Transformer Interpretability

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28 papers in the last four weeks, up 180% on the four weeks before. 0.3% of all new papers.

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Latest papers 224

Jul 27, 2026cs.CL

Grounding latent algorithm routing in transformer reasoning

A central question in the in-context learning literature is whether transformers can organize episode-level adaptation around different inductive-bias families. We study this question in a controlled setting through latent algorithm routing: route-like behavior in which the solver-family preference changes with the latent data-generating regime while prompt form is held fixed, remains stable under nuisance perturbations, and is selectively influenced by targeted activation interventions without large losses in answer quality. We introduce ROUTEBENCH, a diagnostic benchmark whose regimes differentially favor global shrinkage, sparsity, robustness, and locality, operationalized by ridge-like, lasso-like, Huber-like, and kNN-like family representatives. Across dense decoder-only transformers trained from scratch at 44M-612M parameters, a 306M model closes 80.9 percent of the oracle-routing gap and achieves route F1 of 84.1. The effect remains substantial under natural-language renderings, shuffled supports, lexical paraphrases, and a unified four-way routing setting. Stronger adaptive alternatives, including an input-conditioned soft mixture and an unsupervised Gumbel router, narrow the gap but remain below the 306M and 612M models on route F1 and OOD performance. Probe controls and matched activation-patching controls further show that route-relevant internal directions are decodable and functionally involved in solver-family-consistent output behavior. These results provide controlled evidence that dense transformers trained on ROUTEBENCH can develop route-like internal variables, but they do not establish universal routing in pretrained language models or unrestricted natural-language reasoning.

Xiangbo Zhang, Xiaoxu Ma

Georgia Institute of Technology

Transformer Interpretability Decoder-Only Language Models In-Context Learning

Jul 26, 2026cs.LG

LAWFUL: Law-Aligned Witness for Faithful Use of Latents

When a neural network predicts a physical system accurately, has it learned the governing law as formal, structured knowledge, and if so, does the network's internal computation actually use that representation throughout the law's domain of validity? We identify four interpretability gaps that limit answering these questions for {\em physics laws over continuous variables}: the absence of a coverage-aware causal-consistency measure over continuous counterfactuals; of a domain-of-validity test for the identified circuit; of a verification of the law's invariants and forbidden behaviors; and of a quantification of how a derived physical quantity flows through the circuit. We develop a foundational framework, LAWFUL, that closes the first two and lays groundwork for the remaining two, and illustrate it on the Mocap2Radar transformer, validating whether it learns and internally uses the Doppler frequency law

f(t) = \frac{2 v(t)}λ

from motion-capture and radar data in which neither

f(t)

nor

v(t)

appears.

Kevin Chen, Kenneth W. Parker, Anish Arora

Computer Science & Engineering, The Ohio State University, Columbus, Ohio, USA · Independent Researcher, Waterford, Virginia, USA

Transformer Interpretability Mechanistic Interpretability Neural Network Interpretability Scientific ML Causal Interpretability

Jul 25, 2026cs.LG

Through the Bottleneck: How Multi-head Latent Attention Separates Content from Position in Language Models

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

Dhruvil S, Fenil Sojitra, Ravirajsinh Chauhan

1Indian Institute of Technology Madras · 2P P Savani University

Transformer Interpretability Low-Rank Attention Attention Head Analysis Attention Mechanisms Representation Geometry in Language Models Multi-Head Attention+1

Jul 24, 2026cs.LG

Interior interpretability with attention rollout: contraction and propagation profiles in Transformers

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

Umberto Biccari, Qian Huang, Enrique Zuazua

Transformer Interpretability Transformer

Jul 22, 2026cs.LG

Scaling Interpretable Transformers with Parity Bottleneck Layers

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

Andrew Mack, Kraig Yuheng Tou, Mark Henry +2

Principles of Intelligence · Independent

Feature Superposition Transformer Interpretability Activation Sparsity Representation Disentanglement Neural Network Interpretability

