diff --git a/ARENA_Balanced_Brackets.py b/ARENA_Balanced_Brackets.py
new file mode 100644
index 0000000..4e8f532
--- /dev/null
+++ b/ARENA_Balanced_Brackets.py
@@ -0,0 +1,818 @@
+# %%
+
+
+import json
+import sys
+from functools import partial
+from pathlib import Path
+
+import circuitsvis as cv
+import einops
+import torch as t
+from IPython.display import display
+from jaxtyping import Bool, Float, Int
+from sklearn.linear_model import LinearRegression
+from torch import Tensor, nn
+from tqdm import tqdm
+from transformer_lens import ActivationCache, HookedTransformer, HookedTransformerConfig, utils
+from transformer_lens.hook_points import HookPoint
+
+device = t.device("mps" if t.backends.mps.is_available() else "cuda" if t.cuda.is_available() else "cpu")
+t.set_grad_enabled(False)
+
+# Make sure exercises are in the path
+# chapter = "chapter1_transformer_interp"
+# section = "part51_balanced_bracket_classifier"
+# exercises_dir = next(p for p in Path.cwd().parents if p.name == chapter) / "exercises"
+# section_dir = exercises_dir / section
+# if str(exercises_dir) not in sys.path:
+# sys.path.append(str(exercises_dir))
+
+import ARENA_files.part51_balanced_bracket_classifier_tests as tests
+import ARENA_files.arena_plotly_utils as arena_plotly_utils
+# from arena_balanced_bracket_classifier_datasets import BracketsDataset, SimpleTokenizer
+from ARENA_files.arena_plotly_utils import bar, hist
+from ARENA_files.arena_balanced_bracket_classifier_datasets import BracketsDataset, SimpleTokenizer
+
+MAIN = __name__ == "__main__"
+
+# %%
+
+if MAIN:
+ VOCAB = "()"
+
+ cfg = HookedTransformerConfig(
+ n_ctx=42,
+ d_model=56,
+ d_head=28,
+ n_heads=2,
+ d_mlp=56,
+ n_layers=3,
+ attention_dir="bidirectional", # defaults to "causal"
+ act_fn="relu",
+ d_vocab=len(VOCAB) + 3, # plus 3 because of end and pad and start token
+ d_vocab_out=2, # 2 because we're doing binary classification
+ use_attn_result=True,
+ device=device,
+ use_hook_tokens=True,
+ )
+
+ model = HookedTransformer(cfg).eval()
+
+ state_dict = t.load("ARENA_files/brackets_model_state_dict.pt", map_location=device)
+ model.load_state_dict(state_dict)
+
+# %%
+
+if MAIN:
+ tokenizer = SimpleTokenizer("()")
+
+ # Examples of tokenization
+ # (the second one applies padding, since the sequences are of different lengths)
+ print(tokenizer.tokenize("()"))
+ print(tokenizer.tokenize(["()", "()()"]))
+
+ # Dictionaries mapping indices to tokens and vice versa
+ print(tokenizer.i_to_t)
+ print(tokenizer.t_to_i)
+
+ # Examples of decoding (all padding tokens are removed)
+ print(tokenizer.decode(t.tensor([[0, 3, 4, 2, 1, 1]])))
+
+# %%
+
+
+def add_perma_hooks_to_mask_pad_tokens(model: HookedTransformer, pad_token: int) -> HookedTransformer:
+ # Hook which operates on the tokens, and stores a mask where tokens equal [pad]
+ def cache_padding_tokens_mask(tokens: Float[Tensor, "batch seq"], hook: HookPoint) -> None:
+ hook.ctx["padding_tokens_mask"] = einops.rearrange(tokens == pad_token, "b sK -> b 1 1 sK")
+
+ # Apply masking, by referencing the mask stored in the `hook_tokens` hook context
+ def apply_padding_tokens_mask(
+ attn_scores: Float[Tensor, "batch head seq_Q seq_K"],
+ hook: HookPoint,
+ ) -> None:
+ attn_scores.masked_fill_(model.hook_dict["hook_tokens"].ctx["padding_tokens_mask"], -1e5)
+ if hook.layer() == model.cfg.n_layers - 1:
+ del model.hook_dict["hook_tokens"].ctx["padding_tokens_mask"]
+
+ # Add these hooks as permanent hooks (i.e. they aren't removed after functions like run_with_hooks)
+ for name, hook in model.hook_dict.items():
+ if name == "hook_tokens":
+ hook.add_perma_hook(cache_padding_tokens_mask)
+ elif name.endswith("attn_scores"):
+ hook.add_perma_hook(apply_padding_tokens_mask)
+
+ return model
+
+
+if MAIN:
+ model.reset_hooks(including_permanent=True)
+ model = add_perma_hooks_to_mask_pad_tokens(model, tokenizer.PAD_TOKEN)
+
+# %%
+
+if MAIN:
+ N_SAMPLES = 5000
+ with open("ARENA_files/brackets_data.json") as f:
+ data_tuples = json.load(f)
+ print(f"loaded {len(data_tuples)} examples, using {N_SAMPLES}")
+ data_tuples = data_tuples[:N_SAMPLES]
+
+ data = BracketsDataset(data_tuples).to(device)
+ data_mini = BracketsDataset(data_tuples[:100]).to(device)
+
+# %%
+
+if MAIN:
+ hist(
+ [len(x) for x, _ in data_tuples],
+ nbins=data.seq_length,
+ title="Sequence lengths of brackets in dataset",
+ labels={"x": "Seq len"},
+ )
+
+# %%
+
+if MAIN:
+ # Define and tokenize examples
+ examples = ["()()", "(())", "))((", "()", "((()()()()))", "(()()()(()(())()", "()(()(((())())()))"]
+ labels = [True, True, False, True, True, False, True]
+ toks = tokenizer.tokenize(examples)
+
+ # Get output logits for the 0th sequence position (i.e. the [start] token)
+ logits = model(toks)[:, 0]
+
+ # Get the probabilities via softmax, then get the balanced probability (which is the second element)
+ prob_balanced = logits.softmax(-1)[:, 1]
+
+ # Display output
+ print(
+ "Model confidence:\n"
+ + "\n".join(
+ [f"{ex:18} : {prob:<8.4%} : label={int(label)}" for ex, prob, label in zip(examples, prob_balanced, labels)]
+ )
+ )
+
+# %%
+
+
+def run_model_on_data(
+ model: HookedTransformer, data: BracketsDataset, batch_size: int = 200
+) -> Float[Tensor, "batch 2"]:
+ """Return probability that each example is balanced"""
+ all_logits = []
+ for i in tqdm(range(0, len(data.strs), batch_size)):
+ toks = data.toks[i : i + batch_size]
+ logits = model(toks)[:, 0]
+ all_logits.append(logits)
+ all_logits = t.cat(all_logits)
+ assert all_logits.shape == (len(data), 2)
+ return all_logits
+
+
+if MAIN:
+ test_set = data
+ n_correct = (run_model_on_data(model, test_set).argmax(-1).bool() == test_set.isbal).sum()
+ print(f"\nModel got {n_correct} out of {len(data)} training examples correct!")
+
+# %%
+
+
+def is_balanced_forloop(parens: str) -> bool:
+ """
+ Return True if the parens are balanced.
+
+ Parens is just the ( and ) characters, no begin or end tokens.
+ """
+ cumsum = 0
+ for paren in parens:
+ cumsum += 1 if paren == "(" else -1
+ if cumsum < 0:
+ return False
+
+ return cumsum == 0
+
+
+if MAIN:
+ for parens, expected in zip(examples, labels):
+ actual = is_balanced_forloop(parens)
+ assert expected == actual, f"{parens}: expected {expected} got {actual}"
+
+ print("All tests for `is_balanced_forloop` passed!")
+
+# %%
+
+
+def is_balanced_vectorized(tokens: Float[Tensor, "seq_len"]) -> bool:
+ """
+ Return True if the parens are balanced.
+
+ tokens is a vector which has start/pad/end indices (0/1/2) as well as left/right brackets (3/4)
+ """
+ # Convert start/end/padding tokens to zero, and left/right brackets to +1/-1
+ table = t.tensor([0, 0, 0, 1, -1])
+ change = table[tokens]
+ # Get altitude by taking cumulative sum
+ altitude = t.cumsum(change, -1)
+ # Check that the total elevation is zero and that there are no negative altitudes
+ no_total_elevation_failure = altitude[-1] == 0
+ no_negative_failure = altitude.min() >= 0
+
+ return (no_total_elevation_failure & no_negative_failure).item()
+
+
+if MAIN:
+ for tokens, expected in zip(tokenizer.tokenize(examples), labels):
+ actual = is_balanced_vectorized(tokens)
+ assert expected == actual, f"{tokens}: expected {expected} got {actual}"
+
+ print("All tests for `is_balanced_vectorized` passed!")
+
+# %%
+
+
+def get_post_final_ln_dir(model: HookedTransformer) -> Float[Tensor, "d_model"]:
+ """
+ Returns the direction in which final_ln_output[0, :] should point to maximize P(unbalanced)
+ """
+ return model.W_U[:, 0] - model.W_U[:, 1]
+
+
+if MAIN:
+ tests.test_get_post_final_ln_dir(get_post_final_ln_dir, model)
+
+# %%
+
+
+def get_activations(model: HookedTransformer, toks: Int[Tensor, "batch seq"], names: list[str]) -> ActivationCache:
+ """Uses hooks to return activations from the model, in the form of an ActivationCache."""
+ names_list = [names] if isinstance(names, str) else names
+ _, cache = model.run_with_cache(
+ toks,
+ return_type=None,
+ names_filter=lambda name: name in names_list,
+ )
+ return cache
+
+
+def get_activation(model: HookedTransformer, toks: Int[Tensor, "batch seq"], name: str):
+ """Gets a single activation."""
+ return get_activations(model, toks, [name])[name]
+
+
+def LN_hook_names(layernorm: nn.Module) -> tuple[str, str]:
+ """
+ Returns the names of the hooks immediately before and after a given layernorm.
+
+ Example:
+ model.final_ln -> ("blocks.2.hook_resid_post", "ln_final.hook_normalized")
+ """
+ if layernorm.name == "ln_final":
+ input_hook_name = utils.get_act_name("resid_post", 2)
+ output_hook_name = "ln_final.hook_normalized"
+ else:
+ layer, ln = layernorm.name.split(".")[1:]
+ input_hook_name = utils.get_act_name("resid_pre" if ln == "ln1" else "resid_mid", layer)
+ output_hook_name = utils.get_act_name("normalized", layer, ln)
+
+ return input_hook_name, output_hook_name
+
+
+def get_ln_fit(
+ model: HookedTransformer, data: BracketsDataset, layernorm: nn.Module, seq_pos: int | None = None
+) -> tuple[LinearRegression, float]:
+ """
+ Fits a linear regression, where the inputs are the values just before the layernorm given by the
+ input argument `layernorm`, and the values to predict are the layernorm's outputs.
+
+ if `seq_pos` is None, find best fit aggregated over all sequence positions. Otherwise, fit only
+ for the activations at `seq_pos`.
+
+ Returns: A tuple of a (fitted) sklearn LinearRegression object and the r^2 of the fit.
+ """
+ input_hook_name, output_hook_name = LN_hook_names(layernorm)
+
+ activations_dict = get_activations(model, data.toks, [input_hook_name, output_hook_name])
+ inputs = utils.to_numpy(activations_dict[input_hook_name])
+ outputs = utils.to_numpy(activations_dict[output_hook_name])
+
+ if seq_pos is None:
+ inputs = einops.rearrange(inputs, "batch seq d_model -> (batch seq) d_model")
+ outputs = einops.rearrange(outputs, "batch seq d_model -> (batch seq) d_model")
+ else:
+ inputs = inputs[:, seq_pos, :]
+ outputs = outputs[:, seq_pos, :]
+
+ final_ln_fit = LinearRegression().fit(inputs, outputs)
+
+ r2 = final_ln_fit.score(inputs, outputs)
+
+ return (final_ln_fit, r2)
+
+
+if MAIN:
+ tests.test_get_ln_fit(get_ln_fit, model, data_mini)
+
+ _, r2 = get_ln_fit(model, data, layernorm=model.ln_final, seq_pos=0)
+ print(f"r^2 for LN_final, at sequence position 0: {r2:.4f}")
+ _, r2 = get_ln_fit(model, data, layernorm=model.blocks[1].ln1, seq_pos=None)
+ print(f"r^2 for LN1, layer 1, over all sequence positions: {r2:.4f}")
+
+# %%
+
+
+def get_pre_final_ln_dir(model: HookedTransformer, data: BracketsDataset) -> Float[Tensor, "d_model"]:
+ """
+ Returns the direction in residual stream (pre ln_final, at sequence position 0) which
+ most points in the direction of making an unbalanced classification.
