feat(backward_lens): add vocabulary readout of GPT-2 MLP gradient factors

.github/workflows/checks.yml

@@ -430,6 +430,7 @@ jobs:
           - "Activation_Patching_in_TL_Demo"
           - "ARENA_Content"
           - "BERT"
+          - "Backward_Lens_Demo"
           - "Bridge_Evals_Demo"
           - "Exploratory_Analysis_Demo"
           # - "Grokking_Demo"

docs/source/content/backward_lens.md

@@ -0,0 +1,176 @@
+# Backward Lens
+
+Backward Lens projects factors of MLP weight gradients into a language model's
+vocabulary space. It is useful for inspecting which token directions are associated
+with the forward inputs and backward signals that compose a gradient. A readable
+vocabulary projection is a diagnostic, not by itself evidence that a token or neuron
+causes a model behavior.
+
+TransformerLens currently provides a focused GPT-2 implementation through
+`TransformerBridge`. It follows the method introduced by
+[Katz et al. (2024)](https://aclanthology.org/2024.emnlp-main.142/).
+
+## Gradient factorization
+
+For one linear projection and one prompt, let $x_i \in \mathbb{R}^{d_{in}}$ be
+the input at token position $i$, and let
+$\delta_i = \partial L / \partial y_i \in \mathbb{R}^{d_{out}}$ be the loss
+gradient at its output. GPT-2 stores `Conv1D` weights in `[in, out]` order, so
+
+$$
+\nabla_W L = \sum_i x_i \delta_i^\mathsf{T} = X^\mathsf{T}\Delta.
+$$
+
+`BackwardLens` captures both factors and independently computes the weight gradient.
+Each matrix result includes the reconstructed gradient and maximum absolute and
+scale-aware relative reconstruction errors.
+
+### The two GPT-2 MLP matrices
+
+The two projections expose different residual-width factors:
+
+| Result | Weight shape | Projected factor | Shape before vocabulary projection |
+|---|---:|---|---:|
+| `input_projection` (FF1 / `c_fc`) | `[d_model, d_mlp]` | Forward input $x_i$ | `[position, d_model]` |
+| `output_projection` (FF2 / `c_proj`) | `[d_mlp, d_model]` | Backward signal $\delta_i$ | `[position, d_model]` |
+
+The FF1 readout therefore describes the residual-stream directions entering the MLP.
+The FF2 readout describes raw loss gradients at the MLP output. These are different
+quantities and should not be interpreted interchangeably.
+
+## Vocabulary projection
+
+For each residual-width row $v$, the lens computes a fresh readout
+
+$$
+P(v) = \operatorname{Unembed}(\operatorname{LN}_{final}(v)).
+$$
+
+Final-normalization statistics are recomputed independently for every factor. The
+implementation does not reuse normalization scales cached during the model's forward
+pass. `vocabulary_logits` contains signed, pre-softmax logits; it does not contain
+probabilities.
+
+When `normalized=True`, the analysis also computes the Normalized Logit Lens:
+
+$$
+P_{norm}(v) = P\left(\frac{v}{\lVert v\rVert_2}\right).
+$$
+
+Exact-zero rows remain zero before projection and are identified by `zero_norm_mask`.
+The original float32 norms are retained in `factor_norms`. Normalization is most useful
+when comparing directions whose norms differ greatly, especially very small backward
+signals. Because final LayerNorm has an epsilon and may have a bias, raw and normalized
+projections need not be identical.
+
+## Sign convention
+
+All backward signals and weight gradients preserve the raw `d(loss) / d(tensor)`
+sign. Gradient descent subtracts them:
+
+$$
+W_{new} = W - \eta \nabla_W L.
+$$
+
+For FF2 backward signals, `bottom(...)` and
+`gradient_descent_target_ranks(...)` inspect the smallest raw-gradient logits, which
+are often the most relevant ordering for the subtracted update. Do not simply negate
+projected logits: final LayerNorm bias and epsilon mean that projection is not exactly
+sign-symmetric.
+
+## Minimal example
+
+```python
+import torch
+
+from transformer_lens.model_bridge import TransformerBridge
+from transformer_lens.tools.analysis import BackwardLens
+
+model = TransformerBridge.boot_transformers(
+    "openai-community/gpt2",
+    device="cuda" if torch.cuda.is_available() else "cpu",
+    dtype=torch.float32,
+)
+
+result = BackwardLens(model).analyze(
+    prompt="The capital of France is",
+    target_token=" Paris",
+    layers=[0, 6, 11],
+    normalized=True,
+)
+
+last_layer = result.layer(11)
+ff1 = last_layer.input_projection
+ff2 = last_layer.output_projection
+
+ff1_tokens = ff1.top_tokens(model.tokenizer, k=5)
+ff2_update_tokens = ff2.bottom_tokens(model.tokenizer, k=5)
+target_ranks = ff2.gradient_descent_target_ranks(
+    result.target_token_id,
+    normalized=True,
+)
+```
+
+`target_token` must encode to exactly one token without a beginning-of-sequence token.
