Posterior-Calibrated Causal Circuits in Variational Autoencoders: Why Image-Domain Interpretability Fails on Tabular Data

Abstract: Although mechanism-based interpretability has generated an abundance of insight for discriminative network analysis, generative models are less understood -- particularly outside of image-related applications. We investigate how much of the causal circuitry found within image-related variational autoencoders (VAEs) will generalize to tabular data, as VAEs are increasingly used for imputation, anomaly detection, and synthetic data generation. In addition to extending a four-level causal intervention framework to four tabular and one image benchmark across five different VAE architectures (with 75 individual training runs per architecture and three random seed values for each run), this paper introduces three new techniques: posterior-calibration of Causal Effect Strength (CES), path-specific activation patching, and Feature-Group Disentanglement (FGD). The results from our experiments demonstrate that: (i) Tabular VAEs have circuits with modularity that is approximately 50% lower than their image counterparts. (ii) $β$-VAE experiences nearly complete collapse in CES scores when applied to heterogeneous tabular features (0.043 CES score for tabular data compared to 0.133 CES score for images), which can be directly attributed to reconstruction quality degradation (r = -0.886 correlation coefficient between CES and MSE). (iii) CES successfully captures nine of eleven statistically significant architecture differences using Holm--Šidák corrections. (iv) Interventions with high specificity predict the highest downstream AUC values (r = 0.460, p < .001). This study challenges the common assumption that architectural guidance from image-related studies can be transferred to tabular datasets.

Dip Roy
Rajiv Misra
Sanjay Kumar Singh
Anisha Roy


Shift-Invariant Feature Attribution in the Application of Wireless Electrocardiograms

Abstract: Assigning relevance scores to the input features of a machine learning model enables to measure the contributions of the features in achieving a correct outcome. It is regarded as one of the approaches towards developing explainable models. For biomedical assignments, this is very useful for medical experts to comprehend machine-based decisions. In the analysis of electro cardiogram (ECG) signals, in particular, understanding which of the electrocardiogram samples or features contributed most for a given decision amounts to understanding the underlying cardiac phases or conditions the machine tries to explain. For the computation of relevance scores, determining the proper baseline is important. Moreover, the scores should have a distribution which is at once intuitive to interpret and easy to associate with the underline cardiac reality. The purpose of this work is to achieve these goals. Specifically, we propose a shift-invariant baseline which has a physical significance in the analysis as well as interpretation of electrocardiogram measurements. Moreover, we aggregate significance scores in such a way that they can be mapped to cardiac phases. We demonstrate our approach by inferring physical exertion from cardiac exertion using a residual network. We show that the ECG samples which achieved the highest relevance scores (and, therefore, which contributed most to the accurate recognition of the physical exertion) are those associated with the P and T waves. Index Terms Attribution, baseline, cardiovascular diseases, electrocardiogram, activity recognition, machine learning

Yalemzerf Getnet
Abiy Tasissa
Waltenegus Dargie


Sparse Autoencoders Reveal Interpretable and Steerable Features in VLA Models

Abstract: Vision-Language-Action (VLA) models have emerged as a promising approach for general-purpose robot manipulation. However, little research has mechanistically explored when and why they generalize across objects, scenes, and instructions. To probe internal representations, we train Sparse Autoencoders (SAEs) on the VLA's hidden-layer activations. SAEs learn sparse dictionaries over model activations, often revealing features that correspond to interpretable directions in the model's representation space. We identify SAE features corresponding to motion primitives and semantic concepts, including features that are general across episodes and causally steerable. We propose a metric to categorize features as general transferable primitives or episode-specific memorizations, offering a promising glimpse towards VLA generalization. We validate these findings through steering experiments on both the LIBERO simulation benchmark and on real-world DROID hardware. We find that amplifying general and semantic features induces behaviors consistent with their meanings, whereas ablating them destroys model performance. Furthermore, we demonstrate steering as a way to control behavior in unpromptable directions. Together, these results provide mechanistic evidence that VLAs can learn reusable internal features linking perception, language, and action across tasks and scenes. Our project page is located at https://drvla.github.io

Aiden Swann
Lachlain McGranahan
Hugo Buurmeijer
Monroe Kennedy
Mac Schwager


Counting Circuits: Mechanistic Interpretability of Visual Reasoning in Large Vision-Language Models

Abstract: Counting serves as a simple but powerful test of a Large Vision-Language Model's (LVLM's) reasoning; it forces the model to identify each individual object and then add them all up. In this study, we investigate how LVLMs implement counting using controlled synthetic and real-world benchmarks, combined with mechanistic analyses. Our results show that LVLMs display a human-like counting behavior, with precise performance on small numerosities and noisy estimation for larger quantities. We introduce two novel interpretability methods, Visual Activation Patching and HeadLens, and use them to uncover a structured "counting circuit" that is largely shared across a variety of visual reasoning tasks. Building on these insights, we propose a lightweight intervention strategy that exploits simple and abundantly available synthetic images to fine-tune arbitrary pretrained LVLMs exclusively on counting. Despite the narrow scope of this fine-tuning, the intervention not only enhances counting accuracy on in-distribution synthetic data, but also yields an average improvement of +8.36% on out-of-distribution counting benchmarks and an average gain of +1.54% on complex, general visual reasoning tasks for Qwen2.5-VL. These findings highlight the central, influential role of counting in visual reasoning and suggest a potential pathway for improving overall visual reasoning capabilities through targeted enhancement of counting mechanisms.

Liwei Che
Zhiyu Xue
Yihao Quan
Benlin Liu
Zeru Shi
Michelle Hurst
Jacob Feldman
Ruixiang Tang
Ranjay Krishna
Vladimir Pavlovic


Interpretability without actionability: mechanistic methods cannot correct language model errors despite near-perfect internal representations

Abstract: Language models encode task-relevant knowledge in internal representations that far exceeds their output performance, but whether mechanistic interpretability methods can bridge this knowledge-action gap has not been systematically tested. We compared four mechanistic interpretability methods -- concept bottleneck steering (Steerling-8B), sparse autoencoder feature steering, logit lens with activation patching, and linear probing with truthfulness separator vector steering (Qwen 2.5 7B Instruct) -- for correcting false-negative triage errors using 400 physician-adjudicated clinical vignettes (144 hazards, 256 benign). Linear probes discriminated hazardous from benign cases with 98.2% AUROC, yet the model's output sensitivity was only 45.1%, a 53-percentage-point knowledge-action gap. Concept bottleneck steering corrected 20% of missed hazards but disrupted 53% of correct detections, indistinguishable from random perturbation (p=0.84). SAE feature steering produced zero effect despite 3,695 significant features. TSV steering at high strength corrected 24% of missed hazards while disrupting 6% of correct detections, but left 76% of errors uncorrected. Current mechanistic interpretability methods cannot reliably translate internal knowledge into corrected outputs, with implications for AI safety frameworks that assume interpretability enables effective error correction.

Sanjay Basu
Sadiq Y. Patel
Parth Sheth
Bhairavi Muralidharan
Namrata Elamaran
Aakriti Kinra
John Morgan
Rajaie Batniji


Do Language Models Encode Semantic Relations? Probing and Sparse Feature Analysis

Abstract: Understanding whether large language models (LLMs) capture structured meaning requires examining how they represent concept relationships. In this work, we study three models of increasing scale: Pythia-70M, GPT-2, and Llama 3.1 8B, focusing on four semantic relations: synonymy, antonymy, hypernymy, and hyponymy. We combine linear probing with mechanistic interpretability techniques, including sparse autoencoders (SAE) and activation patching, to identify where these relations are encoded and how specific features contribute to their representation. Our results reveal a directional asymmetry in hierarchical relations: hypernymy is encoded redundantly and resists suppression, while hyponymy relies on compact features that are more easily disrupted by ablation. More broadly, relation signals are diffuse but exhibit stable profiles: they peak in the mid-layers and are stronger in post-residual/MLP pathways than in attention. Difficulty is consistent across models (antonymy easiest, synonymy hardest). Probe-level causality is capacity-dependent: on Llama 3.1, SAE-guided patching reliably shifts these signals, whereas on smaller models the shifts are weak or unstable. Our results clarify where and how reliably semantic relations are represented inside LLMs, and provide a reproducible framework for relating sparse features to probe-level causal evidence.


Towards Interpretable Framework for Neural Audio Codecs via Sparse Autoencoders: A Case Study on Accent Information

Abstract: Neural Audio Codecs (NACs) are widely adopted in modern speech systems, yet how they encode linguistic and paralinguistic information remains unclear. Improving the interpretability of NAC representations is critical for understanding and deploying them in sensitive applications. Hence, we employ Sparse Autoencoders (SAEs) to decompose dense NAC representations into sparse, interpretable activations. In this work, we focus on a challenging paralinguistic attribute-accent-and propose a framework to quantify NAC interpretability. We evaluate four NAC models under 16 SAE configurations using a relative performance index. Our results show that DAC and SpeechTokenizer achieve the highest interpretability. We further reveal that acoustic-oriented NACs encode accent information primarily in activation magnitudes of sparse representations, whereas phonetic-oriented NACs rely more on activation positions, and that low-bitrate EnCodec variants show higher interpretability.

