse onto one curve against each cell's sample threshold. Koopman modes beat random directions but lose to principal components on indirect-object identification, with the gap decaying $4.1\times$ in depth-distance, as the theorem predicts. The Koopman spectrum is an identifiable, model-intrinsic fingerprint with a stated error bar, not a legible decomposition.

Uncovering the internal mechanisms underlying the safety capabilities of large language models (LLMs) is crucial for developing trustworthy artificial intelligence. Currently, mechanistic interpretability studies on multilingual safety are largely confined to local components, such as isolated neurons. However, this static and fragmented perspective overlooks the synergy among components and fails to elucidate how safety signals dynamically propagate within the model to drive safety decisions ultimately. In this work, we move beyond isolated neurons to identify and target the cross-layer functional pathways formed during safety signal propagation, thereby uncovering the mechanisms driving the cross-lingual safety gap. Specifically, we first identify monolingual safety pathways and validate their impact on refusing harmful requests. Subsequent cross-lingual analyses reveal a sparse subset of cross-lingual shared safety pathways, confirming that this intersection acts as the internal bridge transferring safety capabilities from high-resource (HR) languages to non-high-resource (NHR) languages. Building on these mechanistic findings, we propose a pathways-targeted alignment method based on the cross-lingual shared safety pathways. Experimental results show that updating only a small fraction of pathway parameters significantly improves safety in NHR languages while largely preserving the model's general capabilities.

As machine learned models increase in complexity and expressive power, features of simpler models, such as interpretability and control over the shape of the modeled function are lost. On the one edge of the spectrum we have simple linear models are transparent and possess good interpretability and explainability properties, but have a limited expressive power. On the other edge we have neural networks, that have expressive power that improves with scaling, but are mostly opaque. In this work we develop the \emph{spectral neuron} concept: a scalar model given by $f(\vx)=λ_k \left(A_0+\sum_{i=1}^n x_i A_i\right)$, with learned real symmetric matrices $A_0,\ldots,A_n$. The input enters the model through an affine matrix function, but the prediction is obtained by reading one of its eigenvalues. Thus, the model is nonlinear, but the source of nonlinearity is still mathematically explicit. This gives us a useful middle ground: the model can become more expressive as the matrix dimension grows, while retaining a degree of structural interpretability through the learned matrices. For example, extremal eigenvalues yield convex or concave functions, semidefinite constraints on the coefficient matrices impose monotonicity, and the associated eigenspaces characterize local feature sensitivity. We study the robustness, structural interpretability, and shape-control properties of this model family, and then test whether it can be learned and scaled in practice. We develop a systematic study of this model family, bringing together spectral results from several mathematical literatures to characterize its expressivity, robustness, interpretability, and shape-control properties.

Mixed strategy equilibrium predicts i.i.d play: past actions should not help predict future decisions. Human players, however, systematically depart from this benchmark, and in O'Neill's zero sum card game, these departures can be predicted by black box sequence models such as LSTMs. This paper asks whether that predictive power can be achieved by transparent alternatives that also reveal the behavioural structure behind it. Using 84,060 decisions from 2,802 pairs, the analysis first benchmarks naive and behavioral models against interpretable machine learning and deep learning models, then evaluates the modified EWA specifications of prior work against these benchmarks and uses the LASSO diagnostics to motivate a further nested frequency tracking extension. The results show that repeat or avoid behavior, especially players' management of their own recent action histories, accounts for most of the interpretable and strategically exploitable signal, while frequency tracking adds little out of sample.

Transformers have had a profound impact on the world of language processing and computer vision. As efforts to answer the million-dollar question of ``How does a Transformer learn?" have been increasing, existing interpretability studies primarily analyze representations at isolated layers or the network as a whole, while the developmental evolution of individual representations and its manifolds across transformer layers remains underexplored. With this work, we aim at providing a comprehensive analysis of the evolution of representations as the representation point cloud transforms across the layers; thereby attempting to isolate layers or establish a trend which comes closer to justifying how and when raw input representations evolve into task-relevant feature representations. Thus, Transformer Geometry Observatory-TGO-IV introduces a topological framework for analysing the evolution of Transformer representations through the lens of Persistent Homology. Rather than studying local geometric properties alone, TGO-IV constructs Vietoris--Rips simplicial complexes from token-level representation point clouds and investigates the evolution of their persistent topological signatures across Transformer layers. The proposed framework comprises complementary topological observatories including Persistence Diagrams, Barcode Diagrams, Betti Curves, Persistence Landscapes, Bottleneck Distance, and Wasserstein Distance, enabling a comprehensive analysis of how the global topology of representation point clouds develops throughout the forward pass.

