Mechanistic Interpretability

Sparse autoencoders (SAEs) are standard tools for mechanistic interpretability, but current SAE families are constrained by fixed encoder nonlinearities such as ReLU, JumpReLU, and TopK. This hard-codes a particular sparsity mechanism into the model and can distort the reconstruction-versus-sparsity trade-off. We introduce the Rational Sparse Autoencoder (RSAE), which replaces the fixed encoder activation with a trainable rational function. Rational activations are flexible enough to uniformly approximate the activation primitives used by existing SAE families on compact domains (for TopK, the thresholded gate obtained after a separating top-k threshold is supplied), while also providing a richer function class for adapting to the observed pre-activation geometry. We realise this idea through a two-stage pipeline: an initialisation procedure that copies the pre-trained baseline SAE weights, plugs in rational coefficients obtained by the relaxed Remez exchange on synthetic data, and calibrates the scale parameters along with the rational coefficients; followed by a fine-tuning step under the standard sparsity-regularised reconstruction objective. Empirically, on residual-stream activations of three open-weight language models and across all three baseline activation families, the RSAE strictly improves on it after the fine-tuning step, both on reconstruction-side metrics and on downstream-behaviour metrics, without sacrificing feature-level interpretability under sparse probing. These gains are consistent across host language models, across baseline activation families, and across the full range of baseline sparsity we tested, while the upgrade itself adds only a handful of scalar parameters per autoencoder and runs in minutes on a single consumer GPU.

Alzheimer's Disease (AD) is a complex neurodegenerative disorder that continues to impact millions of people worldwide. Predicting AD conversion during the prodromal stage remains critical for disease understanding and patient care. As such, survival models are widely used for AD risk prediction, yet they are typically static predictors with limited interpretability and no capacity for natural language reasoning. In this work, we propose iLENS, an interpretable large language model (LLM) guided framework based on mixture-of-experts (MoE) for survival prediction in AD conversion. Our approach uses LLM to synthesize structured neuroimaging measurements and unstructured information to guide expert routing. Our framework demonstrates competitive predictive performance and capability in patient subtyping. Furthermore, our framework provides transparent, biologically grounded rationales for its routing decisions, bridging the gap between high-performance survival analysis and interpretable clinical decision support.

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.

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

Language-model post-training is the main stage at which model behavior is shaped, yet it still largely involves optimization of scalar rewards that summarize diverse desiderata. This abstraction gives practitioners little visibility into what their data actually teaches models, allowing spurious correlations to be learned by a model and inducing undesirable behaviors such as over-stylization and sycophancy. To address this problem, we ask: can we inspect a preference dataset before optimization and decide, at the level of concepts, which behaviors a model should be allowed to learn? Motivated by this, we introduce a data-centric post-training pipeline that uses interpretability protocols to develop statistical hypotheses for the latent concepts separating preferred from dispreferred generations, making them explicit for fine-grained user feedback. Building on this view, we unify several interpretability-based training protocols as ways of shaping rewards via feature or data interventions. Empirically, we show that our pipeline diagnoses undesirable signals in existing preference data, mitigates off-target learning, and can also help amplify or shape desired properties such as safeguards and model personality. More broadly, our results suggest that interpretability can turn post-training from optimizing opaque proxy rewards into a process of auditing and sculpting the learning signal itself.

As Artificial Intelligence models grow in complexity, interpretability has become an indispensable tool for understanding, debugging, and controlling their computations. However, interpretability lacks general theories to deductively design interpretable methods. This gap between theories and methods results in a fragmented literature and inconsistent evaluation protocols. To fill this gap, we introduce the Standard Interpretable Model (SIM), a general theory grounded in Lagrangian mechanics that enables the deductive design of interpretable methods. Specifically, the SIM summarises, in a set of premises, what interpretability is for a target user. From these premises, the SIM systematically derives interpretability symmetries and corresponding constraints, which shape the landscape of a Lagrangian whose minima correspond to optimal interpretable models. To reach the minima, one can either update the parameter values of an opaque model to make it more interpretable or compile constraints into an interpretable architecture. We empirically show that the SIM identifies and solves limitations of existing methods (including traditional, concept-based, and mechanistic interpretability), highlights underexplored research directions, and informs the design of core programming interfaces. Beyond being a research method, the deductive nature of the SIM offers pedagogical grounding for interpretability curricula and may shift the scientific community's perspective of a discipline that has long been fragmented.

Finding interpretable directions in language-model representations is critical for understanding and controlling model behavior. Sparse autoencoders (SAEs) have become the standard tool for this purpose, but using them as the default first lens often requires training, storing, and evaluating large overcomplete dictionaries. This bottleneck limits rapid exploration and raises a fundamental question: how much interpretable structure is already visible from activation geometry before training another neural dictionary? Our intuition is simple: many interpretable directions are selective on tokens, and these directions should look less Gaussian than random directions. We therefore revisit independent component analysis (ICA), a classical method for finding non-Gaussian directions, as a compact lens for language-model interpretability. We find that ICA has been underestimated for LLM interpretability, because prior uses often relied on off-the-shelf ICA implementations that are brittle on LLM activations and lacked systematic tools for inspecting and evaluating the recovered directions. To bridge these gaps, we introduce ICALens, the first practical workflow for stable, efficient, and auditable ICA analysis of LLM representations. It combines an optimized GPU-parallel FastICA pipeline with LLM-specific stability recipes and better fitting diagnostics, enabling efficient and reliable layer-wise analysis. Across GPT-2 Small, Gemma 2 2B, and Qwen 3.5 2B Base, ICALens efficiently recovers compact, human-interpretable directions without per-layer gradient-based dictionary training. On SAEBench, ICA is competitive with public SAEs in sparse probing and outperforms them in targeted probe perturbation under small-to-medium budgets. These results suggest that ICA should not be viewed as a weak baseline, but as an efficient and complementary first lens for exploring language-model representations.

Data attribution is a promising field in interpretability that aims to explain model behavior through the influence of its training data, with applications including debugging undesirable model behavior and training dataset curation. However, significant engineering effort is required to perform it at scale, and many cutting edge techniques lack open-source tooling and support. Bergson is an open source library that aims to enable faster progress in the field by providing a host of techniques that scale to very large language models and pre-training datasets. The library natively supports on-disk gradient stores and multi-node distributed training, and provides quality of life tools for researchers. Finally, we introduce the first open-source implementations of three leading data attribution methods: MAGIC, SOURCE, and TrackStar. The library is available at https://github.com/EleutherAI/bergson .

Generative AI emulators are increasingly used in scientific domains where we already have strong theory, benchmarks, and physical intuition. This raises a central evaluation and interpretability question: when a foundation-style model can reproduce known continuum dynamics, what internal mechanism supports that behavior, is the internal behaviour consistent with known physics, and how does it relate to where the emulator succeeds or fails? We investigate a cross-domain foundation model for continuum dynamics, Walrus by Polymathic, using mechanistic interpretability guided by physical principles. We apply a sparse autoencoder (SAE) to probe a selected layer, and address the practical challenge of triaging a large feature set (over 20,000) using enstrophy as a physically grounded metric. As a deliberately simple testbed, we focus on shear flow and compare feature recruitment across multiple shear-flow setups, i.e. parameter values in the numerical simulation. Across setups we find evidence of piecewise consistency, with subsets of features recurring in similar roles, but this structure is intermittent and does not map cleanly onto standard physical decompositions. In parallel, direct comparisons between numerical simulation and the emulator reveal systematic output-level discrepancies, including regimes where energy/structures become too diffuse or too localized. We connect parts of these discrepancies to changes in specific SAE feature usage. Our work highlights open questions for scientific foundation models: how to robustly prioritize mechanistically meaningful features, how to separate stable structure from analysis artifacts (including single-layer and SAE limitations), and how to use established benchmarks to decide when "different" internal representations are genuinely informative rather than merely effective.