Shih-Heng Wang
Tiantian Feng
Aditya Kommineni
Thanathai Lertpetchpun
Bowen Yi
Xuan Shi
Shrikanth Narayanan


Sparse but not Simpler: A Multi-Level Interpretability Analysis of Vision Transformers

Abstract: Sparse neural networks are often hypothesized to be more interpretable than dense models, motivated by findings that weight sparsity can produce compact circuits in language models. However, it remains unclear whether structural sparsity itself leads to improved semantic interpretability. In this work, we systematically evaluate the relationship between weight sparsity and interpretability in Vision Transformers using DeiT-III B/16 models pruned with Wanda. To assess interpretability comprehensively, we introduce \textbf{IMPACT}, a multi-level framework that evaluates interpretability across four complementary levels: neurons, layer representations, task circuits, and model-level attribution. Layer representations are analyzed using BatchTopK sparse autoencoders, circuits are extracted via learnable node masking, and explanations are evaluated with transformer attribution using insertion and deletion metrics. Our results reveal a clear structural effect but limited interpretability gains. Sparse models produce circuits with approximately $2.5\times$ fewer edges than dense models, yet the fraction of active nodes remains similar or higher, indicating that pruning redistributes computation rather than isolating simpler functional modules. Consistent with this observation, sparse models show no systematic improvements in neuron-level selectivity, SAE feature interpretability, or attribution faithfulness. These findings suggest that structural sparsity alone does not reliably yield more interpretable vision models, highlighting the importance of evaluation frameworks that assess interpretability beyond circuit compactness.


GradCFA: A Hybrid Gradient-Based Counterfactual and Feature Attribution Explanation Algorithm for Local Interpretation of Neural Networks

Abstract: Explainable Artificial Intelligence (XAI) is increasingly essential as AI systems are deployed in critical fields such as healthcare and finance, offering transparency into AI-driven decisions. Two major XAI paradigms, counterfactual explanations (CFX) and feature attribution (FA), serve distinct roles in model interpretability. This study introduces GradCFA, a hybrid framework combining CFX and FA to improve interpretability by explicitly optimizing feasibility, plausibility, and diversity - key qualities often unbalanced in existing methods. Unlike most CFX research focused on binary classification, GradCFA extends to multi-class scenarios, supporting a wider range of applications. We evaluate GradCFA's validity, proximity, sparsity, plausibility, and diversity against state-of-the-art methods, including Wachter, DiCE, CARE for CFX, and SHAP for FA. Results show GradCFA effectively generates feasible, plausible, and diverse counterfactuals while offering valuable FA insights. By identifying influential features and validating their impact, GradCFA advances AI interpretability. The code for implementation of this work can be found at: https://github.com/jacob-ws/GradCFs .

IEEE Transactions on Artificial Intelligence


Embedding-Aware Feature Discovery: Bridging Latent Representations and Interpretable Features in Event Sequences

Abstract: Industrial financial systems operate on temporal event sequences such as transactions, user actions, and system logs. While recent research emphasizes representation learning and large language models, production systems continue to rely heavily on handcrafted statistical features due to their interpretability, robustness under limited supervision, and strict latency constraints. This creates a persistent disconnect between learned embeddings and feature-based pipelines. We introduce Embedding-Aware Feature Discovery (EAFD), a unified framework that bridges this gap by coupling pretrained event-sequence embeddings with a self-reflective LLM-driven feature generation agent. EAFD iteratively discovers, evaluates, and refines features directly from raw event sequences using two complementary criteria: \emph{alignment}, which explains information already encoded in embeddings, and \emph{complementarity}, which identifies predictive signals missing from them. Across both open-source and industrial transaction benchmarks, EAFD consistently outperforms embedding-only and feature-based baselines, achieving relative gains of up to $+5.8\%$ over state-of-the-art pretrained embeddings, resulting in new state-of-the-art performance across event-sequence datasets.

Artem Sakhno
Ivan Sergeev
Alexey Shestov
Omar Zoloev
Elizaveta Kovtun
Gleb Gusev
Andrey Savchenko
Maksim Makarenko


Whether, Not Which: Mechanistic Interpretability Reveals Dissociable Affect Reception and Emotion Categorization in LLMs

Abstract: Large language models appear to develop internal representations of emotion -- "emotion circuits," "emotion neurons," and structured emotional manifolds have been reported across multiple model families. But every study making these claims uses stimuli signalled by explicit emotion keywords, leaving a fundamental question unanswered: do these circuits detect genuine emotional meaning, or do they detect the word "devastated"? We present the first clinical validity test of emotion circuit claims using mechanistic interpretability methods grounded in clinical psychology -- clinical vignettes that evoke emotions through situational and behavioural cues alone, emotion keywords removed. Across six models (Llama-3.2-1B, Llama-3-8B, Gemma-2-9B; base and instruct variants), we apply four convergent mechanistic interpretability methods -- linear probing, causal activation patching, knockout experiments, and representational geometry -- and discover two dissociable emotion processing mechanisms. Affect reception -- detecting emotionally significant content -- operates with near-perfect accuracy (AUROC 1.000), consistent with early-layer saturation, and replicates across all six models. Emotion categorization -- mapping affect to specific emotion labels -- is partially keyword-dependent, dropping 1-7% without keywords and improving with scale. Causal activation patching confirms keyword-rich and keyword-free stimuli share representational space, transferring affective salience rather than emotion-category identity. These findings falsify the keyword-spotting hypothesis, establish a novel mechanistic dissociation, and introduce clinical stimulus methodology as a rigorous standard for testing emotion processing claims in large language models -- with direct implications for AI safety evaluation and alignment. All stimuli, code, and data are released for replication.


Abstract: Attribution methods for Vision Transformers (ViTs) aim to identify image regions that influence model predictions, but producing faithful and well-localized attributions remains challenging. Existing attribution methods face several limitations, with gradient-based, relevance-propagation, and attention-based methods relying on local approximations, while perturbation or optimization-based methods intervene on inputs, tokens, or surrogates rather than internal patch representations. The key challenge is that class-relevant evidence is formed through interactions between patch tokens across layers; methods that operate only on input changes, attention weights, or backward relevance signals may therefore provide indirect proxies for patch importance rather than directly testing the predictive effect of contextualized patch representations. We propose Causal Attribution via Activation Patching (CAAP), which estimates the contribution of individual image patches to the ViT's prediction by directly intervening on internal activations rather than using learned masks or synthetic perturbation patterns. For each patch, CAAP inserts the corresponding source-image activations into a neutral target context over an intermediate range of layers and uses the resulting target-class score as the attribution signal. The resulting attribution map reflects the causal contribution of patch-associated internal representations on the model's prediction. The causal intervention serves as a principled measure of patch influence by capturing semantic evidence after initial representation formation, while avoiding late-layer global mixing that can reduce spatial specificity. Across multiple ViT backbones and standard metrics, CAAP consistently outperforms existing methods in various settings and produces more faithful and localized attributions.

Amirmohammad Izadi
Mohammadali Banayeeanzade
Alireza Mirrokni
Hosein Hasani
Mobin Bagherian
Faridoun Mehri
Mahdieh Soleymani Baghshah


From Data Statistics to Feature Geometry: How Correlations Shape Superposition

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

Lucas Prieto
Edward Stevinson
Melih Barsbey
Tolga Birdal
Pedro A. M. Mediano


Dissecting Chronos: Sparse Autoencoders Reveal Causal Feature Hierarchies in Time Series Foundation Models

Abstract: Time series foundation models (TSFMs) are increasingly deployed in high-stakes domains, yet their internal representations remain opaque. We present the first application of sparse autoencoders (SAEs) to a TSFM, training TopK SAEs on activations of Chronos-T5-Large (710M parameters) across six layers. Through 392 single-feature ablation experiments, we establish that every ablated feature produces a positive CRPS degradation, confirming causal relevance. Our analysis reveals a depth-dependent hierarchy: early encoder layers encode low-level frequency features, the mid-encoder concentrates causally critical change-detection features, and the final encoder compresses a rich but less causally important taxonomy of temporal concepts. The most critical features reside in the mid-encoder (max single-feature Delta CRPS = 38.61), not in the semantically richest final encoder layer, where progressive ablation paradoxically improves forecast quality. These findings demonstrate that mechanistic interpretability transfers effectively to TSFMs and that Chronos-T5 relies on abrupt-dynamics detection rather than periodic pattern recognition.


Class Visualizations and Activation Atlases for Enhancing Interpretability in Deep Learning-Based Computational Pathology

Abstract: The rapid adoption of transformer-based models in computational pathology has enabled prediction of molecular and clinical biomarkers from H&E whole-slide images, yet interpretability has not kept pace with model complexity. While attribution- and generative-based methods are common, feature visualization approaches such as class visualizations (CVs) and activation atlases (AAs) have not been systematically evaluated for these models. We developed a visualization framework and assessed CVs and AAs for a transformer-based foundation model across tissue and multi-organ cancer classification tasks with increasing label granularity. Four pathologists annotated real and generated images to quantify inter-observer agreement, complemented by attribution and similarity metrics. CVs preserved recognizability for morphologically distinct tissues but showed reduced separability for overlapping cancer subclasses. In tissue classification, agreement decreased from Fleiss k = 0.75 (scans) to k = 0.31 (CVs), with similar trends in cancer subclass tasks. AAs revealed layer-dependent organization: coarse tissue-level concepts formed coherent regions, whereas finer subclasses exhibited dispersion and overlap. Agreement was moderate for tissue classification (k = 0.58), high for coarse cancer groupings (k = 0.82), and low at subclass level (k = 0.11). Atlas separability closely tracked expert agreement on real images, indicating that representational ambiguity reflects intrinsic pathological complexity. Attribution-based metrics approximated expert variability in low-complexity settings, whereas perceptual and distributional metrics showed limited alignment. Overall, concept-level feature visualization reveals structured morphological manifolds in transformer-based pathology models and provides a framework for expert-centered interrogation of learned representations across label granularities.

