Many Circuits, One Mechanism: Input Variation and Evaluation Granularity in Circuit Discovery

• URL: http://arxiv.org/abs/2606.06267v1
• Date: Thu, 04 Jun 2026 15:10:14 GMT
• Title: Many Circuits, One Mechanism: Input Variation and Evaluation Granularity in Circuit Discovery
• Abstract summary: We show that structural differences between circuits are not sufficient evidence for distinct mechanisms.<n>Standard evaluation practice obscures this pattern, while edge-level evaluation reveals the many-to-one mapping from structure to function.
• Score: 49.50794188352666
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Circuit discovery methods identify subgraphs that explain specific model behaviors, and structural differences between discovered circuits are commonly interpreted as evidence of distinct mechanisms. We test this assumption by varying input statistics while holding the task fixed, and show that the resulting structural differences exhibit apparent specialization but do not correspond to functional differences, a pattern we term phantom specialization. Using Literal Sequence Copying across four token-frequency bands plus a control condition in five Pythia models (70M-1.4B), we extract 75 circuits and find that structurally distinct circuits implement the same computation: band-specific edges transfer broadly across bands, a core shared across most bands recovers at least 99% of circuit performance, and causal interchange interventions confirm that internal representations are interchangeable across frequency bands. Repeated extractions within the same frequency band further suggest that discovery algorithms sample from an equivalence class of valid subgraphs rather than recovering a unique mechanism. Standard evaluation practice obscures this pattern: source-level evaluation inflates apparent faithfulness, while edge-level evaluation reveals the many-to-one mapping from structure to function. Our results show that structural differences between circuits are not sufficient evidence for distinct mechanisms, and that exposing this requires edge-level evaluation and cross-condition transfer tests.

Related papers

• Differentiable Interval Bottlenecks for Interpretable Anomaly Detection in Numerical Data [0.5213778368155993]
  DIFFINT is an autoencoder whose latent bottleneck is structured as a set of soft, axis-aligned interval memberships.<n>It is the only interpretable detector in the statistically-tied leading cluster of seven methods.
  arXiv  Detail & Related papers  (2026-09-03T14:05:27Z)
• Circuit Claims Depend on What Is Extracted and How It Is Compared [10.373302428063091]
  We argue that 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.<n>We make this concrete in a synthetic Lean tactic-prediction benchmark.<n>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.
  arXiv  Detail & Related papers  (2026-07-21T10:04:29Z)
• Demystifying Variance in Circuit Discovery of LLMs [51.97489679448601]
  We develop a new circuit discovery method that substantially lessens resampling variance.<n>We show that rephrasing variance arises because prompts with different templates tend to activate different circuits in the model.<n>We argue that sparsity, which has been claimed to form more compact and interpretable task circuits, fails to solve this problem.
  arXiv  Detail & Related papers  (2026-06-15T16:25:07Z)
• Decompose to Understand, Fuse to Detect: Frequency-Decoupled Anomaly Detection for Encrypted Network Traffic [38.99819352589072]
  This work pioneers the identification of a pervasive full-frequency'' characteristic and an associated limitation termed spectral mismatch''<n>FreeUp is a novel frequency-decoupled framework designed explicitly for encrypted traffic analysis.
  arXiv  Detail & Related papers  (2026-05-03T13:44:41Z)
• From Tensor Networks to Tractable Circuits, and back [4.942278642834429]
  We show that some classes of tensor networks that are appealing in practice correspond to classes of circuits with specific properties.<n>In particular, we prove that matrix product states (tensor trains) coincide with nondeterministic edge-valued decision diagrams.
  arXiv  Detail & Related papers  (2026-04-30T18:01:40Z)
• Quantum hardware noise learning via differentiable Kraus representation on tensor networks [0.0]
  We present a method for learning quantum hardware noise from a measurement distribution of a single device experiment.<n>Independent channels are attached to each native gate type, to each nearest-neighbor crosstalk interaction, and to state preparation and measurement.<n>On ibm_fez, training on a ripple-carry adder circuit reproduces the device output distribution, and the same learned parameters, applied without retraining, also track the device distribution of an unrelated multiplier circuit.
  arXiv  Detail & Related papers  (2026-04-22T17:35:01Z)
• Formal Mechanistic Interpretability: Automated Circuit Discovery with Provable Guarantees [5.156069978876762]
  We propose a suite of automated algorithms that yield circuits with provable guarantees.<n>We focus on three types of guarantees: *input domain robustness*, *robust patching*, and *minimality*.<n>We uncover a diverse set of novel theoretical connections among these three families of guarantees, with critical implications for the convergence of our algorithms.
  arXiv  Detail & Related papers  (2026-02-18T19:41:01Z)
• Noise & pattern: identity-anchored Tikhonov regularization for robust structural anomaly detection [58.535473924035365]
  Anomaly detection plays a pivotal role in automated industrial inspection, aiming to identify subtle or rare defects in otherwise uniform visual patterns.<n>We tackle structural anomaly detection using a self-supervised autoencoder that learns to repair corrupted inputs.<n>We introduce a corruption model that injects artificial disruptions into training images to mimic structural defects.
  arXiv  Detail & Related papers  (2025-11-10T15:48:50Z)
• Wavelet-Based Feature Extraction and Unsupervised Clustering for Parity Detection: A Feature Engineering Perspective [0.0]
  This paper explores a deliberately over-engineered approach to the classical problem of parity detection.<n>Instead of relying on modular arithmetic, integers are transformed into wavelet-domain representations.<n>The resulting feature space reveals meaningful structural differences between odd and even numbers, achieving a classification accuracy of approximately 69.67%.
  arXiv  Detail & Related papers  (2025-10-29T11:41:36Z)
• Tractable Bounding of Counterfactual Queries by Knowledge Compilation [51.47174989680976]
  We discuss the problem of bounding partially identifiable queries, such as counterfactuals, in Pearlian structural causal models. A recently proposed iterated EM scheme yields an inner approximation of those bounds by sampling the initialisation parameters. We show how a single symbolic knowledge compilation allows us to obtain the circuit structure with symbolic parameters to be replaced by their actual values.
  arXiv  Detail & Related papers  (2023-10-05T07:10:40Z)
• Which Tokens to Use? Investigating Token Reduction in Vision Transformers [64.99704164972513]
  We study the reduction patterns of 10 different token reduction methods using four image classification datasets. We find that the Top-K pruning method is a surprisingly strong baseline. The similarity of reduction patterns is a moderate-to-strong proxy for model performance.
  arXiv  Detail & Related papers  (2023-08-09T01:51:07Z)
• Self-Supervised Training with Autoencoders for Visual Anomaly Detection [61.62861063776813]
  We focus on a specific use case in anomaly detection where the distribution of normal samples is supported by a lower-dimensional manifold. We adapt a self-supervised learning regime that exploits discriminative information during training but focuses on the submanifold of normal examples. We achieve a new state-of-the-art result on the MVTec AD dataset -- a challenging benchmark for visual anomaly detection in the manufacturing domain.
  arXiv  Detail & Related papers  (2022-06-23T14:16:30Z)
• Tractable Inference in Credal Sentential Decision Diagrams [116.6516175350871]
  Probabilistic sentential decision diagrams are logic circuits where the inputs of disjunctive gates are annotated by probability values. We develop the credal sentential decision diagrams, a generalisation of their probabilistic counterpart that allows for replacing the local probabilities with credal sets of mass functions. For a first empirical validation, we consider a simple application based on noisy seven-segment display images.
  arXiv  Detail & Related papers  (2020-08-19T16:04:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.