#01Nov 5, 2026
cs.LG
Module-Aware Optimization for Graph Neural Networks
Guy Hadad, Haggai Roitman, Moshe Eliasof and 1 more
Different optimizers impose different geometries on parameter updates. Adaptive methods such as Adam and AdamW use coordinate-wise updates, while matrix-aware optimizers such as Muon utilize weight-matrix structure through orthogonalized updates. For Graph Neural Networks (GNNs), however, the effective geometry of its weight matrices is shaped not only by its learned channel-mixing weights, but also by the graph-propagated representations it acts on. Thus, even if an update is well normalized as a matrix, its effect on the layer output can be amplified when applied to graph-propagated features. To address this gap, we introduce GraphMuon, a graph-aware optimizer that adapts Muon's matrix updates to the covariance structure of graph-propagated layer inputs. GraphMuon performs orthogonalization in a metric defined by these propagated representations and normalizes step sizes according to the update's induced effect on the layer representation. We show that theoretically, vanilla Muon can suffer from graph-induced update amplification, while our GraphMuon can mitigate this effect. As such, our GraphMuon yields a graph-metric analogue of Muon's polar update step. Empirically, GraphMuon achieves $1.32\times$-$2.42\times$ validation-loss time-to-target speedups over AdamW on three large-scale OGB benchmarks. Across 15 dataset-architecture configurations spanning node classification, inductive graph classification, and graph regression, it achieves lower time-to-target in 13 cases, while maintaining competitive or superior predictive performance. Code is available at https://github.com/guy-hadad/GraphMuon.
#02Nov 5, 2026
cs.LG
Muir: Linear Attention with Sensitivity-Allocated Gating and Matched-Filter Readout
Tushaar Gangavarapu, Gil Tabak, Clemens JS Schaefer
Linear attention compresses context into a fixed-size key-value state for linear-time training and constant-memory inference. Gated delta-rule models decay this state and erase its prediction for an incoming key before writing a new value; Gated DeltaNet-2 (GDN-2) generalizes this with channel-wise decay and decoupled, full-rank erase and write gates. However, we show that state updates are far less sensitive to erasure than to writes: key activation and unit normalization concentrate key energy onto a sparse subset of channels, whereas value writes scale all channels, so the erase gate can be parameterized at lower rank. Furthermore, slow-decaying state rows accumulate much larger norms than fast rows, dominating unweighted readout and forcing stronger write-time erasure to suppress interference. Guided by this analysis, we introduce Muir, which fuses all gates into a sensitivity-allocated low-rank projection, re-weights state rows with a matched-filter readout gate, and reinvests the saved parameters in a wider feed-forward network. Because standard chunkwise algorithms become numerically unstable at the large chunk sizes needed to saturate wide matrix units, we design a parallel update for stable, efficient training. Across 166M-1.34B parameters, Muir lowers perplexity by 1.8-2.0% over GDN-2 and 2.5-3.6% over Transformer, raises commonsense accuracy by up to 1.9 points, and improves extractive recall over GDN-2. At 1.34B, Muir outperforms both baselines on multi-hop and multi-needle recall, extrapolates 2,560x from its 4K training length to 10M-token streams without perplexity drift, and maintains near-100% passkey retrieval to 1M tokens with static readout. Muir achieves these gains while matching GDN-2 throughput, reaching its 100B-token validation loss 1.2x faster, and training 2.7x faster than Transformer at 32K.