Marco Gustav
Fabian Wolf
Christina Glasner
Nic G. Reitsam
Stefan Schulz
Kira Aschenbroich
Bruno Märkl
Sebastian Foersch
Jakob Nikolas Kather


Learning Concept Bottleneck Models from Mechanistic Explanations

Abstract: Concept Bottleneck Models (CBMs) aim for ante-hoc interpretability by learning a bottleneck layer that predicts interpretable concepts before the decision. State-of-the-art approaches typically select which concepts to learn via human specification, open knowledge graphs, prompting an LLM, or using general CLIP concepts. However, concepts defined a-priori may not have sufficient predictive power for the task or even be learnable from the available data. As a result, these CBMs often significantly trail their black-box counterpart when controlling for information leakage. To address this, we introduce a novel CBM pipeline named Mechanistic CBM (M-CBM), which builds the bottleneck directly from a black-box model's own learned concepts. These concepts are extracted via Sparse Autoencoders (SAEs) and subsequently named and annotated on a selected subset of images using a Multimodal LLM. For fair comparison and leakage control, we also introduce the Number of Contributing Concepts (NCC), a decision-level sparsity metric that extends the recently proposed NEC metric. Across diverse datasets, we show that M-CBMs consistently surpass prior CBMs at matched sparsity, while improving concept predictions and providing concise explanations. Our code is available at https://github.com/Antonio-Dee/M-CBM.

Antonio De Santis
Schrasing Tong
Marco Brambilla
Lalana Kagal


NOTAI.AI: Explainable Detection of Machine-Generated Text via Curvature and Feature Attribution

Abstract: We present NOTAI.AI, an explainable framework for machine-generated text detection that extends Fast-DetectGPT by integrating curvature-based signals with neural and stylometric features in a supervised setting. The system combines 17 interpretable features, including Conditional Probability Curvature, ModernBERT detector score, readability metrics, and stylometric cues, within a gradient-boosted tree (XGBoost) meta-classifier to determine whether a text is human- or AI-generated. Furthermore, NOTAI.AI applies Shapley Additive Explanations (SHAP) to provide both local and global feature-level attribution. These attributions are further translated into structured natural-language rationales through an LLM-based explanation layer, which enables user-facing interpretability. The system is deployed as an interactive web application that supports real-time analysis, visual feature inspection, and structured evidence presentation. A web interface allows users to input text and inspect how neural and statistical signals influence the final decision. The source code and demo video are publicly available to support reproducibility.

Oleksandr Marchenko Breneur
Adelaide Danilov
Aria Nourbakhsh
Salima Lamsiyah


Stable and Steerable Sparse Autoencoders with Weight Regularization

Abstract: Sparse autoencoders (SAEs) are widely used to extract human-interpretable features from neural network activations, but their learned features can vary substantially across random seeds and training choices. To improve stability, we studied weight regularization by adding L1 or L2 penalties on encoder and decoder weights, and evaluate how regularization interacts with common SAE training defaults. On MNIST, we observe that L2 weight regularization produces a core of highly aligned features and, when combined with tied initialization and unit-norm decoder constraints, it dramatically increases cross-seed feature consistency. For TopK SAEs trained on language model activations (Pythia-70M-deduped), adding a small L2 weight penalty increased the fraction of features shared across three random seeds and roughly doubles steering success rates, while leaving the mean of automated interpretability scores essentially unchanged. Finally, in the regularized setting, activation steering success becomes better predicted by auto-interpretability scores, suggesting that regularization can align text-based feature explanations with functional controllability.


Step-Level Sparse Autoencoder for Reasoning Process Interpretation

Abstract: Large Language Models (LLMs) have achieved strong complex reasoning capabilities through Chain-of-Thought (CoT) reasoning. However, their reasoning patterns remain too complicated to analyze. While Sparse Autoencoders (SAEs) have emerged as a powerful tool for interpretability, existing approaches predominantly operate at the token level, creating a granularity mismatch when capturing more critical step-level information, such as reasoning direction and semantic transitions. In this work, we propose step-level sparse autoencoder (SSAE), which serves as an analytical tool to disentangle different aspects of LLMs' reasoning steps into sparse features. Specifically, by precisely controlling the sparsity of a step feature conditioned on its context, we form an information bottleneck in step reconstruction, which splits incremental information from background information and disentangles it into several sparsely activated dimensions. Experiments on multiple base models and reasoning tasks show the effectiveness of the extracted features. By linear probing, we can easily predict surface-level information, such as generation length and first token distribution, as well as more complicated properties, such as the correctness and logicality of the step. These observations indicate that LLMs should already at least partly know about these properties during generation, which provides the foundation for the self-verification ability of LLMs. Our code is available at https://github.com/Miaow-Lab/SSAE.

Xuan Yang
Jiayu Liu
Yuhang Lai
Hao Xu
Zhenya Huang
Ning Miao


A Polynomial-Time Axiomatic Alternative to SHAP for Feature Attribution

Abstract: In this paper, we provide a theoretically grounded and computationally efficient alternative to SHAP. To this end, we study feature attribution through the lens of cooperative game theory by formulating a class of XAI--TU games. Building on this formulation, we investigate equal-surplus-type and proportional-allocation-type attribution rules and propose a low-cost attribution rule, ESENSC_rev2, constructed by combining two polynomial-time closed-form rules while ensuring the null-player property in the XAI--TU domain. Extensive experiments on tabular prediction tasks demonstrate that ESENSC_rev2 closely approximates exact SHAP while substantially improving scalability as the number of features increases. These empirical results indicate that equal-surplus-type attribution rules can achieve favorable trade-offs between computational cost and approximation accuracy in high-dimensional explainability settings. To provide theoretical foundations for these findings, we establish an axiomatic characterization showing that ESENSC_rev2 is uniquely determined by efficiency, the null-player axiom, a restricted differential marginality principle, an intermediate inessential-game property, and axioms that reduce computational requirements. Our results suggest that axiomatically justified and computationally efficient attribution rules can serve as practical and theoretically principled substitutes for SHAP-based approximations in modern explainability pipelines.

Kazuhiro Hiraki
Shinichi Ishihara
Takumi Kongo
Junnosuke Shino


Learning Retrieval Models with Sparse Autoencoders

Abstract: Sparse autoencoders (SAEs) provide a powerful mechanism for decomposing the dense representations produced by Large Language Models (LLMs) into interpretable latent features. We posit that SAEs constitute a natural foundation for Learned Sparse Retrieval (LSR), whose objective is to encode queries and documents into high-dimensional sparse representations optimized for efficient retrieval. In contrast to existing LSR approaches that project input sequences into the vocabulary space, SAE-based representations offer the potential to produce more semantically structured, expressive, and language-agnostic features. Building on this insight, we introduce SPLARE, a method to train SAE-based LSR models. Our experiments, relying on recently released open-source SAEs, demonstrate that this technique consistently outperforms vocabulary-based LSR in multilingual and out-of-domain settings. SPLARE-7B, a multilingual retrieval model capable of producing generalizable sparse latent embeddings for a wide range of languages and domains, achieves top results on MMTEB's multilingual and English retrieval tasks. We also developed a 2B-parameter variant with a significantly lighter footprint.

Thibault Formal
Maxime Louis
Hervé Dejean
Stéphane Clinchant


Certified Circuits: Stability Guarantees for Mechanistic Circuits

Abstract: Understanding how neural networks arrive at their predictions is essential for debugging, auditing, and deployment. Mechanistic interpretability pursues this goal by identifying circuits--minimal subnetworks responsible for specific behaviors. However, existing circuit discovery methods are brittle: circuits depend strongly on the chosen concept dataset and often fail to transfer out-of-distribution, raising doubts whether they capture the concept or merely dataset-specific artifacts. We introduce Certified Circuits, which provide provable stability guarantees for circuit discovery. Our framework wraps any black-box discovery algorithm with randomized data subsampling to certify that inclusion decisions over circuit components--neurons or edges of the model graph, depending on the base algorithm--are invariant to bounded edit-distance perturbations of the concept dataset. Unstable components are abstained from, yielding circuits that are more compact and more accurate. We validate across three architectures (ResNet, ViT, GPT-2) on vision (ImageNet and four OOD datasets) and language (IOI, IOI-Hard, Greater-Than) tasks. Certified circuits achieve up to 56% higher accuracy and up to 80% fewer components, and remain reliable where baselines degrade. Certified Circuits puts circuit discovery on formal ground by producing mechanistic explanations that are provably stable and better aligned with the target concept. Code: https://github.com/AlaaAnani/certified-circuits.

Alaa Anani
Tobias Lorenz
Bernt Schiele
Mario Fritz
Jonas Fischer


Fair feature attribution for multi-output prediction: a Shapley-based perspective

Abstract: In this article, we provide an axiomatic characterization of feature attribution for multi-output predictors within the Shapley framework. While SHAP explanations are routinely computed independently for each output coordinate, the theoretical necessity of this practice has remained unclear. By extending the classical Shapley axioms to vector-valued cooperative games, we establish a rigidity theorem showing that any attribution rule satisfying efficiency, symmetry, dummy player, and additivity must necessarily decompose component-wise across outputs. Consequently, any joint-output attribution rule must relax at least one of the classical Shapley axioms. This result identifies a previously unformalized structural constraint in Shapley-based interpretability, clarifying the precise scope of fairness-consistent explanations in multi-output learning. Numerical experiments on a biomedical benchmark illustrate that multi-output models can yield computational savings in training and deployment, while producing SHAP explanations that remain fully consistent with the component-wise structure imposed by the Shapley axioms.

Umberto Biccari
Alain Ibáñez de Opakua
José María Mato
Óscar Millet
Roberto Morales
Enrique Zuazua


MINAR: Mechanistic Interpretability for Neural Algorithmic Reasoning

Abstract: The recent field of neural algorithmic reasoning (NAR) studies the ability of graph neural networks (GNNs) to emulate classical algorithms like Bellman-Ford, a phenomenon known as algorithmic alignment. At the same time, recent advances in large language models (LLMs) have spawned the study of mechanistic interpretability, which aims to identify granular model components like circuits that perform specific computations. In this work, we introduce Mechanistic Interpretability for Neural Algorithmic Reasoning (MINAR), an efficient circuit discovery toolbox that adapts attribution patching methods from mechanistic interpretability to the GNN setting. We show through two case studies that MINAR recovers faithful neuron-level circuits from GNNs trained on algorithmic tasks. Our study sheds new light on the process of circuit formation and pruning during training, as well as giving new insight into how GNNs trained to perform multiple tasks in parallel reuse circuit components for related tasks. Our code is available at https://github.com/pnnl/MINAR.

