Coreference resolution is an important task in contextual reasoning. In this paper, we investigate the mechanism for representing and retrieving singular and plural entities for plural reference. We use a combination of mechanistic interpretability and attention pattern analysis to study the process in which LLMs predict a pronoun to refer back to previously mentioned entities. Using a range of causal intervention techniques, we find a set of attention heads that are responsible for (1) representing coreference information in the input, (2) identifying entities that form a plural reference, (3) transferring the information to the component that is responsible for selecting the antecedents and predicting the pronoun. We also find that LLMs align with humans in preference for plural pronoun. Specifically, entities in a plural construction are more likely to be referred to as a plural entity if they are ontologically similar and are linked by the conjunction "and".
LLM-based evaluators of natural language generation (NLG) quality are widely deployed as scoring tools and as automated training signals, yet the internal procedure by which they assign a rating remains poorly understood. We investigate this procedure mechanistically through an eight-attack perturbation taxonomy across the Readability and Adequacy dimensions of NLG quality, a generation pipeline that produces paired clean and corrupt summaries with controlled error intensity and explicit token-level modification maps, and a four-experiment battery of causal tracing, logit-lens vocabulary projection, and attention-head knockout applied to Themis (Llama-3-8B) and Prometheus (Mistral-7B). Both evaluators implement a structured, coherent evaluation pipeline operating in two stages: below layer 15, attention performs local error comparison and routes the result to the final input position; above it, the MLP cascade integrates the signal and writes the rating, with the decision crystallizing in the residual stream at a sharp late layer (L = 26 on Themis, L = 25 on Prometheus). Furthermore, a base-model control at the same scale (Llama-3-8B) reproduces the routing architecture and crystallization but not the stage separation, isolating the two mechanisms that fine-tuning specifically installs, suppression of below-L15 MLP contribution at the last position and a two-layer advance of the crystallization depth, indicating that fine-tuning sculpts an existing substrate rather than building the pipeline from scratch. We release the source code and data at https://github.com/himil-v/judge-mech
Multilingual large language models (mLLMs) achieve strong performance in machine translation, yet our understanding of the mechanisms by which they transform representations from one language to another remains incomplete. Prior work suggests that translation decomposes into separable processes within an mLLM, where conceptual content is first represented independently, followed by a production into language-specific form. In this work, we show that translation is even more modular than previously assumed and that the output language production in translation processes is actually further separable into a syntax and a surface language process. We construct controlled multilingual datasets that isolate cross-linguistic differences in word-order and use causal interventions and probing to track how representations are transformed during translation. We find that models first construct target-side word-order before realizing the target language surface form. We identify individual attention heads that are selectively sensitive to syntactic transformations while remaining largely invariant to language identity. These results establish the commitment to a syntactic structure as an independent stage in translation, extending prior decompositions and showing how translation is implemented by functionally different components within mLLMs.
Large Language Models (LLMs) have demonstrated remarkable performance across diverse tasks, from text summarization to question answering. Despite these capabilities, their black-box nature obscures internal decision-making processes. Mechanistic interpretability (MI) aims to address this by reverse-engineering neural networks into human-understandable algorithms. Current MI approaches for LLMs typically follow a two-stage paradigm: first identifying important components (circuit discovery), where components are typically individual nodes such as an attention head or feedforward neuron, and second determining the role they play in a certain task (functional interpretation). However, this sequential approach overlooks a fundamental insight: a component's importance and its functional role are inherently codependent. Unifying these stages presents two key challenges: (1) functional roles are often tied to specific nodes or components, limiting generalization, and (2) their identification relies on subjective interpretation rather than quantifiable metrics. To address these challenges, we propose S^3martCirc (Self-supervised Smart Circuit Discovery), a unified framework that simultaneously discovers circuits and interprets functionality. S^3martCirc abstracts node behavior into two general computational roles that generalize across tasks and defines a quantitative metric for assigning them, enabling importance and functional role to be discovered jointly rather than in sequence. Extensive experiments show that our framework outperforms existing methods in circuit discovery.