+ """
+ post_final_ln_dir = get_post_final_ln_dir(model)
+
+ final_ln_fit = get_ln_fit(model, data, layernorm=model.ln_final, seq_pos=0)[0]
+ final_ln_coefs = t.from_numpy(final_ln_fit.coef_).to(device)
+
+ return final_ln_coefs.T @ post_final_ln_dir
+
+
+if MAIN:
+ tests.test_get_pre_final_ln_dir(get_pre_final_ln_dir, model, data_mini)
+
+# %%
+
+
+def get_out_by_components(
+ model: HookedTransformer, data: BracketsDataset
+) -> Float[Tensor, "component batch seq_pos emb"]:
+ """
+ Computes a tensor of shape [10, dataset_size, seq_pos, emb] representing the output of the model's components when run on the data.
+ The first dimension is [embeddings, head 0.0, head 0.1, mlp 0, head 1.0, head 1.1, mlp 1, head 2.0, head 2.1, mlp 2]
+ """
+ embedding_hook_names = ["hook_embed", "hook_pos_embed"]
+ head_hook_names = [utils.get_act_name("result", layer) for layer in range(model.cfg.n_layers)]
+ mlp_hook_names = [utils.get_act_name("mlp_out", layer) for layer in range(model.cfg.n_layers)]
+
+ all_hook_names = embedding_hook_names + head_hook_names + mlp_hook_names
+ activations = get_activations(model, data.toks, all_hook_names)
+
+ out = (activations["hook_embed"] + activations["hook_pos_embed"]).unsqueeze(0)
+
+ for head_hook_name, mlp_hook_name in zip(head_hook_names, mlp_hook_names):
+ out = t.concat(
+ [
+ out,
+ einops.rearrange(activations[head_hook_name], "batch seq heads emb -> heads batch seq emb"),
+ activations[mlp_hook_name].unsqueeze(0),
+ ]
+ )
+
+ return out
+
+
+if MAIN:
+ tests.test_get_out_by_components(get_out_by_components, model, data_mini)
+
+# %%
+
+if MAIN:
+ biases = model.b_O.sum(0)
+ out_by_components = get_out_by_components(model, data)
+ summed_terms = out_by_components.sum(dim=0) + biases
+
+ final_ln_input_name, final_ln_output_name = LN_hook_names(model.ln_final)
+ final_ln_input = get_activation(model, data.toks, final_ln_input_name)
+
+ t.testing.assert_close(summed_terms, final_ln_input)
+ print("Tests passed!")
+
+# %%
+
+if MAIN:
+ # Get output by components, at sequence position 0 (which is used for classification)
+ out_by_components_seq0 = out_by_components[:, :, 0, :] # [component=10 batch d_model]
+ # Get the unbalanced direction for tensors being fed into the final layernorm
+ pre_final_ln_dir = get_pre_final_ln_dir(model, data) # [d_model]
+ # Get the size of the contributions for each component
+ out_by_component_in_unbalanced_dir = einops.einsum(
+ out_by_components_seq0,
+ pre_final_ln_dir,
+ "comp batch d_model, d_model -> comp batch",
+ )
+ # Subtract the mean
+ out_by_component_in_unbalanced_dir -= out_by_component_in_unbalanced_dir[:, data.isbal].mean(dim=1).unsqueeze(1)
+
+ tests.test_out_by_component_in_unbalanced_dir(out_by_component_in_unbalanced_dir, model, data)
+
+ arena_plotly_utils.hists_per_comp(out_by_component_in_unbalanced_dir, data, xaxis_range=[-10, 20])
+
+# %%
+
+
+def is_balanced_vectorized_return_both(
+ toks: Int[Tensor, "batch seq"],
+) -> tuple[Bool[Tensor, "batch"], Bool[Tensor, "batch"]]:
+ table = t.tensor([0, 0, 0, 1, -1]).to(device)
+ change = table[toks.to(device)].flip(-1)
+ altitude = t.cumsum(change, -1)
+ total_elevation_failure = altitude[:, -1] != 0
+ negative_failure = altitude.max(-1).values > 0
+ return total_elevation_failure, negative_failure
+
+
+if MAIN:
+ total_elevation_failure, negative_failure = is_balanced_vectorized_return_both(data.toks)
+
+ h20_in_unbalanced_dir = out_by_component_in_unbalanced_dir[7]
+ h21_in_unbalanced_dir = out_by_component_in_unbalanced_dir[8]
+
+ tests.test_total_elevation_and_negative_failures(data, total_elevation_failure, negative_failure)
+
+# %%
+
+if MAIN:
+ failure_types_dict = {
+ "both failures": negative_failure & total_elevation_failure,
+ "just neg failure": negative_failure & ~total_elevation_failure,
+ "just total elevation failure": ~negative_failure & total_elevation_failure,
+ "balanced": ~negative_failure & ~total_elevation_failure,
+ }
+
+ arena_plotly_utils.plot_failure_types_scatter(h20_in_unbalanced_dir, h21_in_unbalanced_dir, failure_types_dict, data)
+
+# %%
+
+if MAIN:
+ arena_plotly_utils.plot_contribution_vs_open_proportion(
+ h20_in_unbalanced_dir, "Head 2.0 contribution vs proportion of open brackets '('", failure_types_dict, data
+ )
+
+# %%
+
+if MAIN:
+ arena_plotly_utils.plot_contribution_vs_open_proportion(
+ h21_in_unbalanced_dir, "Head 2.1 contribution vs proportion of open brackets '('", failure_types_dict, data
+ )
+
+# %%
+
+
+def get_attn_probs(model: HookedTransformer, data: BracketsDataset, layer: int, head: int) -> t.Tensor:
+ """
+ Returns: (N_SAMPLES, max_seq_len, max_seq_len) tensor that sums to 1 over the last dimension.
+ """
+ return get_activation(model, data.toks, utils.get_act_name("pattern", layer))[:, head, :, :]
+
+
+if MAIN:
+ tests.test_get_attn_probs(get_attn_probs, model, data_mini)
+
+# %%
+
+if MAIN:
+ attn_probs_20 = get_attn_probs(model, data, 2, 0) # [batch seqQ seqK]
+ attn_probs_20_open_query0 = attn_probs_20[data.starts_open].mean(0)[0]
+
+ bar(
+ attn_probs_20_open_query0,
+ title="Avg Attention Probabilities for query 0, first token '(', head 2.0",
+ width=700,
+ template="simple_white",
+ labels={"x": "Sequence position", "y": "Attn prob"},
+ )
+
+# %%
+
+
+def get_WOV(model: HookedTransformer, layer: int, head: int) -> Float[Tensor, "d_model d_model"]:
+ """
+ Returns the W_OV matrix for a particular layer and head.
+ """
+ return model.W_V[layer, head] @ model.W_O[layer, head]
+
+
+def get_pre_20_dir(model, data) -> Float[Tensor, "d_model"]:
+ """
+ Returns the direction propagated back through the OV matrix of 2.0 and then through the layernorm before the layer 2
+ attention heads.
+ """
+ W_OV = get_WOV(model, 2, 0)
+
+ layer2_ln_fit, r2 = get_ln_fit(model, data, layernorm=model.blocks[2].ln1, seq_pos=1)
+ layer2_ln_coefs = t.from_numpy(layer2_ln_fit.coef_).to(device)
+
+ pre_final_ln_dir = get_pre_final_ln_dir(model, data)
+
+ return layer2_ln_coefs.T @ W_OV @ pre_final_ln_dir
+
+
+if MAIN:
+ tests.test_get_pre_20_dir(get_pre_20_dir, model, data_mini)
+
+# %%
+
+if MAIN:
+ # YOUR CODE HERE - define `out_by_component_in_pre_20_unbalanced_dir` (for all components before head 2.0)
+ pre_layer2_outputs_seqpos1 = out_by_components[:-3, :, 1, :]
+ out_by_component_in_pre_20_unbalanced_dir = einops.einsum(
+ pre_layer2_outputs_seqpos1,
+ get_pre_20_dir(model, data),
+ "comp batch emb, emb -> comp batch",
+ )
+ out_by_component_in_pre_20_unbalanced_dir -= out_by_component_in_pre_20_unbalanced_dir[:, data.isbal].mean(-1, True)
+
+ tests.test_out_by_component_in_pre_20_unbalanced_dir(out_by_component_in_pre_20_unbalanced_dir, model, data)
+
+ arena_plotly_utils.hists_per_comp(out_by_component_in_pre_20_unbalanced_dir, data, xaxis_range=(-5, 12))
+
+# %%
+
+if MAIN:
+ arena_plotly_utils.mlp_attribution_scatter(out_by_component_in_pre_20_unbalanced_dir, data, failure_types_dict)
+
+# %%
+
+
+def get_out_by_neuron(
+ model: HookedTransformer, data: BracketsDataset, layer: int, seq: int | None = None
+) -> Float[Tensor, "batch *seq neuron d_model"]:
+ """
+ If seq is None, then out[batch, seq, i, :] = f(x[batch, seq].T @ W_in[:, i] + b_in[i]) @ W_out[i, :],
+ i.e. the vector which is written to the residual stream by the ith neuron (where x is the input to the
+ residual stream (i.e. shape (batch, seq, d_model)).
+
+ If seq is not None, then out[batch, i, :] = f(x[batch, seq].T @ W_in[:, i]) @ W_out[i, :], i.e. we just
+ look at the sequence position given by argument seq.
+
+ (Note, using * in jaxtyping indicates an optional dimension)
+ """
+ # Get the W_out matrix for this MLP
+ W_out = model.W_out[layer] # [neuron d_model]
+
+ # Get activations of the layer just after the activation function, i.e. this is f(x.T @ W_in)
+ f_x_W_in = get_activation(model, data.toks, utils.get_act_name("post", layer)) # [batch seq neuron]
+
+ # f_x_W_in are activations, so they have batch and seq dimensions - this is where we index by seq if necessary
+ if seq is not None:
+ f_x_W_in = f_x_W_in[:, seq, :] # [batch neuron]
+
+ # Calculate the output by neuron (i.e. so summing over the `neurons` dimension gives the output of the MLP)
+ out = einops.einsum(
+ f_x_W_in,
+ W_out,
+ "... neuron, neuron d_model -> ... neuron d_model",
+ )
+ return out
+
+
+def get_out_by_neuron_in_20_dir(
+ model: HookedTransformer, data: BracketsDataset, layer: int
+) -> Float[Tensor, "batch neurons"]:
+ """
+ [b, s, i]th element is the contribution of the vector written by the ith neuron to the residual stream in the
+ unbalanced direction (for the b-th element in the batch, and the s-th sequence position).
+
+ In other words we need to take the vector produced by the `get_out_by_neuron` function, and project it onto the
+ unbalanced direction for head 2.0 (at seq pos = 1).
+ """
+ # Get neuron output at sequence position 1
+ out_by_neuron_seqpos1 = get_out_by_neuron(model, data, layer, seq=1)
+
+ # For each neuron, project the vector it writes to residual stream along the pre-2.0 unbalanced direction
+ return einops.einsum(
+ out_by_neuron_seqpos1, get_pre_20_dir(model, data), "batch neuron d_model, d_model -> batch neuron"
+ )
+
+
+if MAIN:
+ tests.test_get_out_by_neuron(get_out_by_neuron, model, data_mini)
+ tests.test_get_out_by_neuron_in_20_dir(get_out_by_neuron_in_20_dir, model, data_mini)
+
+# %%
+
+
+def get_out_by_neuron_in_20_dir_less_memory(
+ model: HookedTransformer, data: BracketsDataset, layer: int
+) -> Float[Tensor, "batch neurons"]:
+ """
+ Has the same output as `get_out_by_neuron_in_20_dir`, but uses less memory (because it never stores the output
+ vector of each neuron individually).
+ """
+ W_out = model.W_out[layer] # [neurons d_model]
+
+ f_x_W_in = get_activation(model, data.toks, utils.get_act_name("post", layer))[:, 1, :] # [batch neurons]
+
+ pre_20_dir = get_pre_20_dir(model, data) # [d_model]
+
+ # Multiply along the d_model dimension
+ W_out_in_20_dir = W_out @ pre_20_dir # [neurons]
+ # Multiply elementwise, over neurons (we're broadcasting along the batch dim)
+ out_by_neuron_in_20_dir = f_x_W_in * W_out_in_20_dir # [batch neurons]
+
+ return out_by_neuron_in_20_dir
+
+
+if MAIN:
+ tests.test_get_out_by_neuron_in_20_dir_less_memory(get_out_by_neuron_in_20_dir_less_memory, model, data_mini)
+
+# %%
+
+if MAIN:
+ for layer in range(2):
+ # Get neuron significances for head 2.0, sequence position #1 output
+ neurons_in_unbalanced_dir = get_out_by_neuron_in_20_dir_less_memory(model, data, layer)[
+ utils.to_numpy(data.starts_open), :
+ ]
+
+ # Plot neurons' activations
+ arena_plotly_utils.plot_neurons(neurons_in_unbalanced_dir, model, data, failure_types_dict, layer)
+
+# %%
+
+
+def get_q_and_k_for_given_input(
+ model: HookedTransformer,
+ tokenizer: SimpleTokenizer,
+ parens: str,
+ layer: int,
+) -> tuple[Float[Tensor, "seq n_heads d_model"], Float[Tensor, "seq n_heads d_model"]]:
+ """
+ Returns the queries and keys for the given parens string, for all attention heads in the given layer.
