# Filtering Training Data to the Universal Weight Subspace

Boundary: one controlled mechanism check and one small-scale digits MLP. No ViT, LLM, or production-training result.

Canonical URL: https://www.contextjamming.com/universal-weight-subspace-filtered-training
Author: Bret Kerr
Author profile: https://www.linkedin.com/in/bretkerr/
Source paper: https://arxiv.org/abs/2512.05117
Repository: https://github.com/BretKerrAI/founderfile/tree/main/research/universal_weight_subspaces/portfolio/repo
Digits record: https://www.contextjamming.com/research/universal-weight-subspace/digits-results.json
Stability record: https://www.contextjamming.com/research/universal-weight-subspace/stability-results.json

## Question

If related trained models occupy a shared low-rank layer-wise weight subspace, can examples be scored by the fraction of their gradient energy inside that basis and then used for filtering, importance sampling, or hard update projection?

## Measured here

- Controlled planted-rank recovery: eight of eight directions.
- Digits MLP, four regimes, three deterministic seeds.
- Constraint alignment: 9.04% baseline versus 64.81% constrained.
- Matched 5,040-example delta: +0.67 percentage points IID and +0.67 points synthetic noisy OOD.
- Final filtering tradeoff: +0.74 points noisy OOD and -1.19 points IID.
- Effective rank: 7.77 baseline versus 11.54 constrained; cleaner-spectrum criterion NOT MET.
- Leave-one-source-out rank-eight worst principal angle: 89.81 degrees; weakest included direction unstable.
- Rank nine after holdout: NOT IDENTIFIABLE.

## Evidence policy

The source paper's claims are attributed to the paper. Conceptual diagrams are labeled as reconstructions. JSON experiment records are self-hashed. The serialized PyTorch basis has a tested schema and SHA-256. Missing ViT, LLM, natural-shift, and diverse-source experiments remain missing.