Alireza Bayat Makou, Emirhan Böge, Phu Gia Hoang +5cs.CL
This paper presents Murano, an open source framework for designing, running, and reproducing mechanistic interpretability studies of large language models, intended for researchers across disciplines. These studies often combine loading, recording, attribution, intervention, and evaluation, while existing libraries tend to focus on different parts of this workflow. As a result, researchers using several libraries may need to adapt outputs from one for use by another. To bridge this gap, Murano represents operations from these five areas as composable steps. Steps exchange named result artifacts and declare the inputs they require and the outputs they produce. A pipeline executes its steps in the order supplied, and Murano uses canonical addresses when component identities pass between operations. Murano builds on existing interpretability and machine learning libraries. We demonstrate Murano through two reproductions of established interpretability studies and one illustrative sparse autoencoder case study.
Minju Song, Hyeon Hwang, Junhyun Lee +1cs.CL cs.AI
Large language models exhibit substantial performance variation across languages, even when solving semantically equivalent tasks. Existing analyses often treat this phenomenon as an observational disparity caused by differences in pretraining data, tokenization, or benchmark coverage. We study a complementary hypothesis: high-resource languages (HRLs) may more reliably elicit latent computations useful for task-specific (i.e. mathematical) reasoning, while lower-resource languages (LRLs) may under-activate those computations despite expressing the same task. To test this hypothesis, we introduce a mechanistic intervention framework for identifying and transferring task-relevant sparse latent features across languages. Using sparse autoencoders over residual-stream activations, we isolate features enriched in successful HRL task-specific reasoning while filtering out source-language and generic-generation features. We then construct steering directions from these features and inject them during LRL inference. The resulting interventions test whether the selected features are functionally involved in the observed reasoning gap: suppressing them should impair source-language reasoning, while activating them should partially recover target-language reasoning beyond random and non-task controls. Our framework reframes some cross-lingual reasoning gaps as failures of mechanism elicitation rather than capability absence, and offers a causally testable route to feature-mediated transfer without translation, fine-tuning, or changing the user-facing language.
A wide range of methods have been proposed for interpreting language models, delivering important insights into their inner workings. However, different methods and their resulting insights stand in relative isolation: what could the underlying structure of language models be, such that they give rise to all our interpretations? In this work, we propose using Tensor Product Representations (TPRs) as a unifying hypothesis. TPRs give a concrete proposal for how compositional structure could be represented in vector space --- as filler-role bindings. We show, both mathematically and empirically, that TPRs can unify several prior interpretability methods: additive analogies, linear probing, sparse autoencoders, and activation patching. Mathematically, we show that these methods can all be derived from TPRs. Empirically, we apply the derivations to a range of different models --- from small toy models to LLMs --- to construct instances of each of the above interpretability methods; these constructed variants perform comparably to their standard variants. We view this work as a step toward what interpretability will ideally provide: a unified account of the nature of neural networks, corroborated not just by individual observations but also by an explanation of the connections between them.
Linguistic theory has long recognized cross-linguistic syntactic regularities, leading to claims that these similar structures are processed by similar mechanisms. However, this hypothesis has been difficult to test empirically due to our lack of fine-grained, manipulable access of human processing mechanisms. In this work, we take advantage of techniques from mechanistic interpretability to study such a question in multilingual LMs. We first isolate language-internal mechanisms before attempting to transfer them cross-lingually. Across four models and three well-studied constructions (subject--verb number agreement, anaphoric pronoun gender agreement, and filler--gap object extraction) we find consistent cross-lingual mechanism transfer. We further find transfer to be graded, with more transfer between more typologically similar languages. We believe our work provides novel hypotheses about cross-linguistic syntactic structures and multilingual processing, and more broadly shows how the study of language models can help inform linguistic theory.
One approach to mechanistic interpretability explains behavior through circuits: the components and connections that carry it. Frozen discovery often returns hundreds of edges, making them hard to inspect, compare, or verify exhaustively. We introduce Circuit Condensation, which post-trains models to concentrate behaviors into smaller causal graphs. Each round prunes low-attribution edges and trains a low-rank adapter to match the original through what remains, retaining the cut only if task performance and general capability survive. Across four behaviors and eight models, condensed circuits are smaller than the strongest frozen baseline in 30 of 32 settings, by $8.1\times$ on average and up to $316\times$. Repeating the search without weight updates produces larger circuits in 29 of 32 settings, showing that weight updates, rather than search alone, drive the reduction. Testing every subset of 19 circuits finds 11 that cannot be reduced and reveals removable edges in the rest. Pair ablations expose dependencies between edges, showing that their effects cannot be understood independently. On indirect object identification, condensation isolates 24 heads, 17 of them with documented roles, against 61 heads and 36 undocumented ones for the matched frozen circuit: a sufficient sub-circuit of the published mechanism rather than a reconstruction of it. The resulting circuit tracks the original model's next-token distribution and predicts its errors.
