Finding Usable Weight Mechanisms with Tiled SVD
TL;DR
This work proposes extracting mechanism mounts directly from linear sites by column-tiled SVD: each mount is a triple read as trigger, write, and strength, and evaluates mounts with a pre-registered suite judged on full-write energy lift rather than tile-local lift.
Abstract
The dominant approach to mechanistic interpretability trains proxy dictionaries such as sparse autoencoders and labels features from max-activating text. The best such atlases identify con- cepts, but that identity lives in the learned dictionary rather than in the network weights them- selves. We propose extracting mechanism mounts directly from linear sites by column-tiled SVD: each mount is a triple (v,u,{\sigma}) read as trigger, write, and strength. Identity is the weight rule. We evaluate mounts with a pre-registered suite judged on full-write energy lift rather than tile-local lift. On Gemma-2-2B with WikiText-2 (16,384-token subsample), all seven linear maps are scored: residual writes (mlp.down, attn.o) receive full A/B/C with steer after post-sublayer RMSNorm and pass 52/52 site-layers; other maps receive A/B only (mlp.gate/attn.q/attn.k/effective mlp.up/attn.v 26/26 each). Aggregate: 182/182 GO. We release library code, the corpus builder, the experiment entrypoint, and unit tests.