+For GPT-2 tokenization, a leading space is often significant. The prompt is tokenized
+normally, including its prepended BOS token; all position-indexed factors and readouts
+align with `result.prompt_token_ids`.
+
+## Result structure
+
+`BackwardLens.analyze(...)` returns a detached `BackwardLensResult`:
+
+- `prompt`, `prompt_token_ids`, `target_token`, and `target_token_id` record the inputs.
+- `loss` is final-position cross-entropy against the one-token target.
+- `layers` preserves the requested layer order; `result.layer(index)` retrieves one.
+- Each layer has `input_projection` and `output_projection` matrix results.
+- Each matrix exposes `factors`, `factor_norms`, `zero_norm_mask`, and raw vocabulary
+  logits. `normalized_vocabulary_logits` is present only when requested.
+- `top(...)` and `bottom(...)` return signed values and token ids.
+- `top_tokens(...)` and `bottom_tokens(...)` decode ids with a caller-provided
+  tokenizer. Results deliberately retain no model or tokenizer reference.
+- Target ranks are zero-based competition ranks, so tied logits receive the same rank.
+- Maximum reconstruction errors summarize both MLP matrices over all requested layers.
+
+Returned tensors are detached, owned CPU copies. Factors, reconstructed gradients,
+norms, and vocabulary logits use float32; token ids and ranks use int64.
+
+## Requirements and non-goals
+
+The current implementation requires:
+
+- A freshly booted, raw `TransformerBridge` using `GPT2ArchitectureAdapter`.
+- Original, trainable GPT-2 `Conv1D` weights and a dense, non-gated MLP.
+- Compatibility mode and weight processing to remain disabled.
+- One non-empty prompt, one single-token target, and unique valid layer indices.
+
+It does not currently support batched prompts, multi-token target losses, gated MLPs,
+other architecture families, compatibility-mode weights, model editing, or causal
+claims about the displayed vocabulary rankings.
+
+## Model-state safety
+
+An analysis uses one gradient-enabled forward pass and one `torch.autograd.grad` call.
+It does not call `backward()` or modify parameter `.grad` buffers. It preserves model
+weights, `requires_grad` flags, train/eval state, existing hooks, and CPU/CUDA/MPS RNG
+state, and it removes only its own temporary hooks on success or failure. Existing
+activation-editing hooks still affect the analyzed computation.
+
+## Troubleshooting
+
+| Symptom | Cause and resolution |
+|---|---|
+| Raw-Bridge or processed-weight error | Reboot with `TransformerBridge.boot_transformers(...)`; do not enable compatibility mode or process weights. |
+| Target encodes to zero or multiple tokens | Choose text that maps to one GPT-2 token without BOS; check leading whitespace. |
+| Duplicate or out-of-range layer error | Pass a non-empty sequence of unique indices in `[0, model.cfg.n_layers)`. |
+| Normalized logits were not requested | Call `analyze(..., normalized=True)` before using `logits(normalized=True)` or normalized ranks. |
+| FF2 ranking appears sign-reversed | Remember that results are raw loss gradients and gradient descent subtracts them; inspect bottom tokens or ascending target ranks. |
+| Results change when custom hooks are installed | Existing hooks are intentionally respected; remove them to analyze the unmodified model computation. |
+
+## References
+
+- Shahar Katz, Yonatan Belinkov, Mor Geva, and Lior Wolf. 2024.
+  [Backward Lens: Projecting Language Model Gradients into the Vocabulary Space](https://aclanthology.org/2024.emnlp-main.142/).
+  *Proceedings of EMNLP 2024*, pages 2390–2422.
+- [Authors' research demonstration](https://github.com/shacharKZ/BackwardLens).
+  TransformerLens does not import, vendor, or depend on that repository's code.

docs/source/index.md

@@ -58,6 +58,7 @@ content/hook_system
 content/compatibility_mode
 content/ssm_interpretability
 content/jacobian_lens_fitting
+content/backward_lens
 content/debugging_numerical_divergence
 generated/demos/Main_Demo
 generated/demos/Exploratory_Analysis_Demo

makefile

@@ -45,6 +45,7 @@ docstring-test:
 
 notebook-test:
 	$(RUN) pytest --nbval-sanitize-with demos/doc_sanitize.cfg demos/BERT.ipynb $(RERUN_ARGS)
+	$(RUN) pytest --nbval-sanitize-with demos/doc_sanitize.cfg demos/Backward_Lens_Demo.ipynb $(RERUN_ARGS)
 	$(RUN) pytest --nbval-sanitize-with demos/doc_sanitize.cfg demos/Bridge_Evals_Demo.ipynb $(RERUN_ARGS)
 	$(RUN) pytest --nbval-sanitize-with demos/doc_sanitize.cfg demos/Exploratory_Analysis_Demo.ipynb $(RERUN_ARGS)
 	$(RUN) pytest --nbval-sanitize-with demos/doc_sanitize.cfg demos/Main_Demo.ipynb $(RERUN_ARGS)