Vedant Palit, Florent Draye, Terry Jingchen Zhang +2cs.CL cs.LG
Transcoder attribution graphs are usually trained to explain why a model assigns high probability to a particular next token. We introduce Concept-Targeted Attribution (CTA), which instead trains attribution graphs with respect to a linear probe direction. CTA therefore yields probe-specific circuits that explain why an internal concept representation arises in a prompt, independently of whether it is expressed in the generated token. Using Cross-Layer Transcoders, we show that these probe-targeted graphs contain predictive structure: graph-level features predict probe accuracy across four widely studied concept categories ($ρ= 0.91$, $R^2 = 0.84$), while local features identify the sparse components driving per-prompt classification. This connects probe performance to interpretable circuit structure, allowing us to ask not only whether a probe works, but which internal computations make it work. Causal ablations further show that probe-targeted and logit-targeted graphs capture functionally distinct mechanisms. Removing probe-relevant features reduces internal concept scores while largely preserving generated tokens, whereas removing logit-relevant features changes the generated token in 92% to 100% of cases with near-zero effect on probe scores. CTA provides a framework for moving from behavioral probe accuracy to mechanistic explanations of probe performance, enabling more detailed audits of internal concept representations, including safety-critical ones. Our code is available at https://github.com/vedantpalit/concept-targeted-attribution
Discovering stable neuron behavior across entire domains remains a challenge in mechanistic interpretability. Existing methods often rely on instance-level point estimates or computationally expensive procedures, which either obscure population-level variability or limit scalable domain-wide analysis. We present RACE (Residual Alignment for Consistency Estimation), a forward-pass statistical framework that evaluates the domain-wide functional consistency of Transformer neurons. Perturbation experiments demonstrate that RACE achieves superior domain specificity compared to gradient-based point estimates. Meanwhile, token-distribution-level results verify the association between the selected neurons and the target domain. Furthermore, its computational overhead is two orders of magnitude lower than that of gradient-based methods.
Hang Chen, Jiaying Zhu, Wenya Wangcs.LG cs.AI cs.CL
Mechanistic Localization bridges mechanistic interpretability and post-training optimization by isolating critical parameters via interpretative approaches and then guiding parameter-efficient Supervised Fine-Tuning (SFT) in a ``locating-then-tuning'' paradigm. However, due to the retrospective nature of mechanistic interpretability, directly interpreting pre-SFT models introduces misleading conclusions. Specifically for novel tasks, initially identified neurons differ drastically from those governing the final model, introducing biases that actively disrupt SFT. To address this, we propose a forward-looking localization framework that accurately estimates the post-SFT interpretability state using only pre-SFT parameters and the target dataset. Theoretically, we model SFT as a continuous parameter evolution, leveraging Taylor expansion to rigorously bridge the post-tuning mechanistic objective with the pre-SFT model's dynamic gradients. Practically, we design dual-granularity (neuron- and component-level) localization pipelines. Extensive experiments demonstrate that our approach not only provides superior SFT guidance but also exhibits robust performance and temporal scalability across increasing model sizes. This work transcends the fundamental limitation of traditional interpretability-its inability to identify task-critical mechanisms before they are trained-pioneering a predictive frontier that unites mechanistic interpretability with targeted optimization.
When a context asserts two values for one fact, a model commits to a cue -- recency, repetition, position -- but natural data rarely makes these disagree, so behavior cannot reveal which. We train 26M-parameter transformers on a synthetic language where recency and rarity are exactly coextensive, and separate them with a minimal causal edit that inverts one cue while holding the truth, token count and answer position fixed. All 75 runs reach accuracy >= 0.999, including where the trivial heuristic fails, so no held-in evaluation distinguishes them. Under intervention the per-cell readout does not replicate: 13 of 25 cells differ by more than 0.3 in sign fraction across three seeds, the largest by 0.879 against a standard error of 0.025. The construction predicts this -- coextensive rules leave the objective indifferent between them -- and the variance is ordered by how much of the optimization each comparison releases. What replicates is timing: escape from a positional shortcut with a closed-form ceiling, monotone in redundancy. Probed before that escape, attribution reverses sign in 32 of 75 runs at unchanged accuracy, and gating on circuit formation is necessary but not sufficient. The corpus fixes when a mechanism appears, not which one -- a criterion for when mechanistic attribution to data is available at all, and our construction makes the unavailable case exact.