Jesse He
Helen Jenne
Max Vargas
Davis Brown
Gal Mishne
Yusu Wang
Henry Kvinge


ADAPT: Hybrid Prompt Optimization for LLM Feature Visualization

Abstract: Understanding what features are encoded by learned directions in LLM activation space requires identifying inputs that strongly activate them. Feature visualization, which optimizes inputs to maximally activate a target direction, offers an alternative to costly dataset search approaches, but remains underexplored for LLMs due to the discrete nature of text. Furthermore, existing prompt optimization techniques are poorly suited to this domain, which is highly prone to local minima. To overcome these limitations, we introduce ADAPT, a hybrid method combining beam search initialization with adaptive gradient-guided mutation, designed around these failure modes. We evaluate on Sparse Autoencoder latents from Gemma 2 2B, proposing metrics grounded in dataset activation statistics to enable rigorous comparison, and show that ADAPT consistently outperforms prior methods across layers and latent types. Our results establish that feature visualization for LLMs is tractable, but requires design assumptions tailored to the domain.

João N. Cardoso
Arlindo L. Oliveira
Bruno Martins


Formal Mechanistic Interpretability: Automated Circuit Discovery with Provable Guarantees

Abstract: *Automated circuit discovery* is a central tool in mechanistic interpretability for identifying the internal components of neural networks responsible for specific behaviors. While prior methods have made significant progress, they typically depend on heuristics or approximations and do not offer provable guarantees over continuous input domains for the resulting circuits. In this work, we leverage recent advances in neural network verification to propose a suite of automated algorithms that yield circuits with *provable guarantees*. We focus on three types of guarantees: (1) *input domain robustness*, ensuring the circuit agrees with the model across a continuous input region; (2) *robust patching*, certifying circuit alignment under continuous patching perturbations; and (3) *minimality*, formalizing and capturing a wide array of various notions of succinctness. Interestingly, we uncover a diverse set of novel theoretical connections among these three families of guarantees, with critical implications for the convergence of our algorithms. Finally, we conduct experiments with state-of-the-art verifiers on various vision models, showing that our algorithms yield circuits with substantially stronger robustness guarantees than standard circuit discovery methods, establishing a principled foundation for provable circuit discovery.


Interpretability-by-Design with Accurate Locally Additive Models and Conditional Feature Effects

Abstract: Generalized additive models (GAMs) offer interpretability through independent univariate feature effects but underfit when interactions are present in data. GA$^2$Ms add selected pairwise interactions which improves accuracy, but sacrifices interpretability and limits model auditing. We propose \emph{Conditionally Additive Local Models} (CALMs), a new model class, that balances the interpretability of GAMs with the accuracy of GA$^2$Ms. CALMs allow multiple univariate shape functions per feature, each active in different regions of the input space. These regions are defined independently for each feature as simple logical conditions (thresholds) on the features it interacts with. As a result, effects remain locally additive while varying across subregions to capture interactions. We further propose a principled distillation-based training pipeline that identifies homogeneous regions with limited interactions and fits interpretable shape functions via region-aware backfitting. Experiments on diverse classification and regression tasks show that CALMs consistently outperform GAMs and achieve accuracy comparable with GA$^2$Ms. Overall, CALMs offer a compelling trade-off between predictive accuracy and interpretability.

Vasilis Gkolemis
Loukas Kavouras
Dimitrios Kyriakopoulos
Konstantinos Tsopelas
Dimitrios Rontogiannis
Giuseppe Casalicchio
Theodore Dalamagas
Christos Diou


Quantifying LLM Attention-Head Stability: Implications for Circuit Universality

Abstract: In mechanistic interpretability, recent work scrutinizes transformer "circuits" - sparse, mono or multi layer sub computations, that may reflect human understandable functions. Yet, these network circuits are rarely acid-tested for their stability across different instances of the same deep learning architecture. Without this, it remains unclear whether reported circuits emerge universally across labs or turn out to be idiosyncratic to a particular estimation instance, potentially limiting confidence in safety-critical settings. Here, we systematically study stability across-refits in increasingly complex transformer language models of various sizes. We quantify, layer by layer, how similarly attention heads learn representations across independently initialized training runs. Our rigorous experiments show that (1) middle-layer heads are the least stable yet the most representationally distinct; (2) deeper models exhibit stronger mid-depth divergence; (3) unstable heads in deeper layers become more functionally important than their peers from the same layer; (4) applying weight decay optimization substantially improves attention-head stability across random model initializations; and (5) the residual stream is comparatively stable. Our findings establish the cross-instance robustness of circuits as an essential yet underappreciated prerequisite for scalable oversight, drawing contours around possible white-box monitorability of AI systems.

Karan Bali
Jack Stanley
Praneet Suresh
Danilo Bzdok


Causally Grounded Mechanistic Interpretability for LLMs with Faithful Natural-Language Explanations

Abstract: Mechanistic interpretability identifies internal circuits responsible for model behaviors, yet translating these findings into human-understandable explanations remains an open problem. We present a pipeline that bridges circuit-level analysis and natural language explanations by (i) identifying causally important attention heads via activation patching, (ii) generating explanations using both template-based and LLM-based methods, and (iii) evaluating faithfulness using ERASER-style metrics adapted for circuit-level attribution. We evaluate on the Indirect Object Identification (IOI) task in GPT-2 Small (124M parameters), identifying six attention heads accounting for 61.4% of the logit difference. Our circuit-based explanations achieve 100% sufficiency but only 22% comprehensiveness, revealing distributed backup mechanisms. LLM-generated explanations outperform template baselines by 64% on quality metrics. We find no correlation (r = 0.009) between model confidence and explanation faithfulness, and identify three failure categories explaining when explanations diverge from mechanisms.


Finding Interpretable Prompt-Specific Circuits in Language Models

Abstract: Understanding the internal circuits that language models use to solve tasks remains a central challenge in mechanistic interpretability. A crucial part of finding circuits is understanding why each attention head attends where it does. To this end, we introduce ACC++, an improved circuit-tracing method based on the principle of attention-causal communication (ACC) [1], which identifies signals, i.e., contents of low dimensional subspaces that cause attention on a token pair. ACC++ extracts circuits from a single forward pass, without replacement models or patching. Circuits identified by ACC++ consist of components that are causal for the model's attention decisions, together with the low-dimensional signals used to communicate between them. Here, we first detail the conceptual advances that ACC++ makes over previous work. We then show that across multiple models, a substantial portion of ACC++ signals are interpretable: many signals admit a short natural-language description. We next present a number of new insights into model behavior obtained via ACC++. First, we use ACC++'s interpretable circuits to characterize the sensitivity of indirect object identification (IOI) circuits to prompt structure. We find that prompt-specific circuits form well-defined clusters, and across clusters, heads receive systematically different signals corresponding to distinct mechanisms for identifying the IO name. Next, in multilingual IOI, ACC++ circuits show that while model components are reused across languages, signals are often language-specific. In a four-language IOI case study, cross-language circuit distances are consistent with linguistic relatedness. Together, these results show that ACC++ can shed light on a broad spectrum of model behaviors.

Gabriel Franco
Lucas M. Tassis
Azalea Rohr
Mark Crovella


Singular Vectors of Attention Heads Align with Features

Abstract: Identifying feature representations in language models is a central task in mechanistic interpretability. Several recent studies have made the observation that feature representations can be inferred in some cases from singular vectors of attention matrices. However, sound justification for this phenomenon is lacking. In this paper we address that question, asking: why and when do singular vectors align with features? First, we demonstrate that singular vectors robustly align with features in a model where features can be directly observed. We then show theoretically that such alignment is expected under a range of conditions. We close by asking how, operationally, alignment may be recognized in real models where feature representations are not directly observable. We identify sparse attention decomposition as a testable prediction of alignment, and show evidence that it emerges in real models in a manner consistent with predictions. Together these results suggest that alignment of singular vectors with features can be a sound and theoretically justified basis for feature identification in language models.

Gabriel Franco
Carson Loughridge
Mark Crovella


From Atoms to Trees: Building a Structured Feature Forest with Hierarchical Sparse Autoencoders

Abstract: Sparse autoencoders (SAEs) have proven effective for extracting monosemantic features from large language models (LLMs), yet these features are typically identified in isolation. However, broad evidence suggests that LLMs capture the intrinsic structure of natural language, where the phenomenon of "feature splitting" in particular indicates that such structure is hierarchical. To capture this, we propose the Hierarchical Sparse Autoencoder (HSAE), which jointly learns a series of SAEs and the parent-child relationships between their features. HSAE strengthens the alignment between parent and child features through two novel mechanisms: a structural constraint loss and a random feature perturbation mechanism. Extensive experiments across various LLMs and layers demonstrate that HSAE consistently recovers semantically meaningful hierarchies, supported by both qualitative case studies and rigorous quantitative metrics. At the same time, HSAE preserves the reconstruction fidelity and interpretability of standard SAEs across different dictionary sizes. Our work provides a powerful, scalable tool for discovering and analyzing the multi-scale conceptual structures embedded in LLM representations.