This research introduces a framework for incorporating Concept Bottleneck Models (CBMs) into 3D generative architectures to address the inherent 'semantic gap' in deep geometric learning. As deep models become central to 3D content creation, explainability shifts from a peripheral feature to a fundamental requirement for trust and accountability in safety-critical domains such as healthcare and manufacturing. CBMs provide an intrinsic interpretability solution by constraining latent representations to align with human-defined concepts, yet their application to unstructured 3D data remains largely unexplored. We design, implement, and validate a formal 3D-CBM architecture that maps raw geometric inputs, including point clouds and meshes, into a multi-tiered taxonomy of interpretable primitives and functional attributes. The framework further identifies strategic datasets, such as PartNet and ShapeNet, specialized for concept-based supervision. Experimental results from a 3D part-manipulation proof-of-concept experiment demonstrate the framework's efficacy, achieving a concept prediction accuracy of 88.8% and a Chamfer Distance of 0.0115. Critically, the model enables precise test-time intervention, allowing for the interactive correction of structural errors. This work establishes a foundation for semantically-steerable 3D generation and invites further exploration into collaborative human-in-the-loop design systems.

Interpretability methods routinely use population-level summary statistics over observed model behaviour to license claims about the effects of targeted interventions on specific computations; in Pearl's terms, they treat rung-1 associational evidence as if it supported rung-2 interventional conclusions, a move whose validity is rarely tested. We examine one concrete instance: the use of routing statistics in Mixture-of-Experts (MoE) pruning, where utilization rates, activation norms, and routing weight distributions are treated as predictors of which experts can be removed without functional cost. A token-level interventional audit across three high-redundancy MoE architectures (OLMoE-1B-7B-0924, Qwen1.5-MoE-A2.7B, DeepSeek-V2-Lite) finds no observational metric predicts causal expert importance in any model: across all 60 metric-layer combinations effect sizes stay below Cohen's $d = 0.23$, and no metric is reliably positive under our corrected, dual-test criterion. A per-token routing weight control, run with identical $n$, rules out insufficient power, recovering a signal whose CI excludes zero at OLMoE's final MoE layer ($d = +0.231$, 95% CI $[+0.09, +0.37]$, $p = 0.0013$). Existing pruning methods succeed in this regime not by identifying dispensable experts but because early-layer redundancy renders most selection criteria interchangeable. Our results provide an explicit counterexample to the common inferential step from population-level observational summaries to token-level interventional claims about expert importance, and illustrate how interventional audits can calibrate the evidential standards for interpretability claims.

Concept-based models (CMs), deep neural networks that ground their predictions on representations aligned with human-understandable concepts (e.g., "round", "stripes", etc.), have been shown to learn representations that leak concept-irrelevant information. As the traditional narrative goes, this leakage is undesirable and should be eradicated as it leads to uninterpretable models. In this paper, we posit that this conventional view of leakage in CMs is not only ill-posed, as the evidence of how leakage makes a model less interpretable is often inconclusive, but also bound to lead to impractical CMs under common real-world constraints. Specifically, we argue that in real-world settings where concept incompleteness is the norm, some leakage is often necessary for constructing accurate and intervenable CMs. To this end, we propose that there is such a thing as benign leakage and show that, by optimizing a reframing of the typical CM training objective, CMs can encourage and exploit this form of leakage without sacrificing accuracy or intervenability.

Generative models have shown remarkable progress in a variety of domains such as protein design, but such power enables the opaque generation of hazardous proteins. In this work, we introduce VFUSE (Virulent Feature Understanding with Sparse autoEncoders), a mechanistic interpretability approach that trains SAEs on diffusion-transformer activations to audit protein models for hazard-aware features. We apply VFUSE to RoseTTAFold3 and RFDiffusion3, popular open-weight models for protein folding and synthesis. We find that for certain blocks, linear probes detect hazardous designs significantly better when fit in the SAE latent space over the original model's representations: improving interpretability without sacrificing model performance. Furthermore, we identify monosemantic features from the SAE that fire only on hazardous designs at up to AUROC $0.84$ ($q < 10^{-13}$). To our knowledge this is the first SAE trained on an all-atom diffusion model and the first feature-level virulence audit of a protein design model, paving the way towards safe and interpretable protein design.

Interpretability increasingly treats groups of components, not individual units, as the basic object, and proposes to find them by clustering co-activation statistics. We ask whether such a cheap signal actually identifies an attention-head circuit. Adapting a sparse-autoencoder clustering recipe to attention heads -- but validating by causal ablation rather than reconstruction -- we cluster heads and then run a closure test: ablate the discovered community and compare per-example damage to matched-random controls. Across two dense 1B-scale models (Pythia 1B, OLMo 1B) and two input distributions, the communities pass closure. In a Mixture-of-Experts model (OLMoE-1B-7B), route-conditional clustering recovers a statistically real signal that nonetheless does not survive closure -- ablation improves loss, the wrong direction. Extending closure across training, attention-target selectivity and participation ratio decouple from function in both directions. We conclude that a cheap signal is a circuit proposal, not a confirmed circuit; closure is what separates them.

Understanding how transformer representations evolve across layers, not merely what they encode, remains an open problem in mechanistic interpretability. We recast the transformer forward pass as a discrete population trajectory through a high-dimensional representation manifold, drawing on geometric tools from computational neuroscience. Rather than probing for pre-specified features, we characterize trajectory geometry using five metrics computed directly in the ambient space: trajectory length, curvature, a semantic convergence index, layerwise cosine similarity, and representational stability. Across three model families (GPT-2, TinyLlama, Qwen2.5) and five controlled prompt families, we report four findings. First, semantically related prompts converge significantly in middle-to-late layers (peak CI 0.41--0.58, p<0.001, Mann-Whitney U), consistent with attractor-like dynamics. Second, reasoning tasks produce trajectories of greater curvature than lexical variations (0.71--0.83 rad vs. 0.27--0.31 rad), suggesting curvature encodes computational complexity. Third, ambiguous tokens exhibit trajectory bifurcation with up to 5.6x representational separation by the final layer, absent in unambiguous controls. Fourth, layerwise cosine similarity reveals a universal three-phase structure: encoding, elaboration, and output preparation, consistent across all three architectures. All four effects vanish under shuffled-layer and random-embedding controls. We release a fully open-source, model-agnostic pipeline and argue that trajectory geometry constitutes a principled, probe-free lens for mechanistic interpretability.

As Vision-Language Models are increasingly deployed in safety-critical applications, the trustworthiness of their explanations becomes crucial. Explainable AI (XAI) methods for Vision-Language Models often suffer from semantic hallucination, where attribution maps highlight prominent image regions even when prompted with incorrect text descriptions (e.g., highlighting a dog when prompted ``cat''). Although this problem is widespread, a formal mathematical analysis of XAI methods and CLIP embeddings is largely missing in the literature. We demonstrate that this phenomenon is not specific to a single architecture but is a fundamental consequence of Linear Semantic Leakage in high-dimensional embedding spaces. We propose a unified theoretical framework, Linear Semantic Attribution (LSA), which generalizes across discriminative methods. We introduce OSP, a geometric intervention that utilizes the residual property of OMP to disentangle unique semantic signals from shared concepts. We prove theoretically and demonstrate empirically that OSP minimizes hallucination by orthogonalizing the query vector against distractor concepts, rendering the attribution model blind to shared features while preserving fidelity for correct prompts. Our code is available at: https://github.com/emirhanbilgic/Orthogonal-Semantic-Projection

