The paper investigates how post‑training modifies the weights of Large Language Models relative to their pretrained state. By expressing weight updates in the pretrained matrix’s singular value decomposition, the authors separate changes into three geometric components: diagonal (reshaping singular values), off‑diagonal (rotating input‑output coupling), and null‑space (routing outside the original SVD core). Experiments on a math evaluation suite show that removing the diagonal component largely preserves post‑training gains, indicating that improvements stem mainly from reconfiguring and extending pretrained pathways rather than altering singular values.
arXiv:2608. 11674v1 Announce Type: cross Abstract: On-policy rollout methods such as GRPO are central to post-training of large language models, yet they frequently suffer from training instabilities, cross-task capability degradation, and response-length inflation.
arXiv:2602.02848v2 Announce Type: replace Abstract: Advances in large language models have driven strong performance across many tasks, but their memory and compute costs still hinder deployment. SVD...
arXiv:2608. 10850v1 Announce Type: new Abstract: We study continual pre-training (CPT) as a mechanism for adapting general-purpose large language models to specialized domains: mathematics, instruction, code, and natural text.
arXiv:2606. 16454v1 Announce Type: cross Abstract: Low-Rank Adaptation (LoRA) enables efficient adaptation of large pre-trained models to downstream tasks by parameterizing weight updates with low-rank matrices.
arXiv:2607. 01232v1 Announce Type: new Abstract: Reinforcement learning (RL) has become a central component of post-training large language models (LLMs), yet little is understood about how RL adaptation is distributed across transformer layers.
arXiv:2606. 13657v2 Announce Type: replace Abstract: On-policy distillation (\textsc{OPD}) has recently become a prominent post-training recipe by combining two desirable ingredients: on-policy student trajectories and dense teacher supervision.
arXiv:2606. 07098v1 Announce Type: cross Abstract: We present SigmaScale, a method for learning auxiliary scaling matrices $S$ to aid truncated Singular Value Decomposition (SVD) based Large Language Model (LLM) compression.
arXiv:2606. 31813v1 Announce Type: cross Abstract: Low-rank adaptation (LoRA) and its variants enable parameter-efficient fine-tuning of large language models under the supervised fine-tuning (SFT) paradigm.
arXiv:2605.28573v2 Announce Type: replace-cross Abstract: LLM pretraining is extremely costly; therefore, parameter-efficient LLM architectures have recently emerged as a compelling research directio...
arXiv:2608. 12332v1 Announce Type: cross Abstract: In recent years, low-rank adaptation (LoRA) has emerged as a significant paradigm that freezes pre-trained weights and introduces small, learnable adapters instead of fine-tuning the full set of parameters.
arXiv:2609.36262v1 Announce Type: new Abstract: Recent studies have observed that parameter changes during language-model post-training can be concentrated in a small subset of coordinates. This phen...
arXiv:2607. 11505v1 Announce Type: cross Abstract: Post-training is essential for refining the domain-specific capabilities of large language models (LLMs), yet existing reward optimization and distribution matching methods tightly couple policy exploration with distribution alignment.