#03Nov 5, 2026
cs.CL
Understanding AI from the Inside: The State of Mechanistic Interpretability for AI Safety
Fazl Barez, Tung-Yu Wu, Hunar Batra and 24 more
Neural networks are likely to be among the most consequential artefacts in human history. As these systems become more capable and autonomous, their potential to cause societal harm also grows, making AI safety one of the defining challenges of our time. Yet we continue to build increasingly powerful systems without fully understanding how they work, how they will behave in unfamiliar situations, or how to reliably control them. Mechanistic interpretability offers a path towards understanding these systems by studying their internal representations and computations, with the aim of evaluating, predicting, and controlling behaviour. We survey mechanistic interpretability for AI safety in order to answer the question: Does understanding how models work actually make them safer? We place mechanistic interpretability in the broader context of interpretability research and compare its mechanistic evidence with behavioural evaluation. We introduce the foundations of mechanistic interpretability, including features, polysemanticity, transformer computation, and circuits, and survey methods for feature extraction and analysis, circuit discovery and causal verification, explaining intermediate representations in natural language, learning dynamics, and training-data attribution. Beyond surveying existing methods, we propose a unified framework for evaluating mechanistic interpretability claims and characterise six research orientations by their goals, assumptions, and trade-offs. Finally, we examine how mechanistic understanding can support AI safety, including knowledge editing, steering, and monitoring, and assess its limitations, failure modes, open problems, and relationship to behavioural safety measures. We also release a repository of code notebooks with worked examples that reproduce key findings from surveyed methods, allowing readers to build intuition through hands-on experimentation.
#04Nov 5, 2026
cs.LG
Adversarial Training with Large Step Sizes: Implicit Bias, Optimization, and Sharpness
Yi Feng, Andrea Paudice
Adversarial Training (AT) is an important method for improving model robustness. We study the dynamics of deterministic Gradient Descent (GD) in AT. Most existing works in this direction focus on the small or vanishing step sizes regime, where GD resembles a continuous-time flow. However, such step sizes can make training inefficient and are rarely used in practice. In this paper, we study the AT dynamics of GD with large constant step sizes. We first study GD in adversarial linear logistic regression, focusing on two aspects: where the model parameters converge (implicit bias) and how quickly the losses decrease (optimization). We then turn to neural networks training and study how the sharpness of losses evolve during AT. Our results advance the understanding of the behaviors of GD with large step sizes in AT and highlight three key differences from its behavior in Standard Training (ST): (i) the implicit bias gap between AT and ST, previously established only for small step sizes, persists for arbitrarily large constant step sizes, (ii) different from ST, there is no uniform rate of convergence for the optimization error in AT, and (iii) sharpness can exhibit two-stage dynamics that differ from the Edge-of-Stability behavior observed in ST.
#05Nov 5, 2026
cs.AI
Benchmarking Large Language Models on Heterogeneous Cognitive and Biomedical Knowledge Graphs: The Role of Graph Grounding in Multi-Hop Reasoning and Hallucination Mitigation
Ali Sarabadani, Kheirolah Rahsepar Fard, Tahereh Jeirani
Large language models (LLMs) are increasingly used in biomedical and cognitive neuroscience, but their ability to reason reliably over heterogeneous knowledge graphs (KGs) remains unclear. We benchmark five LLMs (GPT-5.1, Gemini 2.0 Pro, Llama 3, Qwen, and BioGPT) across five KGs: DrugBank, NeuroSynth, Cognitive Atlas, Brain Map, and GDPKG. We introduce a multitier query dataset to evaluate reasoning depth and factual accuracy under KG-aware (graph-grounded) and KG-agnostic conditions. Inter-annotator agreement was substantial, with Cohen's kappa of 0.781 (range: 0.753-0.807) and Fleiss' kappa of 0.77. Results show that general-purpose models, particularly GPT-5.1 and Gemini 2.0 Pro, generally outperform domain-specific models on multi-hop and high-level reasoning tasks, although performance declines as query complexity increases. KG grounding reduces hallucination rates across all evaluated models. Contrary to our initial hypothesis, domain-specific models do not consistently outperform general-purpose models on specialized tasks without graph grounding. These findings highlight the value of combining broad language-model capabilities with structured domain knowledge. We provide practical guidance for selecting LLM-KG integration strategies based on task complexity and computational constraints, and discuss hybrid neurosymbolic architectures for personalized medicine, cognitive disorder diagnosis, and explainable AI.