Fundamental investigations into how different molecular encoding methods affect molecular property prediction remain relatively limited. In this study, we extensively examined the optimal molecular encoding methods for molecular properties prediction using two prevalent structure designs: a classical neural network model (MLP) and a Transformer encoder-based model (MLP+TL). For molecular encoding methods, we investigated several types of fingerprints, including traditional topological fingerprints, substructure-based fingerprints, and string-based representations. These two models were trained on seven well-known molecular datasets to evaluate different input molecular encoding methods based on evaluation metrics. On several biologically relevant classification tasks, including toxicity, mutagenicity, and side-effect prediction, our models consistently achieved average AUC values above 0.9. Rather than relying on external post-hoc explanation methods such as the local interpretable model-agnostic explanation (LIME) or the Deep SHapley Additive exPlanations (SHAP), we leveraged the model's intrinsic attention weights as an internal interpretability signal for identifying potentially important feature. The MLP+TL model using MACCS and PubChem as input can capture chemically interpretable groups that determined the major blood-brain barrier (BBB) permeability and mutagenicity in Salmonella typhimurium. In particular, a comparison between Morphine and Heroin highlighted the role of hydroxyl-related substructures in BBB permeability prediction, which was consistently reflected in the attention weights. Overall, our findings provide practical guidance for selecting effective molecular encoding methods and contribute to the development of interpretable molecular informatics approaches for drug discovery.

World models are now built on substantially different computational substrates. Latent recurrent state-space models such as PlaNet and the Dreamer family compress observations into recurrent states; token-based models such as IRIS quantize observations into a learned codebook and predict autoregressively with a transformer; and joint-embedding predictive architectures such as I-JEPA predict in a learned latent space with no pixel decoder. The interpretability methods applied to these models, including probing, activation patching, sparse autoencoders, and surprise analysis, share a common set of primitives, yet they are re-implemented from scratch for each architecture because existing hook-and-cache tooling assumes a transformer language model with no notion of actions, environment steps, or imagined rollouts. We argue that this fragmentation reflects the tooling rather than the models, and that the shared structure of world models is captured by a small typed interface. We present WorldModelLens, an open-source interpretability substrate organized around a capability-typed adapter: every model implements four required methods (encode, transition, initial state, sample) and declares a set of optional heads (decode, reward, continue, actor, critic) through an explicit capability descriptor, so that reinforcement-learning and self-supervised world models are first-class without either imitating the other. A single hook and cache layer exposes time-indexed activations, imagination rollouts, and intervention replay over this interface, allowing each analysis to be written once.

Purpose - Quotation error refers to the inconsistency between cited information and its original source. This phenomenon leads to a series of negative impacts, such as misinterpretation of the original research, undermining the academic community's collective understanding of relevant issues, and weakening the accuracy and fairness of the citation-based academic evaluation system. Existing studies have shown that quotation error is prevalent in the academic community; moreover, manual verification of quotation error is not only labor-intensive but also inefficient. Therefore, this paper proposes the task of 'automated detection of quotation errors'. Methodology - Adopting a large language model (LLM)-based approach, this paper improves detection performance from two aspects on the basis of existing research: first, employ the fine-tuning approach for LLMs to detect quotation errors; second, incorporating full-text data of the cited literature into dataset construction, and exploring the optimal scheme for building such datasets by comparing three types of full-text integration methods. Based on this, this paper further uses the TokenSHAP tool to conduct interpretability experimental analysis on the model's prediction results. Findings - The fine-tuning approach for LLMs has improved the performance in detecting quotation errors. Among the different methods for incorporating full-text information, the approach based on using the source abstract yielded the best performance. Originality - The fine-tuning approach for large language models (LLMs) is applied to the task of automated detection of quotation errors, and interpretability analysis is conducted on the model's output results.

As deep language models (DLMs) are increasingly deployed in high-stakes domains such as healthcare, understanding their decision rationale becomes paramount for ensuring trust, safety, and accountability. However, achieving this vital level of interpretability is particularly challenging when these DLMs operate as black-box systems (e.g., via APIs), where access to internal model states (e.g., parameters, gradients) is restricted. Despite numerous efforts, existing explanation methods often fail to concurrently satisfy three key desiderata: (i) inference-time efficiency, (ii) black-box compatibility without inducing out-of-distribution behavior, and (iii) comprehensible explanations grounded in the input's linguistic structure. To address these challenges, we propose a method that explains predictions of DLMs by selecting a small, informative subset of input words. We formulate this as an amortized optimization problem, enabling efficient one-shot inference without the need for input-specific search. Our selection policy is trained via REINFORCE-style policy gradients, allowing discrete word selection in a fully gradient-free setting. To enhance interpretability and align with human linguistic intuition, we integrate graph-structured knowledge into this selection process, fostering linguistically coherent subsets that result in explanations both highly informative and cognitively meaningful to end-users. We evaluated our method on diverse DLM architectures and multiple real-world datasets. It consistently identifies word subsets with enhanced discriminative power and stronger alignment with linguistically salient cues, outperforming both conventional black-box compatible methods and gradient-based approaches that are given oracle access to the black-box model's gradients for a more challenging benchmark. Our code is available at here.

In mechanistic interpretability, attention heads are commonly elevated to role claims (e.g., "this head represents addition") when they are necessary for a behavior, encode it linearly, and recover that behavior when restored after ablation. We show this evidence is insufficient: across three 7-8B instruction-tuned models and five computation families, heads passing all three checks routinely fail to transfer the computation when their activations are patched into a different prompt under matched controls. We introduce KID (Knowing / Intent / Doing), a role-assignment lens for attention heads, and pair it with a three-stage pipeline: capability-selective screening (CSS), singular value decomposition (SVD), and activation transduction under matched controls. Our results document a preliminary role taxonomy (including prompt-trajectory stabilizers, answer-side logit-bias heads, and soft computation-pattern carriers) and show that the same-answer control (a transduction target sharing the answer string but not the requested computation) is an underused check that exposes broad state transfer masquerading as semantic specificity.

As large language models are increasingly deployed in high-stakes settings, there is a growing need for tools that audit not only model outputs but also the internal computations that produce them. Circuit analysis is a central approach in mechanistic interpretability, but it is typically target-conditioned, explaining a single prompt paired with a chosen completion. This target-conditioned setup can obscure heterogeneity across a model's continuation distribution. We introduce distribution-level unsupervised feature discovery, which clusters sampled continuations using both semantic content and sequence-level mechanistic attributions, without manually specifying target outputs. Our method represents each continuation with a semantic embedding and a prefix-to-continuation attribution signature, then optimizes a rate-distortion objective that trades off semantic coherence, mechanistic consistency, and cluster granularity. Across clustering and steering analyses, the discovered clusters expose continuation modes that single-view baselines miss and provide interventional evidence that cluster signatures correspond to actionable mechanistic factors. Overall, our approach complements circuit analysis and behavioral evaluation by providing a scalable audit of the mechanisms underlying a model's continuation distribution.

Recent advances in generative AI, especially powerful Large Language Models (LLMs) and Large Reasoning Models (LRMs), raise concerns over the interpretability, safety and sustainability of these large and opaque AI models. The power of such architectures is derived not only from the scalability of deep neural networks, but also massively parallel hardware such as GPU clusters. The diffuse nature of deep neural networks gives them great function-approximation capability when provided with sufficient training data but imposes a cost in interpretability and computational efficiency. Observing that localised machine learning (ML) models tend to be more interpretable and computationally efficient than deep neural networks on small datasets, we reason by analogy that similar advantages may apply to specific localised hardware ML architectures. We argue that localised architectures with lower bandwidth but higher expressivity per node have the potential to be fundamentally more interpretable than deep neural networks running on GPU clusters while remaining competitive for smaller datasets. We then evaluate the suitability of various hardware ML paradigms for implementing such localised architectures and evaluate their per-node expressivity, energy efficiency and practical maturity of the technology required.