Yifan Luo
Yang Zhan
Jiedong Jiang
Tianyang Liu
Mingrui Wu
Zhennan Zhou
Bin Dong


Control Reinforcement Learning: Interpretable Token-Level Steering of LLMs via Sparse Autoencoder Features

Abstract: Sparse autoencoders (SAEs) decompose language model activations into interpretable features, but existing methods reveal only which features activate, not which change model outputs when amplified. We introduce Control Reinforcement Learning (CRL), which trains a policy to select SAE features for steering at each token, producing interpretable intervention logs: the learned policy identifies features that change model outputs when amplified. Adaptive Feature Masking encourages diverse feature discovery while preserving singlefeature interpretability. The framework yields new analysis capabilities: branch point tracking locates tokens where feature choice determines output correctness; critic trajectory analysis separates policy limitations from value estimation errors; layer-wise comparison reveals syntactic features in early layers and semantic features in later layers. On Gemma 2 2B across MMLU, BBQ, GSM8K, HarmBench, and XSTest, CRL achieves improvements while providing per-token intervention logs. These results establish learned feature steering as a mechanistic interpretability tool that complements static feature analysis with dynamic intervention probes


Less is Enough: Synthesizing Diverse Data in LLM Feature Space with Sparse Autoencoders

Abstract: The diversity of post-training data is critical for effective downstream performance in large language models (LLMs). Many existing approaches to constructing post-training data quantify diversity using text-based metrics that capture linguistic variation, but such metrics provide only weak signals for the task-relevant features that determine downstream performance. In this work, we introduce Feature Activation Coverage (FAC) which measures data diversity in an interpretable feature space. Building upon this metric, we further propose a diversity-driven data synthesis framework, named FAC Synthesis, that first uses a sparse autoencoder to identify missing features from a seed dataset, and then generates synthetic samples that explicitly reflect these features. Experiments show that our approach consistently improves both data diversity and downstream performance on various tasks, including instruction following, toxicity detection, reward modeling, and behavior steering. Interestingly, we identify a shared, interpretable feature space across model families (i.e., LLaMA, Mistral, and Qwen), enabling cross-model knowledge transfer. Our work provides a solid and practical methodology for exploring data-centric optimization of LLMs.

Zhongzhi Li
Xuansheng Wu
Yijiang Li
Lijie Hu
Ninghao Liu


Triggers Hijack Language Circuits: A Mechanistic Analysis of Backdoor Behaviors in Large Language Models

Abstract: Backdoor attacks pose significant security risks for Large Language Models (LLMs), yet the internal mechanisms by which triggers operate remain poorly understood. We present the first mechanistic analysis of language-switching backdoors, studying the GAPperon model family (1B, 8B, 24B parameters) which contains triggers injected during pretraining that cause output language switching. Using activation patching, we localize trigger formation to early layers (7.5-25% of model depth) and identify which attention heads process trigger information. Our central finding is that trigger-activated heads substantially overlap with heads naturally encoding output language across model scales, with Jaccard indices between 0.18 and 0.66 over the top heads identified. This suggests that backdoor triggers do not form isolated circuits but instead co-opt the model's existing language components. These findings have implications for backdoor defense: detection methods may benefit from monitoring known functional components rather than searching for hidden circuits, and mitigation strategies could potentially leverage this entanglement between injected and natural behaviors.

Théo Lasnier
Wissam Antoun
Francis Kulumba
Djamé Seddah


Improving Interpretability of Lexical Semantic Change with Neurobiological Features

Abstract: Lexical Semantic Change (LSC) is the phenomenon in which the meaning of a word change over time. Most studies on LSC focus on improving the performance of estimating the degree of LSC, however, it is often difficult to interpret how the meaning of a word change. Enhancing the interpretability of LSC is a significant challenge as it could lead to novel insights in this field. To tackle this challenge, we propose a method to map the semantic space of contextualized embeddings of words obtained by a pre-trained language model to a neurobiological feature space. In the neurobiological feature space, each dimension corresponds to a primitive feature of words, and its value represents the intensity of that feature. This enables humans to interpret LSC systematically. When employed for the estimation of the degree of LSC, our method demonstrates superior performance in comparison to the majority of the previous methods. In addition, given the high interpretability of the proposed method, several analyses on LSC are carried out. The results demonstrate that our method not only discovers interesting types of LSC that have been overlooked in previous studies but also effectively searches for words with specific types of LSC.

Kohei Oda
Hiroya Takamura
Kiyoaki Shirai
Natthawut Kertkeidkachorn


Feature salience - not task-informativeness - drives machine learning model explanations

Abstract: Explainable AI (XAI) promises to provide insight into machine learning models' decision processes, where one goal is to identify failures such as shortcut learning. This promise relies on the field's assumption that input features marked as important by an XAI must contain information about the target variable. However, it is unclear whether informativeness is indeed the main driver of importance attribution in practice, or if other data properties such as statistical suppression, novelty at test-time, or high feature salience substantially contribute. To clarify this, we trained deep learning models on three variants of a binary image classification task, in which translucent watermarks are either absent, act as class-dependent confounds, or represent class-independent noise. Results for five popular attribution methods show substantially elevated relative importance in watermarked areas (RIW) for all models regardless of the training setting ($R^2 \geq .45$). By contrast, whether the presence of watermarks is class-dependent or not only has a marginal effect on RIW ($R^2 \leq .03$), despite a clear impact impact on model performance and generalisation ability. XAI methods show similar behaviour to model-agnostic edge detection filters and attribute substantially less importance to watermarks when bright image intensities are encoded by smaller instead of larger feature values. These results indicate that importance attribution is most strongly driven by the salience of image structures at test time rather than statistical associations learned by machine learning models. Previous studies demonstrating successful XAI application should be reevaluated with respect to a possibly spurious concurrency of feature salience and informativeness, and workflows using feature attribution methods as building blocks should be scrutinised.

Benedict Clark
Marta Oliveira
Rick Wilming
Stefan Haufe


LUCID-SAE: Learning Unified Vision-Language Sparse Codes for Interpretable Concept Discovery

Abstract: Sparse autoencoders (SAEs) offer a natural path toward comparable explanations across different representation spaces. However, current SAEs are trained per modality, producing dictionaries whose features are not directly understandable and whose explanations do not transfer across domains. In this study, we introduce LUCID (Learning Unified vision-language sparse Codes for Interpretable concept Discovery), a unified vision-language sparse autoencoder that learns a shared latent dictionary for image patch and text token representations, while reserving private capacity for modality-specific details. We achieve feature alignment by coupling the shared codes with a learned optimal transport matching objective without the need of labeling. LUCID yields interpretable shared features that support patch-level grounding, establish cross-modal neuron correspondence, and enhance robustness against the concept clustering problem in similarity-based evaluation. Leveraging the alignment properties, we develop an automated dictionary interpretation pipeline based on term clustering without manual observations. Our analysis reveals that LUCID's shared features capture diverse semantic categories beyond objects, including actions, attributes, and abstract concepts, demonstrating a comprehensive approach to interpretable multimodal representations.

Difei Gu
Yunhe Gao
Gerasimos Chatzoudis
Zihan Dong
Guoning Zhang
Bangwei Guo
Yang Zhou
Mu Zhou
Dimitris Metaxas


DLM-Scope: Mechanistic Interpretability of Diffusion Language Models via Sparse Autoencoders

Abstract: Sparse autoencoders (SAEs) have become a standard tool for mechanistic interpretability in autoregressive large language models (LLMs), enabling researchers to extract sparse, human-interpretable features and intervene on model behavior. Recently, as diffusion language models (DLMs) have become an increasingly promising alternative to the autoregressive LLMs, it is essential to develop tailored mechanistic interpretability tools for this emerging class of models. In this work, we present DLM-Scope, the first SAE-based interpretability framework for DLMs, and demonstrate that trained Top-K SAEs can faithfully extract interpretable features. Notably, we find that inserting SAEs affects DLMs differently than autoregressive LLMs: while SAE insertion in LLMs typically incurs a loss penalty, in DLMs it can reduce cross-entropy loss when applied to early layers, a phenomenon absent or markedly weaker in LLMs. Additionally, SAE features in DLMs enable more effective diffusion-time interventions, often outperforming LLM steering. Moreover, we pioneer certain new SAE-based research directions for DLMs: we show that SAEs can provide useful signals for DLM decoding order; and the SAE features are stable during the post-training phase of DLMs. Our work establishes a foundation for mechanistic interpretability in DLMs and shows a great potential of applying SAEs to DLM-related tasks and algorithms.

Xu Wang
Bingqing Jiang
Yu Wan
Baosong Yang
Lingpeng Kong
Difan Zou


Identifying Intervenable and Interpretable Features via Orthogonality Regularization

Abstract: With recent progress on fine-tuning language models around a fixed sparse autoencoder, we disentangle the decoder matrix into almost orthogonal features. This reduces interference and superposition between the features, while keeping performance on the target dataset essentially unchanged. Our orthogonality penalty leads to identifiable features, ensuring the uniqueness of the decomposition. Further, we find that the distance between embedded feature explanations increases with stricter orthogonality penalty, a desirable property for interpretability. Invoking the $\textit{Independent Causal Mechanisms}$ principle, we argue that orthogonality promotes modular representations amenable to causal intervention. We empirically show that these increasingly orthogonalized features allow for isolated interventions. Our code is available under $\texttt{https://github.com/mrtzmllr/sae-icm}$.

Moritz Miller
Florent Draye
Bernhard Schölkopf


ShapBPT: Image Feature Attributions Using Data-Aware Binary Partition Trees

Abstract: Pixel-level feature attributions are an important tool in eXplainable AI for Computer Vision (XCV), providing visual insights into how image features influence model predictions. The Owen formula for hierarchical Shapley values has been widely used to interpret machine learning (ML) models and their learned representations. However, existing hierarchical Shapley approaches do not exploit the multiscale structure of image data, leading to slow convergence and weak alignment with the actual morphological features. Moreover, no prior Shapley method has leveraged data-aware hierarchies for Computer Vision tasks, leaving a gap in model interpretability of structured visual data. To address this, this paper introduces ShapBPT, a novel data-aware XCV method based on the hierarchical Shapley formula. ShapBPT assigns Shapley coefficients to a multiscale hierarchical structure tailored for images, the Binary Partition Tree (BPT). By using this data-aware hierarchical partitioning, ShapBPT ensures that feature attributions align with intrinsic image morphology, effectively prioritizing relevant regions while reducing computational overhead. This advancement connects hierarchical Shapley methods with image data, providing a more efficient and semantically meaningful approach to visual interpretability. Experimental results confirm ShapBPT's effectiveness, demonstrating superior alignment with image structures and improved efficiency over existing XCV methods, and a 20-subject user study confirming that ShapBPT explanations are preferred by humans.

