Circuit Condensation: Post-Training that Concentrates a Behavior's Causal Circuit

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.

The Communication Map of a Transformer

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.

The Kinetics of Training: A Driven-Nucleation Rate Law for Emergence, Plasticity Loss, and Circuit Control in Language Models

A capability appears in a language model when the last parts of its circuit align in one stochastic attempt, and getting all but one right is worth nothing. We show this no-partial-credit joint alignment is the rate-limiting step of capability formation. Two fingerprints: in a shortcut-free apparatus a five-part circuit missing three waits as long as a three-part circuit missing three (1.19-1.37), so the wait counts missing parts, not size; and on Pythia across seven capabilities and three scales, ablating one part leaves a median 17% of the capability in 32 of 32 discriminating cells, where partial credit predicts 50-83% (p = 2e-10), while a random non-part head leaves 100%. One rare event whose barrier grows with missing parts yields a rate equation -- sites x attempts x drive x exp(-beta*K), minus destruction -- read three ways, each preregistered with frozen constants. Forward: a capability flat at baseline ignites at a step of our choosing once the mix passes a concentration floor (10/10 above, 0/12 below), and while still flat its arrival is datable from its precursor to 5% median error on six held-out models. Backward: the delay to learn a withheld capability grows with waiting until, past a critical step, it never ignites -- yet validation loss falls smoothly throughout, so standard monitors are blind to it. We locate the damage (heads commit to the base data) and isolate the cure: re-initializing only the query-key slices restores learnability (6/6) while the value slices do nothing (0/6). We prove the mechanism in a controlled gated-attention model: occupation forces a deadline whose consequences need no mixing assumption. Completed: SGD's noise fails the fluctuation-dissipation test, so we install one and anneal, melt and pin circuits on schedule. Scope: conjunction circuits in transformers to 1.4B.

What, Where, and How: Disentangling the Roles of Task, Language, and Model in Code Model Representations

Do independently trained language models come to represent the same thing in the same way? We answer for code, extending a recently introduced concept-circuit extraction method to a 2x2 design -- Python and Rust crossed with Qwen2.5-Coder-7B and DeepSeek-Coder-V1-6.7B -- and measuring a complete inventory of grammatical concepts (58 Python, 57 Rust) identically in all four cells: the smallest design that separates what depends on the task, the language, and the model. The answer splits into three parts. What earns dedicated circuitry is set by the task: the models agree on which concepts receive circuits (Spearman $ρ$ = 0.638 for Python, 0.673 for Rust, both p < $10^{-7}$). Where those circuits sit is set by the model: Qwen processes concepts in a late band (~L17-19), DeepSeek at L6-7, for both languages. How circuits grow across layers is also set by the model: Qwen gives its atomic concepts an early spike that DeepSeek does not. "Are circuits universal?" thus has no single answer: yes for What, no for Where and How -- universality is a property of representational content, not of computational organisation. None of this structure was fixed in advance. The agreement could have landed anywhere between independence and identity; it lands at $ρ\approx 0.65$. Rust constructs receive 2-3x more concept-specific circuitry than their Python equivalents, in both models. Both models share neurons between the languages (6/7 and 7/7 paired constructs), DeepSeek 1.94x more than Qwen -- a direction no prior result predicts. And Qwen binds nine keywords of Rust's type-and-trait machinery into one tight neuron cluster (Jaccard 0.535 vs null 0.112, p < 0.001), a semantic dimension invisible in surface syntax. Ablation and linear probes confirm the circuits are functional. All claims are scoped to this 2x2; whether the per-model profile predicts a third model is the designed next test.

A Multi-Dimensional Evaluation of Explainability in Media Bias Detection

Detecting media bias automatically is difficult because biased framing is often subtle, yet in domains such as news analysis, accurate predictions alone are insufficient without explanations that reflect the model's underlying reasoning. We present a multi-dimensional evaluation of explainability in encoder-based media bias detection using the Bias Annotations By Experts (BABE) dataset. Specifically, we study BERT and RoBERTa as classifiers (base and large variants) along three complementary axes: predictive performance, explanation plausibility (token-level alignment with expert rationales), and mechanistic faithfulness (whether compact sets of attention heads recover predictive signal under counterfactual rationale masking). To induce variation in plausibility, we additionally investigate attention-supervised finetuning, which incorporates expert rationale annotations as an auxiliary training signal. Attention supervision serves as an intervention on attribution plausibility, while the effectiveness of attribution methods varies substantially across architectures. Circuit analysis further reveals substantial variation in mechanistic recoverability across architectures, suggesting that model scale alone does not determine circuit compressibility. Taken together, our findings suggest that predictive performance, attribution plausibility, and mechanistic faithfulness characterize different aspects of model behavior and should be evaluated separately when studying explainability in media bias detection.