A central goal of mechanistic interpretability is to identify which internal components causally drive a language model's behavior. Because these importance estimates serve as the evidence for identifying circuits, systematic errors can lead to the misidentification of the underlying mechanisms. While activation patching provides a gold-standard causal metric, its computational cost is prohibitive at scale. Practitioners instead rely on attribution patching, a gradient-based, first-order approximation whose reliability remains poorly understood. In this work, we characterize the source of this unreliability, demonstrating that the dominant error stems from the non-linearities in the downstream network rather than local curvature at the patched component. This insight yields three practical tools: (i) a reliability score to detect untrustworthy estimates, (ii) error bounds quantifying potential attribution mis-specifications, and (iii) a Hessian-vector-product (HVP) correction that eliminates the leading-order error with only one additional backward pass. In evaluations across five model families (124M-9B parameters) and both random-token and naturalistic (name-swap) perturbations, HVP is the only second-order correction feasible at larger scale, where standard baselines like Integrated Gradients become computationally prohibitive. In comparative experiments, a multi-step HVP variant matches or exceeds the accuracy of Integrated Gradients at significantly lower compute, outperforming prior second-order baselines. These improvements lead to higher-fidelity circuit recovery on standard benchmarks and support a Screen-Flag-Fix workflow that targets computational effort only toward the components flagged as unreliable.

Understanding nonlinear feature interactions is crucial in science and engineering, yet standard multilayer perceptrons (MLPs) often capture such interactions only implicitly, leading to entangled representations that can impair robustness and interpretability. We investigate product-unit residual networks (PURe) that integrate multiplicative product units with residual connections to explicitly model cross-feature couplings while stabilizing optimization. We conduct a systematic evaluation on an interaction-driven synthetic benchmark and two real-world datasets, assessing predictive accuracy, robustness to Gaussian feature noise, and performance under limited training data, and we compare real- and complex-valued variants under a matched parameter budget. Beyond accuracy, SHapley Additive exPlanations (SHAP)-based interaction analyses show that PURe learns more concentrated and structurally coherent interaction patterns than MLP baselines. Overall, PURe achieves competitive or improved performance, better robustness and sample efficiency in low-data regimes, and enhanced interaction-level interpretability.

Qualitative product feedback can reveal nuanced user experiences, but its implicit sentiment is difficult to measure. This paper presents a scalable and interpretable framework that uses large language models (LLMs) to quantify product desirability from such data. Using two Product Desirability Toolkit (PDT) datasets from ZORQ and CARMA comprising 106 respondent term groupings with gold-standard human annotation, zero-shot continuous numerical sentiment scoring and categorical sentiment classification are evaluated without relying on explicit review scores. Across the datasets, LLMs generated numerical sentiment scores directly from qualitative responses and closely matched expert labels, achieving Pearson correlations up to 0.97 and classification accuracy up to 94%. LLMs maintained robustness even when handling data presented in multiple forms and consistently expressed high confidence. In contrast, lexicon-based and transformer baselines did not produce statistically significant results. Among the models tested, GPT-4o-mini achieved performance comparable to larger models at 94% lower cost, supporting scalable deployment. The framework also incorporates model confidence ratings and human-readable rationale explanations (xAI), improving interpretability, transparency, and trust while supporting practical use in product satisfaction assessment. In general, using the PDT tool as a survey method along with a cost efficient LLM for sentiment analysis has the potential to provide for product evaluation with results that are rich in terms of sentiment scores (both numerical and classified sentiment) and in terms of the high-level user impressions of the product that can be used to identify ideas for product development and improvement, as well as marketing ideas for target audiences.

Despite high accuracy, Vision Transformer (ViT) predictions can be driven by spurious cues, raising the need to understand their inner workings before safe deployment. Sparse autoencoders (SAEs) provide a promising lens for decomposing model representations into human-interpretable concepts, yet adapting SAE-based interpretation to ViTs remains challenging due to limited control over concept coverage and subjective, non-scalable feature interpretation. To fill the gaps, motivated by neuroscience-inspired principles, we propose ViSAE, a mechanistic interpretability toolbox for understanding ViT inner workings through concept circuits. ViSAE consists of three components: (1) A probing suite with 64K images and a 16K visually grounded concept vocabulary, improving concept coverage efficiency by 20x over ImageNet and interpretation accuracy by 28.7% over existing concept sets. (2) Top-down concept reading and Bottom-up circuit tracing algorithms that automatically recover ViT inner workings via concept circuits. (3) Applications for auditing and steering ViT behavior. Through concept editing, ViSAE improves the worst-group accuracy on WaterBirds by 48.2%, outperforming existing methods by 23.8%. Our data and code: https://github.com/deep-real/ViSAE.

Sparse Autoencoders (SAEs) are widely used for mechanistic interpretability in large language models, yet their formulation assigns each latent feature a single decoder direction, implicitly assuming features to be one-dimensional. We show that this assumption mismatches with the multi-dimensional structure of model features, provably inducing feature splitting through two distinct mechanisms. Geometrically, reconstructing a feature of intrinsic dimension $d_i \ge 2$ to error $\varepsilon$ with single-direction decoders forces a number of atoms that is exponential in $d_i$. From an end-to-end optimization perspective, this splitting is not merely possible but actively preferred. We prove that there exists a continuous path from the true $d_i$-dimensional basis to a strictly lower risk of the $\ell_1$-regularized SAE objective, whose descent directions drive any trained dictionary into that exponential regime. A single coherent feature is therefore fragmented across many near-collinear latents, producing spurious multiplicity and obscuring the intrinsic geometry. Motivated by this, we introduce Subspace-Aware Sparse Autoencoders (SASA), which replace single-vector decoders with learned decoder subspaces, enforce block sparsity via Top-$s$ group gating, and adapt each group's effective rank with a nuclear-norm regularizer. We then show that once the block size satisfies $r \ge d_i$, a single group not only can represent the entire feature slice but is the global minimizer of the SASA objective. This consolidation yields a sample complexity polynomial in $d_i$ rather than exponential -- a decisive advantage given that every training activation costs an LLM forward pass. Empirically, on GPT-2 and Mistral-7B, SASA reduces feature splitting and absorption, improves monosemanticity and interpretability, and matches or exceeds standard SAEs while training on roughly half the token budget.

Recent advances in interpretability suggest that large language models (LLMs) implicitly encode signals in their generated text that enable self-recognition of their outputs. We demonstrate that this capability is reliable, even in low-entropy scenarios, and that it can be amplified through targeted intervention. By steering the internal residual stream during generation with a random sparse vector, we create a detectable fingerprint that enables attribution of a given text to a specific LLM. This signal is recoverable from the activations of an LLM used as a detector, achieving over 98% accuracy across multiple detection settings while preserving the quality of generated text. As AI-generated content proliferates, this approach offers a practical alternative to traditional detectors by leveraging the model's natural representation structure for attribution rather than embedding a signal externally. Our contributions include: (i) establishing reliable self-recognition capabilities in LLMs, (ii) a simple steering mechanism enabling multi-LLM identification with no quality degradation, (iii) demonstrating that activation spaces contain exploitable structure for encoding signals without semantic interference.