While recent advances in data synthesis aim to curate high-quality datasets, most generation pipelines still rely on heuristic prompt-based control. This black-box paradigm provides limited insight into how individual samples interact with a model's underlying learning dynamics. To bridge this gap, we propose a circuit-grounded framework that connects training-dynamics-based data valuation with mechanistic interpretability (MI). Specifically, we conceptualize data quality along three complementary utility axes, learnability, challenge, and alignment. First, we uncover specialized model-internal circuits that causally govern these utility signals. Then, moving beyond heuristic prompting toward mechanistic control, we leverage these circuits as controllable interfaces, actively steering generation to produce utility-targeted data. Building on this capability, we introduce SAMS (Stage-Aware Mechanistic Scheduling), which schedules circuit-steered data according to the model's evolving optimization needs. Experiments on multiple-choice QA tasks demonstrate that our approach yields precisely controlled data with greater diversity than prompt-based baselines, consistently improving downstream performance and calibration. Ultimately, this work establishes a principled white-box paradigm for interpretable data generation, pioneering the use of MI not just as an analytical tool, but as a practical, controllable interface.
Large Language Models (LLMs) demonstrate remarkable problem-solving capabilities when guided by Chain-of-Thought (CoT) prompting, yet the internal mechanisms underlying these improvements remain poorly understood. In this work, we investigate where CoT-related causal effects emerge across the generated reasoning trajectory and which attention heads carry signals that contribute to final-answer computation. Because CoT reasoning unfolds over multiple generated tokens, standard activation patching at a single static token position is insufficient to characterize these temporally distributed effects. To address this limitation, we introduce a sequential activation patching framework that traces CoT-conditioned attention-head activations across token positions and aggregates their effects using Part-of-Speech-guided analysis. We further introduce Sequential Multi-Head Patching to evaluate the joint contribution of distributed head sets, together with cross-question and random activation controls. Targeted zero-ablation experiments show that the identified heads are functionally important for successful answer generation and affect several overlapping mechanisms, including reasoning-trajectory maintenance, answer anchoring, exemplar-target separation, and numerical generation. Overall, our results provide evidence for distributed reasoning-support sub-circuits associated with CoT-conditioned computation.
Mechanistic interpretability has identified transformer circuits, but lacks a shared vocabulary for describing how their functions compose across tasks and architectures. We introduce Coherentist Probabilistic Compositionalism (CPC), an interpretive framework that grounds transformer computation in coherentist theories of interpretation and describes it through four operator roles. Alignment identifies candidate relations, unification integrates supporting information, suppression reduces incompatible alternatives, and routing carries selected information to the output. Across 15 models from five architecture families, the suppression, unification, and routing weight-space signatures correlate with held-out activation-level role measures above random baselines. Suppression is more stable across tasks than unification. Ablating alignment heads reduces downstream suppressive activity beyond a random-head control in 10 models, but similar effects on no-conflict prompts indicate a general upstream dependency, not contradiction-specific coupling. Explicit contradictions significantly shift a layerwise coherence proxy in 14 models; after removing shared residual covariance, the gap has the predicted direction in every model. Base and instruction-tuned variants preserve induction-head score structure ($r{\geq}0.98$) without a consistent shift of operator signatures towards later layers. These results support CPC as a shared vocabulary for comparing transformer mechanisms while showing that their depth and geometric expression remain architecture-specific.
The components of a transformer communicate by writing to and reading from a shared residual stream, and mechanistic interpretability has mapped these connections by hand, one circuit at a time. We present the communication map, which charts every potential communication channel in a language model from weights alone, generalizing the composition score of Elhage et al. (2021) into a single coupling coefficient covering all 18 connection classes, from entire attention head circuits to single neurons. The census of all candidate channels, from $6.3\times10^{8}$ in GPT-2 to $1.3\times10^{11}$ in Pythia-6.9B, finds that 70-89% of head pairs are oriented far from chance, some coupled strongly and others actively avoiding each other. The full map costs 15 seconds for GPT-2 and 11 minutes for Pythia-6.9B on one consumer GPU. Two applications demonstrate the utility of the map. In Application 1, the strongest head-to-head couplings recover the known induction circuits blind and group them into communities, and ablating one such community destroys the model's in-context copying. In Application 2, pooling every head's coupling coefficients identifies a distinct two-dimensional stream subspace, whose deletion abolishes the induction capability in six models up to Pythia-6.9B. This subspace is different from those identified by either activation PCA or outlier dimensions. We release the map, the statistical machinery, and the intervention suite.
