Gerald Penn

Lei Yu, Jingcheng Niu, Zining Zhu et al. · utoronto

In this paper, we introduce DiscoGP, a novel framework for extracting self-contained modular units, or sheaves, within neural language models (LMs). Sheaves extend the concept of functional circuits, a unit widely explored in interpretability research, by considering not only subsets of edges in an LM's computation graph but also the model's weight parameters. Our framework identifies sheaves through a gradient-based pruning algorithm that operates on both of these in such a way that reduces the original LM to a sparse skeleton that preserves certain core capabilities. Experimental results demonstrate that, across a range of linguistic and reasoning tasks, DiscoGP extracts sheaves that preserve 93%-100% of a model's performance on the identified task while comprising only 1%-7% of the original weights and connections. Furthermore, our analysis reveals that, compared to previously identified LM circuits, the sheaves discovered by DiscoGP exhibit superior modularity and functional fidelity. Extending our method to the neuron level also unveils novel insights into the inner workings of LLMs

Xi Chen, Mingyu Jin, Jingcheng Niu et al.

In this paper, we present empirical and theoretical evidence against a central but largely implicit assumption in circuit and sheaf discovery (CSD), which we term the Functional Anisotropy Hypothesis: the idea that functions in large language models (LLMs) are localised to a unique or near-unique internal mechanism. We show that a single LLM task can instead be supported by multiple, structurally distinct circuits or sheaves that are simultaneously faithful, sparse, and complete. To systematically uncover such competing mechanisms, we introduce Overlap-Aware Sheaf Repulsion, a method that augments the CSD objective with an explicit penalty on structural overlap across multiple discovery runs, enabling the discovery of circuits or sheaves with strong task performance but minimal shared structure across a plethora of common CSD benchmarks. We find that this phenomenon becomes increasingly pronounced as the number of discovered sheaves grows and persists robustly across major CSD methods. We further identify an ultra-sparse three-edge sheaf and show that none of its edges is individually indispensable, undermining even weakened notions of canonical or essential components. To explain these findings, we propose a Distributive Dense Circuit Hypothesis and provide a theoretical analysis demonstrating that non-unique, low-overlap circuit explanations arise naturally from high-dimensional superposition under mild assumptions. Together, our results suggest that mechanistic explanations in LLMs are inherently non-canonical and call for a rethinking of how CSD results should be interpreted and evaluated.

Sean Robertson, Gerald Penn, Yingxue Wang

Triangular, overlapping Mel-scaled filters ("f-banks") are the current standard input for acoustic models that exploit their input's time-frequency geometry, because they provide a psycho-acoustically motivated time-frequency geometry for a speech signal. F-bank coefficients are provably robust to small deformations in the scale. In this paper, we explore two ways in which filter banks can be adjusted for the purposes of speech recognition. First, triangular filters can be replaced with Gabor filters, a compactly supported filter that better localizes events in time, or Gammatone filters, a psychoacoustically-motivated filter. Second, by rearranging the order of operations in computing filter bank features, features can be integrated over smaller time scales while simultaneously providing better frequency resolution. We make all feature implementations available online through open-source repositories. Initial experimentation with a modern end-to-end CNN phone recognizer yielded no significant improvements to phone error rate due to either modification. The result, and its ramifications with respect to learned filter banks, is discussed.

Sean Robertson, Gerald Penn, Ewan Dunbar

A long-standing question in automatic speech recognition research is how to attribute errors to the ability of a model to model the acoustics, versus its ability to leverage higher-order context (lexicon, morphology, syntax, semantics). We validate a novel approach which models error rates as a function of relative textual predictability, and yields a single number, $k$, which measures the effect of textual predictability on the recognizer. We use this method to demonstrate that a Wav2Vec 2.0-based model makes greater stronger use of textual context than a hybrid ASR model, in spite of not using an explicit language model, and also use it to shed light on recent results demonstrating poor performance of standard ASR systems on African-American English. We demonstrate that these mostly represent failures of acoustic--phonetic modelling. We show how this approach can be used straightforwardly in diagnosing and improving ASR.