Reinforcement learning policies are difficult to inspect, but interpreting them is a prerequisite for trustworthiness. Converting a trained policy into explicit decision-tree rules improves transparency and the resulting artifacts often remain too complex for human understanding. We present a pruning process that simplifies such rule-based policies while preserving task performance and making edits to the policy auditable. The process defines a small set of structural and usage-aware operators and evaluates candidate edits by re-executing the policy to measure return and interpretability proxies. This exposes an transformation process from complex to compact policy structures. We investigate this approach on classic control and MuJoCo benchmarks, where pruning traces reveal consistent interpretability improvements while maintaining high performance.

The dominant approach to mechanistic interpretability trains proxy dictionaries such as sparse autoencoders and labels features from max-activating text. The best such atlases identify con- cepts, but that identity lives in the learned dictionary rather than in the network weights them- selves. We propose extracting mechanism mounts directly from linear sites by column-tiled SVD: each mount is a triple (v,u,σ) read as trigger, write, and strength. Identity is the weight rule. We evaluate mounts with a pre-registered suite judged on full-write energy lift rather than tile-local lift. On Gemma-2-2B with WikiText-2 (16,384-token subsample), all seven linear maps are scored: residual writes (mlp.down, attn.o) receive full A/B/C with steer after post-sublayer RMSNorm and pass 52/52 site-layers; other maps receive A/B only (mlp.gate/attn.q/attn.k/effective mlp.up/attn.v 26/26 each). Aggregate: 182/182 GO. We release library code, the corpus builder, the experiment entrypoint, and unit tests.

A standard self-attention layer consists of two interacting circuits: the query-key circuit that governs attention allocation, and the output-value circuit that maps attended representations to predictions. Collapsed and factorized parameterizations of the query-key and output-value circuits lead to qualitatively different attention patterns. In particular, some parameterizations give sharper attention to task-relevant tokens, at a similar training loss. We analyze how the parameterizations of these circuits shape the parameter trajectories in single-layer self-attention models trained for next-token prediction. Through gradient-flow analysis, we show that factorization induces implicit rescaling of the two circuits' learning rates. We derive closed-form dynamics showing that output-value and query-key parameters move along a line, with relative speeds determined by their learning rates. Faster query-key learning relative to output-value learning thus produces sharper attention, as the model compensates for slower output-value learning by increasing attention mass on relevant tokens. Experiments show that differences in the relative learning rates of the two circuits govern attention concentration. This improves attention interpretability proxies while maintaining comparable predictive performance.

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.

Interpretability is often treated as a tax on capability: language models are trained as opaque systems, then explained after the fact, with methods whose reliability is difficult to establish. In this work, we challenge this premise. Rather than reverse-engineering a model, we make interpretability a constraint of the training pipeline, optimized alongside the language modeling objective. Across three orders of magnitude of compute, on both autoregressive and diffusion language models, interpretability scales with capability rather than against it. Surprisingly, model representations become more disentangled and aligned with human-understandable concepts with scale. We instantiate the training-time recipe with Steerling-8B, a diffusion language model with a causal attention mask. For any group of generated tokens, Steerling-8B attributes the output to relevant input tokens, human-understandable concepts, and training data. This enables closed-loop intervention: diagnose an output through its concept or feature attribution, retrieve similar training data, and correct the behavior through concept steering without retraining. Steerling-8B remains competitive with open peer models trained on substantially 2-16x more compute, suggesting a different scaling paradigm: interpretability can be designed into training, and it improves with scale.

