Mechanistic Interpretability

Mechanistic interpretability has largely focused on language models and deterministic toy tasks. Much less is known about how sequence models internally represent latent stochastic dynamics under noisy, partially observed observations. We study this question in a controlled multivariate stochastic volatility setting, where models observe only returns while the ground-truth latent volatility state is known to the researcher. This setting provides a useful benchmark for mechanistic interpretability under partial observability: the latent state is hidden from the model but directly available for evaluation. Across architectures, losses, and output heads, we find evidence for a two-stage computation. Hidden representations encode substantial information about the next latent volatility state, and the output head maps this representation to squared return forecasts. Furthermore, in Transformers, latent-state decodability emerges at identifiable architectural stages whose location depends on the volatility period. In long-cycle regimes, this computation simplifies into an explicit latent-state filter consisting of a learned linear projection followed by $\ell^2$ normalization. Output-head replacement further shows that part of the degradation under noisy MSE training arises from readout misalignment rather than representation failure. These results suggest that stochastic volatility models provide a useful benchmark for mechanistic interpretability under noisy latent dynamics and partial observability.

Computer vision models have become highly effective for medical applications, yet their black-box nature continues to undermine clinician trust. In clinical workflows, chest X-ray classifiers are increasingly paired with Vision-Language Models (VLMs) to generate natural-language explanations. However, these systems add linguistic fluency without addressing the underlying opacity of the visual model. With the emergence of Kolmogorov-Arnold Networks (KANs), whose spline-based components provide inherently interpretable functional units, we investigate whether this architectural transparency can be leveraged to produce more trustworthy textual explanations. We introduce KANEx, the first ever framework that leverages the symbolic transparency of KANs to ground VLM reasoning. This interpretability also made it possible to design KAN-Map, a novel heatmap generation method derived directly from KAN models rather than gradient approximations. We feed these grounded contexts into downstream VLMs for enhanced explainability. Benchmarked on the MIMIC-CXR dataset, we demonstrate that KAN-based architectures with ResNet/ViT baselines demonstrate improved semantic similarity while producing significantly more faithful saliency maps. KAN architectures improve visual localization and downstream reasoning quality by 10%. Our findings suggest that grounding linguistic explanations and visual attributions in mathematically interpretable units is a necessary step toward trustworthy medical AI.

Large language models may easily assign personality labels from text, but model interpretability remains an open problem. To address this gap, we introduce LEX-EC, a reusable black-box audit framework combining prevalence and agreement diagnostics with controlled lexical ablation to distinguish marginal-distribution effects from trait-associated signal recoverable under restricted evidence. Using this framework, we illustrate how various text genres may exhibit sharply different profiles: free-form essay text contains the broadest, but still weak, signal; in graduate student introductions, an observable Extraversion association weakened after masking; and single Facebook statuses yield little stable evidence even in a trait-balanced sample, indicating a possible lower bound of content or length. Masking topical and demographic content weakened some associations while leaving others detectable from function words, affective terms, and cognitive-style vocabulary. Linguistic prompting shifted model self-explanations but did not eliminate topical content. LEX-EC jointly evaluates classification prevalence, item-level association, chance-corrected agreement, persistence under lexical restriction, and prompt sensitivity in model-generated explanations. Across datasets, models, and prompts, LEX-EC characterizes how trait associations may vary with available lexical evidence, introducing a novel application of lexical methods to black-box interpretability in personality labeling.

Safety-aligned large language models are trained to refuse harmful requests, yet embedding the same requests in particular scenarios can bypass their safeguards. Existing red-teaming methods empirically identify effective scenarios through observed attack outcomes, but why particular scenarios weaken refusal remains mechanistically unclear. Meanwhile, mechanistic interpretability studies have characterized both refusal directions and jailbreak-associated features, without explaining the relationship between the two representations. In this work, we show that scenario-wrapped prompts activate internal scenario directions whose causal steering consistently reduces refusal scores. Building on this finding, we propose \textsc{Concept2Scenario}, a concept-based attribution framework for vulnerable scenario discovery. It instantiates a broad concept space with a sparse autoencoder, attributes refusal suppression to individual concepts, translates the identified concepts into interpretable natural-language scenarios, and identifies synergistic scenario combinations through interaction attribution. Across three open-source models, two safety benchmarks, and six black-box jailbreak methods, the discovered scenarios serve as reusable priors that improve average attack success rates by up to $18.2$ percentage points. They also transfer to GPT-5, Claude-Haiku-4.5, and Gemini-3-Flash, suggesting that some scenario-level refusal vulnerabilities are shared across model families. Moreover, the identified combinations outperform their individual constituents and enable iterative attacks to succeed in fewer turns.

When a neural network predicts a physical system accurately, has it learned the governing law as formal, structured knowledge, and if so, does the network's internal computation actually use that representation throughout the law's domain of validity? We identify four interpretability gaps that limit answering these questions for {\em physics laws over continuous variables}: the absence of a coverage-aware causal-consistency measure over continuous counterfactuals; of a domain-of-validity test for the identified circuit; of a verification of the law's invariants and forbidden behaviors; and of a quantification of how a derived physical quantity flows through the circuit. We develop a foundational framework, LAWFUL, that closes the first two and lays groundwork for the remaining two, and illustrate it on the Mocap2Radar transformer, validating whether it learns and internally uses the Doppler frequency law $f(t) = \frac{2 v(t)}λ$ from motion-capture and radar data in which neither $f(t)$ nor $v(t)$ appears.

Gene regulatory network modeling often requires balancing predictive accuracy and mechanistic interpretability. In this work, we compare continuous surrogate models and a discrete mechanistic model on the same \textit{Arabidopsis thaliana} induced systemic resistance (ISR) dataset, using both the raw continuous gene-expression measurements and their sign-binarized representation. The study considers eight defense-related genes measured over nine time points and evaluates two continuous predictors, Random Forest (RF) regression and a Multi-Layer Perceptron (MLP), against a threshold Boolean network (TBN). The models are assessed using rolling-origin one-step prediction, recursive multi-step rollout, and interpretability analysis. RF achieved the best average one-step numerical performance in the continuous domain, with an MAE of 1.910 and an RMSE of 2.836, compared with 2.089 and 3.106 for the MLP. In the binary domain, the TBN obtained the best average one-step qualitative performance, with a binary accuracy of 0.550 and a Hamming distance of 3.600, compared with 0.500 and 4.000 for RF, and 0.495 and 4.040 for the MLP. In recursive rollout, the TBN exactly reproduced the observed binarized trajectory, while the MLP also showed near-perfect fidelity, with a trajectory binary accuracy of 0.986, and RF accumulated substantially larger deviation, with a trajectory binary accuracy of 0.708. These results highlight that local numerical accuracy and global qualitative dynamical fidelity are not necessarily aligned, and suggest that continuous surrogates and threshold Boolean networks should be viewed as complementary tools for modeling biological regulation.

Multi-head Latent Attention (MLA), introduced in DeepSeek-V2, compresses key-value pairs through a shared low-rank bottleneck (cKV), achieving 81% KV-cache reduction during inference. Despite its adoption in massive production models, no prior work has studied what information this bottleneck preserves or discards, nor how it reshapes internal transformer circuits. We present the first comprehensive mechanistic interpretability study of MLA, training a 114M-parameter transformer (pretrained on a web/code/math mixture, fine-tuned on TinyStories) and analyzing its representations through SVD, attention head taxonomy, linear probing, and a disruption-attribution analysis. Our key findings are: (1) the cKV bottleneck learns a pure content representation, preserving entity identity (98% retention) while discarding positional information, validating MLA's separation of content from position via RoPE; (2) induction heads co-locate at a single layer (Layer 12), unlike their distributed formation in standard MHA; (3) a single "semantic hub" layer (Layer 15) simultaneously exhibits the highest SVD effective rank and strongest disruption-attribution score; and (4) the bottleneck is globally over-provisioned, using only 46% of its capacity on average. These findings suggest MLA does not merely compress attention passively, but reshapes how the model organizes content, position, and circuit structure. We view this as an initial data point and detail scope limitations in Section 5.