Neural network (NN)-based nonlinear causal discovery methods recover DAG structure but leave each causal mechanism as a black box. Waxman et al. argued that extracting causal mechanisms from NN weights is ill-posed. We propose EML-CD, a framework that integrates the EML operator (capable of composing elementary functions from a single binary operator) into causal structure learning, with interpretable mechanism recovery as the primary objective. EML-CD represents each edge mechanism as a gated EML binary tree and automatically discovers closed-form causal equations. Analytical Jacobians can be directly computed from the output equations, enabling quantitative understanding of causal effects. On real data (Sachs protein signaling, d=11), EML-CD achieves SHD=11.2 +/- 0.4 (5-seed mean; baselines are single deterministic runs), on par with PC/GES within seed variance and below CAM, while attaching closed-form equations to each detected edge (precision 0.756, recall 0.365). In a controlled bivariate test with known mechanisms, EML-CD recovers 10 of 11 elementary function families faithfully (held-out shape correlation >= 0.96; only high-frequency sine is partial). On a symbolic synthetic benchmark, EML-CD attains a substantially lower and more stable held-out mechanism f-MSE than a fixed SINDy dictionary (mean 3.67 vs. 7644, the latter inflated by catastrophic extrapolation on one seed), although its structure recovery (SHD 14.0) only matches the dictionary and stays below specialized optimizers; on the Causal Chambers light-tunnel subset, a depth-2 model improves F1 over linear OLS-BIC (0.444 vs. 0.273).

What would it mean to have a scientific understanding of AI? Models are not static objects: they are snapshots of time-evolving processes shaped by data, objectives, architectures, and optimization dynamics. Yet much of AI research treats models as fixed artifacts, analyzing behaviors after training rather than asking why they emerge. This position paper argues that a science of AI must move beyond post-hoc fixes and study the training dynamics that produce model behavior. Such a science should support progressively stronger forms of understanding: predicting outcomes from early training signals, intervening when trajectories go wrong, and ultimately designing training procedures that more reliably produce desired properties. Scaling laws have made prediction routine for loss; the challenge is extending this success to capabilities, biases, robustness, and safety-relevant behaviors. We articulate requirements for such theories grounded in the history and philosophy of science, examine progress in mechanistic interpretability, fairness, memorization, and simplicity bias, and identify concrete open problems.

Large Language Models (LLMs) are increasingly deployed across diverse applications, raising critical questions for governance, accountability, and data provenance. Understanding which training data most influenced a model's output remains a fundamental open problem. We address this challenge through training data attribution (TDA) for auto-regressive LLMs by expanding upon the inverse formulation: How would training data be affected if the model had seen the generated output during training? Our method perturbs the base model using bidirectional gradient optimization (gradient ascent and descent) on a generated text sample and measures the resulting change in loss across training samples. Our framework supports attribution at arbitrary data granularity, enabling both factual and stylistic attribution. We evaluate our method against baselines on pretrained models with known datasets, and show that it outperforms previous work on influence metrics, thereby enhancing model interpretability, an essential requirement for accountable AI systems.

Mechanical ventilation for Acute Respiratory Distress Syndrome (ARDS) requires balancing competing physiological goals, including oxygenation, lung protection, and acid-base homeostasis. However, current data-driven methods, especially those imitating retrospective Electronic Health Records (EHR), often suffer from imitation bias. They may capture superficial correlations from inconsistent clinical demonstrations, such as associating passive ventilator settings with survival because such settings are common in stable patients, and thus fail to generalize to volatile or out-of-distribution phenotypes. Standard Reinforcement Learning (RL) methods also struggle with the adversarial trade-offs of critical care and often produce opaque policies with limited clinical interpretability. To address these limitations, we introduce VentAgent, a hierarchical framework in which Large Language Models (LLMs) act as transparent arbitrators for mechanical ventilation. We reformulate ventilation control as a dynamic Multi-Objective Arbitration process rather than single-objective optimization. VentAgent decomposes decision-making into three interpretable stages: Perception, Planning, and Orchestration. By leveraging the semantic reasoning capabilities of LLMs, it synthesizes strategies from heterogeneous experts and resolves conflicting clinical priorities through an explicit coordination mechanism. Evaluations on a high-fidelity physiological simulator show that VentAgent outperforms state-of-the-art RL and classical control baselines. Moreover, it converts control decisions into human-readable reasoning chains, offering a safer, more interpretable, and adaptable paradigm for critical care automation.

Quantization is a standard path to deploying large language models, and quantized models are typically judged acceptable when perplexity or downstream accuracy remains close to the full-precision original. But behavioral parity need not imply feature fidelity: the sparse-autoencoder (SAE) features used to interpret a full-precision model may change after weight rounding. We test this directly by using a frozen SAE as a fixed measurement basis, encoding full-precision and round-to-nearest (RTN) quantized activations on identical tokens, and measuring per-feature survival by Pearson correlation across bit-widths from INT8 to INT4 on Pythia-70M and Gemma-2-2B. Our central finding is that perplexity can miss feature damage: on Gemma-2-2B, INT7 improves perplexity while degrading 18.7% of active SAE features, and under sliding-window evaluation INT6 also improves perplexity while only 51.3% of active features survive. Feature survival is graded rather than cliff-like, with 62.4% of active Pythia features and 51.3% of active Gemma features surviving at INT6; most non-surviving features are blurred rather than fully damaged. Survival is also predictable from full-precision feature statistics alone, with cross-validated AUC 0.92--0.97 and peak activation as the strongest marginal predictor. Finally, RTN quantization and matched-perplexity magnitude pruning damage strongly overlapping feature sets, with Jaccard overlap 0.79--0.86 and damage-score Spearman correlation 0.98. These results show that behavioral metrics alone are insufficient evidence that full-precision interpretability findings transfer to quantized models, motivating feature-level audits of compression.

Linear probing of large language model (LLM) hidden states is widely used to claim that models learn distinct representations for different reasoning types. We test this by probing Qwen3-14B on three benchmarks spanning the classical trichotomy: LogiQA 2.0 (deductive), ARC-Challenge (inductive), and $α$NLI (abductive). At layer 32 of 40, linear probes achieve 100% cross-validated accuracy with well-separated geometry (intrinsic dimensionalities: 20.6, 28.5, 33.6; convex hull contamination $\leq$1.5%). However, this separation is entirely driven by format confounds. Residualizing source identity, option count, and response length reduces accuracy to chance. Trace-anchor similarity indicates largely shared reasoning across tasks (42.5% agreement vs.\ 33.3% chance), and causal steering with random controls ($n=20$) shows no functional link between geometry and reasoning mode ($p=0.286$). Thus, high probe accuracy reflects task format rather than computational structure, motivating routine format deconfounding in mechanistic interpretability.

Deep neural networks learn representations where individual features often lack interpretable meaning; a single neuron may activate for scattered, unrelated inputs. We introduce coherence, a geometric property inspired by neural coding in the brain, where neurons like grid cells and head direction cells respond to contiguous regions of state space. A non-negative matrix is coherent if each row (sample) attends to geometrically clustered columns (features) and vice versa, and in addition every sample is well described by some feature and every feature is needed by some sample. We prove that coherent matrices induce a bounded interleaving between the Vietoris-Rips filtrations of samples and features, guaranteeing that both spaces share compatible topological structure. This geometric constraint facilitates interpretability. For example, if data lies on a circle, coherent features must tile that circle into contiguous arcs. We introduce Coh, a differentiable objective function based on Fréchet variance that enforces coherence during training. Unlike sparsity, which bounds how many samples a feature activates on, coherence bounds which samples, requiring geometric connectivity rather than only rarity. This yields not just interpretable features but an interpretable feature space. We validate Coh in an auto-encoder using synthetic and rotated MNIST datasets and in a token embedding of BERT using language data.