Dense pretrained transformers do not naturally expose interpretable units for circuit extraction. Existing approaches obtain such units by learning auxiliary sparse representations or training sparse models, incurring substantial additional computation while potentially introducing a fidelity gap between the representation being analyzed and the original pretrained model. We propose Sparse Weight Decomposition (SWD), which reparameterizes pretrained linear projections by factorizing each weight matrix into two sparse factors whose shared intermediate coordinates serve as individually addressable circuit units. Without training a separate replacement network, this parametric representation supports the same scoring, selection, and ablation circuit extraction workflow used for methods that learn sparse features. Across single-matrix replacements, SWD matches the held-out fidelity achieved by Transcoder and other strong baselines while using less than 1% of the data that those baselines use to train their replacements. For matched replacement fidelity, SWD reaches the same circuit sufficiency and necessity targets with fewer active read/write edges and selected units across tasks on GPT-2, Qwen2.5, and Qwen3.5-27B. We further show that SWD remains effective for full-model replacement of all attention and MLP weight matrices after fine-tuning the nonzero factor values. Finally, SWD also features a zero-data variant, allowing broader use of mechanistic interpretability analysis (e.g., per-step analysis).

Electronic Health Records (EHRs) are widely used for clinical risk prediction using machine learning. International Classification of Diseases (ICD) codes provide structured information about patient diagnoses, but representing them effectively remains challenging. Existing approaches often face a trade-off between predictive performance and interpretability: grouping-based representations are interpretable but may lose information, while embedding-based representations achieve strong predictive performance but are difficult to interpret. We propose Explainable Representation of Multiple ICD Codes (xMICD), a method for constructing low-dimensional patient representations from sets of ICD codes. xMICD combines clinically meaningful diagnostic groupings with similarity in a pre-trained ICD embedding space. Instead of using binary group membership, the method assigns codes to groups via similarity-based relative assignments, yielding features that reflect how closely a patient's diagnoses align with each clinical group. Experiments on large-scale EHR datasets demonstrate that xMICD achieves predictive performance comparable to embedding-based representations such as ICD2Vec across multiple clinical prediction tasks. At the same time, the resulting features remain clinically interpretable because each dimension corresponds to a recognizable diagnostic group. xMICD therefore provides a practical way to integrate embedding-based semantic relationships into interpretable clinical feature spaces for machine learning models.

Tool-integrated vision-language agents have made remarkable progress on compositional and multi-step visual reasoning. Yet their outputs frequently exhibit unfaithfulness: the stated reasoning path diverges from the computation that actually produced the answer, undermining reliability in safety-critical applications. We present DiffuseAgent-MI, a self-evolving agent whose perceptual grounding is governed by a KL-minimal energy model over feature units, providing a distributional view of visual mechanistic interpretability. The agent learns an energy landscape that softly constrains generated samples to lie near the native prior conditioned on the chosen interpretable unit, closing the gap between the explanation and the internal representation. A verifier then supplies trajectory-level faithfulness rewards, and a repair branch re-conditions the energy when the verifier flags an unfaithful step. On GeoQA, SciVis, VQA-v2 and an in-house multimodal reasoning set, DiffuseAgent-MI improves accuracy by up to 5.1 points over prior self-evolving agents while more than doubling mutual-information faithfulness and human-interpretability agreement. Our analysis shows the energy term and the verifier are complementary: the former guarantees distributional faithfulness, the latter trajectory-level faithfulness, and only their combination closes both gaps.

Modern opaque AI models prize performance over interpretability, which makes testing difficult. However, formal statistical tests conducted on a model's embedding space can provide robust characterizations of semantic structure, concept separation, and knowledge graph alignment. Model developers would benefit from a model comparison technique that leverages human-curated knowledge structures to test alignment. The scale of the input space for even relatively simple tasks motivates the need for alignment checks that augment standard outcome reasoning. This work develops and demonstrates a topology-based multi-modal alignment test to make deployment, selection, and comparison of opaque models more interpretable. These methods also offer an intuitive connection to possibility theory and a unified decision theoretic framework from data to deployment.