Post-training quantization (PTQ) has become a practical solution for deploying deep learning models on resource-constrained edge devices by compressing high-precision floating-point weights into low-precision representations without requiring retraining. Past research has demonstrated that quantization largely preserves classification accuracy; however, whether it also preserves the model's internal reasoning remains an open question. This study presents a systematic evaluation on how static PTQ affects the interpretability / explainability of five widely used CNN architectures: VGG19, ResNet18, EfficientNet-B0, DenseNet161, and MobileNetV2 at INT8 and INT4 precision. We employ a dual interpretability framework that combines Grad-CAM for spatial attention analysis with LIME for input-level feature attribution, and systematically compare full-precision and quantized models on two binary classification datasets. Interpretability is evaluated using three complementary metrics: the Pearson correlation coefficient, structural similarity index, and top-20% IoU to capture distributional and structural variations in model explanations, supplemented by deletion/insertion faithfulness analysis. The results show that classification accuracy is not a reliable indicator of interpretability stability under reduced precision. DenseNet161 maintains strong feature consistency across both precision levels, whereas EfficientNet-B0, despite achieving competitive spatial attention and classification accuracy at INT8 precision, exhibits a substantial degradation in input-level feature attribution. These findings have direct implications for the trustworthy deployment of quantized models in applications with high interpretability requirements, demonstrating that architecture selection is as important as the quantization strategy.

Feature-attribution methods assign scores relating input variables to a model's output, but do not by themselves characterize how explicitly defined interaction operators compose across its intermediate layers. We introduce \emph{interior interpretability}, a propagation-based perspective on internal model organization, and instantiate it for tabular Transformers using attention rollout. We interpret rollout as a row-stochastic operator encoding attention-mediated propagation between feature tokens. By applying classical Doeblin--Dobrushin contraction theory, we show that a rollout operator with a small Dobrushin coefficient is quantitatively close to a rank-one stochastic matrix whose common row is determined by its normalized column sums. This result gives a structural interpretation to the corresponding rollout propagation profile. In Transformers trained for metabolomic age prediction, the measured rollout contraction strengthens with depth. Trained and randomly initialized models also exhibit different propagation profiles, although the present experiments do not establish the predictive relevance of individual rollout-ranked variables. Exploratory comparisons with PCA and GradientExplainer approximations to SHAP reveal localized agreement among highly ranked variables but weak agreement across complete rankings. Attention rollout is therefore used here as a diagnostic of attention-mediated propagation, not as a causal explanation or faithful attribution of the complete Transformer.

Large language models may infer demographic attributes from subtle linguistic cues even when those attributes are not explicitly stated. This pilot study examines whether Qwen2.5-7B-Instruct internally represents Colombian identity, socioeconomic status, or stereotype-related information when processing Colombian-Spanish and English prompts. We use Natural Language Autoencoders (NLA) to verbalize residual-stream activations from layer 20 across four positional quartiles per prompt. Our dataset contains 30 prompts arranged as 15 matched Spanish-English pairs, spanning explicit Colombian cues, implicit Colombian cues, and neutral controls. We report descriptive rates and qualitative evidence rather than statistically powered effects, focusing on whether latent nationality or stereotype representations appear before they are verbalized in the model output. This work connects activation-level interpretability with bias evaluation for underrepresented Spanish varieties.

Neural network compression and interpretability remain open challenges in modern deep learn- ing, where billion-parameter architectures deliver impressive accuracy at the cost of trans- parency, computational efficiency, and reliable uncertainty quantification. This paper introduces Neural Atom Prevalence (NAP), a principled Bayesian framework for structured node-level model selection in feedforward neural networks. NAP introduces the neural atom (activation unit) and functions as a hybrid method operating through a four-phase pipeline: Bayesian Lottery Ticket (BLT) identification via Iterative Magnitude Pruning (IMP), soft variational training of the Spike and Slab Independent Gaussian (SS-IG) model, Poisson-Binomial (PB) optimal layer-size selection, and Bayesian fine-tuning to produce a sparse, stable, interpretable, and accurate model. Extensive empirical validation across simulated nonlinear regression, two UCI benchmark datasets (Concrete, YearPredictionMSD), and the MNIST image classification task demonstrates that NAP achieves state-of-the-art structural sparsity, reducing active nodes to as few as 8% of the original dense architecture on MNIST, while well-calibrated probabilisti- cally: the aleatoric-epistemic uncertainty decomposition reveals that model ignorance accounts for only 3 to 4% of total predictive variance across all experiments, and regression reliability diagrams confirm a near-nominal predictive interval coverage (93.4% observed against a 95% target). These results establish NAP as a reliable, theoretically grounded, and computation- ally tractable solution to the simultaneous pursuit of sparsity, accuracy, interpretability, and uncertainty quantification in Bayesian neural networks.

Body-based emotion recognition is important for real-time affective systems, but graph-based skeleton models can be computationally expensive. This paper studies whether lightweight temporal convolutional networks (TCNs) can provide an efficient and interpretable alternative for body-based emotion classification. We evaluate a family of TCN models on DIEM-A and compare them with a graph-based time-series graph (G-TSG) baseline using accuracy, macro-F1, parameter count, and inference latency. Although G-TSG achieves the highest mean performance, TCN-Base remains within $1.58$ accuracy points and $1.25$ macro-F1 points while using $79.18\%$ fewer parameters and reducing classifier latency by approximately $12.5\times$. We also analyze body-region contributions using region-specific TCN models, zero-based occlusion, and G-TSG gradient saliency. The results show that upper-body motion provides the strongest standalone regional cue, that the usefulness of body regions varies across emotions, and that different interpretability methods capture distinct aspects of model behavior. These findings suggest that lightweight TCNs can support efficient body-based emotion recognition while also providing practical insight into how motion cues contribute to classification.

Weather forecasting foundation models (FMs) are increasingly fine-tuned to predict air quality, offering fast global pollution forecasts at lower computational cost than conventional chemical transport models. These FMs are typically trained on reanalysis data and generate forecasts through autoregressive rollout. They do not explicitly represent governing physical or chemical processes. Therefore, high forecast skill does not reveal whether a model has learned physical mechanisms or exploits statistical regularities in its training data. Here, we present the first study of what a FM fine-tuned for atmospheric chemistry has learned by examining Microsoft's Aurora model. We impose controlled chemical perturbations on its forecasts and test them against known photochemical relationships. We then examine the internal representations that generate these forecasts. We find that Aurora captures a first-order ozone response to reactive nitrogen but does not enforce the chemical constraints that a process-based model encodes. It generates chemically inconsistent combinations of related species and relaxes localized emission features such as wildfire plumes toward background. Internally, its representations remain largely organized around the meteorology inherited during pretraining, with little structure specific to chemistry. Using sparse autoencoders, we identify internal components that causally control the chemical forecast but do not map cleanly onto individual atmospheric processes. This work provides a framework for testing whether AI forecasting systems learn atmospheric chemistry from reanalysis data. As these models are increasingly positioned to inform environmental policy decisions, we argue that composition forecasts should also be judged by their internal mechanisms rather than by benchmark skill alone.

Language models are thought to exhibit the phenomenon of superposition, representing many more features than dimensions in their residual streams. Sparse autoencoders (SAEs) are designed to recover such features post-hoc, but training models that are interpretable by construction has remained impractical, as a per-layer over-complete bottleneck is prohibitively expensive in both memory and compute. To overcome this issue, we introduce the ParityTransformer, a GPT-2-scale architecture whose intermediate representations are efficient and wide / sparse by design. At each layer, a Deep Parity Bottleneck (DPB) replaces a learned over-complete basis with a parameter-free algebraic dictionary, providing a deterministic incoherence guarantee and eliminating the memory requirements that have prevented per-layer interpretable bottlenecks at scale. A DPB is a hierarchically structured sparse bottleneck which efficiently enforces sparsity using a multi-level mixture-of-experts approach: a hardware-aware implementation that closes the cost gap between activation sparse and dense training to a manageable interpretability tax. Empirically, ParityTransformers perform at least as well as post-hoc SAEs on sparse probing tasks, while out-performing on measures of feature absorption, steering effectiveness, and fine-grained causal interventions. Because subsequent computation acts only on features that survive the sparse bottleneck, the ParityTransformer's features are native to the model's forwards pass by construction, addressing the question of whether SAEs probe features the model actually uses during computation. We see this as a step toward training models whose internal representations are interpretable by design rather than recovered post hoc.