Recent work in mechanistic interpretability has studied how large language models recall facts stored in their weights. This paper argues that factual recall points to something broader: a general kind of operation in deep learning models, which I call feature recall. The core observation is that a linear projection can be read as retrieving stored information scaled by input activations. I define feature recall, show it applies across architectures, and contrast it with the established paradigm of feature combination. I also consider how cases of feature recall might be mechanistically identified. The account gives philosophers a new conceptual tool for understanding deep learning, and points to empirical directions for mechanistic interpretability research.
Mechanistic interpretability seeks quantities that models do not expose directly: represented states, component effects, interactions, and responses to interventions. Patching, gradients, Hessian-vector products, and subset interventions provide different measurements under different access assumptions and may target different quantities. We formulate their shared measurement structure as mechanistic tomography: designed measurement for recovering internal mechanisms and intervention effects. For a chosen basis and intervention family, measurements take the form y = Ax + w, where A describes the interventions, x is the target map, and w contains nonlinear response, sampling error, and basis misspecification. This language gives a practical procedure: start with the least costly measurements, test on held-out interventions at the intended scale, calibrate simple mismatch, and expand the measurement family when structured residuals remain. Control provides a demanding validation setting because an estimate that guides an intervention acts as an observer. In a two-HMM model, control error rises with observer error, while target improvement can hide nuisance-state movement. Under forward-only access, sparse aggregate measurements recover a finite-effect map with fewer interventions than coordinate patching. With gradient access, finite probes improve a local attribution map. Lifted measurements and Hessian-vector products recover interactions missed by first-order maps, while Tracr shows that the required family depends on the basis. On GPT-2-small IOI, the Name Mover-Negative Name Mover interaction is the largest held-out predictive term among three tested cross-group pairs. On Qwen-2.5-7B, finite calibration makes an additive refusal-response map adequate, so held-out error does not support pairwise lifting.
Rahul Chowdhury, Timothy A Rupprecht, Senhao Cao +5cs.LG cs.AI
Recent work has shown that large language models (LLMs) exhibit strong numerical sequence modeling capabilities and show promise in time-series prediction. While LLMs display in-context learning capabilities, the mechanisms with which they accomplish time-series prediction remain unclear. Specifically, whether they truly understand the underlying structure, which at a minimum requires reasoning over first differences in the sequence of numbers. To study this, we investigate Llama 3.1-8B from a mechanistic interpretability point of view. Mechanistic interpretability is an emerging field concerned with the reverse engineering of the algorithms learned by neural networks such as LLMs. To assess Llamas' numerical sequence modeling capabilities and to facilitate our mechanistic interpretability analysis, we create a sequence modeling task that cannot be solved without picking up structural cues. Specifically, we sample n random numbers and repeat them with an offset. We find that Llama displays strong performance on our tasks suggesting that it can pick up on the underlying structure. To understand the mechanisms that allow it to do so, we perform probing experiments and activation patching based counterfactual analysis. Probing reveals that the model computes and stores first differences in its internal representations without explicit supervision, indicating that it tracks structural information about the sequence. Activation patching reveals that Llama retrieves the relevant first-difference with a mechanism similar to an induction circuit and subsequently adds it to the current value. Notably, our work represents one of the first studies to identify this form of concept induction in LLMs.
Language models hold latent quantities in a form they can report on, and more of a quantity is present in that form when the task requires reusing it flexibly. What causes a representation to enter that form is open, and the word workspace invites an admission story: a gate that decides what gets in. Testing it on open-weight models with Jacobian lenses, over a benchmark whose five arms share an identical context, we find no gate where it predicts one. Demand raises a concept's lens visibility beyond what applying an operator to a supplied value produces: +0.050 [+0.045, +0.057] in percentile rank on our primary checkpoint, positive on all four we measure, though that arm answers at ceiling and the accuracymatched contrast is stronger under that readout. At the same time one shared linear map decodes the variable from every arm, the control included, at 6.4-9.0x its selection-corrected floor. What produces the later readable form at the queried position is attention-mediated gathering inside a mid-depth window: separating patch depth from readout depth puts transport there at least 17x above anywhere shallower under non-saturating readouts, with no tested MLP output contributing positively inside it. Under the saturating percentile rank the same grid does not localise the window, which is a fact about that measure. An arm that needs the variable for nothing concentrates sevenfold less, so the window is demand-specific. That window has two measured edges, a survival failure below and destruction above, and it falls at the same fractional depth in a 64-layer hybrid and a 62-layer dense model from another family. We localise where the variable is installed and read, not the route from the passage, which transports nothing. But the readout is not a calibrated measure of use: three components move it to within 12% of one another and differ 7.4x in what they do to the answer.