+ """
+ q_name = utils.get_act_name("q", layer)
+ k_name = utils.get_act_name("k", layer)
+
+ activations = get_activations(model, tokenizer.tokenize(parens), [q_name, k_name])
+
+ return activations[q_name][0], activations[k_name][0]
+
+
+if MAIN:
+ tests.test_get_q_and_k_for_given_input(get_q_and_k_for_given_input, model, tokenizer)
+
+# %%
+
+if MAIN:
+ layer = 0
+ all_left_parens = "".join(["(" * 40])
+ all_right_parens = "".join([")" * 40])
+
+ model.reset_hooks()
+ q0_all_left, k0_all_left = get_q_and_k_for_given_input(model, tokenizer, all_left_parens, layer)
+ q0_all_right, k0_all_right = get_q_and_k_for_given_input(model, tokenizer, all_right_parens, layer)
+ k0_avg = (k0_all_left + k0_all_right) / 2
+
+ # Define hook function to patch in q or k vectors
+ def hook_fn_patch_qk(
+ value: Float[Tensor, "batch seq head d_head"],
+ hook: HookPoint,
+ new_value: Float[Tensor, "... seq d_head"],
+ head_idx: int | None = None,
+ ) -> None:
+ if head_idx is not None:
+ value[..., head_idx, :] = new_value[..., head_idx, :]
+ else:
+ value[...] = new_value[...]
+
+
+# Define hook function to display attention patterns (using plotly)
+def hook_fn_display_attn_patterns(
+ pattern: Float[Tensor, "batch heads seqQ seqK"], hook: HookPoint, head_idx: int = 0
+) -> None:
+ avg_head_attn_pattern = pattern.mean(0)
+ labels = ["[start]", *[f"{i + 1}" for i in range(40)], "[end]"]
+ display(
+ cv.attention.attention_heads(
+ tokens=labels,
+ attention=avg_head_attn_pattern,
+ attention_head_names=["0.0", "0.1"],
+ max_value=avg_head_attn_pattern.max(),
+ mask_upper_tri=False, # use for bidirectional models
+ )
+ )
+
+
+if MAIN:
+ # Run our model on left parens, but patch in the average key values for left vs right parens
+ # This is to give us a rough idea how the model behaves on average when the query is a left paren
+ model.run_with_hooks(
+ tokenizer.tokenize(all_left_parens).to(device),
+ return_type=None,
+ fwd_hooks=[
+ (utils.get_act_name("k", layer), partial(hook_fn_patch_qk, new_value=k0_avg)),
+ (utils.get_act_name("pattern", layer), hook_fn_display_attn_patterns),
+ ],
+ )
+
+# %%
+
+
+def hook_fn_display_attn_patterns_for_single_query(
+ pattern: Float[Tensor, "batch heads seqQ seqK"], hook: HookPoint, head_idx: int = 0, query_idx: int = 1
+):
+ bar(
+ utils.to_numpy(pattern[:, head_idx, query_idx].mean(0)),
+ title="Average attn probabilities on data at posn 1, with query token = '('",
+ labels={"index": "Sequence position of key", "value": "Average attn over dataset"},
+ height=500,
+ width=800,
+ yaxis_range=[0, 0.1],
+ template="simple_white",
+ )
+
+
+if MAIN:
+ data_len_40 = BracketsDataset.with_length(data_tuples, 40).to(device)
+
+ model.reset_hooks()
+ model.run_with_hooks(
+ data_len_40.toks[data_len_40.isbal],
+ return_type=None,
+ fwd_hooks=[
+ (utils.get_act_name("q", 0), partial(hook_fn_patch_qk, new_value=q0_all_left)),
+ (utils.get_act_name("pattern", 0), hook_fn_display_attn_patterns_for_single_query),
+ ],
+ )
+
+# %%
+
+
+def embedding(model: HookedTransformer, tokenizer: SimpleTokenizer, char: str) -> Float[Tensor, "d_model"]:
+ assert char in ("(", ")")
+ idx = tokenizer.t_to_i[char]
+ return model.W_E[idx]
+
+
+if MAIN:
+ W_OV = model.W_V[0, 0] @ model.W_O[0, 0]
+
+ layer0_ln_fit = get_ln_fit(model, data, layernorm=model.blocks[0].ln1, seq_pos=None)[0]
+ layer0_ln_coefs = t.from_numpy(layer0_ln_fit.coef_).to(device)
+
+ v_L = embedding(model, tokenizer, "(") @ layer0_ln_coefs.T @ W_OV
+ v_R = embedding(model, tokenizer, ")") @ layer0_ln_coefs.T @ W_OV
+
+ print(f"Cosine similarity: {t.cosine_similarity(v_L, v_R, dim=0).item():.4f}")
+
+# %%
+
+
+def cos_sim_with_MLP_weights(
+ model: HookedTransformer, v: Float[Tensor, "d_model"], layer: int
+) -> Float[Tensor, "d_mlp"]:
+ """
+ Returns a vector of length d_mlp, where the ith element is the cosine similarity between v and the
+ ith in-direction of the MLP in layer `layer`.
+
+ Recall that the in-direction of the MLPs are the columns of the W_in matrix.
+ """
+ v_unit = v / v.norm()
+ W_in_unit = model.W_in[layer] / model.W_in[layer].norm(dim=0)
+
+ return einops.einsum(v_unit, W_in_unit, "d_model, d_model d_mlp -> d_mlp")
+
+
+def avg_squared_cos_sim(v: Float[Tensor, "d_model"], n_samples: int = 1000) -> float:
+ """
+ Returns the average (over n_samples) cosine similarity between v and another randomly chosen vector.
+
+ We can create random vectors from the standard N(0, I) distribution.
+ """
+ v2 = t.randn(n_samples, v.shape[0]).to(device)
+ v2 /= v2.norm(dim=1, keepdim=True)
+
+ v1 = v / v.norm()
+
+ return (v1 * v2).pow(2).sum(1).mean().item()
+
+
+if MAIN:
+ print("Avg squared cosine similarity of v_R with ...\n")
+
+ cos_sim_mlp0 = cos_sim_with_MLP_weights(model, v_R, 0)
+ print(f"...MLP input directions in layer 0: {cos_sim_mlp0.pow(2).mean():.4f}")
+
+ cos_sim_mlp1 = cos_sim_with_MLP_weights(model, v_R, 1)
+ print(f"...MLP input directions in layer 1: {cos_sim_mlp1.pow(2).mean():.4f}")
+
+ cos_sim_rand = avg_squared_cos_sim(v_R)
+ print(f"...random vectors of len = d_model: {cos_sim_rand:.4f}")
+
+# %%
+
+if MAIN:
+ adversarial_examples = ["()", "(())", "))"]
+
+ def tallest_balanced_bracket(length: int) -> str:
+ return "".join(["(" for _ in range(length)] + [")" for _ in range(length)])
+
+ i_max = 30
+ adversarial_examples.append(
+ tallest_balanced_bracket(i_max // 2) + ")(" + tallest_balanced_bracket((40 - i_max) // 2 - 1)
+ )
+
+ m = max(len(ex) for ex in adversarial_examples)
+ toks = tokenizer.tokenize(adversarial_examples)
+ probs = model(toks)[:, 0].softmax(-1)[:, 1]
+ print("\n".join([f"{ex:{m}} -> {p:.4%} balanced confidence" for (ex, p) in zip(adversarial_examples, probs)]))
+
+# %%
diff --git a/ARENA_Indirect_Object_Identification.py b/ARENA_Indirect_Object_Identification.py
new file mode 100644
index 0000000..3fa8632
--- /dev/null
+++ b/ARENA_Indirect_Object_Identification.py
@@ -0,0 +1,1722 @@
+# %%
+
+
+import re
+import sys
+from functools import partial
+from itertools import product
+from pathlib import Path
+from typing import Callable, Literal
+
+import circuitsvis as cv
+import einops
+import numpy as np
+import plotly.express as px
+import torch as t
+from IPython.display import HTML, display
+from jaxtyping import Bool, Float, Int
+from rich import print as rprint
+from rich.table import Column, Table
+from torch import Tensor
+from tqdm.notebook import tqdm
+from transformer_lens import ActivationCache, HookedTransformer, utils
+from transformer_lens.components import MLP, Embed, LayerNorm, Unembed
+from transformer_lens.hook_points import HookPoint
+
+t.set_grad_enabled(False)
+device = t.device("mps" if t.backends.mps.is_available() else "cuda" if t.cuda.is_available() else "cpu")
+
+
+import ARENA_files.arena_part41_ioi_tests as tests
+from ARENA_files.arena_plotly_utils import bar, imshow, line, scatter
+
+MAIN = __name__ == "__main__"
+
+# %%
+
+if MAIN:
+ model = HookedTransformer.from_pretrained(
+ "gpt2-small",
+ center_unembed=True,
+ center_writing_weights=True,
+ fold_ln=True,
+ refactor_factored_attn_matrices=True,
+ )
+
+# %%
+
+if MAIN:
+ # Here is where we test on a single prompt
+ # Result: 70% probability on Mary, as we expect
+
+ example_prompt = "After John and Mary went to the store, John gave a bottle of milk to"
+ example_answer = " Mary"
+ utils.test_prompt(example_prompt, example_answer, model, prepend_bos=True)
+
+# %%
+
+if MAIN:
+ prompt_format = [
+ "When John and Mary went to the shops,{} gave the bag to",
+ "When Tom and James went to the park,{} gave the ball to",
+ "When Dan and Sid went to the shops,{} gave an apple to",
+ "After Martin and Amy went to the park,{} gave a drink to",
+ ]
+ name_pairs = [
+ (" Mary", " John"),
+ (" Tom", " James"),
+ (" Dan", " Sid"),
+ (" Martin", " Amy"),
+ ]
+
+ # Define 8 prompts, in 4 groups of 2 (with adjacent prompts having answers swapped)
+ prompts = [prompt.format(name) for (prompt, names) in zip(prompt_format, name_pairs) for name in names[::-1]]
+ # Define the answers for each prompt, in the form (correct, incorrect)
+ answers = [names[::i] for names in name_pairs for i in (1, -1)]
+ # Define the answer tokens (same shape as the answers)
+ answer_tokens = t.concat([model.to_tokens(names, prepend_bos=False).T for names in answers])
+
+ rprint(prompts)
+ rprint(answers)
+ rprint(answer_tokens)
+
+ table = Table("Prompt", "Correct", "Incorrect", title="Prompts & Answers:")
+
+ for prompt, answer in zip(prompts, answers):
+ table.add_row(prompt, repr(answer[0]), repr(answer[1]))
+
+ rprint(table)
+
+# %%
+
+if MAIN:
+ tokens = model.to_tokens(prompts, prepend_bos=True)
+ # Move the tokens to the GPU
+ tokens = tokens.to(device)
+ # Run the model and cache all activations
+ original_logits, cache = model.run_with_cache(tokens)
+
+# %%
+
+if MAIN:
+
+ def logits_to_ave_logit_diff(
+ logits: Float[Tensor, "batch seq d_vocab"],
+ answer_tokens: Int[Tensor, "batch 2"] = answer_tokens,
+ per_prompt: bool = False,
+ ) -> Float[Tensor, "*batch"]:
+ """
+ Returns logit difference between the correct and incorrect answer.
+
+ If per_prompt=True, return the array of differences rather than the average.