Jul 21, 2026cs.CV

Text Template Tokens Are Implicit Semantic Registers in Diffusion Transformers

Modern text-to-image diffusion transformers (DiTs) generate images through joint attention, in which text and image tokens interact directly within a single sequence. In large-scale DiTs, the conditioning input contains not only the user prompt but also chat-template tokens introduced by LLM-based text encoders. Yet how these tokens participate in the denoising computation remains poorly understood. To probe this, we introduce a causal interpretability framework. Using it to separate prompt-content tokens from chat-template tokens, we find that the template tokens carry little prompt-specific information at the encoder output. Yet surprisingly, they emerge as dominant image-to-text attention sinks and causally maintain object identity inside the DiT, acting as implicit semantic registers. We show that they acquire this identity indirectly. Rather than reading the prompt tokens, they draw the identity from the image latents into which the prompt semantics have already been injected at the very first layer. We further reveal a division of labor across heads and depth in DiTs, where distinct heads route semantics or render visual structure, and identity is committed in early blocks, carried by middle blocks, and refined in late ones. As a practical payoff, this analysis yields a training-free pruning rule that removes the causally inert prompt-reading heads and cuts

20\%

of joint-attention FLOPs at a

1.4

-point cost in GenEval accuracy. Overall, our work not only reveals that the tokens encoding semantics at the input need not be those that maintain them during generation, but also provides a causal view of internal mechanisms in diffusion transformers.

Maohua Li, Qirui Li, Yanke Zhou +10

Nanjing University · Alibaba Group · Zhejiang University

Transformer Interpretability Diffusion Transformer Attention Sinks Attention Head Pruning T2I Diffusion Models

Jul 21, 2026cs.LG

Circuit Claims Depend on What Is Extracted and How It Is Compared

Circuit extraction identifies a small set of model components whose presence preserves a target behavior under ablation, and the resulting circuit is often read as the mechanism behind that behavior. We argue that this reading is under-determined: preserving behavior does not single out one circuit, because the claim it supports depends on which circuit is reported and how two circuits are compared. We make this concrete in a synthetic Lean tactic-prediction benchmark -- predicting the next step of a proof -- where fixed proof rules with randomized surface form let differences between extracted circuits be attributed to these choices rather than to the task. Across dense and weight-sparse checkpoints (most weights constrained to zero) of the same transformer, evaluated on atomic (single-rule) and compositional (multi-rule) proofs, we vary which extracted object is reported (a compact prediction-preserving circuit, a broader graph that also keeps surrounding read, write, and routing structure, or the smallest subgraph meeting a post-ablation loss threshold), and whether each attention head's query and key are represented jointly or separately. Exact component-to-component edge overlap is low and sensitive to these choices, at times dropping to a random baseline, while two coarser summaries stay stable: the set of selected attention heads, and the circuit-size ranking of conditions that differ in which supervised checkpoint initializes reinforcement learning (RL). The largest accuracy gains from RL on compositional proofs come with the most structure beyond the atomic circuits. A circuit-level claim is therefore well defined only once one states which circuit is reported, the pruning threshold used to extract it, and the level at which circuits are compared. We distill these requirements into a reporting practice for circuit-extraction studies.

Yang Sheng, Jie Fu

1Fudan University · 2Shanghai Innovation Institute · 3IQuest Research

Transformer Interpretability Circuit Discovery Circuits in Language Models

Jul 20, 2026cs.CL

For What Reason? Interpreting Models' Encoding of Causation and Antithesis

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

Abhidip Bhattacharyya, Shira Wein

University of Massachusetts Amherst · University of South Florida

Transformer Interpretability Causal Reasoning in Language Models

Jul 20, 2026cs.LG

An Analysis of Residual-Stream Geometry Across Transformer Depth

We propose a transition-centred geometric analysis of transformer residual streams. Relative displacement measures how \emph{far} representations move between consecutive layers, and orthogonal Procrustes analysis separates each transition into a rigid rotation and a non-rigid residual. Across six instruction-tuned models, on code generation and cross-lingual translation, these measurements reveal reproducible depth regularities. Relative displacement is strongly layer-dependent; typically larger early and late, with a quieter middle third; and nearly invariant across conditions within each model. Rotation magnitude is nearly constant across depth, while Procrustes residual and angle concentration remain depth-modulated, with residual peaking at the final transition. During generation, non-English targets show larger final-layer displacement and residual than English targets. We present these as descriptive geometric regularities, not as measures of computational effort or causal explanations. The contribution is a measurement framework for residual-stream transitions and evidence that, in the settings studied here, depth curves are model-dependent and largely condition-stable.