Natural-language autoencoders score explanations of hidden activations by reconstruction: an explanation is deemed faithful if the activation can be regenerated from it. The test is structurally insensitive to individual false claims: if flipping a claim does not change the reconstruction, the claim is never penalized. We show the test is passed in two ways, neither faithful. On a released Qwen-2.5-7B verbalizer, explanations reconstruct well above chance while ~2% of specific claims are reconstruction-dependent, so the score tracks gist, not specific facts. Under exact synthetic ground truth, the standard recipe develops co-adapted private codes (false wording the reconstruction depends on) in 5/5 runs, and fixes that leave the target model unchanged do not help. We contribute two audit protocols, the grounded-vs-true cross and the evaluator swap, and RECAP (Readable Encodings via Co-trained Auxiliary Predictors): linear heads trained alongside the target model to keep designated content decodable. On RECAP-trained sandbox models, fresh verbalizers state the designated content truly and the codes vanish, at a +0.001-nat cost. This replicates on a pretrained Pythia-160M: the content becomes reliably probe-decodable, though a fresh verbalizer conveys it only in part (truth 0.44-0.46 vs a near-zero control). For interpretability, high reconstruction does not certify individual claims. For AI safety, RECAP makes designated internal content independently checkable against probes rather than asserted by prose a model can game: an independent probe scores the verbalizer's true claims above its false ones (AUC 0.96, vs 0.82 without RECAP). Against an adversary that edits an explanation to maximize the reconstruction score while lying (suppressing ~87% of its lie penalty), the RECAP probe still flags the lies (AUC 0.95) while the control probe collapses to chance (0.51).

Machine learning models achieve high predictive accuracy in regression tasks, but their deployment in safety-critical and regulated domains requires interpretability. While fuzzy rule-based systems offer transparent, linguistically explicit interpretable models, Mamdani-style fuzzy regression remains underrepresented in modern machine learning software libraries. This paper presents an interpretable regression extension for the Ex-Fuzzy library, enabling Mamdani fuzzy inference with scalar consequents learned directly from data. For this, a target-aware partition initialisation strategy based on Fuzzy C-Means clustering is introduced, in which linguistic variables are derived from an augmented input-output space to emphasise output-relevant regions of the feature space. The proposed extension is evaluated on ten regression datasets from the KEEL repository, comparing Gaussian and trapezoidal partition strategies against standard baselines including linear regression, multilayer perceptron, and random forests. Experimental results show that Gaussian partitions consistently outperform uniform trapezoidal partitions, achieving a mean coefficient of determination of approximately 0.86 while producing compact rule bases of 10-15 human-readable rules. The proposed implementation provides a transparent and competitive alternative to black-box regression models, supporting practical interpretability with competitive predictive performance.

Discourse relations provide document structure, critical to language understanding and enabling language model performance and ethicality. In this work, we investigate how instruction-tuned Transformer models (LLaMA and Mistral) encode discourse relations in English, with a particular focus on the contrasting relations of causation and antithesis. Framing the task as a next-token prediction task and applying a suite of interpretability techniques to test model internals, our findings show that certain early layers make predictive decisions at mid-sequence tokens, while some mid-level layers finalize their decisions closer to the last token. Most of the remaining layers primarily propagate earlier decisions rather than actively influencing them. Additionally, we observe that some layers exhibit a preference for one answer over alternatives, suggesting asymmetric representation of discourse-based reasoning.\footnote{Our code is available at https://github.com/abhidipbhattacharyya/causation_vs_antithesis}

Highly nonlinear chaotic dynamical systems remain difficult to model due to fundamental trade-offs between complexity, expressivity, and data efficiency. Modern machine learning methods achieve strong predictive performance but often rely on a-priori system knowledge or curated data with limited interpretability. Koopman operator theory offers a promising direction via linear representation in an infinite-dimensional observable space. However, many data-driven Koopman methods seek globally valid operators for which useful finite-dimensional spectral embeddings remain difficult to identify under these constraints. To overcome associated limitations, we introduce Fuzzy Spectral Region Decomposition (fSRD), a fully automated learning framework for estimating finite Koopman representation via multiple operators. The proposed method realizes a data-adaptive framework for assembling locally invariant embeddings, termed Invariant Decomposition. fSRD achieves highly accurate linear reconstructions of nonlinear systems while learning finite-dimensional representations of their induced evolution operators, bridging interpretable operator-theoretic models with expressive data-driven sequence learning. These embeddings are adaptively constructed via a global fuzzy tree model, drawing inspiration from fuzzy neural architectures to learn the induced dynamics while prioritizing parsimonious solutions. Empirical results across canonical chaotic systems (e.g., Lorenz and Duffing) and high-dimensional real-world data demonstrate strong predictive accuracy, interpretability, and robust expressivity across data-rich and data-limited regimes, highlighting the method's generality.

Within Explainable Artificial Intelligence, mechanistic interpretability uses Sparse Autoencoders (SAEs) to extract more interpretable features from neural representations. However, assessing their monosemanticity, and thus explanation quality, remains challenging. Existing metrics require external concept labels or depend on pretrained embedding models, making them sensitive to encoder's geometry. We introduce the Tversky Monosemanticity Score (TMS), a label-free metric that operationalizes monosemanticity as activation-set coherence of binarized SAE latents, and does not require external embedding encoders. We evaluate TMS on SAEs trained on features from pretrained vision and vision-language models (DINOv3, CLIP, BLIP2), two common SAE regimes (TopK, BatchTopK), multiple sparsity levels, and expansion factors. Our results show that TMS is less affected by encoder anisotropy than its embedding-based alternative, while remaining aligned with established monosemanticity indicators. TMS also reveals distinct SAE training dynamics across base models. Moreover, under encoder anisotropy, TMS provides a stronger indication of probe-based concept deletion effectiveness, while being competitive otherwise.

A Bayes-filtered transformer (BFT) is a transformer trained on sequences that are generated in two steps: first a latent task is drawn from a prior, then observations are drawn conditional on that task. Trained under autoregressive log loss, the BFT's next-token prediction, in the idealized limit, is the Bayesian posterior predictive distribution (PPD) induced by that prior and that conditional law. In practice the trained BFT is only an approximation of this ideal PPD, raising an interpretive question: what prior and posterior over the latent task has the trained BFT actually internalized? Existing work answers this question by comparing the trained BFT's predictions against the predictions of various "reference" posteriors, each standing in for a different candidate algorithm or computation the BFT might be implementing. This prediction-space comparison is fragile: different posteriors can share the same posterior-mean predictions. We use predictive Monte Carlo (PMC) as a general interpretability tool for any BFT: using only next-token generation, PMC returns an approximation to the implicit prior and posterior over the latent task, answering the interpretive question directly in latent space. We apply PMC to three stylized task families spanning 0-Markov and 1-Markov exchangeability. The phenomena previously reported in these settings remain visible in latent space. Code is available at https://github.com/afiq-aswadi/bft-pmc

Air pollution and climate-related stressors are increasingly important concerns for respiratory health, especially in settings with unequal environmental exposure and healthcare capacity. This study evaluates an interpretable machine learning framework for predicting respiratory disease rates and air-quality status using structured country-level weekly data. Two supervised learning tasks were considered: regression of respiratory disease rate per 100,000 population and binary classification of air-quality status. Nine regression models and nine classification models were compared using nested cross-validation. Model interpretation was conducted using SHAP values, and subgroup analysis was performed across income levels and geographic regions. The results showed that PM2.5 concentration was the dominant predictor of respiratory disease rate, with linear and regularized linear models achieving the strongest regression performance. For air-quality classification, models achieved high balanced accuracy when PM2.5 was included, but performance decreased substantially when PM2.5 was removed, indicating strong dependence on pollutant-related information. SHAP analysis showed that, without PM2.5, socioeconomic and meteorological variables such as GDP per capita, precipitation, and healthcare access became more influential. Subgroup analysis showed similar aggregate regression error across income groups, but PM2.5 contributed more strongly to predictions in lower-middle-income countries. These results show that model accuracy alone is not sufficient for climate-health prediction. Interpretable models can help identify dominant pollution-related signals, test whether results depend on key pollutant variables, and show whether prediction patterns differ across socioeconomic groups.