+ """
+ # Only the final logits are relevant for the answer
+ final_logits: Float[Tensor, "batch d_vocab"] = logits[:, -1, :]
+ # Get the logits corresponding to the indirect object / subject tokens respectively
+ answer_logits: Float[Tensor, "batch 2"] = final_logits.gather(dim=-1, index=answer_tokens)
+ # Find logit difference
+ correct_logits, incorrect_logits = answer_logits.unbind(dim=-1)
+ answer_logit_diff = correct_logits - incorrect_logits
+ return answer_logit_diff if per_prompt else answer_logit_diff.mean()
+
+ tests.test_logits_to_ave_logit_diff(logits_to_ave_logit_diff)
+
+ original_per_prompt_diff = logits_to_ave_logit_diff(original_logits, answer_tokens, per_prompt=True)
+ print("Per prompt logit difference:", original_per_prompt_diff)
+ original_average_logit_diff = logits_to_ave_logit_diff(original_logits, answer_tokens)
+ print("Average logit difference:", original_average_logit_diff)
+
+ cols = [
+ "Prompt",
+ Column("Correct", style="rgb(0,200,0) bold"),
+ Column("Incorrect", style="rgb(255,0,0) bold"),
+ Column("Logit Difference", style="bold"),
+ ]
+ table = Table(*cols, title="Logit differences")
+
+ for prompt, answer, logit_diff in zip(prompts, answers, original_per_prompt_diff):
+ table.add_row(prompt, repr(answer[0]), repr(answer[1]), f"{logit_diff.item():.3f}")
+
+ rprint(table)
+
+# %%
+
+if MAIN:
+ answer_residual_directions = model.tokens_to_residual_directions(answer_tokens) # [batch 2 d_model]
+ print("Answer residual directions shape:", answer_residual_directions.shape)
+
+ correct_residual_directions, incorrect_residual_directions = answer_residual_directions.unbind(dim=1)
+ logit_diff_directions = correct_residual_directions - incorrect_residual_directions # [batch d_model]
+ print("Logit difference directions shape:", logit_diff_directions.shape)
+
+# %%
+
+if MAIN:
+ # cache syntax - resid_post is the residual stream at the end of the layer, -1 gets the final layer. The general syntax is [activation_name, layer_index, sub_layer_type].
+ final_residual_stream: Float[Tensor, "batch seq d_model"] = cache["resid_post", -1]
+ print(f"Final residual stream shape: {final_residual_stream.shape}")
+ final_token_residual_stream: Float[Tensor, "batch d_model"] = final_residual_stream[:, -1, :]
+
+ # Apply LayerNorm scaling (to just the final sequence position)
+ # pos_slice is the subset of the positions we take - here the final token of each prompt
+ scaled_final_token_residual_stream = cache.apply_ln_to_stack(final_token_residual_stream, layer=-1, pos_slice=-1)
+
+ average_logit_diff = einops.einsum(
+ scaled_final_token_residual_stream, logit_diff_directions, "batch d_model, batch d_model ->"
+ ) / len(prompts)
+
+ print(f"Calculated average logit diff: {average_logit_diff:.10f}")
+ print(f"Original logit difference: {original_average_logit_diff:.10f}")
+
+ t.testing.assert_close(average_logit_diff, original_average_logit_diff)
+
+# %%
+
+if MAIN:
+
+ def residual_stack_to_logit_diff(
+ residual_stack: Float[Tensor, "... batch d_model"],
+ cache: ActivationCache,
+ logit_diff_directions: Float[Tensor, "batch d_model"] = logit_diff_directions,
+ ) -> Float[Tensor, "..."]:
+ """
+ Gets the avg logit difference between the correct and incorrect answer for a given stack of components in the
+ residual stream.
+ """
+ batch_size = residual_stack.size(-2)
+ scaled_residual_stack = cache.apply_ln_to_stack(residual_stack, layer=-1, pos_slice=-1)
+ return (
+ einops.einsum(scaled_residual_stack, logit_diff_directions, "... batch d_model, batch d_model -> ...")
+ / batch_size
+ )
+
+ # Test function by checking that it gives the same result as the original logit difference
+ t.testing.assert_close(
+ residual_stack_to_logit_diff(final_token_residual_stream, cache), original_average_logit_diff
+ )
+
+# %%
+
+if MAIN:
+ accumulated_residual, labels = cache.accumulated_resid(layer=-1, incl_mid=True, pos_slice=-1, return_labels=True)
+ # accumulated_residual has shape (component, batch, d_model)
+
+ logit_lens_logit_diffs: Float[Tensor, "component"] = residual_stack_to_logit_diff(accumulated_residual, cache)
+
+ line(
+ logit_lens_logit_diffs,
+ hovermode="x unified",
+ title="Logit Difference From Accumulated Residual Stream",
+ labels={"x": "Layer", "y": "Logit Diff"},
+ xaxis_tickvals=labels,
+ width=800,
+ )
+
+# %%
+
+if MAIN:
+ per_layer_residual, labels = cache.decompose_resid(layer=-1, pos_slice=-1, return_labels=True)
+ per_layer_logit_diffs = residual_stack_to_logit_diff(per_layer_residual, cache)
+
+ line(
+ per_layer_logit_diffs,
+ hovermode="x unified",
+ title="Logit Difference From Each Layer",
+ labels={"x": "Layer", "y": "Logit Diff"},
+ xaxis_tickvals=labels,
+ width=800,
+ )
+
+# %%
+
+if MAIN:
+ per_head_residual, labels = cache.stack_head_results(layer=-1, pos_slice=-1, return_labels=True)
+ per_head_residual = einops.rearrange(
+ per_head_residual, "(layer head) ... -> layer head ...", layer=model.cfg.n_layers
+ )
+ per_head_logit_diffs = residual_stack_to_logit_diff(per_head_residual, cache)
+
+ imshow(
+ per_head_logit_diffs,
+ labels={"x": "Head", "y": "Layer"},
+ title="Logit Difference From Each Head",
+ width=600,
+ )
+
+# %%
+
+
+def topk_of_Nd_tensor(tensor: Float[Tensor, "rows cols"], k: int):
+ """
+ Helper function: does same as tensor.topk(k).indices, but works over 2D tensors.
+ Returns a list of indices, i.e. shape [k, tensor.ndim].
+
+ Example: if tensor is 2D array of values for each head in each layer, this will
+ return a list of heads.
+ """
+ i = t.topk(tensor.flatten(), k).indices
+ return np.array(np.unravel_index(utils.to_numpy(i), tensor.shape)).T.tolist()
+
+
+if MAIN:
+ k = 3
+
+ for head_type in ["Positive", "Negative"]:
+ # Get the heads with largest (or smallest) contribution to the logit difference
+ top_heads = topk_of_Nd_tensor(per_head_logit_diffs * (1 if head_type == "Positive" else -1), k)
+
+ # Get all their attention patterns
+ attn_patterns_for_important_heads: Float[Tensor, "head q k"] = t.stack(
+ [cache["pattern", layer][:, head][0] for layer, head in top_heads]
+ )
+
+ # Display results
+ display(HTML(f"Top {k} {head_type} Logit Attribution Heads
"))
+ display(
+ cv.attention.attention_patterns(
+ attention=attn_patterns_for_important_heads,
+ tokens=model.to_str_tokens(tokens[0]),
+ attention_head_names=[f"{layer}.{head}" for layer, head in top_heads],
+ )
+ )
+
+# %%
+
+from transformer_lens import patching
+
+# %%
+
+if MAIN:
+ clean_tokens = tokens
+ # Swap each adjacent pair to get corrupted tokens
+ indices = [i + 1 if i % 2 == 0 else i - 1 for i in range(len(tokens))]
+ corrupted_tokens = clean_tokens[indices]
+
+ print(
+ "Clean string 0: ",
+ model.to_string(clean_tokens[0]),
+ "\nCorrupted string 0:",
+ model.to_string(corrupted_tokens[0]),
+ )
+
+ clean_logits, clean_cache = model.run_with_cache(clean_tokens)
+ corrupted_logits, corrupted_cache = model.run_with_cache(corrupted_tokens)
+
+ clean_logit_diff = logits_to_ave_logit_diff(clean_logits, answer_tokens)
+ print(f"Clean logit diff: {clean_logit_diff:.4f}")
+
+ corrupted_logit_diff = logits_to_ave_logit_diff(corrupted_logits, answer_tokens)
+ print(f"Corrupted logit diff: {corrupted_logit_diff:.4f}")
+
+# %%
+
+if MAIN:
+
+ def ioi_metric(
+ logits: Float[Tensor, "batch seq d_vocab"],
+ answer_tokens: Int[Tensor, "batch 2"] = answer_tokens,
+ corrupted_logit_diff: float = corrupted_logit_diff,
+ clean_logit_diff: float = clean_logit_diff,
+ ) -> Float[Tensor, ""]:
+ """
+ Linear function of logit diff, calibrated so that it equals 0 when performance is same as on corrupted input, and 1
+ when performance is same as on clean input.
+ """
+ patched_logit_diff = logits_to_ave_logit_diff(logits, answer_tokens)
+ return (patched_logit_diff - corrupted_logit_diff) / (clean_logit_diff - corrupted_logit_diff)
+
+ t.testing.assert_close(ioi_metric(clean_logits).item(), 1.0)
+ t.testing.assert_close(ioi_metric(corrupted_logits).item(), 0.0)
+ t.testing.assert_close(ioi_metric((clean_logits + corrupted_logits) / 2).item(), 0.5)
+
+# %%
+
+if MAIN:
+ act_patch_resid_pre = patching.get_act_patch_resid_pre(
+ model=model, corrupted_tokens=corrupted_tokens, clean_cache=clean_cache, patching_metric=ioi_metric
+ )
+
+ labels = [f"{tok} {i}" for i, tok in enumerate(model.to_str_tokens(clean_tokens[0]))]
+
+ imshow(
+ act_patch_resid_pre,
+ labels={"x": "Position", "y": "Layer"},
+ x=labels,
+ title="resid_pre Activation Patching",
+ width=700,
+ )
+
+# %%
+
+
+def patch_residual_component(
+ corrupted_residual_component: Float[Tensor, "batch pos d_model"],
+ hook: HookPoint,
+ pos: int,
+ clean_cache: ActivationCache,
+) -> Float[Tensor, "batch pos d_model"]:
+ """
+ Patches a given sequence position in the residual stream, using the value
+ from the clean cache.
+ """
+ corrupted_residual_component[:, pos, :] = clean_cache[hook.name][:, pos, :]
+ return corrupted_residual_component
+
+
+def get_act_patch_resid_pre(
+ model: HookedTransformer,
+ corrupted_tokens: Float[Tensor, "batch pos"],
+ clean_cache: ActivationCache,
+ patching_metric: Callable[[Float[Tensor, "batch pos d_vocab"]], float],
+) -> Float[Tensor, "3 layer pos"]:
+ """
+ Returns an array of results of patching each position at each layer in the residual
+ stream, using the value from the clean cache.
+
+ The results are calculated using the patching_metric function, which should be
+ called on the model's logit output.
+ """
+ model.reset_hooks()
+ seq_len = corrupted_tokens.size(1)
+ results = t.zeros(model.cfg.n_layers, seq_len, device=device, dtype=t.float32)
+
+ for layer in tqdm(range(model.cfg.n_layers)):
+ for position in range(seq_len):
+ hook_fn = partial(patch_residual_component, pos=position, clean_cache=clean_cache)
+ patched_logits = model.run_with_hooks(
+ corrupted_tokens,
+ fwd_hooks=[(utils.get_act_name("resid_pre", layer), hook_fn)],
+ )
+ results[layer, position] = patching_metric(patched_logits)
+
+ return results
+
+
+if MAIN:
+ act_patch_resid_pre_own = get_act_patch_resid_pre(model, corrupted_tokens, clean_cache, ioi_metric)
+
+ t.testing.assert_close(act_patch_resid_pre, act_patch_resid_pre_own)
+
+# %%
+
+if MAIN:
+ imshow(
+ act_patch_resid_pre_own,
+ x=labels,
+ title="Logit Difference From Patched Residual Stream",
+ labels={"x": "Sequence Position", "y": "Layer"},
+ width=700,
+ )
+
+# %%
+
+if MAIN:
+ act_patch_block_every = patching.get_act_patch_block_every(model, corrupted_tokens, clean_cache, ioi_metric)
+
+ imshow(
+ act_patch_block_every,
+ x=labels,
+ facet_col=0, # This argument tells plotly which dimension to split into separate plots
+ facet_labels=["Residual Stream", "Attn Output", "MLP Output"], # Subtitles of separate plots
+ title="Logit Difference From Patched Attn Head Output",
+ labels={"x": "Sequence Position", "y": "Layer"},
+ width=1200,
+ )
+
+# %%
+
+
+def get_act_patch_block_every(
+ model: HookedTransformer,
+ corrupted_tokens: Float[Tensor, "batch pos"],
+ clean_cache: ActivationCache,
+ patching_metric: Callable[[Float[Tensor, "batch pos d_vocab"]], float],
+) -> Float[Tensor, "3 layer pos"]:
+ """
+ Returns an array of results of patching each position at each layer in the residual stream, using the value from the
+ clean cache.
+
+ The results are calculated using the patching_metric function, which should be called on the model's logit output.