CircuitKIT : Circuit Discovery, Evaluation, and Application Toolkit for Mechanistic Interpretability

Circuit analysis can support not only model explanation but also downstream interventions such as pruning, editing, steering, and selective fine-tuning. However, conducting such analyses currently requires stitching together separate implementations for discovery, evaluation, and intervention, as well as hand-authoring the contrastive prompts required by many discovery methods. This fragmentation makes methods difficult to compare and limits their application beyond canonical tasks. We introduce CircuitKIT, a source-available library that connects the circuit-analysis workflow through a typed, serializable representation. CircuitKIT provides a suite of discovery algorithms, declarative interfaces for mapping structured data into discovery tasks, complementary circuit diagnostics, and downstream application modules. Together, these components provide common infrastructure for conducting and comparing circuit analyses. The library, examples, notebooks, and documentation are released at https://github.com/Lexsi-Labs/CircuitKIT .

Invariant Learning Dynamics of Transformers in Inductive Reasoning Tasks

We present a theoretical framework to explain the emergence of inductive reasoning abilities in Transformer language models. While previous works on Transformer learning dynamics have so far been mostly tied to specific tasks, we study a generalized class of inductive tasks that unifies several synthetic tasks known in the literature, including in-context n-grams and multi-hop reasoning. In this class, we theoretically prove that the training dynamics of attention models can be confined to a highly interpretable, low-dimensional invariant manifold. On this manifold, the learning dynamics are captured by a handful of interpretable coordinates rather than millions of parameters, making both theoretical and empirical analysis more tractable. Using this framework, we characterize how data statistics govern the competition between in-context and in-weights learning, we study how random initializations determine the `winning' circuit when multiple solutions are possible, and we demonstrate that the coordinate frame associated with the manifold can be used to automatically detect which circuits have been learned in trained models. By casting circuit formation as a low-dimensional dynamical phenomenon, we take a step toward a predictive theory of how Transformers learn.

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.

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.

Conditional Co-Ablation: Recovering Self-Repair Backups in Transformer Circuits

Mechanistic interpretability often relies on component-level interventions to discover how a model produces a behavior. This guides attribution, capability knockout, and model pruning downstream to operate by scoring each unit by the effect of ablation in isolation. Such first-order scoring is natural when component importance is additive, but becomes misleading when a transformer self-repairs: after a primary component is removed, a dormant backup can take over, muting the primary's measured effect while the backup itself appears irrelevant on the intact model. We recast this failure as a recovery task, conditional circuit completion, and introduce Conditional Co-Ablation (CoAx), a label-free, output-grounded score that asks how much each remaining unit's ablation effect grows once a primary set has been removed. This conditional growth exposes the second-order interaction that single-unit scores discard. On the GPT-2-small IOI circuit, CoAx raises backup-head recovery from 0.33 to 0.91 ROC-AUC, outperforming all baselines, including self-repair-aware gradient scores (best 0.82); counterfactual patching verifies that the recovered heads causally carry the repair. The same label-free procedure transfers to induction across eight models. Beyond discovery, the recovered backups correct self-repair-masked attribution, identify the components required for capability knockout, and yield repair-aware structured pruning scaling from 124M to 7B. Component importance is therefore not merely an isolated-unit property: in robust circuits, the components that matter can become visible only under the interventions that make them necessary.

Modular Cognitive Architecture Emerges in Large Language Models

The human brain exhibits a striking degree of functional specialization, with distinct networks supporting language, formal reasoning, reasoning about other minds, and reasoning about the physical world. Is this modular organization a fundamental principle of how intelligent systems must be built, or an evolutionary accident specific to biological brains? Here, we test whether a similar organization emerges in Large Language Models--another class of intelligent systems created through a very different optimization process. Using circuit analyses across N=46 tasks spanning four cognitive domains (language, formal reasoning, social reasoning, physical reasoning), we find that LLMs develop a modular architecture that mirrors the human brain: tasks drawing on the same network in humans recruit overlapping neurons in LLMs, whereas tasks drawing on different networks recruit distinct neurons. The convergent emergence of modularity in brains and neural networks suggests that it may be a fundamental property of intelligent systems.

Targeted Recovery of Weight-Space Mechanisms From Neural Networks

Parameter decomposition (PD) decomposes neural networks into interpretable computational components that faithfully reflect the original network's operations. However, scaling PD to large models requires vast compute, making it a costly and risky endeavor. Here we propose targeted PD (tPD), which identifies only the components that process specific inputs of interest -- from isolated prompts to large subtasks -- by introducing a high-rank catch-all component that handles all non-target data. We validate tPD on toy models and on transformer language models trained on The Pile, where it recovers reproducible, mechanistically faithful circuits. We extract a CSS-only submodel of a 4-block transformer using 7% of the FLOPs of its published decomposition, and in a 12-block transformer we surgically ablate and rewire memorized sequences, with negligible side effects on other inputs.