Multi-agent planning becomes substantially harder when agents must improve specialized decision-making skills while keeping their executable implementations private. This setting arises when independently developed agents expose heterogeneous interfaces, observations, and capabilities, yet must coordinate under a shared team objective. Existing approaches commonly rely on centralized optimization, shared policy access, or common skill representations, assumptions that limit knowledge reuse when function signatures differ. We introduce RELIC, a framework for learning interpretable and composable programmatic skills through revealed principles. Each agent improves its own executable skill locally, while useful decision logic and coordination patterns are distilled into compact textual principles. Rather than requiring direct program exchange, these abstractions can be re-instantiated under agent-specific interfaces and reused across incompatible implementation spaces. A shared principle memory accumulates transferable knowledge and promotes abstractions that repeatedly improve team-level performance. This separation allows discoveries made by one agent to guide others while preserving local executable implementations and decentralized execution. RELIC therefore supports strategic transfer across both heterogeneous-role and shared-role cooperative teams. Extensive experiments across routing, scheduling, combinatorial optimization, and distributed coordination settings demonstrate RELIC's effectiveness against independent and joint LLM-based search methods, together with consistent benefits across task structures and LLM backbones.

Large language models often succeed on one formulation of a problem while failing on an equivalent formulation. Whether these failures arise from distinct internal circuits or different activation states of a shared circuit remains unknown. Recent mechanistic interpretability studies suggest that arithmetic in LLMs emerges from a "bag of heuristics," encoded by a sparse set of MLP neurons that represent distinct arithmetic strategies. We investigate whether arithmetic heuristic neurons are form-invariant across symbolic arithmetic, natural language word problems, and Python code in three Llama-3 models. In each format, we identify arithmetic heuristic neurons using a two-stage pipeline combining attribution patching and activation patching. A compact set of neurons is shared across all three formats, and targeted interventions show this shared circuit is both necessary and sufficient for late-layer arithmetic computation. Transferring the shared neurons' activations from a successful execution in one format to a failed execution in another recovers most incorrect predictions, exceeding 97% for addition and subtraction, indicating that cross-format failures arise from activation states rather than distinct circuits. Moreover, shared neurons consistently belong to the same heuristic families across formats, demonstrating that arithmetic computation in LLMs is largely form-invariant at the neuron level.

Interpretability methods for neural network activations span a wide cost spectrum, from cheap, training-free techniques (such as linear probes, PCA, SVD) to more expensive training-based ones (such as SAEs and activation oracles). Training-based methods are typically more powerful, in part because they leverage large activation datasets during training. This raises a natural question - do they actually surface insights that go beyond what is recoverable from the training dataset itself? To address this, we equip an LLM agent with a vector database of activations paired with their textual contexts, along with tools for manipulating activations - projecting out directions in latent space, computing activation differences and averages. The agent iteratively queries the database, forms hypotheses from the retrieved samples, and validates them by constructing linear probes. We call this method HARP, for Hypothesis-driven Agentic Retrieval and Probing. Despite not involving any training, HARP outperforms both activation oracles and SAE-based agents on concept discovery, concept detection, model steering, and secret elicitation. The training-free design also makes HARP substantially cheaper and more flexible: new datasets can be indexed on demand whenever existing ones prove insufficient. More broadly, our results suggest that current training-based methods do not yet extract insights beyond their training data, and motivate benchmarks that explicitly require interpretability methods to demonstrate such insights. We release our code at https://github.com/SriramB-98/HARP

Black-box models limit the adoption of artificial intelligence in medicine because their predictions are difficult to interpret and reproduce. We present a statistically grounded framework for interpretable, rule-based clinical classification using the Bernoulli Naïve Bayes (BNB) model. Supervised chi-square-guided binarization converts continuous variables into binary indicators by selecting thresholds that maximize association with the clinical outcome within the training folds, which allows BNB to operate on continuous medical data without sacrificing transparency. On three benchmark datasets, Pima Indians Diabetes, Wisconsin Breast Cancer, and Heart Failure Prediction, the framework reached areas under the receiver operating characteristic curve of 0.800, 0.984, and 0.919, respectively. Probabilistic reliability was assessed with a leakage-safe cross-validated calibration analysis reporting Brier score and calibration intercept and slope, and post-hoc beta calibration improved probability calibration across datasets. These results indicate that an interpretable, statistically motivated framework can perform comparably to more complex models while providing explicit decision rules expressed in clinical units and calibrated risk estimates. A complete worked example further shows that model inference can be reproduced from a printed reference table using only basic arithmetic, without software or proprietary tools, supporting trustworthy and auditable use of artificial intelligence in clinical settings.

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

Transcoders have recently emerged as a promising approach for mechanistic interpretability (MI), enabling circuit-level analysis of model behaviour. In this paper, we investigate the use of transcoders to analyse deceptive behaviour in language models, a behaviour that poses a safety and security risk. Using a Qwen3-4B model with pre-trained transcoders, specifically per-layer transcoders (PLTs), we construct attribution graphs that capture feature activations and inter-feature dependencies, allowing circuit-level analysis of deception. Through feature steering and circuit analysis, we identified a dictionary of deception-related features and show that these features exert a stronger influence on deceptive outputs, as they produce predictable shifts between deceptive and non-deceptive responses. These findings suggest that deception emerges from internal model mechanisms and highlight the potential of transcoders for behavioural monitoring and early detection of security vulnerabilities related to malicious behaviours in language models.

In this paper, we study the connection between an LLM's output distribution and the data used to train it. Specifically, we study the degree to which an LLM's next-token distribution agrees with the empirical next-token distribution (ENTD) given the context in the training data. The ENTD is an appealing target because it is the unrestricted global minimizer of the next-token cross entropy loss used for pretraining, as well as an easily interpretable function of the pretraining corpus. We find that for a significant fraction of inputs, the LLM's distribution agrees with the ENTD almost perfectly, and the average agreement increases with model scale and training compute. Nevertheless, there is a long tail of input sequences where the LLM and ENTD differ significantly, and we examine several possible sources of this discrepancy across the transformer architecture, training procedure, and finite-sample noise in the ENTD estimate itself. More broadly, we hope our findings will encourage more work on ``data-centric mechanistic interpretability,'' a complement to standard mechanistic interpretability that opens the black box of how model behaviors arise from the data, rather than how they are encoded in the learned weights.

We propose the AIMO Interpretability Challenge, a competition on distinguishing robust from spurious reasoning in frontier mathematical language models based on the models' internal mechanisms. The challenge is motivated by a central limitation of standard reasoning benchmarks: strong final-answer accuracy does not reveal whether a model relies on stable reasoning mechanisms or exploits brittle reasoning shortcuts. Building on AI Mathematical Olympiad (AIMO) problems and submissions, together with resources from the Fields Model Initiative, the competition will provide (1) newly-published olympiad-level math reasoning problems and their symbolic representations, allowing generation of novel functional variants, (2) access to frontier reasoning models, and (3) assessments of models' adversarial robustness on these problems. Participants will use these resources, along with our computing infrastructure support, to develop methods for identifying which models solve problems robustly. Our competition will also create a new, open robustness benchmark and baseline systems, aiming to provide a lasting foundation for standard benchmarking in mathematical reasoning and interpretability. Scientifically, the competition connects interpretability and generalization research around a central question in AI research: can we determine if, and to what extent, the decision-making of frontier AI models is generalizable and thus, reliable?

Automatic voxel-level grounding of free-text findings in 3D chest Computed Tomography (CT) is critical for clinical interpretability. However, this task remains highly challenging due to the intricate spatial complexity of large 3D volumes and the heterogeneity of free-text findings. Existing end-to-end approaches often struggle to simultaneously learn the localized feature representations required for accurate 3D segmentation and the complex semantic understanding needed for text alignment, leading to suboptimal grounding performance. To overcome this fundamental limitation, we propose a novel decoupled framework that disentangles the problem into two specialized stages: (1) class-agnostic lesion segmentation and (2) text-volume reasoning. This structural separation allows the model to first extract candidate sub-volumes by localizing potential abnormalities. Subsequently, intensive cross-modal reasoning is performed to align these localized sub-volumes with free-text medical findings. To resolve the spatial ambiguities inherent in local regions, the reasoning module is augmented with explicit anatomical guidance, utilizing relative spatial coordinates and lung lobe priors. Evaluated on the ReXGroundingCT benchmark, our method achieves state-of-the-art performance in overall grounding quality on the official leaderboard. These results demonstrate that decoupling detection from reasoning is a highly effective paradigm for handling the complexity of 3D medical visual grounding. Our code is publicly available at https://github.com/khuhm/DAGG.