+ """
+ model.reset_hooks()
+ results = t.zeros(3, model.cfg.n_layers, tokens.size(1), device=device, dtype=t.float32)
+
+ for component_idx, component in enumerate(["resid_pre", "attn_out", "mlp_out"]):
+ for layer in tqdm(range(model.cfg.n_layers)):
+ for position in range(corrupted_tokens.shape[1]):
+ hook_fn = partial(patch_residual_component, pos=position, clean_cache=clean_cache)
+ patched_logits = model.run_with_hooks(
+ corrupted_tokens,
+ fwd_hooks=[(utils.get_act_name(component, layer), hook_fn)],
+ )
+ results[component_idx, layer, position] = patching_metric(patched_logits)
+
+ return results
+
+
+if MAIN:
+ act_patch_block_every_own = get_act_patch_block_every(model, corrupted_tokens, clean_cache, ioi_metric)
+
+ t.testing.assert_close(act_patch_block_every, act_patch_block_every_own)
+
+ imshow(
+ act_patch_block_every_own,
+ x=labels,
+ facet_col=0,
+ facet_labels=["Residual Stream", "Attn Output", "MLP Output"],
+ title="Logit Difference From Patched Attn Head Output",
+ labels={"x": "Sequence Position", "y": "Layer"},
+ width=1200,
+ )
+
+# %%
+
+if MAIN:
+ act_patch_attn_head_out_all_pos = patching.get_act_patch_attn_head_out_all_pos(
+ model, corrupted_tokens, clean_cache, ioi_metric
+ )
+
+ imshow(
+ act_patch_attn_head_out_all_pos,
+ labels={"y": "Layer", "x": "Head"},
+ title="attn_head_out Activation Patching (All Pos)",
+ width=600,
+ )
+
+# %%
+
+
+def patch_head_vector(
+ corrupted_head_vector: Float[Tensor, "batch pos head_index d_head"],
+ hook: HookPoint,
+ head_index: int,
+ clean_cache: ActivationCache,
+) -> Float[Tensor, "batch pos head_index d_head"]:
+ """
+ Patches the output of a given head (before it's added to the residual stream) at every sequence position, using the
+ value from the clean cache.
+ """
+ corrupted_head_vector[:, :, head_index] = clean_cache[hook.name][:, :, head_index]
+ return corrupted_head_vector
+
+
+def get_act_patch_attn_head_out_all_pos(
+ model: HookedTransformer,
+ corrupted_tokens: Float[Tensor, "batch pos"],
+ clean_cache: ActivationCache,
+ patching_metric: Callable,
+) -> Float[Tensor, "layer head"]:
+ """
+ Returns an array of results of patching at all positions for each head in each layer, using the value from the clean
+ cache. The results are calculated using the patching_metric function, which should be called on the model's logit
+ output.
+ """
+ model.reset_hooks()
+ results = t.zeros(model.cfg.n_layers, model.cfg.n_heads, device=device, dtype=t.float32)
+
+ for layer in tqdm(range(model.cfg.n_layers)):
+ for head in range(model.cfg.n_heads):
+ hook_fn = partial(patch_head_vector, head_index=head, clean_cache=clean_cache)
+ patched_logits = model.run_with_hooks(
+ corrupted_tokens, fwd_hooks=[(utils.get_act_name("z", layer), hook_fn)], return_type="logits"
+ )
+ results[layer, head] = patching_metric(patched_logits)
+
+ return results
+
+
+if MAIN:
+ act_patch_attn_head_out_all_pos_own = get_act_patch_attn_head_out_all_pos(
+ model, corrupted_tokens, clean_cache, ioi_metric
+ )
+
+ t.testing.assert_close(act_patch_attn_head_out_all_pos, act_patch_attn_head_out_all_pos_own)
+
+ imshow(
+ act_patch_attn_head_out_all_pos_own,
+ title="Logit Difference From Patched Attn Head Output",
+ labels={"x": "Head", "y": "Layer"},
+ width=600,
+ )
+
+# %%
+
+if MAIN:
+ act_patch_attn_head_all_pos_every = patching.get_act_patch_attn_head_all_pos_every(
+ model, corrupted_tokens, clean_cache, ioi_metric
+ )
+
+ imshow(
+ act_patch_attn_head_all_pos_every,
+ facet_col=0,
+ facet_labels=["Output", "Query", "Key", "Value", "Pattern"],
+ title="Activation Patching Per Head (All Pos)",
+ labels={"x": "Head", "y": "Layer"},
+ width=1200,
+ )
+
+# %%
+
+
+def patch_attn_patterns(
+ corrupted_head_vector: Float[Tensor, "batch head_index pos_q pos_k"],
+ hook: HookPoint,
+ head_index: int,
+ clean_cache: ActivationCache,
+) -> Float[Tensor, "batch pos head_index d_head"]:
+ """
+ Patches the attn patterns of a given head at every sequence position, using the value from the clean cache.
+ """
+ corrupted_head_vector[:, head_index] = clean_cache[hook.name][:, head_index]
+ return corrupted_head_vector
+
+
+def get_act_patch_attn_head_all_pos_every(
+ model: HookedTransformer,
+ corrupted_tokens: Float[Tensor, "batch pos"],
+ clean_cache: ActivationCache,
+ patching_metric: Callable,
+) -> Float[Tensor, "layer head"]:
+ """
+ Returns an array of results of patching at all positions for each head in each layer (using the value from the clean
+ cache) for output, queries, keys, values and attn pattern in turn.
+
+ The results are calculated using the patching_metric function, which should be called on the model's logit output.
+ """
+ results = t.zeros(5, model.cfg.n_layers, model.cfg.n_heads, device=device, dtype=t.float32)
+ # Loop over each component in turn
+ for component_idx, component in enumerate(["z", "q", "k", "v", "pattern"]):
+ for layer in tqdm(range(model.cfg.n_layers)):
+ for head in range(model.cfg.n_heads):
+ # Get different hook function if we're doing attention probs
+ hook_fn_general = patch_attn_patterns if component == "pattern" else patch_head_vector
+ hook_fn = partial(hook_fn_general, head_index=head, clean_cache=clean_cache)
+ # Get patched logits
+ patched_logits = model.run_with_hooks(
+ corrupted_tokens, fwd_hooks=[(utils.get_act_name(component, layer), hook_fn)], return_type="logits"
+ )
+ results[component_idx, layer, head] = patching_metric(patched_logits)
+
+ return results
+
+
+if MAIN:
+ act_patch_attn_head_all_pos_every_own = get_act_patch_attn_head_all_pos_every(
+ model, corrupted_tokens, clean_cache, ioi_metric
+ )
+
+ t.testing.assert_close(act_patch_attn_head_all_pos_every, act_patch_attn_head_all_pos_every_own)
+
+ imshow(
+ act_patch_attn_head_all_pos_every_own,
+ facet_col=0,
+ facet_labels=["Output", "Query", "Key", "Value", "Pattern"],
+ title="Activation Patching Per Head (All Pos)",
+ labels={"x": "Head", "y": "Layer"},
+ width=1200,
+ )
+
+# %%
+
+from ARENA_files.ioi_dataset import NAMES, IOIDataset
+
+# %%
+
+if MAIN:
+ N = 25
+ ioi_dataset = IOIDataset(
+ prompt_type="mixed",
+ N=N,
+ tokenizer=model.tokenizer,
+ prepend_bos=False,
+ seed=1,
+ device=str(device),
+ )
+
+# %%
+
+if MAIN:
+ abc_dataset = ioi_dataset.gen_flipped_prompts("ABB->XYZ, BAB->XYZ")
+
+# %%
+
+
+def format_prompt(sentence: str) -> str:
+ """Format a prompt by underlining names (for rich print)"""
+ return re.sub("(" + "|".join(NAMES) + ")", lambda x: f"[u bold dark_orange]{x.group(0)}[/]", sentence) + "\n"
+
+
+def make_table(cols, colnames, title="", n_rows=5, decimals=4):
+ """Makes and displays a table, from cols rather than rows (using rich print)"""
+ table = Table(*colnames, title=title)
+ rows = list(zip(*cols))
+ f = lambda x: x if isinstance(x, str) else f"{x:.{decimals}f}"
+ for row in rows[:n_rows]:
+ table.add_row(*list(map(f, row)))
+ rprint(table)
+
+
+if MAIN:
+ make_table(
+ colnames=["IOI prompt", "IOI subj", "IOI indirect obj", "ABC prompt"],
+ cols=[
+ map(format_prompt, ioi_dataset.sentences),
+ model.to_string(ioi_dataset.s_tokenIDs).split(),
+ model.to_string(ioi_dataset.io_tokenIDs).split(),
+ map(format_prompt, abc_dataset.sentences),
+ ],
+ title="Sentences from IOI vs ABC distribution",
+ )
+
+# %%
+
+if MAIN:
+
+ def logits_to_ave_logit_diff_2(
+ logits: Float[Tensor, "batch seq d_vocab"], ioi_dataset: IOIDataset = ioi_dataset, per_prompt=False
+ ) -> Float[Tensor, "*batch"]:
+ """
+ Returns logit difference between the correct and incorrect answer.
+
+ If per_prompt=True, return the array of differences rather than the average.
+ """
+ # Only the final logits are relevant for the answer
+ # Get the logits corresponding to the indirect object / subject tokens respectively
+ io_logits: Float[Tensor, "batch"] = logits[
+ range(logits.size(0)), ioi_dataset.word_idx["end"], ioi_dataset.io_tokenIDs
+ ]
+ s_logits: Float[Tensor, "batch"] = logits[
+ range(logits.size(0)), ioi_dataset.word_idx["end"], ioi_dataset.s_tokenIDs
+ ]
+ # Find logit difference
+ answer_logit_diff = io_logits - s_logits
+ return answer_logit_diff if per_prompt else answer_logit_diff.mean()
+
+ model.reset_hooks(including_permanent=True)
+
+ ioi_logits_original, ioi_cache = model.run_with_cache(ioi_dataset.toks)
+ abc_logits_original, abc_cache = model.run_with_cache(abc_dataset.toks)
+
+ ioi_per_prompt_diff = logits_to_ave_logit_diff_2(ioi_logits_original, per_prompt=True)
+ abc_per_prompt_diff = logits_to_ave_logit_diff_2(abc_logits_original, per_prompt=True)
+
+ ioi_average_logit_diff = logits_to_ave_logit_diff_2(ioi_logits_original).item()
+ abc_average_logit_diff = logits_to_ave_logit_diff_2(abc_logits_original).item()
+
+ print(f"Average logit diff (IOI dataset): {ioi_average_logit_diff:.4f}")
+ print(f"Average logit diff (ABC dataset): {abc_average_logit_diff:.4f}")
+
+ make_table(
+ colnames=["IOI prompt", "IOI logit diff", "ABC prompt", "ABC logit diff"],
+ cols=[
+ map(format_prompt, ioi_dataset.sentences),
+ ioi_per_prompt_diff,
+ map(format_prompt, abc_dataset.sentences),
+ abc_per_prompt_diff,
+ ],
+ title="Sentences from IOI vs ABC distribution",
+ )
+
+# %%
+
+if MAIN:
+
+ def ioi_metric_2(
+ logits: Float[Tensor, "batch seq d_vocab"],
+ clean_logit_diff: float = ioi_average_logit_diff,
+ corrupted_logit_diff: float = abc_average_logit_diff,
+ ioi_dataset: IOIDataset = ioi_dataset,
+ ) -> float:
+ """
+ We calibrate this so that the value is 0 when performance isn't harmed (i.e. same as IOI dataset),
+ and -1 when performance has been destroyed (i.e. is same as ABC dataset).
+ """
+ patched_logit_diff = logits_to_ave_logit_diff_2(logits, ioi_dataset)
+ return (patched_logit_diff - clean_logit_diff) / (clean_logit_diff - corrupted_logit_diff)
+
+ print(f"IOI metric (IOI dataset): {ioi_metric_2(ioi_logits_original):.4f}")
+ print(f"IOI metric (ABC dataset): {ioi_metric_2(abc_logits_original):.4f}")
+
+# %%
+
+if MAIN:
+
+ def patch_or_freeze_head_vectors(
+ orig_head_vector: Float[Tensor, "batch pos head_index d_head"],
+ hook: HookPoint,
+ new_cache: ActivationCache,
+ orig_cache: ActivationCache,
+ head_to_patch: tuple[int, int],
+ ) -> Float[Tensor, "batch pos head_index d_head"]:
+ """
+ This helps implement step 2 of path patching. We freeze all head outputs (i.e. set them to their values in
+ orig_cache), except for head_to_patch (if it's in this layer) which we patch with the value from new_cache.
+
+ head_to_patch: tuple of (layer, head)
+ """
+ # Setting using ..., otherwise changing orig_head_vector will edit cache value too
+ orig_head_vector[...] = orig_cache[hook.name][...]
