#01Nov 5, 2026
cs.LG
Spectral and Subspace Dynamics of LoRA in Supervised Fine-Tuning and Reinforcement Learning
Chenruo Liu, Zihan Wang, Yijun Dong and 1 more
Low-rank adaptation (LoRA) is commonly used in both supervised fine-tuning (SFT) and reinforcement learning (RL), often under similar optimizer settings. Yet, how the different dynamics of the two stages manifest in the low-rank increment that LoRA optimizes remains unclear. Tracking the singular spectrum and subspaces of LoRA updates on mathematical reasoning tasks, we find that RL concentrates the spectrum at every learning rate, while SFT expands it at moderate learning rates; moreover, RL rotates the singular subspaces much faster than SFT at small learning rates. Interpolating between SFT and RL one ingredient at a time, we pinpoint group-mean baseline subtraction as the source of both contrasts. A quadratic multi-index model updated via LoRA unveils the underlying mechanism: group-mean baseline subtraction tilts the balance between two competing forces, coherent fitting and gradient noise, toward spectral concentration and faster subspace rotation, while forcing the risk-favorable learning rate to be low. Guided by these dynamics, we tailor LoRA updates to each stage: in SFT, we flatten the spectrum of the full update to spread adaptation across singular directions, whereas in RL, we flatten the part of the update outside the current LoRA increment span to promote subspace rotation. Experiments on mathematical reasoning tasks across multiple models show that the respective configurations for SFT and RL yield the best performance among the compared methods in most evaluated settings.
#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.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.
#04Nov 5, 2026
cs.LG
XStack: A Benchmark for ML Repo Migration
Linrong Cai, Taiming Lu, Haozhe Chen and 1 more
ML code should run where researchers choose, not where it was first written. Today, machine learning code mainly lives in two ecosystems, PyTorch on NVIDIA GPUs and JAX on Google TPUs. Migrating repositories between them means building and testing across frameworks and hardware. This migration is (1) a practical need, since it unlocks different hardware for researchers, and (2) a natural benchmark: it involves different frameworks and hardware, covers whole repositories, and is long-horizon and challenging. We introduce XStack, a benchmark that evaluates agents on migrating ML repositories between these two ecosystems. Each agent receives a PyTorch repository and a clean TPU machine and must deliver a JAX repository. Its output passes if it meets our grading criteria, based on the source repository's published result, authenticated and calibrated by us. Migration by agents remains unreliable: Claude Opus 5 passes 75%, GPT-5.6-sol 45%, and every other agent at most 40%. XStack is a step toward freeing ML code from its ecosystem. We release XStack to make progress toward reliable migration across frameworks and hardware measurable.
#05Nov 5, 2026
cs.LG
On the limitations of molecular representations
Acer Blake, Fergus Imrie, Charlotte M. Deane
Molecular representations such as fingerprints and learned embeddings play a central role in cheminformatics and small-molecule machine learning. They serve as the primary input for a diverse array of tasks, including clustering, dataset splitting, and virtual screening, yet their evaluation is often limited to downstream model performance on narrow benchmark tasks. We carried out a systematic investigation of the quality of molecular representations, finding that none of the state-of-the-art molecular embedding models capture graph structure, 3D shape, or ADMET endpoint similarity better than fingerprints or physicochemical descriptors. However, classical fingerprints also revealed their own material limitations. For example, we show that depending on the representation, between 225M and $\sim$4B molecules have non-unique representations in the 10.8B Enamine REAL database, with implications for virtual screening. Our findings provide an insight into the current limitations of molecular representations, outlining future research directions for the development of more robust encodings of small molecules.