Dictionary learning with sparse autoencoders (SAEs) produces overcomplete bases from neural network activations that are often interpretable and reduces polysemanticity. However, features from SAEs vary substantially across random seeds -- a problem known as instability. Archetypal SAEs (Fel et al., 2025) were proposed as a general dictionary-learning intervention for more reliable concept extraction, and report more stable dictionaries at the end of training. We demonstrate that the stability claimed by archetypal SAEs is a result of setting identical initialization across multiple runs. Through our analyses, we attempt to clarify two distinct notions in mechanistic interpretability that may be ambiguously used: stability is agreement between two independently trained models, whereas stabilization is the convergence of independently initialized runs toward a common solution. This distinction is critical for mechanistic interpretability of natural language processing (NLP), where feature stability is increasingly used as evidence that SAE features are reusable units of analysis. Experiments from archetypal SAEs share a deterministic k-means decoder initialization, setting inter-run dictionary distance to zero before training begins. When this initialization is removed, the archetypal constraint provides no stabilization advantage in our setting. We further identify a preprocessing-dependent cosine geometry issue that complicates interpretation of endpoint stability metrics. Overall, our study supports the value of studying SAEs within the larger dictionary-learning tradition while showing that stability claims require trajectory diagnostics and initialization ablations.

Mechanistic interpretability often assumes that probes identifying a representational signature also identify the circuit executing the corresponding computation. We show that this assumption can fail systematically in Mamba-2. Studying the state sink (disproportionate Delta-gate activation on boundary tokens, analogous to the attention sink), we find that single-bucket probes recover only a small execution layer while missing a much larger detection layer with the same representational signature. In Mamba-2, the state sink decomposes into two functional head sets. Single-bucket BOS-specialist heads (about 5% of heads at 2.7B) causally support both BOS-context and newline-target predictions across model scales and corpora. Dual heads (27-35% of heads, recovered by multi-class aggregation of the same probe) show stronger BOS-newline representational similarity but substantially weaker causal effects under ablation. Representational similarity does not imply functional equivalence. This distinction matters for downstream behaviour: ablating BOS-specialist heads collapses RULER NIAH retrieval accuracy from 1.00 to 0.00 at 1024 context length in both Mamba-1 2.8B and Mamba-2 2.7B, while size-matched complements preserve baseline performance. A random channel-bucketing control rules out substrate granularity alone, implicating Mamba-2's head-shared Delta projection. Probe-derived specialty can identify execution circuits; at coarse granularity the same probe also recovers detection circuits, and separating them requires class-conditional ablation rather than class-conditional cosine.

Modern Machine Learning (ML) and Artificial Intelligence (AI) models, especially large language models (LLMs), are increasingly used to generate scientific hypotheses and mechanistic explanations from observational data. This position paper argues that in the high-dimensional proxy regimes where modern ML excels, mechanistic learning is generically underdetermined: many incompatible mechanisms induce essentially the same observational relationships on the support of the data, so predictive success and coherent explanations are insufficient evidence of mechanism discovery. This underdetermination becomes uniquely hazardous with large language models (LLMs), which tend to collapse large equivalence classes of explanations into a single fluent narrative. This paper proposes concrete standards for ``mechanistic ML,'' and argues these norms are necessary if LLM-centered workflows are to support science rather than merely simulate it.

Deep neural networks (DNNs) are widely used, but interpreting what they actually learn remains difficult. A major obstacle is that individual neurons often encode multiple unrelated concepts, obscuring the decision process of the network. While prior work, such as sparse autoencoders, can separate these mixed signals into more meaningful, "monosemantic" features, this typically requires altering the model in ways that can degrade downstream performance. To overcome this, we introduce ELUDe (explicit, lossless, unsupervised disentanglement), a method for improving the interpretability of DNNs while preserving their functional equivalence. ELUDe breaks latent representations into clear, inspectable sub-units that behave like interpretable features, while guaranteeing that the model's outputs remain exactly the same. It requires no explicit training, no labels, and can be applied to pretrained models. ELUDe works by reorganizing how information flows between layers, re-routing concept-specific contributions while preserving the original computation by construction. Across several vision models, including DINOv2 and supervised ViT-B/16, ELUDe improves interpretability, keeps downstream accuracy unchanged, runs efficiently, and supports practical uses such as steering model representations. In short, ELUDe offers interpretability (almost) without a tradeoff: clearer, scalable, and actionable model insights with no loss in performance.

Transformer-based architectures have significantly advanced the generation of complex symbolic sequences, yet a significant gap remains in achieving fine-grained, interpretable control over discrete signal attributes. This paper investigates the mechanistic interpretability of the Multitrack Music Transformer (MMT) and proposes a framework for deterministic attribute modulation without retraining to bridge this gap via inference-time activation steering. Utilizing the Difference-in-Means (DiffMean) methodology, we isolate latent directions for signal attributes, specifically Pitch and Duration, within the residual stream. We validate the Linear Representation Hypothesis in this domain, achieving high correlation between steering magnitude and attribute shift. To address the inherent feature entanglement in multi-attribute steering, we introduce a Dual Steering framework utilizing Gram-Schmidt Orthogonalization. Experimental results demonstrate that this geometric decoupling reduces conceptual interference and signal degradation compared to naive vector addition, enabling independent deterministic control even against strong autoregressive conditioning.

Advances in machine learning and computational power have unlocked the predictive potential of the human genome, yet biologists now demand that these models also elucidate the underlying biological mechanisms. While interpretable machine learning (IML) techniques have been increasingly applied to bridge this gap, there has been a pervasive reliance on anecdotal validation: the vast majority of research relies on a single IML method and reports only isolated successful instances. Through a benchmarking study on transcription factor binding, we demonstrate the risks of current practices. We show that different IML methods can often (1) yield contradictory explanations for the same predictions, (2) fail to localize known regulatory motifs, and (3) fail to faithfully reflect the model's internal decision process. In light of this, we argue for a validation framework analogous to clinical trials: just as trials require rigorous design and adverse-event reporting, genomic interpretability must move beyond cherry-picked plausibility toward systematic assessment of consistency, faithfulness, and biological validity. To facilitate this, we propose a tiered framework to guide rigorous evaluation and reporting of genomic IML methods.

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.

Recently, thanks to the advent of Multimodal-LLMs, deepfake detectors are striving not only to be generalizable but also interpretable. We propose that these two challenges can effectively be tackled jointly, since describable artifacts typically generalize better, opening the possibility to use language as a regularization mechanism. Since deepfake detection generally suffers from overfitting to low-level domain-specific artifacts, our intuition is that an LLM that has been pretrained on language would prefer high-level artifacts that can be described better. This way, we can use high-level features where possible, while training the model to use low-level features where necessary. We utilize a dual-encoder architecture, pairing a frozen specialist detector with a LoRA-tuned MLLM encoder, and a two-stage training curriculum: first, a binary alignment phase demonstrates that the intrinsic capability of MLLMs can effectively combine features to mitigate overfitting to dataset-specific artifacts. To further bolster generalization and achieve interpretability, we employ a reinforcement learning stage that encourages the model to generate descriptive reasoning before classifying, using only binary labels. By rewarding this "explain-then-classify" behavior, we explicitly incentivize the model to prioritize high-level, robust features. Crucially, this process yields both interpretable descriptions and a further boost in cross-dataset performance, even when reasoning chains are omitted at inference. Extensive experiments on benchmark datasets validate our approach, outperforming state-of-the-art methods by a large margin.

Sparse Autoencoders (SAEs) have been seen as a promising avenue for exploring the internals of Large Language Models (LLMs) and for steering model output generation. When AxBench - a model steering benchmark - was introduced in Wu et al. (2025), SAEs did not seem to live up to their original hype due to poor steering performance relative to a set of simple baselines. This work serves as a partial rebuttal for Sparse Autoencoders and suggests that the results of Wu et al. (2025) did not do them full justice. We find that Sparse Autoencoders can, in fact, perform close to on par with the reference LoRA performance on the AxBench benchmark, when features are selected and labelled with our supervised pipeline. We also find that our pipeline selects features that are surprisingly causal of their identified labels when using only its interpretability-based components. Lastly, we present evidence that high sparsity (low l0) may not be crucial for successful steering based on interpretability, which is in contrast to the earlier findings in Wang et al. (2025).