Sunit Bhattacharya, Ravi Shankar Kolli

ProRata AI

Transformer Interpretability Representation Geometry in Language Models

Jul 19, 2026cs.LG

Explaining and Tuning Transformer-based LLMs in Arithmetic Tasks with Human Strategies

Transformer-based large language models (LLMs) continue to achieve state-of-the-art performance across various natural language processing tasks. However, their subpar performance on seemingly elementary problems, such as basic arithmetic, raises concerns about model reliability, safety, and ethical deployment. In this study, we demonstrate that the performance of a vanilla Transformer model trained on integer arithmetic tasks can be improved using methods effective for human learners. We begin by decomposing the arithmetic task into well-defined subtasks and conducting loss convergence order analysis together with ablation studies for each subtask. Our findings reveal that LLMs exhibit learning patterns similar to those of human learners, with a faster learning speed for simpler subtasks compared to more complex ones. In addition, we successfully improved the accuracy of LLMs by applying problem-solving strategies and cognitive empowerment methods shown to enhance the performance of human learners. This suggests that transformer-based LLMs may share cognitive processes with human learners in arithmetic. Lastly, we provide a comprehensive demonstration of our method's effectiveness, including significant accuracy improvement experiments, visualization verification, and explanation-based analysis to illuminate the intricacies of LLMs in arithmetic learning. In general, this work explores the potential similarities between transformer-based LLMs and human learners, supported by explainable AI (XAI) verifications, ultimately fostering trust in LLMs for critical and high-stakes applications.

Luyu Qiu, Jianing Li, Hwanhee Kim +4

1The Hong Kong University of Science and Technology · 2The Hong Kong Polytechnic University · University of California, Berkeley

Transformer Interpretability Language Modeling LLM Mathematical Reasoning

Jul 19, 2026cs.LG

What does a Bayes-filtered transformer believe? A predictive Monte Carlo approach

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

Afiq Abdillah Effiezal Aswadi, Haotong Ma, Susan Wei

Department of Econometrics and Business Statistics Monash University

Transformer Interpretability Latent Variable Models Transformer Bayesian Inference

Jul 15, 2026cs.AI

Tracing LLM Behavior to the Training Data with Empirical Next-Token Distributions

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

Zachary Izzo

NEC Labs America

Language Model Pretraining Transformer Interpretability LLM Interpretability Mechanistic Interpretability

Jul 13, 2026cs.LG

Sparse Inter-Layer Dependencies of Transformer FFN Neurons

Feedforward network (FFN) blocks account for a large fraction of the parameters and computation in Transformer architectures, yet their internal structure remains difficult to interpret due to the additive superposition induced by the residual stream. We examine whether the activation of an FFN neuron can be explained by a sparse set of preceding neuron activations and attention outputs. We introduce a training-free attribution method that estimates the relative influence of upstream neurons and attention outputs on a target neuron's activation. Empirically, across models and layers, we find that small subsets of preceding activations and attention outputs suffice to preserve neuron activations with high fidelity when all remaining inputs are masked with their average values. Effective sparsity is even greater when accounting for the inherent activation sparsity of upstream layers. Moreover, applying the neuron-specific masks in all layers simultaneously, such that the induced deviations propagate through the network, leaves model perplexity largely unchanged at moderate sparsity levels. These results demonstrate that, despite dense parameterization, FFNs exhibit sparse and structured inter-layer dependencies at the neuron level. Our method provides a practical, scalable tool for circuit-level interpretability and identifies candidate sparse pathways with potential implications for efficient inference.

Johannes Knittel, Hanspeter Pfister

Harvard University

Transformer Interpretability Transformer FFNs Neural Network Interpretability

Jul 12, 2026cs.AI

Laguerre Geometry for Interpreting Large Language Models

Existing hypotheses represent a concept in an LLM as a single point, a linear direction, or a Gaussian cluster, yet it remains unclear how and why such structures emerge. Here, we show that concept geometry can be precisely characterized via Laguerre Geometry, in which a concept is defined as a region--a Laguerre-Voronoi cell or a union of cells--allowing us to strictly define, measure, and separate concepts. Building on this formulation, we show that finer-grained concept structures, such as inclusion and hierarchy, are naturally revealed by the Laguerre weights. We then push this geometry inside the transformer. Decomposing each layer into piecewise-linear operators, we show that a token's hidden trajectory is governed by two coupled mechanisms: a static tree of self-contained piecewise-linear flow, and a dynamic transport that hops the trajectory across trees when cross-token attention fires. This decomposition yields Geometric Lens, a training-free, hyperparameter-free method for reading out the exact concept a hidden vector encodes at any layer. We also develop Laguerre Autoencoder, a 2D visualizer that renders both the decision geometry and a model's full reasoning trajectory in one view. Finally, we move beyond explanatory geometry toward actionable interpretability, showing that Geometric Lens recovers the correct factual token when a model is prompted with in-context interference. The code is available on GitHub.