Muhammad Rashid
Elvio G. Amparore
Enrico Ferrari
Damiano Verda

AAAI Conference on Artificial Intelligence


Momentum Attention: The Physics of In-Context Learning and Spectral Forensics for Mechanistic Interpretability

Abstract: The Mechanistic Interpretability (MI) program has mapped the Transformer as a precise computational graph. We extend this graph with a conservation law and time-varying AC dynamics, viewing it as a physical circuit. We introduce Momentum Attention, a symplectic augmentation embedding physical priors via the kinematic difference operator $p_t = q_t - q_{t-1}$, implementing the symplectic shear $\hat{q}_t = q_t + γp_t$ on queries and keys. We identify a fundamental Symplectic-Filter Duality: the physical shear is mathematically equivalent to a High-Pass Filter. This duality is our cornerstone contribution -- by injecting kinematic momentum, we sidestep the topological depth constraint ($L \geq 2$) for induction head formation. While standard architectures require two layers for induction from static positions, our extension grants direct access to velocity, enabling Single-Layer Induction and Spectral Forensics via Bode Plots. We formalize an Orthogonality Theorem proving that DC (semantic) and AC (mechanistic) signals segregate into orthogonal frequency bands when Low-Pass RoPE interacts with High-Pass Momentum. Validated through 5,100+ controlled experiments (documented in Supplementary Appendices A--R and 27 Jupyter notebooks), our 125M Momentum model exceeds expectations on induction-heavy tasks while tracking a 350M baseline within $\sim$2.9% validation loss. Dedicated associative recall experiments reveal a scaling law $γ^* = 4.17 \times N^{-0.74}$ establishing momentum-depth fungibility. We offer this framework as a complementary analytical toolkit connecting Generative AI, Hamiltonian Physics, and Signal Processing.


Spectral Superposition: A Theory of Feature Geometry

Abstract: Neural networks represent more features than they have dimensions via superposition, forcing features to share representational space. Current methods decompose activations into sparse linear features but discard geometric structure. We develop a theory for studying the geometric structre of features by analyzing the spectra (eigenvalues, eigenspaces, etc.) of weight derived matrices. In particular, we introduce the frame operator $F = WW^\top$, which gives us a spectral measure that describes how each feature allocates norm across eigenspaces. While previous tools could describe the pairwise interactions between features, spectral methods capture the global geometry (``how do all features interact?''). In toy models of superposition, we use this theory to prove that capacity saturation forces spectral localization: features collapse onto single eigenspaces, organize into tight frames, and admit discrete classification via association schemes, classifying all geometries from prior work (simplices, polygons, antiprisms). The spectral measure formalism applies to arbitrary weight matrices, enabling diagnosis of feature localization beyond toy settings. These results point toward a broader program: applying operator theory to interpretability.

Georgi Ivanov
Narmeen Oozeer
Shivam Raval
Tasana Pejovic
Shriyash Upadhyay
Amir Abdullah


PolySAE: Modeling Feature Interactions in Sparse Autoencoders via Polynomial Decoding

Abstract: Sparse autoencoders (SAEs) interpret neural network representations by decomposing activations into sparse combinations of dictionary atoms. However, SAEs assume features combine additively through linear reconstruction, an assumption that cannot capture compositional structure: linear models cannot distinguish whether ''Starbucks'' arises from the composition of ''star'' and ''coffee'' features or merely their co-occurrence. This forces SAEs to allocate monolithic features for compound concepts rather than decomposing them into interpretable constituents. We introduce PolySAE, which extends the SAE decoder with higher-order terms to model feature interactions while preserving the linear encoder essential for interpretability. Through low-rank tensor factorization on a shared projection subspace, PolySAE captures pairwise and triple feature interactions with small parameter overhead (3% on GPT2). Across four language models and three SAE variants, PolySAE achieves an average improvement of $\sim$8% in probing F1 while maintaining comparable reconstruction error, and produces 2--10$\times$ larger Wasserstein distances between class-conditional feature distributions. Critically, learned interaction weights exhibit negligible correlation with co-occurrence frequency ($r = 0.06$ vs $r = 0.82$ for SAE feature covariance), suggesting that polynomial terms capture compositional structure largely independent of surface statistics. Finally, the learned interaction directions causally steer model outputs toward the corresponding compositional semantics.

Panagiotis Koromilas
Andreas D. Demou
James Oldfield
Yannis Panagakis
Mihalis Nicolaou


Hidden Heroes and Gradient Bloats: Layer-Wise Redundancy Inverts Attribution in Transformers

Abstract: Gradient-based attribution is the workhorse of mechanistic interpretability, yet whether it reliably tracks causal importance at the component level remains largely untested. We causally evaluate this assumption across two algorithmic tasks and up to 10 random seeds, uncovering a systematic, layer-wise failure: gradient attribution consistently overvalues early-layer \textbf{Gradient Bloats} and undervalues late-layer \textbf{Hidden Heroes}. Rank correlation collapses from $ρ= 0.72$ on sequence reversal to $0.27$ on sequence sorting, reaching $ρ= -0.18$ in individual seeds. This failure stems from first-order gradient attribution's inability to detect collective redundancy: joint Bloat ablation causes $14\times$ greater damage than individual results predict. Consequently, Bloats dominate gradient rankings despite negligible functional impact, while ablating Hidden Heroes destroys OOD accuracy ($-36.4\% \pm 22.8\%$). This systematic inversion of early-layer feature extraction and late-layer computation motivates causal validation as a prerequisite for circuit-level claims.


Mechanistic Interpretability of Brain-to-Speech Models Across Speech Modes

Abstract: Brain-to-speech decoding models demonstrate robust performance in vocalized, mimed, and imagined speech; yet, the fundamental mechanisms via which these models capture and transmit information across different speech modalities are less explored. In this work, we use mechanistic interpretability to causally investigate the internal representations of a neural speech decoder. We perform cross-mode activation patching of internal activations across speech modes, and use tri-modal interpolation to examine whether speech representations vary discretely or continuously. We use coarse-to-fine causal tracing and causal scrubbing to find localized causal structure, allowing us to find internal subspaces that are sufficient for cross-mode transfer. In order to determine how finely distributed these effects are within layers, we perform neuron-level activation patching. We discover that small but not distributed subsets of neurons, rather than isolated units, affect the cross-mode transfer. Our results show that speech modes lie on a shared continuous causal manifold, and cross-mode transfer is mediated by compact, layer-specific subspaces rather than diffuse activity. Together, our findings give a causal explanation for how speech modality information is organized and used in brain-to-speech decoding models, revealing hierarchical and direction-dependent representational structure across speech modes.


Supervised sparse auto-encoders for interpretable and compositional representations

Abstract: Sparse auto-encoders (SAEs) have re-emerged as a prominent method for mechanistic interpretability, yet they face two significant challenges: the non-smoothness of the $L_1$ penalty, which hinders reconstruction and scalability, and a lack of alignment between learned features and human semantics. In this paper, we address these limitations by adapting unconstrained feature models, a mathematical framework from neural collapse theory, and by supervising the task. We supervise (decoder-only) SAEs to reconstruct feature vectors by jointly learning sparse concept embeddings and decoder weights. Validated on Stable Diffusion 3.5, our approach demonstrates compositional generalization, successfully reconstructing images with concept combinations unseen during training, and enabling feature-level intervention for semantic image editing without prompt modification.

Ouns El Harzli
Hugo Wallner
Yoonsoo Nam
Haixuan Xavier Tao


Beyond Activation Patterns: A Weight-Based Out-of-Context Explanation of Sparse Autoencoder Features

Abstract: Sparse autoencoders (SAEs) have emerged as a powerful technique for decomposing language model representations into interpretable features. Current interpretation methods infer feature semantics from activation patterns, but overlook that features are trained to reconstruct activations that serve computational roles in the forward pass. We introduce a novel weight-based interpretation framework that measures functional effects through direct weight interactions, requiring no activation data. Through three experiments on Gemma-2 and Llama-3.1 models, we demonstrate that (1) 1/4 of features directly predict output tokens, (2) features actively participate in attention mechanisms with depth-dependent structure, and (3) semantic and non-semantic feature populations exhibit distinct distribution profiles in attention circuits. Our analysis provides the missing out-of-context half of SAE feature interpretability.


Learning to Price: Interpretable Attribute-Level Models for Dynamic Markets

Abstract: Dynamic pricing in high-dimensional markets poses fundamental challenges of scalability, uncertainty, and interpretability. Existing low-rank bandit formulations learn efficiently but rely on latent features that obscure how individual product attributes influence price. We address this by introducing an interpretable \emph{Additive Feature Decomposition-based Low-Dimensional Demand (\textbf{AFDLD}) model}, where product prices are expressed as the sum of attribute-level contributions and substitution effects are explicitly modeled. Building on this structure, we propose \textbf{ADEPT} (Additive DEcomposition for Pricing with cross-elasticity and Time-adaptive learning)-a projection-free, gradient-free online learning algorithm that operates directly in attribute space and achieves a sublinear regret of $\tilde{\mathcal{O}}(\sqrt{d}T^{3/4})$. Through controlled synthetic studies and real-world datasets, we show that ADEPT (i) learns near-optimal prices under dynamic market conditions, (ii) adapts rapidly to shocks and drifts, and (iii) yields transparent, attribute-level price explanations. The results demonstrate that interpretability and efficiency in autonomous pricing agents can be achieved jointly through structured, attribute-driven representations.