Recent advances in foundation models have transformed AI for Science, enabling remarkably accurate predictive performance across domains ranging from protein folding to weather forecasting. Yet prediction alone does not constitute scientific discovery. Scientific understanding depends on uncovering the reusable explanatory mechanisms that generate observations, whereas contemporary machine learning remains fundamentally organised around predictive mappings rather than explanatory structure. In this paper, we argue that scientific discovery is fundamentally a problem of knowledge organisation. To this end, we introduce Mechanistic World Models, a new design paradigm that places reusable mechanisms at the centre of representation, computation and learning. Drawing on insights from the philosophy of science, we derive the computational capabilities required for discovery, identify the design principles and inductive pressures that encourage explanatory knowledge to emerge, and formalise the anatomy of a mechanism-centric world model. Finally, we show how diverse research directions including mechanistic interpretability, causal representation learning, equation discovery and modular architectures capture complementary ingredients of this paradigm while lacking a unified framework. We propose Mechanistic World Models as a conceptual foundation and computational blueprint for moving AI beyond predictive forecasting towards autonomous scientific discovery.

We study interaction-aware mixture-of-experts for post-stroke rigidity prediction using multi-level views of structured health records. Despite minimal performance gains, routing attribution reveals systematic importance differences across views, underscoring view construction as key to interpretability.

Online shopping is increasingly shifting toward a model in which AI agents independently search for products, compare options, evaluate constraints, and carry out parts of the purchasing process for users. Website design must now support both human and agent-mediated interaction. This paper introduces the agent-ready website, a design framework for enhancing the readability, interpretability, verifiability, and actionability of e-commerce platforms for AI agents. Existing web design, SEO, and generative engine optimization (GEO) metrics do not fully assess a website's capacity for agent-mediated interaction. The proposed framework is structured around three dimensions agent interpretability, agent executability, and agent decision reliability supported by features such as machine readability, semantic clarity, agent actionability, and contextual decision-reliability signals. The framework is evaluated through a controlled experiment comparing a human-oriented baseline and an agent-ready version of an identical website prototype, with identical catalogs, pricing, stock, and shopping workflows. The evaluation involved five tasks, three browser-agent models (GPT-4.1, Gemini-2.5 Flash, and Grok-4 Fast), and 300 runs, measuring PASS,PARTIAL,FAIL outcomes, strict and functional success rates, error patterns, step counts, and token consumption. The agent-ready website achieved 134 PASS runs out of 150 versus 74 out of 150 for the baseline (strict success rates of 89.3% vs. 49.3%), with the largest gains in product detail extraction, comparison, and multi-constraint selection. It also reduced PARTIAL outcomes from 43 to 3 and lowered the average step count from 9.31 to 6.49. These results provide preliminary evidence that enhanced structural clarity, action cues, evidence signals, and temporal validity indicators can substantially improve the reliability and efficiency of AI browser agents.

Existing studies of LLM-as-judge scoring bias work predominantly at the input-output level: they perturb inputs, measure score deltas, and propose prompt-level mitigations. We argue that the same biases admit a representation-level account in the judge's hidden state, complementary to the input-output view and operationally useful in ways it does not afford. We report three findings, across seven judges, seven bias types, and nine benchmarks. Geometry: baseline judging inputs occupy a tight activation manifold while biased inputs are displaced along a low-dimensional, type-specific subspace that sharpens with depth and is recovered consistently by three families of estimators. Causal control: steering hidden states along this subspace drives scoring in both directions, forward shifts reproducing biased scoring on clean inputs and reverse shifts restoring baseline scoring on biased ones, while matched-norm random directions produce shifts an order of magnitude smaller. Operational: a simple linear projection onto the same bias-direction features anticipates judge failures on three entirely unseen benchmarks, substantially outperforming text-based alternatives. Reading bias as activation geometry, rather than as input-output noise, unifies geometric structure, causal control, and operational prediction within a single framework. The project page is available at https://xzx34.github.io/unfair-judge/

Distributional reinforcement learning agents learn full return distributions that are increasingly read at face value: for interpretability, risk-sensitive control, and safety monitoring. We ask a question theory anticipates but that has not been measured directly: are the risk claims of a trained distributional agent true? Our audit combines a decision-relevant screening metric (the excess Wasserstein gap between the top two actions, which equals the mass by which first-order stochastic dominance is violated), ground truth from snapshot-restart Monte Carlo, and a statistical harness (permutation nulls, bootstrap refutation, FDR control) without which the audit itself manufactures false conclusions. Across QR-DQN, C51, and IQN on MinAtar (33 runs), 40-95% of the strongest claimed risk trade-offs are refuted at 95% confidence, the placement of the strongest claims is statistically indistinguishable from truth-blind, and essentially no claim is confirmable: for these agents, the learned "risk" reflects a training artifact rather than environment stochasticity. The artifact is structural (fully formed early in training, uncorrelated with final score, idiosyncratic to each seed) and appears unchanged at full-Atari scale, with every top Breakout claim of a pretrained near-state-of-the-art QR-DQN refuted. Positive controls of known magnitude confirm 96-100% of real claims (correlation 0.89-0.92): the reading measures the agents, not the audit. Acting on the heads' CVaR advice at their most-flagged states ranges from beneficial to significantly worse than chance. Neither training for risk nor ensembling removes the artifact, and recalibration passes the audit only by nullifying the claims: the head is uninformative, not merely miscalibrated. We release the toolkit and document two silent pitfalls that produced convincing but wrong audits of our own.

The current state of the art in AI/ML rests on deep neural architectures, which, in general, suffer from a lack of interpretability. Interpretability is crucial to gleaning insights while analyzing experimental data, where quantitative predictions may not be adequate for a scientist. We present a three layer neural architecture, SAMPAT (Smooth Approximation via Multivariate Polynomials and Analytic Transformations), that can provably learn a continuous, everywhere differentiable function, that can approximate any smooth function arbitrarily closely. SAMPAT's approximant can be expressed as a closed and compact algebraic, analytic expression, providing complete interpretability. Experiments on synthetic and benchmark datasets indicate that SAMPAT yields competitive performance with simpler representations. For many tasks, a two layer SAMPAT suffices. By imposing restrictions on the connectivity between neurons, SAMPAT may be used to provide a range of approximants, including regular and trigonometric polynomials, rational expressions, Gaussians, mixtures of Gaussians, as well as arbitrary combinations of the same; without restrictions, it learns a suitable structure. SAMPAT may be used to factorize polynomials and model nonlinear systems. With the addition of skip connections, a 4 to 6 layer SAMPAT is adequate to represent a substantive range of methods widely used in AI/ML, allowing the choice of a model's family, not just its parameters, to also be optimized as part of the learning process.

We present a Procrustes-conditioned Joint End-to-end Top-K Sparse Autoencoder (SAE) for extracting cross-seed universal features from independently trained BERT models. Cross-seed feature universality is a fundamental challenge in mechanistic interpretability: because dictionary learning is non-convex, independently trained networks learn misaligned feature spaces, so apparently identical features may differ by random initialization. We address this by computing an orthogonal Procrustes rotation between seeds' activation spaces before joint SAE training, combining Top-K sparsity, end-to-end downstream optimization, and an auxiliary dead-feature revival loss based on previous SAE literature. Evaluating on five independent seed pairs (ten BERT models) across three benchmark datasets (SST-2, Stanford Politeness, TweetEval Emotion), our full pipeline produces more universal features (Pearson r $\geq$ 0.70 across seeds) than post-hoc alignment baselines on all three datasets. A minimal qualitative analysis confirms that high-universality features encode interpretable sociolinguistic patterns.

Mechanistic interpretability often evaluates explanations by intervening on a model: swapping hidden states, patching activations, ablating components, or comparing a compressed model to the original one. These experiments are usually summarized by a point estimate, even though the evaluation may be monitored while it runs or adapted toward suspected failures. This makes it hard to tell whether a reported fidelity or patching effect is a stable causal claim or a consequence of finite sampling and evaluation choices. We introduce Certified Interventional Fidelity (CIF), a statistical layer for interventional interpretability evaluations. CIF first writes the quantity being reported as a causal estimand: an expectation of a bounded score over a stated input distribution and a stated intervention distribution. It then provides confidence intervals and anytime-valid confidence sequences for this estimand, including under adaptive intervention sampling via bounded mixture importance weighting. We instantiate CIF with Hoeffding-style sequences and variance-adaptive betting sequences, the latter reducing certification cost by 10-30x in our experiments. On MNIST abstractions and GPT-2 Small IOI circuits, CIF certifies high-fidelity claims, shows when apparent method differences are not statistically supported, and makes sensitivity to the intervention distribution explicit.

