{"id":"arxiv:2606.23740","title":"Weight-Space Geometry of Offline Reasoning Training","date":"2026-06-26","section":"Post-training","quality":-0.244397,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/","source_url":"https://arxiv.org/abs/2606.23740","text_available":true,"authors":["Aleksandr Nikolich","Igor Kiselev","Vladimir Platonov","Karina Romanova"],"outgoing":[{"source":"arxiv:2606.23740","target":"arxiv:1803.03635","evidence":"title","id":"arxiv:1803.03635","title":"The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/a9d7f0235205afcc709e3e74f28cc7707831bcb1d46239c418cc7e4b624d23bd/"},{"source":"arxiv:2606.23740","target":"arxiv:2402.03300","evidence":"id","id":"arxiv:2402.03300","title":"DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/636fb871904bc06f742cfdea069796f9e9665f95bd58dc63260eaff5154ef985/"},{"source":"arxiv:2606.23740","target":"arxiv:2503.14476","evidence":"id","id":"arxiv:2503.14476","title":"DAPO: An Open-Source LLM Reinforcement Learning System at Scale","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/548e934b912ef84691ace63bf1cfd670e7b0257d9d6986dde926f569e7b2f8b7/"},{"source":"arxiv:2606.23740","target":"arxiv:2508.05629","evidence":"id","id":"arxiv:2508.05629","title":"On the Generalization of SFT: A Reinforcement Learning Perspective with Reward Rectification","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/0a17fccfeffa8a04070bb16903a7217d8adee804cf42e0cfc8dd128d3390474f/"}],"incoming":[],"text_parts":[{"start":0,"end":15840,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html"},{"start":15840,"end":20057,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-2.html"}],"contents":[{"title":"Weight-Space Geometry of Offline Reasoning Training","offset":0,"level":1,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html#text"},{"title":"Abstract","offset":55,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html#text"},{"title":"Keywords:","offset":1813,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html#text"},{"title":"1 Introduction","offset":1831,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html#text"},{"title":"2 Setup","offset":4375,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html#text"},{"title":"Data.","offset":4387,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html#text"},{"title":"Methods.","offset":4796,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html#text"},{"title":"Training.","offset":5926,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html#text"},{"title":"Analysis.","offset":6539,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html#text"},{"title":"3 Results","offset":7217,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html#text"},{"title":"3.1 Downstream accuracy","offset":7231,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html#text"},{"title":"On-policy RL preserves accuracy; SFT-style loses it.","offset":7849,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html#text"},{"title":"3.2 Weight-space convergence","offset":8280,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html#text"},{"title":"3.3 Subspace analysis","offset":9732,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html#text"},{"title":"Top-1 singular directions.","offset":11788,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html#text"},{"title":"3.4 Seed and learning-rate sensitivity","offset":12510,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html#text"},{"title":"3.5 Linear mode connectivity","offset":14950,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html#text"},{"title":"3.6 Representational similarity","offset":15803,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-1.html#text"},{"title":"4 Discussion","offset":16451,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-2.html#text"},{"title":"Reward-weighted MLE is SFT, plus DFT is the surprise.","offset":16468,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-2.html#text"},{"title":"Offline GRPO shifts direction but stays in basin; online GRPO does not.","offset":17400,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-2.html#text"},{"title":"DPO sits apart, geometrically and on accuracy.","offset":17924,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-2.html#text"},{"title":"Limitations.","offset":18540,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-2.html#text"},{"title":"Appendix A Supplementary figures","offset":19056,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-2.html#text"},{"title":"Instructions for reporting errors","offset":19093,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/part-2.html#text"}],"text_code_points":20057,"source_markdown":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/e4479f0d0930797db9347855247f1c640a12d96f63d43b83ba9635561e3ff352/source.md"}