Chunwei Ma, Russell Wolfinger

JMP Statistical Discovery, Cary, NC, USA

Transformer Interpretability LLM Interpretability Representation Geometry in Language Models

Jul 11, 2026cs.LG

The RG-Flow Transformer: Encoding Scale-Free Dynamics in Scarce EEG

Brain field potentials are scale-free: their power spectra follow a

1/f^β

law whose aperiodic exponent

β

tracks cortical state, and sleep depth in particular is a shift in

β

. We ask whether a transformer endowed with an explicit renormalization-group (RG) inductive bias the RG-Flow Transformer, which couples ordinary self-attention to a scale-aware stream with a learnable anomalous dimension

γ

, block-spin coarse-graining, and an entropy-gated synchronization bridge has an advantage over a parameter-matched vanilla transformer on \emph{real, scarce} EEG. Using the PhysioNet Sleep-EDF corpus with a strict leakage-free by-subject hold-out, we (i) benchmark RG-Flow against a param-matched vanilla transformer and a hierarchy-only ablation on 5-class AASM sleep staging, (ii) sweep the per-subject data budget to look for the inductive-bias crossover predicted when data are scarce, and (iii) test whether RG-Flow's learned

γ

tracks the measured spectral exponent

β

out-of-sample a quantity the vanilla model does not possess. Across

5

subjects and

5

seeds under leave-one-subject-out cross-validation, RG-Flow and the vanilla transformer are statistically indistinguishable on 5-class staging (77.3% vs 77.0% accuracy; paired

p=0.294

), and the predicted scarce-data crossover does not appear: vanilla is numerically ahead at every data-limited budget. What does separate the models is interpretability RG-Flow recovers the continuous spectral exponent out-of-sample (

β

-recovery

R^2 = 0.416

), a capability the vanilla architecture has no analogue for.

Dibakar Sigdel

Mindverse Computing LLC, Lynnwood, WA 98087 · 1Mindverse Computing LLC, Lynnwood, WA 98087

Transformer Interpretability Electroencephalography Sleep Stage Classification

Jul 11, 2026cs.CV

Gradient-Skipping Relevance Propagation for Efficient Explainability of Vision Transformers

Vision Transformers (ViTs) are difficult to interpret because current methods of relevance propagation and attention flow do not fully consider some key architectural features, such as the uneven importance of attention heads and residual connections. Prior approaches typically assume uniform importance across attention heads; furthermore, they model skip connections as identity paths, leading to inaccurate relevance attribution. To address these issues, we introduce GradSkip, a novel relevance propagation method for ViTs based on adaptive head weighting and skip-aware propagation. GradSkip models the different importance of the attention heads and dynamically distributes relevance between the attention and residual paths. Experiments on ImageNet1K and BloodMNIST demonstrate a state-of-the-art faithfulness of GradSkip while requiring over 14 times fewer GFLOPs than the best-performing existing approaches. Additional evaluations using transformer-based segmentation confirm improved localization and alignment with ground-truth regions.

Christopher Buratti, Michele Marchetti, Federica Parlapiano +3

DII, Polytechnic University of Marche · CHIMOMO, University of Modena and Reggio Emilia

Transformer Interpretability Vision Transformer Layer-Wise Relevance Propagation

Jul 10, 2026cs.LG

System-Prompt Conditioning and Hidden-State Geometry in Four Open-Weight Models: Corrections and What Survives