We consider establishing the interpretability theory of deep learning through constructing a corresponding relationship between the renormalization group (RG) method in statistical physics and the training process of deep neural networks (DNNs). We have proved the constructed relationship using the one-dimensional Ising model as the input data. In this paper we generalize our results to the case of continuous input data, which is a necessary preparation for applying the corresponding framework to real-world data. To be representative, we consider a class of data distribution in the exponential family. We prove that when the parameters of fully connected (FC) DNNs achieve their optimal value after training, the characteristic parameters of the feature layer output of DNNs are equal to the fixed points of the characteristic parameters of input data under RG method for continuous fields. This conclusion shows that the training process of DNNs is equivalent to RG calculation on this kind of data and therefore the network can extract main features from the input data just like RG. Also, the equivalence further validates the correspondence framework we have established, providing an explanation for the outstanding performance of DNNs on real-world data.

Machine learning is increasingly used in mathematical discovery, but in mathematics the desired output is often not a prediction itself, but an explicit construction that can be checked independently. We study this setting through the zeta map on Dyck paths, a classical bijection in the combinatorics of the q,t-Catalan numbers. We train a deliberately small one-layer, one-head encoder-decoder transformer on this map and analyze its learned computation using mechanistic interpretability tools, including decoder cross-attention analysis, linear probing, and causal intervention. The analysis reveals a level-based mechanism: encoder representations make path levels linearly accessible, while the decoder selects and traverses input positions in a structured way. Translating these signals into combinatorics leads to the scaffolding map, an explicit peak-centered traversal algorithm for Dyck paths. We prove that this algorithm agrees with the zeta map, modulo a reversal convention in the labeling. This gives a controlled example of AI-assisted mathematical discovery in which mechanistic interpretability turns model behavior into a precise, human-verifiable combinatorial algorithm.

Clustering is an unsupervised technique for grouping data points by similarity. While explainability methods exist for supervised machine learning, they are not directly applicable to clustering, making it challenging to understand cluster assignments. This interpretability gap is particularly evident in the popular density-based method DBSCAN, which assigns points as inliers (cluster members in dense regions) or outliers (noise points in sparse regions). DBSCAN does not provide insight into why a particular point receives its assignment or whether its assignment is robust to small changes in the data. To address the lack of explainability, we introduce ExDBSCAN, a density-aware, post-hoc explanation method. ExDBSCAN offers actionable counterfactual explanations, with theoretical guarantees for validity. It generates multiple counterfactuals using a density connected weighted graph, adopting a physics-inspired model that repels counterfactual candidates from one another (diversity), while pulling them toward the instance to explain (proximity). Empirical evaluation on 30 tabular datasets comparing against four baselines shows that ExDBSCAN outperforms all baselines while attaining perfect validity and retrieving diverse, proximal counterfactuals.

Human tactile perception of materials relies on complex multisensory touch cues, yet the relationship between low-level tactile signals and perceptual representations remains poorly understood. This knowledge gap hinders the integration of touch in digital environments and the development of robots capable of human-like tactile perception. Here, we present an interpretable computational framework for modeling human material perception and recognition using multisensory touch data. Our framework comprises three interconnected models: Model 1 maps finger-surface interaction features to psychophysical sensory attributes, Model 2 classifies materials based on these perceptual representations, and Model 3 directly classifies materials from tactile features. The results showed that combining information from pressing, static contact, and sliding interactions improves prediction accuracy, and that thermal cues are particularly informative for both perceptual modeling and material classification. These findings highlight the importance of thermal and compliance cues, which remain underrepresented in current robotic fingers and haptic displays. Incorporating such cues may enhance artificial systems' ability to approximate human material perception and guide the design of more perceptually grounded haptic interfaces.

We demonstrate that sparse autoencoders can extract interpretable features from Claude 3 Sonnet, a production-scale language model, addressing the open question of whether dictionary learning methods scale beyond small transformers. We trained sparse autoencoders with up to 34 million features on the model's middle layer residual stream, using scaling laws to guide hyperparameter selection. The resulting features are multilingual and multimodal (generalizing to images despite text-only training), respond to both concrete instances and abstract discussions of concepts, and can be used to steer model behavior in ways consistent with their interpretations. We find features corresponding to famous entities and locations, as well as more abstract concepts like sarcasm or errors in code. We also identify features relevant to ways in which language models might cause harm--including features representing deception, power-seeking, sycophancy, and bias--and show that these causally influence model outputs when manipulated. Additionally, we conduct analyses of feature interpretability, geometry, and computational function. However, significant limitations remain: our suite of features is incomplete, and we lack rigorous methods for evaluating whether our features faithfully capture model computations.

Image quality in modern imaging systems emerges from the coupled effects of the sensor, optics, and computational reconstruction. Ultra-thin metalenses offer a path toward substantial miniaturization of optical modules, but practical designs often exhibit pronounced chromatic and field-dependent aberrations that necessitate computational reconstruction. In current metalens pipelines, reconstruction models are commonly trained and selected using distortion-based fidelity objectives, such as PSNR, yet these proxies can be weakly correlated with human preference and downstream utility, reflecting the well-known perception--distortion trade-off. We introduce MetaRanker, a human-in-the-loop active ranking framework that formalizes metalens image quality in terms of semantic interpretability, defined as the degree to which humans can reliably recognize objects and structures in the presence of optical artifacts. MetaRanker combines a probabilistic preference model with uncertainty-aware query selection, and leverages vision--language models to provide lightweight semantic priors. Importantly, these priors are used only to guide the sampling of informative comparisons; human judgments remain the primary supervision signal throughout. Across real-world and synthetic metalens datasets with distinct degradation profiles, MetaRanker produces rankings that align most closely with human assessments, while reducing the number of pairwise annotations required by approximately 80% relative to exhaustive pairwise evaluation. Finally, we show that standard image quality assessment metrics exhibit limited alignment with human interpretability in the metalens domain, positioning MetaRanker as a practical step toward perceptually grounded metalens evaluation and co-design.

A linear probe can decode a representation almost perfectly and yet be completely irrelevant to how the model uses it. On calendar-date duration reasoning in language models, a $\sin$/$\cos$ probe recovers day-of-year from a layer's activations, yet ablating its direction has no effect on the model's answers -- while ablating a four-dimensional subspace found by Distributed Alignment Search (DAS) at the same layer collapses performance entirely. We measure the angle between these two subspaces -- the \emph{readout-mediator angle} -- and find it indistinguishable from the angle between two random subspaces (the Haar-uniform null), meaning the probe has learned a direction orthogonal to the model's actual computation. Reverse-engineering the circuit reveals why: attention heads route month-grained context through learned QK offsets at ${\pm}30$ and ${\pm}61$ days, and MLPs then convert \emph{when} (absolute date) into \emph{how long} (duration) -- all downstream of the causal subspace the probe never touches. Sparse-autoencoder decomposition confirms the split: probe-aligned and DAS-aligned features encode semantically disjoint concepts with negligible causal overlap. The dissociation replicates across four scales ($1.5$-$9\,$B) and two model families, with preliminary evidence on two further domains (spatial displacement, symbolic arithmetic), suggesting that readout-mediator orthogonality is a general failure mode of probe-based interpretability. This directly undermines proposals to deploy probes as runtime safety monitors: the probe can report high confidence on a direction the model has silently abandoned.