Optimal decision trees (ODTs) are compact, interpretable machine learning models that globally optimize a given objective, but their scalability remains challenging. While recent work has proposed a variety of search strategies to improve scalability, the precise contribution of each strategy remains unclear. To address this gap, we introduce a general algorithmic framework for ODTs that instantiates previously used search strategies and enables the definition of new ones. This provides a common lens through which to understand and compare different strategies, which we use to empirically investigate the effect of 18 search strategies. Compared to the state of the art, the best strategy in our evaluation achieves significantly better anytime performance for classification, and improves runtime by more than an order of magnitude for regression.

Wearable sensors continuously capture fine-grained multivariate time-series data, providing opportunities to model behavioural patterns associated with health outcomes. However, existing deep learning methods prioritise predictive accuracy over interpretability, limiting their application in health research. In this study, we present HealthCAT, a flexible framework that integrates an Encoder-only Transformer with an Attentive Class Activation Token (AttentiveCAT) to generate class-specific, time-step-level interpretations. These interpretations can be mapped back onto behavioural cycles that are relevant to the domain (e.g., time-of-day), supporting individual-level analysis of wearable sensor data. We evaluated HealthCAT using two real-world wearable sensor datasets (306 participants in total). HealthCAT outperformed deep learning baselines by up to 17% in F1-score and 12% in accuracy on both datasets ($p<0.05$). In masking experiments, the time steps identified by HealthCAT carried significantly more predictive value than random selection across all masking conditions ($p<0.05$), indicating that the identified time steps are predictively informative. By coupling predictive performance with validated time-step-level interpretability, HealthCAT moves wearable sensor analysis beyond aggregated metrics towards temporal patterns that support health monitoring, behavioural pattern analysis, and intervention design in health research. The significance of this work is that it enables accurate prediction of health indicators from wearable sensor data while providing insights into when and how physical activity patterns occur, rather than relying solely on aggregated summary measures.

As decision-making processes grow more complex, machine learning tools have become essential for tackling business and societal challenges. However, many existing methods rely on decision-making procedures that are difficult to interpret. Since humans naturally make decisions by comparing new cases with a few representative examples, we aim to design an approach that selects such pivots to construct an interpretable predictive model. Inspired by decision trees, we propose a hierarchical, interpretable-by-design pivot selection model based on the similarity between pivots and input instances. Our method functions both as a pivot selection technique and a standalone predictive model. Extending beyond single pivots, we incorporate pairs of pivots that are used by proximity and oblique trees, as well as ensembles, which enhance the versatility and effectiveness of our proposal. Additionally, our approach is data modality-agnostic, leveraging pre-trained networks for data transformation. Experiments across diverse datasets, including tabular data, text, images, and time series, demonstrate the effectiveness of our approach, outperforming alternative instance selection strategies and achieving competitive results against state-of-the-art interpretable models while maintaining a minimal number of pivots.

Existing benchmarks for electrocardiogram foundation models primarily evaluate downstream predictive performance, providing limited insight into whether their internal representations can be faithfully decomposed, clinically interpreted, or reproduced across independent analyses. We introduce ECG-InterpBench, a benchmark designed to systematically evaluate the interpretability of ECG foundation-model representations. ECG-InterpBench uses sparse autoencoders as standardized measurement instruments and matches their capacity across models to enable controlled comparisons. We evaluate six frozen ECG foundation models across five standardized encoder depths, five matched dictionary widths, and three random seeds, producing a 450-cell interpretability atlas comprising 75 exactly matched six-model comparison blocks. The benchmark evaluates complementary dimensions of representation interpretability, including sparse reconstruction fidelity, single-feature accessibility and coverage of 49 clinically meaningful ECG measurements, and cross-seed feature reproducibility. The evaluation further quantifies patient-sampling uncertainty, depth- and seed-dependent variation, and sensitivity to the sparsity parameterization. The benchmark reveals that ECG foundation models exhibit distinct interpretability profiles. A matched replication on MIMIC-IV-ECG confirms that reconstruction fidelity and clinical accessibility identify different leading models. The benchmark is accompanied by executable evaluation code, standardized manifests, cell-level metrics, and reproducibility audits. ECG-InterpBench complements performance-centered ECG benchmarks by providing a capacity-controlled and reproducible framework for comparing ECG foundation models across distinct dimensions of representation interpretability.