+ if head_to_patch[0] == hook.layer():
+ orig_head_vector[:, :, head_to_patch[1]] = new_cache[hook.name][:, :, head_to_patch[1]]
+ return orig_head_vector
+
+ def get_path_patch_head_to_final_resid_post(
+ model: HookedTransformer,
+ patching_metric: Callable,
+ new_dataset: IOIDataset = abc_dataset,
+ orig_dataset: IOIDataset = ioi_dataset,
+ new_cache: ActivationCache | None = abc_cache,
+ orig_cache: ActivationCache | None = ioi_cache,
+ ) -> Float[Tensor, "layer head"]:
+ """
+ Performs path patching (see algorithm in appendix B of IOI paper), with:
+
+ sender head = (each head, looped through, one at a time)
+ receiver node = final value of residual stream
+
+ Returns:
+ tensor of metric values for every possible sender head
+ """
+ model.reset_hooks()
+ results = t.zeros(model.cfg.n_layers, model.cfg.n_heads, device=device, dtype=t.float32)
+
+ resid_post_hook_name = utils.get_act_name("resid_post", model.cfg.n_layers - 1)
+ resid_post_name_filter = lambda name: name == resid_post_hook_name
+
+ # ========== Step 1 ==========
+ # Gather activations on x_orig and x_new
+
+ # Note the use of names_filter for the run_with_cache function. Using it means we
+ # only cache the things we need (in this case, just attn head outputs).
+ z_name_filter = lambda name: name.endswith("z")
+ if new_cache is None:
+ _, new_cache = model.run_with_cache(new_dataset.toks, names_filter=z_name_filter, return_type=None)
+ if orig_cache is None:
+ _, orig_cache = model.run_with_cache(orig_dataset.toks, names_filter=z_name_filter, return_type=None)
+
+ # Looping over every possible sender head (the receiver is always the final resid_post)
+ for sender_layer, sender_head in tqdm(list(product(range(model.cfg.n_layers), range(model.cfg.n_heads)))):
+ # ========== Step 2 ==========
+ # Run on x_orig, with sender head patched from x_new, every other head frozen
+
+ hook_fn = partial(
+ patch_or_freeze_head_vectors,
+ new_cache=new_cache,
+ orig_cache=orig_cache,
+ head_to_patch=(sender_layer, sender_head),
+ )
+ model.add_hook(z_name_filter, hook_fn)
+
+ _, patched_cache = model.run_with_cache(
+ orig_dataset.toks, names_filter=resid_post_name_filter, return_type=None
+ )
+ # if (sender_layer, sender_head) == (9, 9):
+ # return patched_cache
+ assert set(patched_cache.keys()) == {resid_post_hook_name}
+
+ # ========== Step 3 ==========
+ # Unembed the final residual stream value, to get our patched logits
+
+ patched_logits = model.unembed(model.ln_final(patched_cache[resid_post_hook_name]))
+
+ # Save the results
+ results[sender_layer, sender_head] = patching_metric(patched_logits)
+
+ return results
+
+ path_patch_head_to_final_resid_post = get_path_patch_head_to_final_resid_post(model, ioi_metric_2)
+
+ imshow(
+ 100 * path_patch_head_to_final_resid_post,
+ title="Direct effect on logit difference",
+ labels={"x": "Head", "y": "Layer", "color": "Logit diff. variation"},
+ coloraxis=dict(colorbar_ticksuffix="%"),
+ width=600,
+ )
+
+# %%
+
+if MAIN:
+
+ def patch_head_input(
+ orig_activation: Float[Tensor, "batch pos head_idx d_head"],
+ hook: HookPoint,
+ patched_cache: ActivationCache,
+ head_list: list[tuple[int, int]],
+ ) -> Float[Tensor, "batch pos head_idx d_head"]:
+ """
+ Function which can patch any combination of heads in layers,
+ according to the heads in head_list.
+ """
+ heads_to_patch = [head for layer, head in head_list if layer == hook.layer()]
+ orig_activation[:, :, heads_to_patch] = patched_cache[hook.name][:, :, heads_to_patch]
+ return orig_activation
+
+ def get_path_patch_head_to_heads(
+ receiver_heads: list[tuple[int, int]],
+ receiver_input: str,
+ model: HookedTransformer,
+ patching_metric: Callable,
+ new_dataset: IOIDataset = abc_dataset,
+ orig_dataset: IOIDataset = ioi_dataset,
+ new_cache: ActivationCache | None = None,
+ orig_cache: ActivationCache | None = None,
+ ) -> Float[Tensor, "layer head"]:
+ """
+ Performs path patching (see algorithm in appendix B of IOI paper), with:
+
+ sender head = (each head, looped through, one at a time)
+ receiver node = input to a later head (or set of heads)
+
+ The receiver node is specified by receiver_heads and receiver_input, for example if receiver_input = "v" and
+ receiver_heads = [(8, 6), (8, 10), (7, 9), (7, 3)], we're doing path patching from each head to the value inputs of
+ the S-inhibition heads.
+
+ Returns:
+ tensor of metric values for every possible sender head
+ """
+ model.reset_hooks()
+
+ assert receiver_input in ("k", "q", "v")
+ receiver_layers = set(next(zip(*receiver_heads)))
+ receiver_hook_names = [utils.get_act_name(receiver_input, layer) for layer in receiver_layers]
+ receiver_hook_names_filter = lambda name: name in receiver_hook_names
+
+ results = t.zeros(max(receiver_layers), model.cfg.n_heads, device=device, dtype=t.float32)
+
+ # ========== Step 1 ==========
+ # Gather activations on x_orig and x_new
+
+ # Note the use of names_filter for the run_with_cache function. Using it means we
+ # only cache the things we need (in this case, just attn head outputs).
+ z_name_filter = lambda name: name.endswith("z")
+ if new_cache is None:
+ _, new_cache = model.run_with_cache(new_dataset.toks, names_filter=z_name_filter, return_type=None)
+ if orig_cache is None:
+ _, orig_cache = model.run_with_cache(orig_dataset.toks, names_filter=z_name_filter, return_type=None)
+
+ # Note, the sender layer will always be before the final receiver layer, otherwise there will
+ # be no causal effect from sender -> receiver. So we only need to loop this far.
+ for sender_layer, sender_head in tqdm(list(product(range(max(receiver_layers)), range(model.cfg.n_heads)))):
+ # ========== Step 2 ==========
+ # Run on x_orig, with sender head patched from x_new, every other head frozen
+
+ hook_fn = partial(
+ patch_or_freeze_head_vectors,
+ new_cache=new_cache,
+ orig_cache=orig_cache,
+ head_to_patch=(sender_layer, sender_head),
+ )
+ model.add_hook(z_name_filter, hook_fn, level=1)
+
+ _, patched_cache = model.run_with_cache(
+ orig_dataset.toks, names_filter=receiver_hook_names_filter, return_type=None
+ )
+ # model.reset_hooks(including_permanent=True)
+ assert set(patched_cache.keys()) == set(receiver_hook_names)
+
+ # ========== Step 3 ==========
+ # Run on x_orig, patching in the receiver node(s) from the previously cached value
+
+ hook_fn = partial(
+ patch_head_input,
+ patched_cache=patched_cache,
+ head_list=receiver_heads,
+ )
+ patched_logits = model.run_with_hooks(
+ orig_dataset.toks, fwd_hooks=[(receiver_hook_names_filter, hook_fn)], return_type="logits"
+ )
+
+ # Save the results
+ results[sender_layer, sender_head] = patching_metric(patched_logits)
+
+ return results
+
+ model.reset_hooks()
+
+ s_inhibition_value_path_patching_results = get_path_patch_head_to_heads(
+ receiver_heads=[(8, 6), (8, 10), (7, 9), (7, 3)], receiver_input="v", model=model, patching_metric=ioi_metric_2
+ )
+
+ imshow(
+ 100 * s_inhibition_value_path_patching_results,
+ title="Direct effect on S-Inhibition Heads' values",
+ labels={"x": "Head", "y": "Layer", "color": "Logit diff.
variation"},
+ width=600,
+ coloraxis=dict(colorbar_ticksuffix="%"),
+ )
+
+# %%
+
+
+def scatter_embedding_vs_attn(
+ attn_from_end_to_io: Float[Tensor, "batch"],
+ attn_from_end_to_s: Float[Tensor, "batch"],
+ projection_in_io_dir: Float[Tensor, "batch"],
+ projection_in_s_dir: Float[Tensor, "batch"],
+ layer: int,
+ head: int,
+):
+ scatter(
+ x=t.concat([attn_from_end_to_io, attn_from_end_to_s], dim=0),
+ y=t.concat([projection_in_io_dir, projection_in_s_dir], dim=0),
+ color=["IO"] * N + ["S"] * N,
+ title=f"Projection of the output of {layer}.{head} along the name
embedding vs attention probability on name",
+ title_x=0.5,
+ labels={"x": "Attn prob on name", "y": "Dot w Name Embed", "color": "Name type"},
+ color_discrete_sequence=["#72FF64", "#C9A5F7"],
+ width=650,
+ )
+
+
+if MAIN:
+
+ def calculate_and_show_scatter_embedding_vs_attn(
+ layer: int,
+ head: int,
+ cache: ActivationCache = ioi_cache,
+ dataset: IOIDataset = ioi_dataset,
+ ) -> None:
+ """
+ Creates and plots a figure equivalent to 3(c) in the paper.
+
+ This should involve computing the four 1D tensors:
+ attn_from_end_to_io
+ attn_from_end_to_s
+ projection_in_io_dir
+ projection_in_s_dir
+ and then calling the scatter_embedding_vs_attn function.
+ """
+ # Get the value written to the residual stream at the end token by this head
+ z = cache[utils.get_act_name("z", layer)][:, :, head] # [batch seq d_head]
+ N = z.size(0)
+ output = z @ model.W_O[layer, head] # [batch seq d_model]
+ output_on_end_token = output[t.arange(N), dataset.word_idx["end"]] # [batch d_model]
+
+ # Get the directions we'll be projecting onto
+ io_unembedding = model.W_U.T[dataset.io_tokenIDs] # [batch d_model]
+ s_unembedding = model.W_U.T[dataset.s_tokenIDs] # [batch d_model]
+
+ # Get the value of projections, by multiplying and summing over the d_model dimension
+ projection_in_io_dir = (output_on_end_token * io_unembedding).sum(-1) # [batch]
+ projection_in_s_dir = (output_on_end_token * s_unembedding).sum(-1) # [batch]
+
+ # Get attention probs, and index to get the probabilities from END -> IO / S
+ attn_probs = cache["pattern", layer][:, head] # [batch seqQ seqK]
+ attn_from_end_to_io = attn_probs[t.arange(N), dataset.word_idx["end"], dataset.word_idx["IO"]] # [batch]
+ attn_from_end_to_s = attn_probs[t.arange(N), dataset.word_idx["end"], dataset.word_idx["S1"]] # [batch]
+
+ # Show scatter plot
+ scatter_embedding_vs_attn(
+ attn_from_end_to_io, attn_from_end_to_s, projection_in_io_dir, projection_in_s_dir, layer, head
+ )
+
+ calculate_and_show_scatter_embedding_vs_attn(9, 9) # name mover head 9.9
+
+ calculate_and_show_scatter_embedding_vs_attn(11, 10) # negative name mover head 11.10
+
+# %%
+
+
+def get_copying_scores(model: HookedTransformer, k: int = 5, names: list = NAMES) -> Float[Tensor, "2 layer-1 head"]:
+ """
+ Gets copying scores (both positive and negative) as described in page 6 of the IOI paper, for every (layer, head)
+ pair in the model.
+
+ Returns these in a 3D tensor (the first dimension is for positive vs negative).
+
+ Omits the 0th layer, because this is before MLP0 (which we're claiming acts as an extended embedding).