Xiang Guan, Roger D. Newman-Norlund, Yong Yang +8cs.LG cs.CL
Mechanistic interpretability of large language models lacks spatially resolved, falsifiable tools for testing whether internal components are specialized for distinct cognitive operations. We adapt subtraction analysis, the standard framework of human neuroimaging, from biological brains to perturbed transformers, and apply the same logic to both substrates in parallel. Building on the Brain-LLM Unified Model (BLUM), which showed that layer-perturbed LLaVA-1.6-Vicuna-13B error profiles match the lesion patterns of aphasic patients, we develop PRISM (Perturbation-based Regional Interpretability through Subtraction Mapping). PRISM maps the seven clinical Philadelphia Naming Test categories, subtracts error classes pairwise, and treats each perturbation seed as a subject in a group analysis with threshold-free cluster enhancement along the layer axis. We run a structurally matched analysis on 213 chronic post-stroke aphasia patients using correlation-difference lesion-symptom mapping, and replicate both sides on held-out splits. The designs match in subject dimension (seeds, patients), spatial dimension (layers, atlas-parcellated cortex) and thresholding, but the contrast operator differs: a within-subject error-proportion difference for the LLM, a between-subject correlation difference for the cortex. Both substrates recover a robust phonemic-favoring dissociation, a deep layer cluster and a frontal-perisylvian cortical cluster, both replicating; the semantic-favoring direction is a consistently signed but non-significant trend on both. PRISM thus gives a falsifiable, spatially resolved test of functional-specialization claims in transformer language models. A confirmatory ROI-level intervention (PRISM Stage 3) licensing the strongest causal-mechanism claim is left to subsequent work.
Trained transformer models develop privileged bases: coordinate axes whose statistics differ from the rest of the residual stream. But what kind of direction does such a basis select? We investigate the prediction direction, the unembedding direction of the token a model currently predicts, and find that it functions as a content-defined privileged anchor. Measured with respect to this anchor, residual-stream variation is geometrically and behaviorally stratified by proximity to the prediction. The stratification holds in all eighteen models tested (dense and mixture-of-experts, 7B-120B, base and instruction-tuned). A narrow, scale-invariant prediction interface concentrates readout-relevant structure, while the vast prediction-distal complement expands with model scale. Because the prediction direction sits nearly orthogonal to the principal variance axes, variance-based analyses recover this organization only partly, and the shortfall grows with prompt heterogeneity. Anchoring reveals a steep geometric gradient: prediction-proximal regions are highly structured and cluster related prompts, while the complement is flatter and anti-discriminates among prompt groups. The interface is a narrow slice but functionally decisive. Disrupting the variance directions closest to the prediction causes immediate divergence and frequent task-frame shifts; disrupting the next level down delays divergence and preserves framing. The complement is weakly readout-aligned per direction yet causally and temporally load-bearing, and behavior is driven by direction rather than magnitude. These results establish the prediction direction as a privileged anchor distinct from previously described coordinate axes, and give a geometric account of how high-dimensional computation coexists with linear readout.
A growing body of work reports that language models represent task-relevant latent structure that they fail to use. Whether such structure, once located, can be converted into behavior is a separate question that is rarely tested end to end. We submit the complete pipeline -- detect, localize, and release -- to a fully preregistered stress test on a 25.7M transformer trained on causal-evidence discrimination, where a known suppression phenomenon (latent causal structure present but behaviorally unused) has previously been documented. Every threshold, claim template, and decision-tree branch was hashed and archived before any corresponding data existed. Three findings. (i) Localization succeeds: interventions at observation-evidence channels of mid layers restore target behavior on otherwise-suppressed worlds (paired release advantages $0.563$ and $0.854$, 97.5% CIs excluding zero; best-site release rate $0.889$). (ii) Gating fails out of distribution: a detector calibrated to trigger on zero out-of-distribution calibration worlds triggers on 6.9-7.3% of held-out in-distribution generations and on zero of the 2,400 held-out generations that actually need it -- a complete inversion that silently reduces the gated pipeline to its base model. (iii) Linear release is capped: removing the gate and injecting a per-instance linear direction unconditionally yields a monotone dose-response that plateaus far below the preregistered release margin (intercept $0.382 \to 0.311 \to 0.264$ vs. threshold $\le 0.08$); per-instance adaptivity adds less than $\pm 0.03$. The failure is doubly located: the detector is OOD-inverted, and the entire family of linear release directions at this site and resolution is bounded away from sufficiency. The two failures are dissociable, and neither overturns localization. Every number traces to a hashed artifact in the released audit chain.
