Understanding and Exploiting Anisotropy in Post-Training
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 activations. Anisotropy is widely documented and usually treated as a defect, yet its function and its interaction with post-training remain unclear. We first analyze it. A label-free outlier rule isolates about 5\% of residual channels that are essential for language modeling: removing them raises perplexity from 10 to over $10^6$, versus 35 for count-matched random channels...
| Authors | Samyak Jha, Harshvardhan Saini, Yizhen Liao et al. |
|---|---|
| Primary category | cs.LG |
| Published | 26 September 2026 |
| Last updated at source | 26 September 2026 |
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