+ """
+ results = t.zeros((2, model.cfg.n_layers, model.cfg.n_heads), device=device)
+
+ # Define components from our model (for typechecking, and cleaner code)
+ embed: Embed = model.embed
+ mlp0: MLP = model.blocks[0].mlp
+ ln0: LayerNorm = model.blocks[0].ln2
+ unembed: Unembed = model.unembed
+ ln_final: LayerNorm = model.ln_final
+
+ # Get embeddings for the names in our list
+ name_tokens: Int[Tensor, "batch 1"] = model.to_tokens(names, prepend_bos=False)
+ name_embeddings: Int[Tensor, "batch 1 d_model"] = embed(name_tokens)
+
+ # Get residual stream after applying MLP
+ resid_after_mlp1 = name_embeddings + mlp0(ln0(name_embeddings))
+
+ # Loop over all (layer, head) pairs
+ for layer in range(1, model.cfg.n_layers):
+ for head in range(model.cfg.n_heads):
+ # Get W_OV matrix
+ W_OV = model.W_V[layer, head] @ model.W_O[layer, head]
+
+ # Get residual stream after applying W_OV or -W_OV respectively
+ # (note, because of bias b_U, it matters that we do sign flip here, not later)
+ resid_after_OV_pos = resid_after_mlp1 @ W_OV
+ resid_after_OV_neg = resid_after_mlp1 @ -W_OV
+
+ # Get logits from value of residual stream
+ logits_pos = unembed(ln_final(resid_after_OV_pos)).squeeze() # [batch d_vocab]
+ logits_neg = unembed(ln_final(resid_after_OV_neg)).squeeze() # [batch d_vocab]
+
+ # Check how many are in top k
+ topk_logits: Int[Tensor, "batch k"] = t.topk(logits_pos, dim=-1, k=k).indices
+ in_topk = (topk_logits == name_tokens).any(-1)
+ # Check how many are in bottom k
+ bottomk_logits: Int[Tensor, "batch k"] = t.topk(logits_neg, dim=-1, k=k).indices
+ in_bottomk = (bottomk_logits == name_tokens).any(-1)
+
+ # Fill in results
+ results[:, layer - 1, head] = t.tensor([in_topk.float().mean(), in_bottomk.float().mean()])
+
+ return results
+
+
+if MAIN:
+ copying_results = get_copying_scores(model)
+
+ imshow(
+ copying_results,
+ facet_col=0,
+ facet_labels=["Positive copying scores", "Negative copying scores"],
+ title="Copying scores of attention heads' OV circuits",
+ width=900,
+ )
+
+ heads = {"name mover": [(9, 9), (10, 0), (9, 6)], "negative name mover": [(10, 7), (11, 10)]}
+
+ for i, name in enumerate(["name mover", "negative name mover"]):
+ make_table(
+ title=f"Copying Scores ({name} heads)",
+ colnames=["Head", "Score"],
+ cols=[
+ list(map(str, heads[name])) + ["[dark_orange bold]Average"],
+ [f"{copying_results[i, layer - 1, head]:.2%}" for (layer, head) in heads[name]]
+ + [f"[dark_orange bold]{copying_results[i].mean():.2%}"],
+ ],
+ )
+
+# %%
+
+
+def generate_repeated_tokens(
+ model: HookedTransformer, seq_len: int, batch: int = 1
+) -> Float[Tensor, "batch 2*seq_len"]:
+ """
+ Generates a sequence of repeated random tokens (no start token).
+ """
+ rep_tokens_half = t.randint(0, model.cfg.d_vocab, (batch, seq_len), dtype=t.int64)
+ rep_tokens = t.cat([rep_tokens_half, rep_tokens_half], dim=-1).to(device)
+ return rep_tokens
+
+
+def get_attn_scores(
+ model: HookedTransformer, seq_len: int, batch: int, head_type: Literal["duplicate", "prev", "induction"]
+) -> Float[Tensor, "n_layers n_heads"]:
+ """
+ Returns attention scores for sequence of duplicated tokens, for every head.
+ """
+ rep_tokens = generate_repeated_tokens(model, seq_len, batch)
+
+ _, cache = model.run_with_cache(rep_tokens, return_type=None, names_filter=lambda name: name.endswith("pattern"))
+
+ # Get the right indices for the attention scores
+
+ if head_type == "duplicate":
+ src_indices = range(seq_len)
+ dest_indices = range(seq_len, 2 * seq_len)
+ elif head_type == "prev":
+ src_indices = range(seq_len)
+ dest_indices = range(1, seq_len + 1)
+ elif head_type == "induction":
+ dest_indices = range(seq_len, 2 * seq_len)
+ src_indices = range(1, seq_len + 1)
+
+ results = t.zeros(model.cfg.n_layers, model.cfg.n_heads, device=device, dtype=t.float32)
+ for layer in range(model.cfg.n_layers):
+ for head in range(model.cfg.n_heads):
+ attn_scores = cache["pattern", layer] # [batch seqQ seqK]
+ avg_attn_on_duplicates = attn_scores[:, head, dest_indices, src_indices].mean().item()
+ results[layer, head] = avg_attn_on_duplicates
+
+ return results
+
+
+def plot_early_head_validation_results(seq_len: int = 50, batch: int = 50):
+ """
+ Produces a plot that looks like Figure 18 in the paper.
+ """
+ head_types = ["duplicate", "prev", "induction"]
+
+ results = t.stack([get_attn_scores(model, seq_len, batch, head_type=head_type) for head_type in head_types])
+
+ imshow(
+ results,
+ facet_col=0,
+ facet_labels=[
+ f"{head_type.capitalize()} token attention prob.
on sequences of random tokens"
+ for head_type in head_types
+ ],
+ labels={"x": "Head", "y": "Layer"},
+ width=1300,
+ )
+
+
+if MAIN:
+ model.reset_hooks()
+ plot_early_head_validation_results()
+
+# %%
+
+CIRCUIT = {
+ "name mover": [(9, 9), (10, 0), (9, 6)],
+ "backup name mover": [(10, 10), (10, 6), (10, 2), (10, 1), (11, 2), (9, 7), (9, 0), (11, 9)],
+ "negative name mover": [(10, 7), (11, 10)],
+ "s2 inhibition": [(7, 3), (7, 9), (8, 6), (8, 10)],
+ "induction": [(5, 5), (5, 8), (5, 9), (6, 9)],
+ "duplicate token": [(0, 1), (0, 10), (3, 0)],
+ "previous token": [(2, 2), (4, 11)],
+}
+
+SEQ_POS_TO_KEEP = {
+ "name mover": "end",
+ "backup name mover": "end",
+ "negative name mover": "end",
+ "s2 inhibition": "end",
+ "induction": "S2",
+ "duplicate token": "S2",
+ "previous token": "S1+1",
+}
+
+# %%
+
+
+def get_heads_and_posns_to_keep(
+ means_dataset: IOIDataset,
+ model: HookedTransformer,
+ circuit: dict[str, list[tuple[int, int]]],
+ seq_pos_to_keep: dict[str, str],
+) -> dict[int, Bool[Tensor, "batch seq head"]]:
+ """
+ Returns a dictionary mapping layers to a boolean mask giving the indices of the z output which *shouldn't* be
+ mean-ablated.
+
+ The output of this function will be used for the hook function that does ablation.
+ """
+ heads_and_posns_to_keep = {}
+ batch, seq, n_heads = len(means_dataset), means_dataset.max_len, model.cfg.n_heads
+
+ for layer in range(model.cfg.n_layers):
+ mask = t.zeros(size=(batch, seq, n_heads))
+
+ for head_type, head_list in circuit.items():
+ seq_pos = seq_pos_to_keep[head_type]
+ indices = means_dataset.word_idx[seq_pos]
+ for layer_idx, head_idx in head_list:
+ if layer_idx == layer:
+ mask[:, indices, head_idx] = 1
+
+ heads_and_posns_to_keep[layer] = mask.bool()
+
+ return heads_and_posns_to_keep
+
+
+def hook_fn_mask_z(
+ z: Float[Tensor, "batch seq head d_head"],
+ hook: HookPoint,
+ heads_and_posns_to_keep: dict[int, Bool[Tensor, "batch seq head"]],
+ means: Float[Tensor, "layer batch seq head d_head"],
+) -> Float[Tensor, "batch seq head d_head"]:
+ """
+ Hook function which masks the z output of a transformer head.
+
+ heads_and_posns_to_keep
+ dict created with the get_heads_and_posns_to_keep function. This tells us where to mask.
+
+ means
+ Tensor of mean z values of the means_dataset over each group of prompts with the same template. This tells us
+ what values to mask with.
+ """
+ # Get the mask for this layer, and add d_head=1 dimension so it broadcasts correctly
+ mask_for_this_layer = heads_and_posns_to_keep[hook.layer()].unsqueeze(-1).to(z.device)
+
+ # Set z values to the mean
+ z = t.where(mask_for_this_layer, z, means[hook.layer()])
+
+ return z
+
+
+def compute_means_by_template(
+ means_dataset: IOIDataset, model: HookedTransformer
+) -> Float[Tensor, "layer batch seq head_idx d_head"]:
+ """
+ Returns the mean of each head's output over the means dataset. This mean is computed separately for each group of
+ prompts with the same template (these are given by means_dataset.groups).
+ """
+ # Cache the outputs of every head
+ _, means_cache = model.run_with_cache(
+ means_dataset.toks.long(),
+ return_type=None,
+ names_filter=lambda name: name.endswith("z"),
+ )
+ # Create tensor to store means
+ n_layers, n_heads, d_head = model.cfg.n_layers, model.cfg.n_heads, model.cfg.d_head
+ batch, seq_len = len(means_dataset), means_dataset.max_len
+ means = t.zeros(size=(n_layers, batch, seq_len, n_heads, d_head), device=model.cfg.device)
+
+ # Get set of different templates for this data
+ for layer in range(model.cfg.n_layers):
+ z_for_this_layer = means_cache[utils.get_act_name("z", layer)] # [batch seq head d_head]
+ for template_group in means_dataset.groups:
+ z_for_this_template = z_for_this_layer[template_group]
+ z_means_for_this_template = einops.reduce(
+ z_for_this_template, "batch seq head d_head -> seq head d_head", "mean"
+ )
+ means[layer, template_group] = z_means_for_this_template
+
+ return means
+
+
+def add_mean_ablation_hook(
+ model: HookedTransformer,
+ means_dataset: IOIDataset,
+ circuit: dict[str, list[tuple[int, int]]] = CIRCUIT,
+ seq_pos_to_keep: dict[str, str] = SEQ_POS_TO_KEEP,
+ is_permanent: bool = True,
+) -> HookedTransformer:
+ """
+ Adds a permanent hook to the model, which ablates according to the circuit and seq_pos_to_keep dictionaries.
+
+ In other words, when the model is run on ioi_dataset, every head's output will be replaced with the mean over
+ means_dataset for sequences with the same template, except for a subset of heads and sequence positions as specified
+ by the circuit and seq_pos_to_keep dicts.
+ """
+ model.reset_hooks(including_permanent=True)
+
+ # Compute the mean of each head's output on the ABC dataset, grouped by template
+ means = compute_means_by_template(means_dataset, model)
+
+ # Convert this into a boolean map
+ heads_and_posns_to_keep = get_heads_and_posns_to_keep(means_dataset, model, circuit, seq_pos_to_keep)
+
+ # Get a hook function which will patch in the mean z values for each head, at
+ # all positions which aren't important for the circuit
+ hook_fn = partial(hook_fn_mask_z, heads_and_posns_to_keep=heads_and_posns_to_keep, means=means)
+
+ # Apply hook
+ model.add_hook(lambda name: name.endswith("z"), hook_fn, is_permanent=is_permanent)
+
+ return model
+
+
+# %%
+
+if MAIN:
+ import ARENA_files.ioi_circuit_extraction as ioi_circuit_extraction
+
+ model = ioi_circuit_extraction.add_mean_ablation_hook(
+ model,
+ means_dataset=abc_dataset,
+ circuit=CIRCUIT,
+ seq_pos_to_keep=SEQ_POS_TO_KEEP,
+ )
+ ioi_logits_minimal = model(ioi_dataset.toks)
+
+ print(f"""Average logit difference (IOI dataset, using entire model): {logits_to_ave_logit_diff_2(ioi_logits_original):.4f}
+ Average logit difference (IOI dataset, only using circuit): {logits_to_ave_logit_diff_2(ioi_logits_minimal):.4f}""")
+
+# %%
+
+if MAIN:
+ model = add_mean_ablation_hook(
+ model,
+ means_dataset=abc_dataset,
+ circuit=CIRCUIT,
+ seq_pos_to_keep=SEQ_POS_TO_KEEP,
+ )
+ ioi_logits_minimal = model(ioi_dataset.toks)
+
+ print(f"""Average logit difference (IOI dataset, using entire model): {logits_to_ave_logit_diff_2(ioi_logits_original):.4f}
+ Average logit difference (IOI dataset, only using circuit): {logits_to_ave_logit_diff_2(ioi_logits_minimal):.4f}""")
+
+# %%
+
+K_FOR_EACH_COMPONENT = {
+ (9, 9): set(),
+ (10, 0): {(9, 9)},
+ (9, 6): {(9, 9), (10, 0)},
+ (10, 7): {(11, 10)},
+ (11, 10): {(10, 7)},
+ (8, 10): {(7, 9), (8, 6), (7, 3)},
+ (7, 9): {(8, 10), (8, 6), (7, 3)},
+ (8, 6): {(7, 9), (8, 10), (7, 3)},
+ (7, 3): {(7, 9), (8, 10), (8, 6)},
+ (5, 5): {(5, 9), (6, 9), (5, 8)},
+ (5, 9): {(11, 10), (10, 7)},
+ (6, 9): {(5, 9), (5, 5), (5, 8)},
+ (5, 8): {(11, 10), (10, 7)},
+ (0, 1): {(0, 10), (3, 0)},
+ (0, 10): {(0, 1), (3, 0)},
+ (3, 0): {(0, 1), (0, 10)},
+ (4, 11): {(2, 2)},
+ (2, 2): {(4, 11)},
+ (11, 2): {(9, 9), (10, 0), (9, 6)},
+ (10, 6): {(9, 9), (10, 0), (9, 6), (11, 2)},
+ (10, 10): {(9, 9), (10, 0), (9, 6), (11, 2), (10, 6)},
+ (10, 2): {(9, 9), (10, 0), (9, 6), (11, 2), (10, 6), (10, 10)},
+ (9, 7): {(9, 9), (10, 0), (9, 6), (11, 2), (10, 6), (10, 10), (10, 2)},
+ (10, 1): {(9, 9), (10, 0), (9, 6), (11, 2), (10, 6), (10, 10), (10, 2), (9, 7)},
+ (11, 9): {(9, 9), (10, 0), (9, 6), (9, 0)},
+ (9, 0): {(9, 9), (10, 0), (9, 6), (11, 9)},
+}
+
+# %%
+
+
+def plot_minimal_set_results(minimality_scores: dict[tuple[int, int], float]):
+ """
+ Plots the minimality results, in a way resembling figure 7 in the paper.