Versions 1 and 2 of this preprint reported that an identity-specifying system prompt leaves a geometric fingerprint in the final-layer hidden-state trajectories of four open-weight language models, and that instruction tuning moves this fingerprint from the direction to the magnitude of the hidden-state vector. An audit of their code and data found the following. The curvature statistic described as Ollivier-Ricci curvature on Euclidean k-NN graphs was a non-standard Forman-type edge statistic on graphs built from temporal and cosine k-NN edges. Its released test permuted pooled edges instead of trajectories, and the published p-values came from unreleased code. The quantity reported as the norm of the first generated state is the state at the last prompt position, from which the first output token is predicted. The generic control prompt was matched to the identity prompt in characters, not in tokens. This version corrects the methods, withdraws the regime-specific claims (one model per regime) and the direction-to-magnitude claim, and re-analyzes the data with added controls. What survives is narrower. Centroid distance, maximum mean discrepancy and a linear probe separate every pair of prompt conditions in every model, while the curvature statistic exceeds its split-half noise floor in only four of twelve comparisons. In Gemma-4-E4B-it this state has a lower norm under the identity prompt than under a token-length-matched generic prompt (138.1 vs. 216.5; Cohen's d = -5.45; n = 20). Its direction also separates the conditions, and the effect fits the state's role in planning the output: the identity prompt instructs a pause before every answer, and the model opens 98 of 100 responses with a pause marker. When the first token is fixed, the norm ordering reverses. The base model continues the prompt template instead of answering. A redesigned follow-up study is in preparation.

Jorge Castillo Sepúlveda, Marco Torres Yévenes, Juan Carlos Lanas

Axis Dynamics SpA, Santiago, Chile

Transformer Interpretability Representation Geometry in Language Models Multimodal Instruction Tuning

Jul 10, 2026cs.CV

What Pixels Are Enough? SEAMS: Sufficiency Saliency via MSE-Preservation Soft-Masks

Saliency maps are most useful when they identify the image regions that are sufficient to preserve a model's behaviour. We introduce SEAMS, a sufficiency-based saliency method that directly optimises a soft mask using a preservation objective. Given a frozen differentiable model output, such as a class probability, CLS embedding, or token representation, SEAMS searches for a compact mask that preserves the selected output. The approach relies on a simple optimisation framework based on soft masks, a learnable budget, and a three-way image composite generated entirely from the query image. As a result, it requires no auxiliary distractor dataset, architecture-specific attribution mechanism, or differentiable top-k relaxation. Experiments with frozen ViT-S/16 and ConvNeXt models show that the same optimisation pipeline can generate object-level, class-conditioned, and token-level explanations by changing only the preserved target. The resulting masks are compact, interpretable, stable across random initialisations, and competitive on insertion and deletion benchmarks. Our results also indicate that different architectures often rely on different sufficient evidence while achieving similar preservation fidelity, highlighting the architecture-dependent nature of visual explanations.

Magdalena Trędowicz, Łukasz Struski, Arkadiusz Lewicki +4

Jagiellonian University · University of Information Technology and Management in Rzeszów · Jagiellonian University Medical College

Transformer Interpretability Saliency Map Evaluation Explainable Image Classification Visual Saliency

Jul 9, 2026cs.LG

Training, Reading, and Editing Legible Transformers

A transformer can be built from operators that are legible by construction -- bounded, named units that read as fuzzy set operations rather than dense activations -- but legibility must be pressed for during training, and the pressure has a failure mode. A crispness penalty meant to sharpen a bounded operator into a decisive detector instead collapses it into a dead constant. An identity, E[v(1-v)] = mu(1-mu) - var, shows why -- the penalty is a variance-minimizer blind to the difference between a live detector and a constant -- and names the fix: a per-channel variance floor, the target legibility metric written as a loss, which recovers both legibility and quality. A learned per-unit fraction then retires the hand-set reserved-GELU partition of prior work: given the choice the model keeps no unit as pure GELU and routes 87% of its load-bearing computation through crisp operators. The result is the most legible transformer we have built -- 78% of its feed-forward operands and 50% of its attention value channels are crisp-and-contextual detectors, and per-head legibility rises from 18% in shallow layers to 78% in deep ones. Read in the correct rotated per-layer frame, these units separate a clean detection (what a unit responds to) from a harder naming (what its output decodes to); and because the objective makes each unit crisp and sparse, edits to them are far more local -- 50-184x in the deep layers where the edit sites concentrate -- and can target explicit conjunctions a single neuron cannot express. Finally, a between-unit decorrelation pressure exposes a legibility dial: it trades a circuit's reuse for independence at no quality cost, turning concepts into single, surgically editable units and a prediction into a short explanation read off a handful of named operations. Quality holds at parity with a conventional baseline throughout.

