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README.md

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+---
+tags:
+- sae
+- olmo
+- interpretability
+base_model: allenai/Olmo-3-1025-7B
+datasets:
+- allenai/Dolci-Think-SFT-7B
+---
+
+# MATS sprint SAEs
+
+Sparse autoencoder (SAE) dictionaries and analysis files from a MATS 12.0 sprint project (2026-10-19 to 2026-10-30). The project asks how SFT teaches "diffuse" behaviours that no single training example explains.
+
+The gradient SAEs decompose the gradient of the SFT loss with respect to the residual stream, dLoss/dh, of `allenai/Olmo-3-1025-7B` (the base checkpoint right before SFT) on `allenai/Dolci-Think-SFT-7B`. The loss is the summed cross-entropy over response tokens, and h is the output of decoder block L (`model.model.layers[L]`, 0-indexed). Activation SAEs on h at the same places are the comparison. All dictionaries use a single seed (0), and the analysis files are exploratory.
+
+The code is in the GitHub repo [jason9464/MATS_sprint](https://github.com/jason9464/MATS_sprint), which is private. The loading example at the end of this card needs only this Hub repo.
+
+## Layout
+
+| Path | Content |
+|---|---|
+| `sae/<tag>.pt` | 92 SAE checkpoints |
+| `sae/<tag>.json` | trainer output (config and evaluation) |
+| `sae/<tag>.metrics.json` | metrics re-measured on the same evaluation rows, with the random-dictionary floor |
+| `sae/<tag>.random_lstsq.json` | random dictionary with least-squares coefficients, same rows and support |
+| `baselines/pca_baseline.json` | PCA-k reconstruction baseline (k = 64, 256, 1,024) per unit, layer and signal |
+| `baselines/pca_<unit>_l<L>_<arm>.pt` | all eigenvalues, top 1,024 eigenvectors and the fit mean (30 files) |
+| `whitening.pt` | per-layer whitening matrix `W` and means, shared by all three units |
+| `transforms/<unit>_transforms.pt` | per-unit `mu`, `cap` and `scale` for each layer and signal (`arms[arm][L]`) |
+| `jlens/<tag>_scan.pt` | J-lens readouts of every feature's decoder direction (top-50 token ids for both signs, random-direction readouts, firing frequency) |
+| `jlens/*.json`, `jlens/*_textcross.pt` | summary and comparison tables of the J-lens analysis, and the cross with top-firing texts |
+| `jlens/judge/`, `jlens/judge_gva/` | items and raw outputs of the blind LLM judge |
+| `jlens/tok_position_check_rows.pt` | rows of the firing-position check for token-level layer-23 gradient features |
+
+## Dictionaries
+
+Names are `<unit>_l<layer>_<grad|act>_k<L0>.pt`.
+
+- Unit `tok` (every response position), `chunk` (mean over each full 32-token chunk of the response) or `doc` (mean over all response positions).
+- Layer 7, 15, 19, 23 or 27. Target L0 64, 256 or 1024.
+- Width 32,768 for `tok` and `chunk`, 4,096 for `doc`. Two width-32,768 `doc` references at layer 15 carry a suffix: `doc_l15_grad_k64_w32768.pt`, `doc_l15_act_k64_w32768.pt`.
+- Matryoshka JumpReLU SAEs with nested prefixes at width/4, width/2 and width, trained for 60,000 steps at batch 4,096.
+
+| Unit | Documents | Rows |
+|---|---:|---:|
+| token | 5,280 | 14,552,840 |
+| chunk | 42,242 | 3,628,855 |
+| document | 202,753 | 202,753 |
+
+The holdout is 5% of documents. 2,242 "planted" documents (WildChat documents rewritten into a numbered-list template) are trained on and excluded from every metric.
+
+## Checkpoint keys
+