Srividhya Sethuraman
Chandrashekar Lakshminarayanan


Language Model Circuits Are Sparse in the Neuron Basis

Abstract: The high-level concepts that a neural network uses to perform computation need not be aligned to individual neurons (Smolensky, 1986). Language model interpretability research has thus turned to techniques which decompose the neuron basis into more interpretable units of model computation, such as sparse autoencoders (SAEs). However, not all neuron-based representations are uninterpretable. For the first time, we empirically show that MLP neurons are as sparse a feature basis as SAEs. We use this finding to develop an end-to-end gradient-based attribution pipeline for circuit tracing on the MLP neuron basis, which surfaces causally effective neurons on a variety of tasks. On a standard subject-verb agreement benchmark (Marks et al., 2025), a circuit of $\approx 10^2$ MLP neurons is enough to control model behaviour. On the multi-hop city-state-capital task from (Lindsey et al., 2025), we find a circuit in which small sets of neurons encode specific latent reasoning steps (e.g. mapping a city to its state), and can be steered to change the model's output. This work thus advances automated interpretability of language models without imposing additional training costs.

Aryaman Arora
Zhengxuan Wu
Jacob Steinhardt
Sarah Schwettmann


Learn from A Rationalist: Distilling Intermediate Interpretable Rationales

Abstract: Because of the pervasive use of deep neural networks (DNNs), especially in high-stakes domains, the interpretability of DNNs has received increased attention. The general idea of rationale extraction (RE) is to provide an interpretable-by-design framework for DNNs via a select-predict architecture where two neural networks learn jointly to perform feature selection and prediction, respectively. Given only the remote supervision from the final task prediction, the process of learning to select subsets of features (or rationales) requires searching in the space of all possible feature combinations, which is computationally challenging and even harder when the base neural networks are not sufficiently capable. To improve the predictive performance of RE models that are based on less capable or smaller neural networks (i.e., the students), we propose REKD (Rationale Extraction with Knowledge Distillation) where a student RE model learns from the rationales and predictions of a teacher (i.e., a rationalist) in addition to the student's own RE optimization. This structural adjustment to RE aligns well with how humans could learn effectively from interpretable and verifiable knowledge. Because of the neural-model agnostic nature of the method, any black-box neural network could be integrated as a backbone model. To demonstrate the viability of REKD, we conduct experiments with multiple variants of BERT and vision transformer (ViT) models. Our experiments across language and vision classification datasets (i.e., IMDB movie reviews, CIFAR 10 and CIFAR 100) show that REKD significantly improves the predictive performance of the student RE models.


Mechanistic Data Attribution: Tracing the Training Origins of Interpretable LLM Units

Abstract: While Mechanistic Interpretability has identified interpretable circuits in LLMs, their causal origins in training data remain elusive. We introduce Mechanistic Data Attribution (MDA), a scalable framework that employs Influence Functions to trace interpretable units back to specific training samples. Through extensive experiments on the Pythia family, we causally validate that targeted intervention--removing or augmenting a small fraction of high-influence samples--significantly modulates the emergence of interpretable heads, whereas random interventions show no effect. Our analysis reveals that repetitive structural data (e.g., LaTeX, XML) acts as a mechanistic catalyst. Furthermore, we observe that interventions targeting induction head formation induce a concurrent change in the model's in-context learning (ICL) capability. This provides direct causal evidence for the long-standing hypothesis regarding the functional link between induction heads and ICL. Finally, we propose a mechanistic data augmentation pipeline that consistently accelerates circuit convergence across model scales, providing a principled methodology for steering the developmental trajectories of LLMs.


Putting a Face to Forgetting: Continual Learning meets Mechanistic Interpretability

Abstract: Catastrophic forgetting in continual learning is often measured at the performance or last-layer representation level, overlooking the underlying mechanisms. We introduce a mechanistic framework that offers a geometric interpretation of catastrophic forgetting as the result of transformations to the encoding of individual features. These transformations can lead to forgetting by reducing the allocated capacity of features or by disrupting their readout by downstream computations. Analysis of a tractable toy model formalizes this view, allowing us to identify best- and worst-case scenarios. Through experiments on this model, we empirically test our formal analysis and highlight the detrimental effect of depth. Finally, we demonstrate how our framework can be used in the analysis of practical models through the use of Crosscoders. We do so through a case study example of a Vision Transformer trained on sequential CIFAR-10. Our work provides a new, feature-centric vocabulary for continual learning.

Sergi Masip
Gido M. van de Ven
Javier Ferrando
Tinne Tuytelaars


Decomposing multimodal embedding spaces with group-sparse autoencoders

Abstract: The Linear Representation Hypothesis asserts that the embeddings learned by neural networks can be understood as linear combinations of features corresponding to high-level concepts. Based on this ansatz, sparse autoencoders (SAEs) have recently become a popular method for decomposing embeddings into a sparse combination of linear directions, which have been shown empirically to often correspond to human-interpretable semantics. However, recent attempts to apply SAEs to multimodal embedding spaces (such as the popular CLIP embeddings for image/text data) have found that SAEs often learn "split dictionaries", where most of the learned sparse features are essentially unimodal, active only for data of a single modality. In this work, we study how to effectively adapt SAEs for the setting of multimodal embeddings while ensuring multimodal alignment. We first argue that the existence of a split dictionary decomposition on an aligned embedding space implies the existence of a non-split dictionary with improved modality alignment. Then, we propose a new SAE-based approach to multimodal embedding decomposition using cross-modal random masking and group-sparse regularization. We apply our method to popular embeddings for image/text (CLIP) and audio/text (CLAP) data and show that, compared to standard SAEs, our approach learns a more multimodal dictionary while reducing the number of dead neurons and improving feature semanticity. We finally demonstrate how this improvement in alignment of concepts between modalities can enable improvements in the interpretability and control of cross-modal tasks.

Chiraag Kaushik
Davis Barch
Andrea Fanelli


A Monosemantic Attribution Framework for Stable Interpretability in Clinical Neuroscience Transformer-Based Language Models

Abstract: Interpretability remains a key challenge for deploying language models (LM) in clinical settings such as progression diagnosis of Alzheimer disease, where early and trustworthy predictions are essential. Existing attribution methods exhibit high inter-method variability and unstable explanations due to the polysemantic nature of Transformer-Based LM and LLM representations, while mechanistic interpretability approaches lack direct alignment with model inputs and outputs and do not provide explicit importance scores. We introduce a unified interpretability framework that integrates attributional and mechanistic perspectives through monosemantic feature extraction. By constructing a monosemantic embedding space at the level of an transformer-based LM layer and optimizing the framework to explicitly reduce inter-method variability, our approach produces stable input-level importance scores and highlights salient features via a decompressed representation of the layer of interest, advancing the safe and trustworthy application of LMs in cognitive health and neurodegenerative disease.

Michail Mamalakis
Tiago Azevedo
Cristian Cosentino
Chiara D'Ercoli
Subati Abulikemu
Zhongtian Sun
Richard Bethlehem
Pietro Lio


Mechanistic Interpretability for Large Language Model Alignment: Progress, Challenges, and Future Directions

Abstract: Large language models (LLMs) have achieved remarkable capabilities across diverse tasks, yet their internal decision-making processes remain largely opaque. Mechanistic interpretability (i.e., the systematic study of how neural networks implement algorithms through their learned representations and computational structures) has emerged as a critical research direction for understanding and aligning these models. This paper surveys recent progress in mechanistic interpretability techniques applied to LLM alignment, examining methods ranging from circuit discovery to feature visualization, activation steering, and causal intervention. We analyze how interpretability insights have informed alignment strategies including reinforcement learning from human feedback (RLHF), constitutional AI, and scalable oversight. Key challenges are identified, including the superposition hypothesis, polysemanticity of neurons, and the difficulty of interpreting emergent behaviors in large-scale models. We propose future research directions focusing on automated interpretability, cross-model generalization of circuits, and the development of interpretability-driven alignment techniques that can scale to frontier models.


Hierarchical Sparse Circuit Extraction from Billion-Parameter Language Models through Scalable Attribution Graph Decomposition

Abstract: Mechanistic interpretability seeks to reverse-engineer neural network computations into human-understandable algorithms, yet extracting sparse computational circuits from billion-parameter language models remains challenging due to exponential search complexity and pervasive polysemanticity. The proposed Hierarchical Attribution Graph Decomposition (HAGD) framework reduces circuit discovery complexity from O(2^n) exhaustive enumeration to O(n^2 log n) through multi-resolution abstraction hierarchies and differentiable circuit search. The methodology integrates cross-layer transcoders for monosemantic feature extraction, graph neural network meta-learning for topology prediction, and causal intervention protocols for validation. Empirical evaluation spans GPT-2 variants, Llama-7B through Llama-70B, and Pythia suite models across algorithmic tasks and natural language benchmarks. On modular arithmetic tasks, the framework achieves up to 91% behavioral preservation ($\pm$2.3\% across runs) while maintaining interpretable subgraph sizes. Cross-architecture transfer experiments suggest that discovered circuits exhibit moderate structural similarity (averaging 67%) across model families, indicating potential shared computational patterns. These results provide preliminary foundations for interpretability at larger model scales while identifying significant limitations in current attribution methodologies that require future advances.

Mohammed Mudassir Uddin
Shahnawaz Alam
Mohammed Kaif Pasha


Do Sparse Autoencoders Identify Reasoning Features in Language Models?