Mark Oskin

School of Computer Science and Engineering University of Washington

Transformer Interpretability Transformer FFNs Mechanistic Interpretability

Jul 9, 2026cs.CL

Cross-seed explainability using Procrustes-conditioned Joint End-to-end Top-K Sparse Autoencoders

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

\geq

0.70 across seeds) than post-hoc alignment baselines on all three datasets. A minimal qualitative analysis confirms that high-universality features encode interpretable sociolinguistic patterns.

Bendegúz Váradi, Zoltán Kmetty

Centre for Social Sciences, CSS-RECENS Research Group, Budapest 1097, Hungary. · Department of Sociology, Faculty of Social Sciences, Eötvös Loránd University, Budapest, Hungary.

Transformer Interpretability Sparse Autoencoders Mechanistic Interpretability

Jul 8, 2026cs.LG

Mechanistic Interpretability for Neural Networks: Circuits, Sparse Features and Symbolic Reasoning

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

Pranav Sawant, Jakub Krejčí

The University of Texas at Dallas 800 W Campbell Rd, Richardson, TX 75080, United States · VSB—Technical University of Ostrava 708 00, Ostrava, Czech Republic

Transformer Interpretability Mechanistic Interpretability Circuits in Language Models

Jul 8, 2026cs.LG

Multiplication Beyond Groups: Stratified Fourier Mechanisms in Transformer Circuits

Transformers have demonstrated a remarkable ability to learn algorithmic reasoning, yet mechanistic analyses have mostly focused on globally invertible operations such as cyclic addition and group composition. In this work, we investigate how small transformers learn modular integer multiplication over composite moduli, a fundamentally non-invertible operation due to the presence of zero-divisors. We propose the monoid extension: a localized generalization of Group Composition via Representation (GCR) that suggests the learned computation does not rely on a single global representation space. Instead, the model partitions the input space into local hierarchical algebraic regions, where group-like structure survives and Fourier mechanisms can be applied. In transformers trained on square-free modular multiplication, we find that embeddings organize around these regions, attention exhibits class-sensitive routing and low-rank write directions, and local character features explain a large fraction of the model's output logits. Our results suggest that representation-theoretic mechanisms previously identified for group operations can extend beyond groups to more general structures.

Zitong Andrew Chen, Junaid Hasan, Akhil Srinivasan +2

1UW Math AI Lab, University of Washington.

Transformer Interpretability Transformer Attention Modular Arithmetic LLM Mathematical Reasoning

Jul 6, 2026cs.CL

Faithfulness to Refusal: A Causal Audit of Neuron Selectors

Attribution scores increasingly identify which neuron rows of a language model matter for applications such as pruning, interpretability, and editing for safety, yet whether they identify causally important rows is rarely tested directly. We address this with two paired audits built on one-shot neuron-row zeroing. We first audit selectors at the language-modeling level: attribution methods substantially outperform activation and magnitude-based baselines at identifying dispensable rows across five LLMs. We then adapt the same intervention into a behavior test by driving it with a contrastive harmful-versus-benign signal; the attributed rows are sufficient to install refusal on hate and crime while keeping benign over-refusal low and preserving language model fluency, and specific in that layer-matched random controls at the same depths fail. Highly rank-stable selectors can be among the least causally valid. Refusal moreover lives in a redundant subspace, where different attribution methods install it through largely disjoint row sets, so the recovered edit is one realization of a sufficient set rather than a unique mechanism. Together, these findings show that rank-stability proxies miss the kinds of selector failures a direct causal audit can surface.%

Ananth Eswar, Pratinav Seth, Utsav Avaiya +1

Lexsi Labs · Work done while at Lexsi Labs.

Transformer Interpretability Feature Attribution LLM Auditing LLM Refusal Causal Attribution Causal Interventions in Language Models+1

Jul 5, 2026cs.CL

Legible-by-Construction: Attention and End-to-End Transformers

A companion paper showed that a transformer's feed-forward layer can be rebuilt from explicit fuzzy set operations - intersection, set-difference, and a self-forgetting sequence quantifier - so its hidden units read as named logical operators at no cost to language-model quality. That left the other half of the transformer opaque. Here we carry the same idea into attention and join the two into one model. The mechanism is minimal: a head's value is passed through a sigmoid, so each value channel becomes a readable detector of whether a feature holds at a token. This adds no parameters and leaves the standard head otherwise untouched. A Boolean variant goes further, restructuring the value into an explicit within-token intersection and negation-capable set-difference. In both designs the output projection is left free, not tied to the vocabulary, which is the load-bearing decision: bounding what a head detects while leaving what it writes unconstrained yields selective detectors, whereas constraining the write does not. A bounded value is shaped into a readable detector by two selectivity pressures - one for sparse firing, one for decisive firing at the rails - and which a design wants is not universal. Across five specialized-attention designs at 125M parameters, 44 to 62 percent of value channels become crisp, contextually selective detectors, and their legibility rises with depth rather than crystallizing only on punctuation. Language-model quality is at parity with a conventional baseline. Finally, we couple the Boolean attention to the legible feed-forward layer and train an end-to-end legible-by-construction language model at benchmark parity: its feed-forward units are named set and quantifier operations throughout, and we can take a token it generates and read the named units that compose to produce it.