Diagnostic decision making often relies on a sequence of pathology tests that bridge patient symptoms and final disease diagnosis. Existing clinical decision-support systems typically focus on predicting single diseases and do not explicitly recommend sets of intermediate tests or model dependencies among them. In this paper, we formulate pathology test recommendation as a multi-label classification problem where each case is associated with multiple, interdependent tests. We propose an AI-based framework that applies classifier chains with logistic regression, decision trees, random forests, and their ensemble to capture label dependencies between tests. Experiments on an expert-curated dataset from a private pathology laboratory show that classifier-chain models outperform their independent counterparts, improving F1-score and reducing Hamming loss while maintaining high accuracy across common and rare tests. To enhance trust and transparency, we integrate SHAP-based explainable AI, providing symptom-level attributions that align with established clinical reasoning in most cases. The results demonstrate that classifier chains combined with SHAP offer an effective and interpretable approach for multi-label pathology test recommendation, with potential to support clinicians in selecting appropriate diagnostic tests at an early stage.

Large language models (LLMs) exhibit remarkable capabilities but remain highly vulnerable to adversarial prompts and jailbreak attacks. Existing approaches primarily analyze these failures through input-output behaviors or attribution methods, offering limited insight into how adversarial perturbations alter the model's internal reasoning. Consequently, the mechanisms underlying unsafe or incorrect behaviors remain poorly understood. We introduce a mechanistic framework for diagnosing LLM vulnerabilities using paired internal computation graphs, which represent prompt-specific inference as structured causal interactions among latent features. By constructing and aligning computation graphs for clean and attacked prompts, we reveal that adversarial attacks induce systematic transformations of internal reasoning, including suppression of safety-relevant components, emergence of attack-specific features, and rerouting of computation paths. Building on this representation, we propose a unified framework that (i) decomposes computation into invariant, suppressed, and emergent structures, (ii) identifies recurring vulnerability motifs associated with failure modes, and (iii) performs causal interventions on nodes, paths, and subgraphs to directly evaluate their contributions to attack success. This enables a transition from descriptive attribution to causal diagnosis of model failures. Experiments across multiple open-source LLMs and diverse adversarial and jailbreak benchmarks demonstrate that structural deviations in internal computation graphs strongly correlate with unsafe behaviors. Furthermore, targeted interventions on identified vulnerability motifs improve model robustness, establishing internal computation graphs as a principled foundation for understanding, diagnosing, and mitigating LLM vulnerabilities.

Modern machine learning (ML) increasingly relies on complex models whose behavior is difficult to characterize beyond empirical performance metrics. Across a wide range of tasks, including prediction, generation, and decision-making, models with similar empirical performance can exhibit markedly different properties in terms of their transparency, interpretability, robustness, fairness, privacy, and certifiability. This survey highlights how optimization- and certification-oriented reasoning can provide a useful framework for reasoning about such differences, supporting tasks ranging from model training and selection to auditing and certification. We review and synthesize recent advances at the intersection of combinatorial optimization (CO) and trustworthy ML, covering both training and post-training tasks, including interpretable model learning, explanation generation, robustness analysis, fairness auditing, model compression, and privacy attacks and protections. Across these domains, CO formulations offer additional capabilities over purely heuristic approaches, e.g., gradient-based ones, notably global guarantees, formal certificates, and explicit treatment of trade-offs. While scalability remains an important challenge, continued progress in solvers and hybrid algorithms suggests a growing role for CO in the design and deployment of trustworthy ML systems.

This article offers a comprehensive overview of mechanistic interpretability, an emerging field that seeks to reverse-engineer the internal algorithms of modern neural networks. While traditional explainable AI methods often stop at surface-level input-output correlations, this approach directly addresses the opaque "black box" nature of machine learning models, which is essential for ensuring safety and auditability in high-stakes deployments. The paper provides a detailed examination of Transformer circuit analysis, exploring how internal components like the residual stream, attention mechanisms, and induction heads drive complex tasks and in-context learning. It subsequently tackles the core challenge of superposition and polysemanticity, demonstrating how tools like Sparse Autoencoders (SAEs) and transcoders can decompose tangled network activations into distinct, human-interpretable features. Furthermore, the paper explores methods for actively controlling and modifying model behavior through steering vectors and causal interventions. Finally, it connects these mechanistic insights with neurosymbolic AI frameworks designed to translate neural representations into explicit, executable logical rules.

The XAI community has studied a wide range of queries and scores for explaining predictions of ML models. From a data management perspective, this proliferation of explanation notions calls for declarative query languages in which such notions can be specified, combined, and analyzed uniformly. In this paper, we develop such a framework for Boolean models. We first revisit FOIL, an interpretability query language for black-box models, and show that it has two fundamental limitations: it cannot express central optimality-based explanation queries, and its evaluation problem over decision trees is hard for every level of the polynomial hierarchy. We then introduce ExplAIner, a query language based on FOIL with an extended vocabulary and a layered structure. We show that ExplAIner can express a broad family of explanation notions, including abductive, contrastive, feature-based, and distance-based queries. We also prove that the evaluation problem for each query in ExplAIner belongs to the Boolean hierarchy over every class of Boolean models for which some basic predicates can be evaluated in polynomial time. In particular, that property holds for deterministic and decomposable Boolean circuits. Finally, we introduce Opt-FOIL, an optimization-oriented fragment of ExplAIner for computing explanations that are minimal with respect to strict partial orders, and prove that its evaluation problem is in $\mathrm{FP}^{\mathrm{NP}}$ under the same tractability assumptions. These complexity results have a direct algorithmic consequence: a fixed ExplAIner query can be evaluated with a fixed number of calls to a SAT solver, while a notion of explanation specified in Opt-FOIL can be computed with a polynomial number of such calls. This is particularly relevant in formal XAI, where SAT solvers have been successfully used to compute explanations for several classes of ML models.

In this work, we propose a unified approach for diagnosing misclassification and assessing the robustness of black-box classifiers. Central to our method is an optimization framework that modifies an instance so that the classifier predicts a specified target label, while ensuring that the modification remains easily explainable. The objective function contains two components: an explainability-aware $L_0$ (XA-$L_0$) penalty that promotes sparse and interpretable modifications, and a classifier loss objective that steers the perturbed instance toward the desired output. This integrated optimization formulation is used both to identify the underlying causes of misclassification and to evaluate robustness by determining how an instance can change within a tolerance region before being reassigned to another class. To quantify robustness, we introduce the Tolerance Region Confusion Matrix (TOR-Confusion Matrix), which measures a classifier's susceptibility by modeling the class-to-class transition probabilities induced by tolerance-bounded perturbations. We validate the proposed method on both image and tabular datasets, demonstrating its ability to jointly deliver interpretability and robustness assessment.

The increasing adoption of end-to-end learning for autonomous driving introduces increased model complexity and opacity, raising the risk of learning undesired or erroneous behavior. In this work, we integrate unsupervised dictionary learning as a post hoc interpretability module within state-of-the-art driving models to decompose driving behavior into semantically meaningful concepts while demonstrating their causal influence on the model's driving decisions. We propose a stepwise framework for extracting and interpreting meaningful concepts from the end-to-end model and connecting them to the multifaceted model outputs, thereby revealing the underlying decision-making logic for the prediction of future trajectories. Furthermore, targeted interventions at the concept level allow us to manipulate and correct driving decisions, resulting in measurable improvements in overall driving performance. We thus demonstrate how interpretability can effectively be used to reduce model opacity, uncover erroneous behavior, and enable targeted mitigation, ultimately boosting model performance.