When a language model answers an interventional question, the computation it must perform depends on the type of evidence the query requires. We report a decoupling in how a transformer organizes causal knowledge: slot-by-type structure induced by type-level supervision organizes routing, yet remains functionally decoupled from answer readout. We establish this with a typed mechanism library -- discrete mechanism slots partitioned by evidence type, auditable at the state level -- on a causal-world benchmark with exact interventional ground truth, under a frozen protocol, at two scales (22.6M and 125M). Four preregistered findings. (i) Origin. Slot-by-type organization is induced by type-level supervision: absent in architecturally identical unsupervised controls, not buyable by content-free gating labels, and statistically attributable to the supervision signal, replicating at 125M under a powered preregistered protocol (all nine cells passed). (ii) Boundary. The induced structure is a typed routing index with a sharp routing/readout boundary: slot codes scaffold routing but do not drive answer readout ($|Δ\hat{y}| \le 3.4\times10^{-6}$, zero collateral, three seeds, stable across a 5.6x scale window) -- we therefore make no behavioral-editability claim. (iii) Cost. The structure is free: LM quality matches a parameter-matched monolith within 0.0082 nats. (iv) Trust. The library state is exactly local under edit and bit-exactly revertible -- 250 single-edit and 1,000 stacked reverts per seed, zero failures. We further find that the unsupervised null itself moves with scale, so comparisons reusing a null calibrated at one scale may be confounded at another. Every claim is tied to a preregistered, machine-checkable criterion archived before the data it governs; the full audit trail, including one criterion we failed and how the frozen protocol handled it, is released as an appendix.
Sparse autoencoders (SAEs) have helped uncover mechanistic explanations for LLM behaviours such as reasoning, jailbreaking etc., via understanding the corresponding task-relevant and causally effective features. To evaluate such mechanistic explanations, downstream studies must distinguish surface lexical features from genuinely high-level ones. However, neither an autointerp-based semantic description nor causal steering utility fully resolves the abstraction level of a feature. To this end, we introduce \emph{Feature Nonlocality} (FNL), defined as the entropy of the normalized per-position influence on an SAE feature's activation. We report that FNL correlates with existing LLM-based proxy metrics of feature semantic abstractness, and successfully distinguishes context-dependent reasoning features from token-driven ones, correctly assigning the higher FNL to the contextual feature in $73$--$84\%$ of randomly drawn pairs that consist of one contextual and one token-level feature. We demonstrate two downstream applications. We audit SAE-based features used for jailbreak mitigation and find surprisingly that most effective features are positional features with low FNL rather than genuinely recognizing harmful intents. We report that steering high-FNL features in DeepSeek-R1-Distill-Llama-8B improves MATH-500 accuracy by $4.6$ points over the unsteered model and outperforms steering low-FNL features, though the gains are model-specific. We conclude that FNL provides an LLM-independent, label-free, correlational witness of the abstraction level of an SAE feature, with applications in evaluating mechanistic explanations as well as selecting features for downstream interventions.