Shared Semantics, Divergent Mechanisms: Unsupervised Feature Discovery by Aligning Semantics and Mechanisms

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

Pattern Selectivity is Not Task-Causal Structure: A Cross-Architecture Mechanistic Study of Composed-Task Circuits in 1B-Class Language Models

We test whether a single screen-and-ablate recipe -- identify attention-head circuits by task-pattern selectivity, then verify by causal ablation against a matched-random null -- produces consistent mechanistic claims across model families. The recipe ports across pipelines; the specific circuit it identifies does not. Across four composed tasks (indirect-object identification, greater-than, successor sequences, variable binding) and three 1B-class language models from distinct training pipelines (Pythia 1B / Pile / dense; OLMo 1B / DCLM / dense; OLMoE 1B-7B / DCLM / mixture-of-experts), we run a unified protocol with the matched-random null sampled across ten seeds per cell. The resulting 12 (task, model) cells contain no two that share the same primary causal screen at comparable effect size: the same task, with the same behavioral capability, is implemented through different attention-pattern types across models. We introduce a five-category screen-outcome taxonomy -- primary cause, secondary cause, correlate, interferer, null -- with quantitative thresholds, and show that all five outcomes appear in the panel. We propose a falsifiable hypothesis: the MoE model in our panel builds composed-task circuits on top of a foundational previous-token positional substrate (the prev-token-circuit ablation is the strongest causal screen on 3 of 4 tasks for OLMoE 1B-7B), with the IOI exception consistent with IOI being a final-position name-copying task whose structure directly probes a different pattern. The hypothesis comes with explicit predictions for other MoE language models. We frame the methodology honestly: the spectral participation-ratio signal from the companion methodology paper is a general indicator of specialized computation; what makes a finding task-specific is the task-pattern screen plus a per-model causal verification.

From Circuit Evidence to Mechanistic Theory: An Inductive Logic Approach

Mechanistic interpretability produces circuit-level causal analyses of neural network behaviour, but discovered circuits often remain isolated experimental artefacts: there is no shared formal representation for what circuits compute, how they relate, or when two findings provide evidence for the same mechanism. This work provides a formal infrastructure for cumulative mechanistic science by treating circuit interpretation as inductive theory construction. Each circuit is characterised at two levels: a Causal Functional Signature (CFS), which grounds component behaviour in causal attribution evidence and token role profiles, and an architectural signature $τ_{\mathrm{arch}}$, learned by inductive logic programming (ILP) from scale-invariant structural predicates. Together, these constitute a formal coherence layer that makes mechanistic claims explicit, comparable via $θ$-subsumption, and portable across model scales. CFS reveals qualitatively distinct computational strategies across task types, including attention-mediated copying versus MLP-mediated binding. ILP signatures achieve substantially better structural separation than graph kernel and feature-vector baselines, and support principled transfer across model scales and architecture families.

Perturbation Probing: A Two-Pass-per-Prompt Diagnostic for FFN Behavioral Circuits in Aligned LLMs

Perturbation probing generates task-specific causal hypotheses for FFN neurons in large language models using two forward passes per prompt and no backpropagation, followed by a one-time intervention sweep of about 150 passes amortized across all identified neurons. Across eight behavioral circuits, 13 models, and four architecture families, we identify two circuit structures that organize LLM behavior. Opposition circuits appear when RLHF suppresses a pre-training tendency. In safety refusal, about 50 neurons, or 0.014 percent of all neurons, control the refusal template; ablating them changes 80 percent of response formats on 520 AdvBench prompts while producing near-zero harmful compliance, 3 of 520 cases, all with disclaimers. Routing circuits appear for pre-training behaviors distributed through attention. For language selection, residual-stream direction injection switches English to Chinese output on 99.1 percent of 580 benchmark prompts in the 3 of 19 tested models that satisfy three observed conditions: bilingual training, FFN-to-skip signal ratio between 0.3 and 1.1, and linear representability. The same intervention fails on the other 16 models and on math, code, and factual circuits, defining the limits of directional steering. The FFN-to-skip signal ratio, computed from the same two forward passes, distinguishes the two structures and predicts the appropriate intervention. Circuit topology varies by architecture, from Qwen's concentrated FFN bottleneck to Gemma's normalization-shielded circuit. In Qwen3.5-2B, ablating 20 neurons eliminates multi-turn sycophantic capitulation, while amplifying 10 related neurons improves factual correction from 52 percent to 88 percent on 200 TruthfulQA prompts. These results show that perturbation probing offers mechanistic insight into RLHF-organized behavior and a practical toolkit for precision template-layer editing.