Integrating complex, multi-omics data presents significant challenges. Existing approaches often face a trade-off between model interpretability and representational capacity, with most either relying on post-hoc interpretation or use linear models that may overlook complex interactions. We report Pathway Activity Autoencoders for the multi-omics setting, which embed prior knowledge via pathway-informed architectural constraints, fostering interpretability, while preserving representational power. Our multi-omic framework is applied in the context of breast cancer and is evaluated in survival prediction and subtype classification with results indicating a positive effect of integration. We conduct analysis of individual omics layer impact on end-task performance, revealing that gene, protein, and microRNA expression layers provide the strongest contribution. Repeatability studies indicate that, while dropout improves model robustness and consistency, excessive regularisation can reduce predictive performance. Finally, visualizations of the learned feature space illustrate the framework's intrinsic transparency and clinical relevance. The results underscore the value of multi-omic integration and delineate the impact of individual omics layers, establishing practical guidelines for integration within our framework. Overall, our pathway activity autoencoder frameworks yield superior latent representations that are biologically meaningful and are directly translatable into clinically relevant insights.

The adoption of non-parametric machine learning models for regulatory capital estimation introduces a fundamental governance challenge: the inability to explain model outputs in a manner auditable by supervisory bodies. This 'black box' problem remains a major barrier to the adoption of Gaussian Process Regression (GPR) and related ML architectures in ICAAP and CCAR workflows despite their predictive advantages over traditional parametric approaches. This paper addresses this barrier through SHARC (SHAP for Regulatory Capital), an explainability framework for the Hybrid GPR-HS architecture and its stress-testing extension. SHapley Additive exPlanations (SHAP), derived from cooperative game theory and satisfying the properties of Local Accuracy, Missingness, Consistency, and Efficiency, are applied to Stressed Value-at-Risk (SVaR) outputs under three macro scenarios: West Asia War, Climate Risk, and AI Bubble/Regulatory Burden. SHARC decomposes SVaR into baseline, mean-driven, and volatility-driven components, enabling transparent linkage between scenario design and capital outcomes. Two findings emerge. First, SHARC consistently links non-linear SVaR outputs to underlying scenario inputs, confirming framework fidelity and providing auditable traceability of capital drivers. Second, under stress conditions, the mean return component (directional loss magnitude) dominates the variance component (volatility baseline) in determining capital levels, with implications for capital limit-setting, position management, and hedging strategy. The results establish SHARC as a regulator-aligned explainability layer that makes the Hybrid GPR-HS framework fully auditable and consistent with FRTB, ICAAP Pillar 2, and CCAR transparency requirements.

Minimum Bayes Risk (MBR) decoding yields more robust and higher-quality text generation than maximum a posteriori (MAP) decoding by selecting hypotheses that maximize expected utility over sampled pseudo-references. However, there exists a discrepancy in the design: hypothesis selection calculates expected utility scores conditioned on given pseudo-references, while commonly used evaluation metrics, e.g., BLEU and COMET, are asymmetric. Therefore, it is important to consider both hypothesis-to-reference and reference-to-hypothesis directional effects. In this study, we introduce a noisy channel decomposition of MBR decoding that naturally incorporates bidirectional effects to account for these asymmetries. We decompose MBR decoding into four interacting components: hypothesis-to-reference likelihood, reference-to-hypothesis likelihood, hypothesis prior, and reference prior. This decomposition provides a unified interpretation of existing MBR variants and enables metric- and task-specific interpretability by isolating the contribution of each channel. Our comprehensive analysis reveals that channel-wise contributions exhibit distinct characteristics across metrics while remaining consistent across tasks, and suggests that appropriate channel weighting may lead to improvements over original MBR decoding.

A coding agent solving a software-engineering task spends dozens of steps reasoning, editing code, and running tests, yet little is known about what the underlying language model internally represents about the program it is working on. We show that the residual streams of language models under coding agents linearly encode properties of the evolving program: a logistic-regression probe on hidden states is able to decode whether the current code parses, passes its test suite, reduces the number of failing tests, and introduces regressions, reaching AUC up to 0.83 for correctness across two models and two benchmarks. Our second finding is more surprising: these representations run ahead of the agent's own edits. Probes trained to predict the outcome of future edits (before they are materialized and written on disk) achieve performance above chance up to roughly 25 steps in advance. We call this the agent's latent programming horizon. As a proof of external validity, we show that the probes transfer across benchmarks without retraining. Our positive results open calls for more research in mechanistic interpretability of coding agents.

Interpretability methods aim to reveal the features represented inside large language models (LLMs). Many existing methods begin with labeled examples of a human-defined concept that may reflect human biases, and then identify how that concept is represented within the model, for example in its activation space or through other decomposition methods. We introduce \emph{Mining via Activation Geometry} (MAG), a simple unsupervised framework for extracting reasoning features from model activations by prepending the same natural-language instruction $Q$ to every input $p$, where $Q$ defines the reasoning feature of interest, such as Can this object be found in the desert?'' or Is this prompt malicious?'' We measure how the instruction changes the model's internal representation using $m(Q \mid p) - m(p)$ at a single readout point. We explore eight different MAGs. The extracted reasoning features predict the models' own world understanding and judgment, can be approximated into a single activation direction, we found that some features are more linearly represented and some less, this linear representation, which is vector steering, can change the LLMs' decisions through activation steering by injecting reasoning features. Finally, we use the same method to select the best training datasets for prompt-injection classifier probes: while similarity between ordinary activations is almost unrelated to downstream performance, RFD-based similarity achieves $94.7\%$ Top-1 and $100\%$ Top-2 accuracy.

Dialectal data are scarce relative to Modern Standard Arabic (MSA), causing Arabic LLMs to overproduce MSA and struggle with dialectally accurate generation. This raises a fundamental interpretability question about where and how dialectal features are encoded within model internals and whether these representations can improve dialect generation without fine-tuning. We study two inference-time approaches as interpretability probes and control mechanisms. First, neuron-level analysis identifies sparse populations that encode dialect-specific features and tests whether amplifying or suppressing them steers model outputs toward target dialects. Second, vector steering extracts dialect-specific activation directions and injects them during inference, motivated by feature entanglement at the neuron level. We find that these neurons are real but only partially explanatory. They occupy under 1% of MLP dimensions but span only 5% to 21% of the residual dialect direction. This limited coverage is causally consequential. Neuron steering reinforces dialect in some varieties when the prompt is already dialectal but cannot induce it from MSA prompts, whereas vector steering succeeds in both settings. Arabic dialects are therefore steerable mainly through distributed rather than localized representations

When a person shares something with a language model, the model often answers the surface of the message rather than what the sender was doing by sending it: share a finished project and it critiques the code; share a raw late-night line and it runs a wellness check. We treat the sender's communicative intent, the Gricean what-was-meant, as a first-class interpretability object, and show the failure is one of readout on top of a robust representation. A linear probe decodes the sender's intent, whether they want a thing recognized or evaluated, from a model's default-pass hidden states, cleanly and surface-independently, across six models and four families and in the base checkpoints. The representation generalizes further, to intent that is only pragmatically inferred, and to a second, lexically clean intent (support versus help). The behavioral half of the story, and every causal test, is established on the recognize/evaluate contrast, where what varies is whether the default output acts on the intent. The readout lags the representation in depth within a model (the intent is decodable several layers before it drives the output); across models, which ones act on it by default is model-specific, an observed stratification (three of six show the failure) that we do not read as a scaling law. Where the gap is open, a direction closely tied to the representation, the discriminative direction at a searched-for layer, is a causal handle: steering it recovers the intended behavior, as well as an explicit instruction does and with no prompt at all. This direction is near-orthogonal to the feedback-offering axis, so it routes a represented intent rather than a generic feedback knob, though at the recovery dose the routed intent can override an explicit request. We support each link with controls against obvious deflations and report the nulls as plainly as the confirmations.

A central goal of mechanistic interpretability is to understand how neural networks work and what each individual component does. Dominant circuit-finding approaches focus on a specific behavior and reverse-engineer the role of components on the associated sub-distribution. However, past work has shown that components can have different functions that are active on different subsets of the input distribution. In this work we ask whether a single weight can be understood globally across the full training distribution by characterizing when it matters (the inputs on which ablating it changes the model's predictions). We introduce an automated LLM pipeline that writes a short, human-readable description of when a weight matters and verifies it on held-out text, crediting a weight only if its description generalizes. Across two sparse and two dense transformers, the fraction of weights that are interpretable (in this sense) is higher in sparse transformers than in dense ones, a gap that widens once unreliable descriptions are discarded. Our results show that a meaningful fraction of a sparse transformer model's weights can be interpreted: 12 to 31% of weights have a single short description that identifies what the weight is used for.