+| Key | Content |
+|---|---|
+| `enc` | fp16 [width, 4096] |
+| `dec` | fp16 [4096, width], unit-norm columns |
+| `b_enc`, `theta` | fp32 [width], `theta` is the per-feature JumpReLU threshold |
+| `b_dec` | fp32 [4096] |
+| `groups` | Matryoshka prefix ends, e.g. [8192, 16384, 32768] |
+| `transform` | `cap` and `scale` of this unit, layer and signal |
+| `meta`, `cfg` | tag, unit, layer, arm, width, target L0, and all trainer arguments |
+| `eval_train`, `eval_hold` | FVU per prefix, L0, dead features, row count |
+| `eval_random` | FVU of the untrained initial dictionary |
+
+`whitening.pt` has keys `layers`, `W`, `grad_mu`, `act_mu`, `evals`, `n_tokens`, `damp_c`. `W[L]` is fp32 [4096, 4096] and symmetric, and the means are [4096].
+
+## Input transform
+
+SAEs do not see raw vectors.
+
+- Gradient: x -> clip_norm(W (x - grad_mu), cap) / scale.
+- Activation: x -> clip_norm(x - act_mu, cap) / scale.
+
+`W`, `grad_mu` and `act_mu` come from `whitening.pt` at the checkpoint's layer, and `cap` and `scale` from the checkpoint's `transform`. W = U (Λ + 0.1 λ̄ I)^(-1/2) Uᵀ whitens the token-level gradient covariance, with λ̄ its mean eigenvalue. FVU is measured in this transformed space, so gradient and activation FVUs are errors on different targets. Inputs must be built like the training rows of the same unit.
+
+## Loading
+
+```python
+import torch
+from huggingface_hub import hf_hub_download
+
+repo = "jason9464/mats-sprint-saes"
+sae = torch.load(hf_hub_download(repo, "sae/doc_l23_grad_k64.pt"), map_location="cpu", weights_only=False)
+wh = torch.load(hf_hub_download(repo, "whitening.pt"), map_location="cpu", weights_only=False)
+L, arm = sae["meta"]["layer"], sae["meta"]["arm"]
+cap, scale = sae["transform"]["cap"], sae["transform"]["scale"]
+enc, dec = sae["enc"].float(), sae["dec"].float()  # [width, 4096], [4096, width]
+b_enc, b_dec, theta = sae["b_enc"], sae["b_dec"], sae["theta"]
+
+
+def to_sae_space(x):
+    """Raw rows [n, 4096] (dLoss/dh for arm 'grad', h for arm 'act') -> SAE input."""
+    if arm == "grad":
+        x = (x.float() - wh["grad_mu"][L]) @ wh["W"][L]  # W is symmetric
+    else:
+        x = x.float() - wh["act_mu"][L]
+    x = x * torch.clamp(cap / x.norm(dim=1, keepdim=True), max=1.0)
+    return x / scale
+
+
+def encode(x):
+    z = (x - b_dec) @ enc.T + b_enc
+    return z * (z > theta)  # JumpReLU with a per-feature threshold
+
+
+def decode(f, k=None):
+    """k = Matryoshka prefix size (one of sae["groups"]); None = full width."""
+    k = k or f.shape[1]
+    return f[:, :k] @ dec[:, :k].T + b_dec
+
+
+x = to_sae_space(torch.randn(8, 4096))  # replace with real rows of the same unit
+f = encode(x)
+x_hat = decode(f)
+print(tuple(f.shape), tuple(x_hat.shape), "mean L0", (f > 0).sum(1).float().mean().item())
+```
+
+Encoding is z = (x - b_dec) enc^T + b_enc followed by f = z * (z > theta). Decoding with prefix size k is f[:, :k] dec[:, :k]^T + b_dec. On the training server's holdout rows, this code reproduces the stored holdout FVU and L0 of `doc_l23_grad_k64` (0.7115 and 74.8). Random input only checks shapes, and its L0 means nothing. To take a gradient decoder column d back to raw gradient space, use `torch.linalg.solve(W, d)`. The J-lens analysis reads -W⁻¹d, the direction in which SFT pushes the residual stream.

baselines/pca_baseline.json

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