# Reproduction — *Why Self-Training Helps and Hurts: Denoising vs. Signal Forgetting*

Independent reproduction of ICML 2026 paper **VnA5q5jXVz** (arXiv **2602.14029**),
Wu, Yang & Sun. No official code was released; everything here is written from the paper.

## What is verified

| Claim | Content | Status | Evidence |
|---|---|---|---|
| 1 | Deterministic-equivalent recursion `R*_t = B*_t (forgetting, up) + V*_t (noise, down exp)` | verified | `claim1_decomposition.py`, `general_cov.py` (spiked Thm 3.2 **and** general Thm 4.2) |
| 2 | U-shaped risk & optimal early stopping, **strictly** under anisotropy (s>1) | verified | `claim2_ushape.py` (Fig 1b, Fig 3a) |
| 3 | Direction-dependent spectral filter: survival `(s/(s+tau))^{t+1}`, noise `(1+tau)^{-t}` | verified | `claim3_spectral.py` |
| 4 | iGCV consistently estimates risk & recovers t* with no validation set | verified | `claim4_igcv.py` |
| 5 | Trade-off persists for deep nets (ResNet-50 / CIFAR-10 self-distillation) | verified (GPU Job) | `cifar_selfdistill.py` (Fig 6a) |

## Layout

- `src/linear_selftrain.py` — Algorithm 1 (ridgeless/ridge self-training), spiked Thm 3.2,
  multi-spike Thm 3.6, **general** deterministic-equivalent recursion (Def 4.1 / eq 10),
  iGCV (eq 11-12), fast structured samplers.
- `src/plotting.py` — Plotly + CSV export helpers.
- `claim{1,2,3,4}_*.py`, `general_cov.py` — per-claim reproductions (linear theory, CPU).
- `cifar_selfdistill.py` — PEP-723 UV script for the ResNet-50/CIFAR-10 experiment (HF GPU Job).
- `outputs/` — generated figures (HTML) + raw data (CSV) per claim.

## Reproduce

```bash
# linear-theory claims (CPU, ~1 min each). WSL2 note: single-thread BLAS is faster.
uv run --env-file .env python claim1_decomposition.py   # .env pins OPENBLAS_NUM_THREADS=1
uv run --env-file .env python claim2_ushape.py
uv run --env-file .env python claim3_spectral.py
uv run --env-file .env python claim4_igcv.py
uv run --env-file .env python general_cov.py

# deep-net claim (GPU): run on Hugging Face Jobs
hf jobs uv run --flavor a10g-small --secrets HF_TOKEN cifar_selfdistill.py \
  --n 10000 --K 4 --epochs 40 --etas 0.4,0.6,0.8
```