LLMs have advanced text classification, yet existing paradigms face a trade-off: supervised (label only) fine-tuning is scalable but offers limited reasoning on complex text and lacks broader model transparency, while discrete prompt optimization offers human-readable instructions but struggles with performance and scalability. We introduce eXTC (eXplainable Text Classifier) with three progressive stages: (1) learning a Standard Operating Procedure (SOP, or rulebook) in natural language via a new Structured Prompt Optimization algorithm; (2) SOP-grounded reasoning distillation from a large teacher LLM into a compact LM; and (3) expanding reasoning capabilities beyond the initial SOP via reinforcement learning. This design enables eXTC to provide (i) fast inference via a compact LM, with (ii) inference-time local reasoning traces, alongside a global, modular explanation of its learned domain rules, while (iii) significantly outperforming existing paradigms across diverse benchmarks in both classification performance and explanation quality, with stage-by-stage gains.

Prediction markets such as Polymarket aggregate crowd beliefs into real-time probability estimates, and the comments traders post beneath each market contain rich directional stance signals that prices alone cannot capture. This work introduces the first stance detection study applied to prediction market commentary, a domain characterized by extreme brevity, trader- specific vernacular, and severe class imbalance (only 8.7% of comments oppose the market outcome). RoBERTa-base is fine-tuned across a 4 x 3 ablation: four input configurations ({2- class, 3-class} x {with/without market context}) and three augmentation conditions (baseline, 50% synthetic, 100% synthetic). Synthetic minority-class samples are generated via LLM-driven Pro -> Anti counterfactual flips using the Anthropic API. Results show that (1) market context is the single most impactful factor, raising 3-class Anti recall from 0.10 to 0.45; (2) counterfactual augmentation is conditionally effective, improving Anti F1 in weak configurations (0.10 -> 0.24) while degrading strong ones (2-class-ctx macro F1: 0.68 -> 0.50 at full dose); and (3) 50% augmentation is the optimal dose, with 100% consistently hurting performance. Attention-based interpretability analysis provides mechanistic support for all three findings.

Hybrid interpretable models combine a transparent component with a black-box model by assigning some examples to the former and deferring the rest to the latter. While this design enables flexible tradeoffs between accuracy and interpretability, it also raises a distinct procedural fairness concern: some demographic groups may systematically receive interpretable decisions, while others are disproportionately routed to a black box. We formalize this issue as Interpretability Coverage Disparity (ICD), a demographic-parity-style measure applied to the routing decision of hybrid interpretable models. Using tools from predictive multiplicity, we study ICD across four hybrid interpretable learning methods, three standard fairness benchmark datasets, and multiple sensitive attributes. Our experiments reveal substantial ICD in intermediate transparency regimes, where both the interpretable and black-box components are actively used. We further show that simple coverage-disparity constraints can significantly reduce ICD in exact hybrid learning methods, with marginal impact on accuracy and sparsity. In several settings, ICD mitigation also improves standard algorithmic fairness metrics. These results show that hybrid interpretable models should be audited not only for predictive fairness, but also for how they allocate interpretability across individuals and groups.

LLMs often default to equal treatment across cultural groups, even though context warrants differentiation: this is a lack of difference awareness. Using mechanistic interpretability and a factorial design on the N4 cultural appropriation benchmark from Wang et al. (2025), we identify 2-3 mid-layer attention heads per model that contribute causally to cultural binding across eight models (base and instruct versions of four architectures). Cultural binding is the process of associating a cultural item with its related identity. Knockout of the identity-to-item edges on these heads lowers the binding strength by 9-23%. The identified heads transfer from instruct to base models, suggesting that cultural binding is created during pre-training. An $α$-scaling shows a graded dose-response. Moderate amplification steering at generation ($α= 2-3$) increases cultural differentiation accuracy by 1-3 pp while leaving reasoning on culturally neutral questions mostly intact. A knowledge probing task shows that models know 3-6 times more than they act upon, indicating that the bottleneck lies in routing and not knowledge.

Understanding how LLMs reason is hindered by a practical asymmetry: while their generated outputs are observable, the underlying reasoning patterns remain opaque. Relying on single probes, such as Mutual Information Peak (MIP) or Deep-Thinking Ratio (DTR), risks underestimating the genuine inferential structure. To response this deficiency, we present an Integrated, cross-Architecture Reasoning (IAR) framework, designed to provide a unified approach to LLM reasoning interpretability. Specifically, we first propose to use bandwidth-calibrated MIP coupled with Tukey IQR peak-detection to isolate reasoning-crucial tokens at the output layer. Second, we performed an overlap analysis between MIP-picked tokens and DTR-deep tokens to trace the cross-layer trajectories of those tokens. This also discloses whether reasoning-crucial tokens are computation-intensive as well, further facilitating to understand how reasoning patterns evolve across model layers. Finally, we apply a Jaccard stability metric over multi-domain problems to verify if the MIP-identified tokens are reasoning quality-guaranteed. Extensive experiments on six models across four domains (mathematics, code, logic, and common sense) demonstrate IAR's generalizable interpretation capabilities across architectures. Our code is available at https://github.com/LeonardoMatthew/IAR.

When a language model sees a document contradicting its training knowledge, it must choose: follow the document or trust itself. Prior work proved this choice depends on how well-known the fact is. We ask: does the model's chain-of-thought (CoT) reasoning faithfully report this mechanism? We introduce introspective faithfulness and test it across 200 questions, 8 models, and 4 prompt conditions. We find CoT reasoning is highly stable across opposite decisions: flip pairs retain 96% of same-answer similarity (d=0.34; confirmed by ROUGE-L, d=0.45). Yet self-rated confidence carries a faint genuine signal: for obscure facts where entity fame is uninformative, confidence still predicts decisions (p<0.001) and tracks item-level knowledge (r=0.134). GPT-4o is the only model with statistically reliable reasoning-decision coupling. Claude Sonnet 4.6 shows the widest confidence range (SD=1.39) but near-zero pooled correlation because the confidence-decision relationship reverses between conditions; a temperature ablation confirms this is model-specific. Internal thinking tokens show greater decision-sensitivity than user-facing CoT (p=0.033). CoT decomposes into a decision-invariant knowledge display (~96%) and a thin confidence layer with weak but real signal. For monitoring: read confidence, not the argument.

Soft prompt tuning is a parameter-efficient method for adapting LLMs to specific tasks, but suffers from a lack of interpretability. Building on recent work on interpreting soft prompts (Ramati et al., 2024), we explore how training a dedicated soft prompt to natural language translation model can yield higher translation quality. In particular, in both quantitative and qualitative comparisons on multiple Datasets of Datasets (DoDs), we demonstrate that our translator produces fluent, accurate verbalizations that outperforms existing training-free methods like InSPEcT. In addition to advancing interpretability, our work suggests a promising downstream application: soft prompts optimized on small, open-source models can be translated into portable text prompts that, when deployed on larger closed-API models, exceed the performance of the original soft prompt and, in some cases, even few-shot learning.

Model internals encode rich information about how a large language model (LLM) processes its training data; however, post-training data engineering largely relies on external signals and ignores rich intrinsic signals lying in model internals. We propose SAERL, a data engineering framework for LLM reinforcement learning (RL). It models three intrinsic data properties: diversity, difficulty, and quality, using model internals extracted with Sparse Autoencoder (SAE), an advanced mechanistic interpretability tool. Each property grounds a concrete data engineering operation: SAE-space clustering with moderate batch mixing for batch diversity control, a difficulty proxy for easy-to-hard curriculum ordering, and a quality probe for data filtering. SAERL improves average accuracy by 3.00% over vanilla GRPO and reaches target accuracy with 20% fewer training steps on Qwen2.5-Math-1.5B, with consistent gains across model scales and RL algorithms. Experiments show that SAE transfers effectively across model families and scales, serving as a lightweight and reusable data engineering tool. These results demonstrate that model internals are a powerful and practical source of signals for post-training data engineering.