Mark Oskin

School of Computer Science and Engineering University of Washington

Transformer Interpretability Transformer Attention

Jul 3, 2026cs.LG

Individual Parameters in Weight-Sparse Transformers Appear Interpretable

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

Arnau Marin-Llobet, Stefan Heimersheim

School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138

Transformer Interpretability Transformer Mechanistic Interpretability Neural Network Interpretability Sparse Neural Networks

Jul 2, 2026cs.LG

Induction Heads Interpolate N-Grams

Induction heads are attention circuits believed to underlie in-context learning in transformers, yet a precise characterization of the estimators they implement remains elusive. We study transformers trained on order-

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Markov chains and identify two complementary smoothing mechanisms. First, at finite attention-weight scale, the circuit implements a soft context-matching estimator: it aggregates contributions from exact and partial context matches, weighted exponentially by their overlap, and induces a data-dependent interpolation across context orders analogous to Jelinek-Mercer smoothing. Second, a beginning-of-sequence (BOS) token induces additive pseudo-counts, recovering Dirichlet-style smoothing. We construct a disentangled transformer implementing both mechanisms and show that trained transformers recover the predicted attention patterns. Across settings where pseudo-count smoothing is optimal or lower-order contexts provide structured evidence, trained transformers match or outperform classical count-based baselines. Our results bridge mechanistic interpretability of induction heads with classical statistical smoothing, revealing that transformers learn to regularize in-context estimation rather than simply count.

Francesco D'Angelo, Oguz Kaan Yuksel, Swathi Shree Narashiman +1

1TML Lab, EPFL, Switzerland. · 2IIT Madras, India. · †Work done during an internship at the TML Lab, EPFL.

Transformer Interpretability In-Context Learning Language Modeling Induction Heads

Jul 1, 2026cs.CL

KnowledgeDebugger -- an Exploration Tool for Knowledge Localization and Editing in Transformers

Recent research has increasingly focused on understanding how Transformers store and process knowledge, as well as how this knowledge can be edited. Research work in this area is often conducted in two phases: first, phenomena are explored on individual samples. Then, when results appear promising, more statistically robust experiments follow. To support the first phase, we propose KnowledgeDebugger, a GUI-based exploration tool for knowledge localization and editing in Transformers. Our tool - inspired by LM-Debugger - offers no-code access to the methods in EasyEdit, a widely used library of state-of-the-art Knowledge Editing approaches. We demonstrate the tool's effectiveness through case studies of recent findings in this field.

Eric Benz, Lennart Stöpler, Nikolai Bolik +1

Heidelberg University

Knowledge Editing Transformer Interpretability Model Editing

Jun 30, 2026cs.LG

Representation as a Bottleneck for Mechanistic Interpretability: The Manifestation Unit Protocol

Mechanistic interpretability has produced a rich inventory of component-level analyses that characterise what neural-network components encode and how they interact. Their outputs, however, are not easily reusable: selectivity tables, circuit diagrams, and feature lists remain locked in per-study notebooks - non-composable, not queryable in natural language, and not directly actionable for downstream audit or intervention. We study the representation layer that sits between these analyses and downstream use as a bottleneck that can be evaluated independently, and introduce Manifestation Units, a typed tuple protocol (E, S, R, D, G) extended with attention-head primitives (T) for transformer architectures, organising per-component statistics into structured fields populated automatically and queried through hybrid retrieval. Instantiated across generative vision (beta-VAE), discriminative vision (CNN), and language (GPT-2), the protocol supports two findings: typed structure substantially outperforms unstructured baselines on retrieval, and CNN filters retrieved by the schema satisfy causal sufficiency and necessity criteria under matched-budget controls. The schema absorbs attention-head primitives without modification, set-recovers known IOI circuit members under retrieval-budget-matched controls, and reveals an irreducible two-field core (S+R) with remaining fields either redundant or actively interfering. We present this as schema infrastructure for mechanistic interpretability rather than frontier-scale validation.

