# Finding Usable Weight Mechanisms with Tiled SVD

arXiv: https://arxiv.org/abs/2608.06969 · HTML: https://mlsanity.com/paper/2608.06969/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 2 of its 5 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Placed in

- Mechanistic interpretability / [Circuits and mechanistic analysis](https://mlsanity.com/mechinterp/circuits-and-mechanistic-analysis/)

## Builds on (most cited first, 2 of 2)

- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Beyond Components: Singular Vector-Based Interpretability of Transformer Circuits](https://mlsanity.com/paper/2511.20273/) (2025)

## Abstract (arXiv)

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,σ) 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.