Abstract: We study how reliably sparse autoencoders (SAEs) support claims about reasoning-related internal features in large language models. We first give a stylized analysis showing that sparsity-regularized decoding can preferentially retain stable low-dimensional correlates while suppressing high-dimensional within-behavior variation, motivating the possibility that contrastively selected "reasoning" features may concentrate on cue-like structure when such cues are coupled with reasoning traces. Building on this perspective, we propose a falsification-based evaluation framework that combines causal token injection with LLM-guided counterexample construction. Across 22 configurations spanning multiple model families, layers, and reasoning datasets, we find that many contrastively selected candidates are highly sensitive to token-level interventions, with 45%-90% activating after injecting only a few associated tokens into non-reasoning text. For the remaining context-dependent candidates, LLM-guided falsification produces targeted non-reasoning inputs that trigger activation and meaning-preserving paraphrases of top-activating reasoning traces that suppress it. A small steering study yields minimal changes on the evaluated benchmarks. Overall, our results suggest that, in the settings we study, sparse decompositions can favor low-dimensional correlates that co-occur with reasoning, underscoring the need for falsification when attributing high-level behaviors to individual SAE features. Code is available at https://github.com/GeorgeMLP/reasoning-probing.

George Ma
Zhongyuan Liang
Irene Y. Chen
Somayeh Sojoudi


Interpreting Transformers Through Attention Head Intervention

Abstract: Neural networks are growing more capable on their own, but we do not understand their neural mechanisms. Understanding these mechanisms' decision-making processes, or mechanistic interpretability, enables (1) accountability and control in high-stakes domains, (2) the study of digital brains and the emergence of cognition, and (3) discovery of new knowledge when AI systems outperform humans. This paper traces how attention head intervention emerged as a key method for causal interpretability of transformers. The evolution from visualization to intervention represents a paradigm shift from observing correlations to causally validating mechanistic hypotheses through direct intervention. Head intervention studies revealed robust empirical findings while also highlighting limitations that complicate interpretation. Recent work demonstrates that mechanistic understanding now enables targeted control of model behaviour, successfully suppressing toxic outputs and manipulating semantic content through selective attention head intervention, validating the practical utility of interpretability research for AI safety.


When the Coffee Feature Activates on Coffins: An Analysis of Feature Extraction and Steering for Mechanistic Interpretability

Abstract: Recent work by Anthropic on Mechanistic interpretability claims to understand and control Large Language Models by extracting human-interpretable features from their neural activation patterns using sparse autoencoders (SAEs). If successful, this approach offers one of the most promising routes for human oversight in AI safety. We conduct an initial stress-test of these claims by replicating their main results with open-source SAEs for Llama 3.1. While we successfully reproduce basic feature extraction and steering capabilities, our investigation suggests that major caution is warranted regarding the generalizability of these claims. We find that feature steering exhibits substantial fragility, with sensitivity to layer selection, steering magnitude, and context. We observe non-standard activation behavior and demonstrate the difficulty to distinguish thematically similar features from one another. While SAE-based interpretability produces compelling demonstrations in selected cases, current methods often fall short of the systematic reliability required for safety-critical applications. This suggests a necessary shift in focus from prioritizing interpretability of internal representations toward reliable prediction and control of model output. Our work contributes to a more nuanced understanding of what mechanistic interpretability has achieved and highlights fundamental challenges for AI safety that remain unresolved.

Raphael Ronge
Markus Maier
Frederick Eberhardt


Mechanistic Knobs in LLMs: Retrieving and Steering High-Order Semantic Features via Sparse Autoencoders

Abstract: Recent work in Mechanistic Interpretability (MI) has enabled the identification and intervention of internal features in Large Language Models (LLMs). However, a persistent challenge lies in linking such internal features to the reliable control of complex, behavior-level semantic attributes in language generation. In this paper, we propose a Sparse Autoencoder-based framework for retrieving and steering semantically interpretable internal features associated with high-level linguistic behaviors. Our method employs a contrastive feature retrieval pipeline based on controlled semantic oppositions, combing statistical activation analysis and generation-based validation to distill monosemantic functional features from sparse activation spaces. Using the Big Five personality traits as a case study, we demonstrate that our method enables precise, bidirectional steering of model behavior while maintaining superior stability and performance compared to existing activation steering methods like Contrastive Activation Addition (CAA). We further identify an empirical effect, which we term Functional Faithfulness, whereby intervening on a specific internal feature induces coherent and predictable shifts across multiple linguistic dimensions aligned with the target semantic attribute. Our findings suggest that LLMs internalize deeply integrated representations of high-order concepts, and provide a novel, robust mechanistic path for the regulation of complex AI behaviors.


MAFS: Multi-head Attention Feature Selection for High-Dimensional Data via Deep Fusion of Filter Methods

Abstract: Feature selection is essential for high-dimensional biomedical data, enabling stronger predictive performance, reduced computational cost, and improved interpretability in precision medicine applications. Existing approaches face notable challenges. Filter methods are highly scalable but cannot capture complex relationships or eliminate redundancy. Deep learning-based approaches can model nonlinear patterns but often lack stability, interpretability, and efficiency at scale. Single-head attention improves interpretability but is limited in capturing multi-level dependencies and remains sensitive to initialization, reducing reproducibility. Most existing methods rarely combine statistical interpretability with the representational power of deep learning, particularly in ultra-high-dimensional settings. Here, we introduce MAFS (Multi-head Attention-based Feature Selection), a hybrid framework that integrates statistical priors with deep learning capabilities. MAFS begins with filter-based priors for stable initialization and guide learning. It then uses multi-head attention to examine features from multiple perspectives in parallel, capturing complex nonlinear relationships and interactions. Finally, a reordering module consolidates outputs across attention heads, resolving conflicts and minimizing information loss to generate robust and consistent feature rankings. This design combines statistical guidance with deep modeling capacity, yielding interpretable importance scores while maximizing retention of informative signals. Across simulated and real-world datasets, including cancer gene expression and Alzheimer's disease data, MAFS consistently achieves superior coverage and stability compared with existing filter-based and deep learning-based alternatives, offering a scalable, interpretable, and robust solution for feature selection in high-dimensional biomedical data.


Attribution-Guided Distillation of Matryoshka Sparse Autoencoders

Abstract: Sparse autoencoders (SAEs) aim to disentangle model activations into monosemantic, human-interpretable features. In practice, learned features are often redundant and vary across training runs and sparsity levels, which makes interpretations difficult to transfer and reuse. We introduce Distilled Matryoshka Sparse Autoencoders (DMSAEs), a training pipeline that distills a compact core of consistently useful features and reuses it to train new SAEs. DMSAEs run an iterative distillation cycle: train a Matryoshka SAE with a shared core, use gradient X activation to measure each feature's contribution to next-token loss in the most nested reconstruction, and keep only the smallest subset that explains a fixed fraction of the attribution. Only the core encoder weight vectors are transferred across cycles; the core decoder and all non-core latents are reinitialized each time. On Gemma-2-2B layer 12 residual stream activations, seven cycles of distillation (500M tokens, 65k width) yielded a distilled core of 197 features that were repeatedly selected. Training using this distilled core improves several SAEBench metrics and demonstrates that consistent sets of latent features can be transferred across sparsity levels

Cristina P. Martin-Linares
Jonathan P. Ling


Towards Interpretable AI in Personalized Medicine: A Radiological-Biological Radiomics Dictionary Connecting Semantic Lung-RADS and imaging Radiomics Features; Dictionary LC 1.0

Abstract: Lung cancer remains the leading cause of cancer-related mortality worldwide, with survival strongly dependent on early detection. Standard-dose computed tomography (CT) screening using the Lung Imaging Reporting and Data System (Lung-RADS) standardizes pulmonary nodule assessment but is limited by inter-reader variability and reliance on qualitative descriptors, while radiomics offers quantitative biomarkers that often lack clinical interpretability. To bridge this gap, we propose a radiological-biological dictionary that aligns radiomic features (RFs) with Lung-RADS semantic categories. A clinically informed dictionary translating ten Lung-RADS descriptors into radiomic proxies was developed through literature curation and validated by eight expert reviewers. As a proof of concept, imaging and clinical data from 977 patients across 12 collections in The Cancer Imaging Archive (TCIA) were analyzed; following preprocessing and manual segmentation, 110 RFs per nodule were extracted using PyRadiomics in compliance with the Image Biomarker Standardization Initiative (IBSI). A semi-supervised learning framework incorporating 499 labeled and 478 unlabeled cases was applied to improve generalizability, evaluating seven feature selection methods and ten interpretable classifiers. The optimal pipeline (ANOVA feature selection with a support vector machine) achieved a mean validation accuracy of 0.79. SHapley Additive exPlanations (SHAP) analysis identified key RFs corresponding to Lung-RADS semantics such as attenuation, margin irregularity, and spiculation, supporting the validity of the proposed mapping. Overall, this dictionary provides an interpretable framework linking radiomics and Lung-RADS semantics, advancing explainable artificial intelligence for CT-based lung cancer screening.

Ali Fathi Jouzdani
Shahram Taeb
Mehdi Maghsudi
Arman Gorji
Arman Rahmim
Mohammad R. Salmanpour


Triangulation as an Acceptance Rule for Multilingual Mechanistic Interpretability

Abstract: Multilingual language models achieve strong aggregate performance yet often behave unpredictably across languages, scripts, and cultures. We argue that mechanistic explanations for such models should satisfy a \emph{causal} standard: claims must survive causal interventions and must \emph{cross-reference} across environments that perturb surface form while preserving meaning. We formalize \emph{reference families} as predicate-preserving variants and introduce \emph{triangulation}, an acceptance rule requiring necessity (ablating the circuit degrades the target behavior), sufficiency (patching activations transfers the behavior), and invariance (both effects remain directionally stable and of sufficient magnitude across the reference family). To supply candidate subgraphs, we adopt automatic circuit discovery and \emph{accept or reject} those candidates by triangulation. We ground triangulation in causal abstraction by casting it as an approximate transformation score over a distribution of interchange interventions, connect it to the pragmatic interpretability agenda, and present a comparative experimental protocol across multiple model families, language pairs, and tasks. Triangulation provides a falsifiable standard for mechanistic claims that filters spurious circuits passing single-environment tests but failing cross-lingual invariance.