Hussein Chouman, Wataru Sasaki, Tomokazu Matsui +2

Ubiquitous Computing Systems Laboratory, Nara Institute of Science and Technology, Nara, Japan.

Transformer Interpretability Mechanistic Interpretability Explainability Evaluation

Jun 30, 2026cs.LG

Signed-Permutation Coordinate Transport for RMSNorm Transformers

Modern LLM workflows move coordinate-indexed objects across checkpoints: steering vectors, sparse autoencoders, top-

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neuron sets, attribution lists, and merge alignments. This is only well posed after fixing the model's residual-stream gauge, which we show is architecture-dependent: LayerNorm residual charts have permutation gauge

S_d

(up to a global sign flip), while RMSNorm charts with generic per-channel gain have signed-permutation gauge

B_d = S_d \ltimes \{\pm 1\}^d

. Permutation-only alignment is therefore symmetry-incomplete for RMSNorm models. We introduce sign-marginalized Hungarian matching and prove a sharp failure mode: with decorrelated coordinates, raw signed-correlation matching has a structural permutation-accuracy ceiling at the positive-sign fraction of the true gauge, which sign-marginalization removes. We then make coordinate-preserving transport, not function-level merging, the primary object: composing saved-checkpoint local

B_d

gauges along same-base fine-tuning trajectories recovers 91.1% of cross-run coordinates at 1500 steps versus 60.3% for endpoint matching, and the gain is not explained by merely routing through the base. The recovered gauge transfers tools that permutation-only alignment breaks: TinyLlama SAE reconstruction has NMSE 0.004 under

B_d

versus 1.08 under

S_d

; Qwen sentiment steering preserves 95.8% of its effect versus 17.2%; refusal steering reverses sign under

S_d

; coordinate-preserving merges behave the same way. The same covariance governs stateful training: signed transport of AdamW state preserves the resumed trajectory, while permutation-only state follows a different one from a functionally identical checkpoint. Finally, gauge-sweep audits show index-level interpretability claims are reproducible only relative to an explicit gauge.

John Sweeney

Sideplane AI

Transformer Interpretability Permutation-Invariant Learning Model Merging

Jun 30, 2026cs.CL

Explicit Fuzzy Logic in the Feed-Forward Layer: Self-Forgetting Quantifiers Discover Legible Grammatical-Licensing Detectors

A transformer's feed-forward (FFN) sublayer materializes the distinctions attention gathers, yet gives no account of what it computes. In a parameter-neutral replacement, each hidden unit is an explicit fuzzy set operation on sigmoid-bounded [0,1] memberships: intersection AB and set-difference A(1-B), the latter a bounded positive negation ("A but not B") that gated/bilinear units lack -- a negation-capable FFN (NC-FFN). On N-bit parity they are the most parameter-efficient reasoning basis at shallow depth; at scale (125M, OpenWebText) NC-FFN ties the GELU baseline's perplexity, every unit carrying explicit logical form. Two limits share one cause: two-operand logic localizes to layer 0 and erodes under training, and the one robust grammatical deficit concentrates in licensing and quantifiers, beyond within-token operators. We resolve both with a small block of sequence quantifiers: a soft existential and a soft proportion, each with a per-unit learned forgetting rate from a sticky init. This recovers the deficit at epoch one (halving the wider epoch-two gap), modestly leads on LAMBADA, and makes the FFN legible: the structure now holds and migrates into depth; the decay un-learns its stickiness (median half-life ~1.5 tokens; zero latch units); and at the semantic layers the units read, without dictionary learning, as grammatical licensing detectors: each fires on a licensor (a comparative, a passive participle, a negative-polarity item) and carries its memory forward to predict the licensed word (than, by, nor). This legibility is localized and free only up to a partition (a fully Boolean FFN diverges in training), but the result is a parameter-neutral, language-model-quality transformer with a readable, interpretable-by-construction grammatical mechanism -- an account not just of what a feed-forward layer represents but how it licenses.

Mark Oskin

School of Computer Science and Engineering University of Washington

Transformer Interpretability Transformer FFNs Transformer Fuzzy Logic Language Modeling Feedforward Neural Networks