Jingcheng Niu, Andrew Liu, Zining Zhu et al. · utoronto

We reassess the Knowledge Neuron (KN) Thesis: an interpretation of the mechanism underlying the ability of large language models to recall facts from a training corpus. This nascent thesis proposes that facts are recalled from the training corpus through the MLP weights in a manner resembling key-value memory, implying in effect that "knowledge" is stored in the network. Furthermore, by modifying the MLP modules, one can control the language model's generation of factual information. The plausibility of the KN thesis has been demonstrated by the success of KN-inspired model editing methods (Dai et al., 2022; Meng et al., 2022). We find that this thesis is, at best, an oversimplification. Not only have we found that we can edit the expression of certain linguistic phenomena using the same model editing methods but, through a more comprehensive evaluation, we have found that the KN thesis does not adequately explain the process of factual expression. While it is possible to argue that the MLP weights store complex patterns that are interpretable both syntactically and semantically, these patterns do not constitute "knowledge." To gain a more comprehensive understanding of the knowledge representation process, we must look beyond the MLP weights and explore recent models' complex layer structures and attention mechanisms.

Xutao Mao, Jinman Zhao, Gerald Penn et al.

Agent memory failures are silent: an LLM-based agent can produce a fluent response even when it fails to extract, retain, or retrieve the information needed across sessions. The write-manage-read loop describes the external pipeline of these systems but leaves open which internal computations implement each stage. Tracing internal feature circuits across the Qwen-3 family (0.6B--14B) and two memory frameworks (mem0 and A-MEM), we report three findings. First, control is detectable before content: routing circuitry is causally active at 0.6B, while content circuitry produces no detectable signal until 4B under our tracing setup, creating a deployment regime where small models route with apparent competence but silently fail at extraction and grounding. Second, within the content group, Write and Read share a late-layer hub that operates as a context-grounding substrate already present in the base model; only memory framing recruits a functional grounding direction on this substrate, and the hub transfers across both frameworks. Third, emergence does not imply steerability: although the content circuit becomes detectable at 4B, it becomes reliably steerable only at 8B, indicating that detection and intervention have distinct scale thresholds. As a practical implication, the feature-space separation between the two circuit groups enables per-operation failure localization at 76.2% accuracy without supervision, providing a stage-level diagnostic for otherwise silent agent-memory failures.

Yining Wang, Jinman Zhao, Chuangxin Zhao et al.

Reinforcement Learning with Human Feedback (RLHF) has been the dominant approach for improving the reasoning capabilities of Large Language Models (LLMs). Recently, Reinforcement Learning with Verifiable Rewards (RLVR) has simplified this paradigm by replacing the reward and value models with rule-based verifiers. A prominent example is Group Relative Policy Optimization (GRPO). However, GRPO inherently suffers from a length bias, since the same advantage is uniformly assigned to all tokens of a response. As a result, longer responses distribute the reward over more tokens and thus contribute disproportionately to gradient updates. Several variants, such as DAPO and Dr. GRPO, modify the token-level aggregation of the loss, yet these methods remain heuristic and offer limited interpretability regarding their implicit token preferences. In this work, we explore the possibility of allowing the model to learn its own token preference during optimization. We unify existing frameworks under a single formulation and introduce a learnable parameter $λ$ that adaptively controls token-level weighting. We use $λ$-GRPO to denote our method, and we find that $λ$-GRPO achieves consistent improvements over vanilla GRPO and DAPO on multiple mathematical reasoning benchmarks. On Qwen2.5 models with 1.5B, 3B, and 7B parameters, $λ$-GRPO improves average accuracy by $+1.9\%$, $+1.0\%$, and $+1.7\%$ compared to GRPO, respectively. Importantly, these gains come without any modifications to the training data or additional computational cost, highlighting the effectiveness and practicality of learning token preferences.