Mechanistic interpretability explains models by identifying circuits inside them, but has no way to tell whether a circuit is a property of the model or an artifact of the method that found it. Sparse autoencoders illustrate the problem: different seeds and widths recover materially different features from the same activations, and no theory says whether that variability is incidental or structural. We put dictionary learning for interpretability on an identifiability footing. Treating the forward pass as a controlled dynamical system with depth as time and lifting it with the Koopman operator yields a finite linear realisation whose \emph{spectrum} is a coordinate-free property of the model. We prove the spectrum is recoverable from $M$ calibration samples at rate $M^{-1/2}$ up to permutation - to our knowledge the first identifiability theorem for a mechanistic-interpretability primitive, with a matching minimax lower bound, a median-of-means variant for heavy-tailed activations, and a dissociation theorem: whenever the realisation is non-normal, the directions carrying activation variance and the directions carrying information across depth cannot coincide. The identifiable object and the legible object are not the same object. On GPT-2 small, Gemma-2-2B and Qwen3-8B-Base the spectrum converges everywhere and attains the predicted exponent on Qwen3-8B-Base ($0.506 \pm 0.031$); shortfalls collapse onto one curve against each cell's sample threshold. Koopman modes beat random directions but lose to principal components on indirect-object identification, with the gap decaying $4.1\times$ in depth-distance, as the theorem predicts. The Koopman spectrum is an identifiable, model-intrinsic fingerprint with a stated error bar, not a legible decomposition.
Chester Tan, Moritz Lampert, Courtney Maynard +3cs.LG
Circuit localization is a mechanistic interpretability task whose goal is to identify a sparse subgraph of a transformer's computation graph sufficient to reproduce a particular behavior. Most established methods localize circuits independently for each model--task pair. We instead frame circuit localization as a graph machine learning problem in which the edges of a computation graph represent computational pathways, and graph neural networks (GNNs) model interactions among these pathways. We introduce Graph Circuit Learning (GCL), a supervised, amortized framework that trains a GNN across multiple model--task pairs and applies it to unseen cases. To provide sufficient data, we augment the InterpBench benchmark with additional cases derived from the TracrBench programs. Of the 14 evaluated GCL configurations, the highest scored a median edge AUROC of $0.902$ (interquartile interval $[0.861, 0.942]$) on the 16 original held-out InterpBench cases. This is close to the published InterpBench median of $0.910$ for EAP-IG while remaining below ACDC's $0.959$. Removing all message-passing edges reduces the median to $0.825$. We also adapt PGExplainer, a GNN explainability method, to circuit localization, obtaining a median edge AUROC of $0.858$ on the same cases. These preliminary results suggest that graph machine learning offers a natural and potentially powerful perspective on circuit localization, and we hope this perspective encourages closer exchange between the two communities.
While Large Language Models (LLMs) employing Chain-of-Thought (CoT) exhibit superior reasoning capabilities, the neural mechanisms distinguishing this explicit Thinking mode from direct answer generation (NoThinking mode) remain poorly understood. To deconstruct this cognitive process, we apply Top-K Sparse Autoencoders (SAEs) to the intermediate representations of DeepSeek-R1-Distill-Qwen-7B and examine the model's divergent behaviors across math-solving tasks of three distinct difficulty levels. Observationally, we identify a clear distinction in how the model functions under two reasoning modes: Thinking mode relies on sparse and high-intensity feature activations driving verbal deduction independent of problem complexity, whereas NoThinking mode exhibits an adaptive and diffuse pattern prioritizing symbolic manipulation. Causally, suppressing the three most active sparse features by Total Activation Volume reveals three principles: (i) reasoning and syntactic structure are tightly coupled, as interventions consistently degrade \LaTeX{} and boxed-solution formatting; (ii) Thinking responds to disruption with compensatory over-generation marked by increased metacognitive cues and repetitive, low-information continuations; and (iii) coherent CoT behavior depends on a fragile coordination among specialized features, yielding distinct failure modes under perturbation but a consistently impaired output structure.
Large language models (LLMs) can solve complex multi-hop problems yet exhibit puzzling failures on simple two-hop queries: although a model may correctly store each individual hop, it often fails to combine them. To understand the internal mechanisms of this phenomenon, we train transformers from scratch in a controlled symbolic environment. Our experiments reveal a pattern in two-hop generalization: models generalize reliably when the second hop follows the training distribution, but always fail when it deviates. Through mechanistic analysis, we provide a complete explanation for these distinct generalization behaviors: in settings where models generalize successfully, performance is driven by the emergence of consistent intermediate representations for the same entities across contexts, whereas failures on settings where the second hop is out-of-distribution arise from a mismatch across layers: lower layers correctly construct these intermediate representations, but upper layers, while trained on corresponding atomic facts, primarily learn to map them to outputs rather than to reason over them. Driven by this insight, we propose a recurrent-style training strategy, which enables transformers to reuse their reasoning circuitry across input forms and substantially improves generalization on out-of-distribution two-hop queries. Our data and code are available at https://github.com/zzl-strong/two_hop .