Models trained via Contrastive Language-Image Pretraining (CLIP) serve as the foundational vision encoders for most modern Large Vision Language Models (LVLMs). Despite their widespread adoption, CLIP models exhibit a critical yet underexplored failure mode: irrelevant text appearing within images confounds visual representations, biasing them toward lexical meaning rather than true visual semantics. This robustness issue, commonly described as a Typographic Attack (TA), exposes a vulnerability that poses a significant risk to safety-critical applications such as autonomous driving. To achieve interpretable and effective robustness against TA, we propose a novel, training-free mechanistic interpretability method. Our method provides sampling-based interpretations of hidden state representations and quantitatively attributes semantic versus lexical focus to individual attention heads. Through probabilistic analysis and circuit mining, we isolate specific Vision Transformer (ViT) components that disproportionately encode lexical information, thereby identifying the mechanistic source of TA. We further show that simple interventions applied directly to the identified circuits, without any additional training, can substantially improve robustness against Typographic Attacks in object classification. These interventions, such as selective adjustment of attention weights, also outperform both supervised and training-free defense methods. Our experiments demonstrate that applying the proposed intervention to the vision encoders of several state-of-the-art LVLMs yields substantial gains in Visual Question Answering accuracy under Typographic Attack interference on RIO-Bench. These results confirm both the efficacy and the generalizability of our mechanistic approach. Code is released at https://github.com/Liu-524/SamplingTAR.

Steering and monitoring activations in Large Language Models (LLMs) are increasingly used for both safety and interpretability. Early work assumed behaviours are encoded along single linear directions, but recent findings suggest complex behaviours, such as the refusal to answer harmful queries, live in multi-dimensional subspaces. However, existing methods for extracting these subspaces are computationally expensive, which becomes prohibitive on reasoning models who produce long reasoning traces. By adapting the Recursive Feature Machine (RFM) algorithm -- which can be computed efficiently -- with a probe-informed initialization, we are able to identify the multi-dimensional refusal subspace in seconds, on reasoning (Qwen 3) and non-reasoning (Qwen 2.5) models. While RFM allows for faster subspace identification, it also showed better performances on the ablation task than its alternatives. More work is planned to better understand the relations between subspaces found by different methods. If confirmed, RFM could be a cheap and scalable complement to existing subspace-extraction methods in LLMs.

Mechanistic interpretability seeks to explain transformer behavior through circuits: sets of internal components that causally support a behavior. However, self-repair creates a blind spot: ablating a primary component can activate a dormant backup, so a circuit that explains behavior in the intact model can become incomplete under the intervention used to test it. We formulate this gap as conditional circuit completion: given a primary set, identify components that become causally important after its removal. We introduce conditional co-ablation (CoAx), which ranks candidates by growth in ablation effect after primary-set removal. We show that a perfectly dormant backup can be indistinguishable from an irrelevant component to per-unit intact-state scores, whereas its conditional effect change exactly aggregates all interaction orders linking it to the removed set. On GPT-2-small's Indirect Object Identification (IOI) circuit, CoAx recovers the documented backup heads at 0.941 ROC-AUC, versus 0.815 for the strongest intact-state attribution baseline and 0.758 for the matched conditional-energy control. Recovery drops to 0.40 +/- 0.13 AUC for alternative component sets matched in behavioral effect, output displacement, and depth, showing that recovery is specific to the removed circuit. Beyond recovery, the CoAx-selected heads are causally load-bearing: freezing them after primary removal sharply reduces the IOI margin, while adding them to the incomplete circuit reduces incompleteness from 0.75 to 0.21. More broadly, conditional growth aligns with intervention-derived repair in 11/12 held-out instances across 4 mechanism clusters, and CoAx completions outperform matched random completions on all 8 non-GPT-2 models spanning 6 architecture families. Together, causal explanations of self-repairing transformers must account for backup circuitry when primary components fail.

Sparse autoencoders (SAEs) decompose internal activations of neural networks into sparse linear combinations of learned features by fitting an overcomplete dictionary $\mathbf{W}\in\mathbb{R}^{m\times n}$ with $m<n$, and inferring a sparse code $\mathbf{x}\in\mathbb{R}^n$ from $\mathbf{h}\approx\mathbf{W}\mathbf{x}$. This inference problem closely resembles the canonical setup of compressed sensing, but dense decoders requires $O(mn)$ learned values, which becomes costly at large feature counts. We introduce Expander SAEs: TopK SAEs whose decoder and tied encoder are supported on a left-$d$-regular expander mask with $d\ll m$, learning only $dn$ decoder values while keeping the sparse-coding problem $(m,n,k)$ fixed. The same structure reduces storage and turns the matching-pursuit correlation step $\mathbf{W}^\top \mathbf{r}$ in OMP into an $O(dn)$ gather-and-reduce operation. Our experiments show that across Pythia-70M/160M, Qwen2.5-3B, and Llama-3.2-1B residual-stream activations, varying $d$ traces a consistent storage--fidelity frontier, and that at the most compressed modern-LM setting, Qwen2.5-3B with $d=7$ uses $293\times$ fewer learned decoder values than the full dense decoder while retaining $84$% of dense CE-loss recovered. Control experiments show that the improved storage--fidelity tradeoff is driven by sparse, diverse decoder support structure rather than by fewer learned decoder values, and that when sparse and dense decoders are compared at matched parameter count, part of the remaining gap comes from encoder amortisation. On the theoretical side, we show that expansion and column flatness are sufficient for identifiability of noiseless $k$-sparse codes, and we derive complementary sufficient conditions under which OMP recovers the support exactly.

Neural Quantum States (NQS) are a remarkably expressive class of variational ansätze for quantum many-body wavefunctions, yet little is understood about their internal mechanisms: trained on variational objectives alone, how do NQS accurately capture physical observables that they have never been explicitly optimized for? In this work, we present a systematic approach to analyze the internal activations of NQS using sparse autoencoders. We extract features from the residual stream and demonstrate that these features strongly correlate with physical observables such as order parameters, staggered magnetization, and half-chain correlators, across both ground state representation and real-time dynamics. Remarkably, the discovery of these features is entirely unsupervised, with no physical labels provided. We further establish that such features causally affect the corresponding observables predicted by NQS, by showing that targeted, post-training intervention on a \textit{single} feature smoothly and monotonically steers the corresponding observable, while leaving the variational energy nearly unchanged. These results demonstrate that NQS are not merely functional approximators, but encode rich, interpretable internal representations of physical information. Our approach provides both a diagnostic and an intervention tool for NQS, and serves as a foundation for using mechanistic interpretability towards more reliable, transparent NQS.

Deep learning has outgrown any single mathematical explanation. From Approximation to Emergence develops a unified, proof-oriented account of modern deep learning theory, tracing a path from the classical foundations of approximation, optimization, and generalization to the contemporary mechanisms of overparameterization, robustness, generative modeling, transformers, in-context learning, scaling laws, interpretability, alignment, and emergence. Rather than presenting isolated results, the book organizes a broad literature into a coherent research narrative: each theory is examined through the object it controls, the assumptions that make it valid, and the phenomena it leaves unexplained. Written for researchers, graduate students, and mathematically trained practitioners, this monograph offers a rigorous map of deep learning theory as it stands today: powerful, incomplete, and increasingly centered on the question of how learned mechanisms arise from scale, data, architecture, and training.

Complexity and interpretability rarely coincide: systems rich enough for complex behaviours to emerge are usually too opaque to question, while transparent ones are too simple for anything complex to emerge. A single large language model (LLM) is a static artefact, hardly exhibiting any of the emergent properties we associate with life. This changes through interaction: populations of LLMs display emergent dynamics absent from isolated models. Furthermore, LLMs can be endowed with persistent memory, tools and shared skills, and the capacity to initiate actions unprompted, i.e., turning LLMs agentic. In this paper, we argue that such collectives of agents can serve as a computational substrate for Artificial Life (ALife) research. Critically, since the agents communicate in natural language, their collective behaviour can be directly interrogated by examining textual traces and asking the agents themselves. We outline the notion of interpretability in language-model research and extend it for collectives of agents. Lastly, we survey recent examples of agentic LLM collectives that already instantiate the idea of agentic substrates, from controlled experiments to deployments in the wild.