#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
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.
#03Nov 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.
#04Nov 5, 2026
cs.LG
Unpacking the Compute Efficiency of Strong-to-Weak OPD against GRPO
Zeyu Leo Liu, Yang Li, Bo Pang and 7 more
On-policy distillation (OPD) trains a student on its own rollouts under a frozen teacher's per-token supervision. Does this dense signal reduce the training FLOPs needed to reach a target accuracy compared with reinforcement learning? We systematically compare vanilla reverse-KL OPD with Group Relative Policy Optimization (GRPO) across task difficulty, student and teacher size, domain, and optimization choices, measuring held-out accuracy against training FLOPs. With an external post-trained teacher, OPD generally loses to GRPO in accuracy per training FLOP at matched settings, even when the teacher is further trained with GRPO, and often suffers response-length inflation. Yet a different teacher changes the picture: when the teacher is the student's own GRPO checkpoint, OPD recovers that checkpoint's accuracy on math with $50\times$ fewer distillation FLOPs than GRPO needs to reach the same accuracy. Following the same teacher setting, we consistently observe this high efficiency with a larger student, on code, and in a second model family. On a single domain, however, the GRPO checkpoint is already the desired model, so distilling it adds to total compute. Across domains, separate GRPO checkpoints hold different capabilities, and no single checkpoint serves every domain. Multi-teacher OPD (DeepSeek-AI, 2026) consolidates per-domain GRPO experts into a single student that matches each expert's accuracy, with the distillation stage costing only 5.2% (on 2 domains) and 8.0% (on 4 domains) of the specialist training FLOPs. Counting specialist training and distillation together, this pipeline reaches joint GRPO's performance on the 2-domain mix with 42.0% fewer total FLOPs.
#05Nov 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.