Muon improves large-scale training by applying a spectral-norm steepest-descent update to matrix parameters, but practical models also contain parameter blocks that do not fit dense-matrix geometry. One important case is the tied vocabulary table, which appears in language models and other token generators and can rece …
When designing machine learning models, desirable properties are often in tension: improving one behavior can impair another, so task progress can depend on alleviating the conflict. LLM-based AutoResearch systems, which iteratively edit model code and retain edits based on scalar task-performance feedback, have largel …
Direct Preference Optimization (DPO) aligns language models by optimizing over sequence-level sums of token-wise implicit reward differences. However, we identify a pervasive pathology in this formulation: a disproportionately small subset of high-frequency token types dominates cumulative sequence scores while appeari …
LLM post-training combines supervised fine-tuning (SFT), a mode-covering forward-KL objective, with reinforcement learning (RL), a mode-seeking reverse-KL objective. Frequency-weighted likelihood training leaves a well-known signature: \emph{anisotropy}, in which a few residual channels carry disproportionately large a …
Recent advances in Large Language Models (LLMs) have revolutionized artificial intelligence and how human interact with AIs. Despite impressive advancements, LLMs struggle with complex mathematical, scientific, and logical tasks. Inspired by human cognitive flexibility - our ability to dynamically switch mental perspec …