+
+ minimality_scores:
+ dict with elements like (9, 9): minimality score for head 9.9 (as described
+ in section 4.2 of the paper)
+ """
+
+ CIRCUIT_reversed = {head: k for k, v in CIRCUIT.items() for head in v}
+ colors = [CIRCUIT_reversed[head].capitalize() + " head" for head in minimality_scores.keys()]
+ color_sequence = [px.colors.qualitative.Dark2[i] for i in [0, 1, 2, 5, 3, 6]] + ["#BAEA84"]
+
+ bar(
+ list(minimality_scores.values()),
+ x=list(map(str, minimality_scores.keys())),
+ labels={"x": "Attention head", "y": "Change in logit diff", "color": "Head type"},
+ color=colors,
+ template="ggplot2",
+ color_discrete_sequence=color_sequence,
+ bargap=0.02,
+ yaxis_tickformat=".0%",
+ legend_title_text="",
+ title="Plot of minimality scores (as percentages of full model logit diff)",
+ width=800,
+ hovermode="x unified",
+ )
+
+
+# %%
+
+
+def get_score(
+ model: HookedTransformer,
+ ioi_dataset: IOIDataset,
+ abc_dataset: IOIDataset,
+ K: set[tuple[int, int]],
+ C: dict[str, list[tuple[int, int]]],
+) -> float:
+ """
+ Returns the value F(C \ K), where F is the logit diff, C is the core circuit, and K is the set of circuit components
+ to remove.
+ """
+ C_excl_K = {k: [head for head in v if head not in K] for k, v in C.items()}
+ model = add_mean_ablation_hook(model, abc_dataset, C_excl_K, SEQ_POS_TO_KEEP)
+ logits = model(ioi_dataset.toks)
+ score = logits_to_ave_logit_diff_2(logits, ioi_dataset).item()
+
+ return score
+
+
+def get_minimality_score(
+ model: HookedTransformer,
+ ioi_dataset: IOIDataset,
+ abc_dataset: IOIDataset,
+ v: tuple[int, int],
+ K: set[tuple[int, int]],
+ C: dict[str, list[tuple[int, int]]] = CIRCUIT,
+) -> float:
+ """
+ Returns the value | F(C \ K_union_v) - F(C | K) |, where F is the logit diff, C is the core circuit, K is the set of
+ circuit components to remove, and v is a head (not in K).
+ """
+ assert v not in K
+ K_union_v = K | {v}
+ C_excl_K_score = get_score(model, ioi_dataset, abc_dataset, K, C)
+ C_excl_Kv_score = get_score(model, ioi_dataset, abc_dataset, K_union_v, C)
+
+ return abs(C_excl_K_score - C_excl_Kv_score)
+
+
+if MAIN:
+
+ def get_all_minimality_scores(
+ model: HookedTransformer,
+ ioi_dataset: IOIDataset = ioi_dataset,
+ abc_dataset: IOIDataset = abc_dataset,
+ k_for_each_component: dict = K_FOR_EACH_COMPONENT,
+ ) -> dict[tuple[int, int], float]:
+ """
+ Returns dict of minimality scores for every head in the model (as
+ a fraction of F(M), the logit diff of the full model).
+
+ Warning - this resets all hooks at the end (including permanent).
+ """
+ # Get full circuit score F(M), to divide minimality scores by
+ model.reset_hooks(including_permanent=True)
+ logits = model(ioi_dataset.toks)
+ full_circuit_score = logits_to_ave_logit_diff_2(logits, ioi_dataset).item()
+
+ # Get all minimality scores, using the `get_minimality_score` function
+ minimality_scores = {}
+ for v, K in tqdm(k_for_each_component.items()):
+ score = get_minimality_score(model, ioi_dataset, abc_dataset, v, K)
+ minimality_scores[v] = score / full_circuit_score
+
+ model.reset_hooks(including_permanent=True)
+
+ return minimality_scores
+
+ minimality_scores = get_all_minimality_scores(model)
+ plot_minimal_set_results(minimality_scores)
+
+# %%
+
+if MAIN:
+ model.reset_hooks(including_permanent=True)
+
+ attn_heads = [(5, 5), (6, 9)]
+
+ # Get repeating sequences (note we could also take mean over larger batch)
+ batch = 1
+ seq_len = 15
+ rep_tokens = generate_repeated_tokens(model, seq_len, batch)
+
+ # Run cache (we only need attention patterns for layers 5 and 6)
+ _, cache = model.run_with_cache(
+ rep_tokens,
+ return_type=None,
+ names_filter=lambda name: name.endswith("pattern") and any(f".{layer}." in name for layer, head in attn_heads),
+ )
+
+ # Display results
+ attn = t.stack([cache["pattern", layer][0, head] for (layer, head) in attn_heads])
+ cv.attention.attention_patterns(
+ tokens=model.to_str_tokens(rep_tokens[0]),
+ attention=attn,
+ attention_head_names=[f"{layer}.{head}" for (layer, head) in attn_heads],
+ )
+
+# %%
+
+if MAIN:
+ model.reset_hooks(including_permanent=True)
+
+ induction_head_key_path_patching_results = get_path_patch_head_to_heads(
+ receiver_heads=[(5, 5), (6, 9)], receiver_input="k", model=model, patching_metric=ioi_metric_2
+ )
+
+ imshow(
+ 100 * induction_head_key_path_patching_results,
+ title="Direct effect on Induction Heads' keys",
+ labels={"x": "Head", "y": "Layer", "color": "Logit diff.
variation"},
+ coloraxis=dict(colorbar_ticksuffix="%"),
+ width=600,
+ )
+
+# %%
+
+if MAIN:
+ model.reset_hooks(including_permanent=True)
+
+ ioi_logits, ioi_cache = model.run_with_cache(ioi_dataset.toks)
+ original_average_logit_diff = logits_to_ave_logit_diff_2(ioi_logits)
+
+ s_unembeddings = model.W_U.T[ioi_dataset.s_tokenIDs]
+ io_unembeddings = model.W_U.T[ioi_dataset.io_tokenIDs]
+ logit_diff_directions = io_unembeddings - s_unembeddings # [batch d_model]
+
+ per_head_residual, labels = ioi_cache.stack_head_results(layer=-1, return_labels=True)
+ per_head_residual = einops.rearrange(
+ per_head_residual[:, t.arange(len(ioi_dataset)).to(device), ioi_dataset.word_idx["end"].to(device)],
+ "(layer head) batch d_model -> layer head batch d_model",
+ layer=model.cfg.n_layers,
+ )
+
+ per_head_logit_diffs = residual_stack_to_logit_diff(per_head_residual, ioi_cache, logit_diff_directions)
+
+ top_layer, top_head = topk_of_Nd_tensor(per_head_logit_diffs, k=1)[0]
+ print(f"Top Name Mover to ablate: {top_layer}.{top_head}")
+
+ # Getting means we can use to ablate
+ abc_means = ioi_circuit_extraction.compute_means_by_template(abc_dataset, model)[top_layer]
+
+ # Define hook function and add to model
+ def ablate_top_head_hook(z: Float[Tensor, "batch pos head_index d_head"], hook):
+ """
+ Ablates hook by patching in results
+ """
+ z[range(len(ioi_dataset)), ioi_dataset.word_idx["end"], top_head] = abc_means[
+ range(len(ioi_dataset)), ioi_dataset.word_idx["end"], top_head
+ ]
+ return z
+
+ model.add_hook(utils.get_act_name("z", top_layer), ablate_top_head_hook)
+
+ # Run the model, temporarily adds caching hooks and then removes *all* hooks after running, including the ablation hook.
+ ablated_logits, ablated_cache = model.run_with_cache(ioi_dataset.toks)
+ rprint(
+ "\n".join(
+ [
+ f"{original_average_logit_diff:.4f} = Original logit diff",
+ f"{per_head_logit_diffs[top_layer, top_head]:.4f} = Direct Logit Attribution of top name mover head",
+ f"{original_average_logit_diff - per_head_logit_diffs[top_layer, top_head]:.4f} = Naive prediction of post ablation logit diff",
+ f"{logits_to_ave_logit_diff_2(ablated_logits):.4f} = Logit diff after ablating L{top_layer}H{top_head}",
+ ]
+ )
+ )
+
+# %%
+
+if MAIN:
+ per_head_ablated_residual, labels = ablated_cache.stack_head_results(layer=-1, return_labels=True)
+ per_head_ablated_residual = einops.rearrange(
+ per_head_ablated_residual[:, t.arange(len(ioi_dataset)).to(device), ioi_dataset.word_idx["end"].to(device)],
+ "(layer head) batch d_model -> layer head batch d_model",
+ layer=model.cfg.n_layers,
+ )
+ per_head_ablated_logit_diffs = residual_stack_to_logit_diff(
+ per_head_ablated_residual, ablated_cache, logit_diff_directions
+ )
+ per_head_ablated_logit_diffs = per_head_ablated_logit_diffs.reshape(model.cfg.n_layers, model.cfg.n_heads)
+
+ imshow(
+ t.stack(
+ [per_head_logit_diffs, per_head_ablated_logit_diffs, per_head_ablated_logit_diffs - per_head_logit_diffs]
+ ),
+ title="Direct logit contribution by head, pre / post ablation",
+ labels={"x": "Head", "y": "Layer"},
+ facet_col=0,
+ facet_labels=["No ablation", "9.9 is ablated", "Change in head contribution post-ablation"],
+ width=1200,
+ )
+
+ scatter(
+ y=per_head_logit_diffs.flatten(),
+ x=per_head_ablated_logit_diffs.flatten(),
+ hover_name=labels,
+ range_x=(-1, 1),
+ range_y=(-2, 2),
+ labels={"x": "Ablated", "y": "Original"},
+ title="Original vs Post-Ablation Direct Logit Attribution of Heads",
+ width=600,
+ add_line="y=x",
+ )
+
+# %%
+
+if MAIN:
+ ln_scaling_no_ablation = ioi_cache["ln_final.hook_scale"][
+ t.arange(len(ioi_dataset)), ioi_dataset.word_idx["end"]
+ ].squeeze()
+ ln_scaling_ablated = ablated_cache["ln_final.hook_scale"][
+ t.arange(len(ioi_dataset)), ioi_dataset.word_idx["end"]
+ ].squeeze()
+
+ scatter(
+ y=ln_scaling_ablated,
+ x=ln_scaling_no_ablation,
+ labels={"x": "No ablation", "y": "Ablation"},
+ title=f"Final LN scaling factors compared (ablation vs no ablation)
Average ratio = {(ln_scaling_no_ablation / ln_scaling_ablated).mean():.4f}",
+ width=700,
+ add_line="y=x",
+ )
+
+# %%
+
+if MAIN:
+ datasets: list[tuple[tuple, str, IOIDataset]] = [
+ ((0, 0), "original", ioi_dataset),
+ ((1, 0), "random token", ioi_dataset.gen_flipped_prompts("ABB->CDD, BAB->DCD")),
+ ((2, 0), "inverted token", ioi_dataset.gen_flipped_prompts("ABB->BAA, BAB->ABA")),
+ ((0, 1), "inverted position", ioi_dataset.gen_flipped_prompts("ABB->BAB, BAB->ABB")),
+ ((1, 1), "inverted position, random token", ioi_dataset.gen_flipped_prompts("ABB->DCD, BAB->CDD")),
+ ((2, 1), "inverted position, inverted token", ioi_dataset.gen_flipped_prompts("ABB->ABA, BAB->BAA")),
+ ]
+
+ results = t.zeros(3, 2).to(device)
+
+ s2_inhibition_heads = CIRCUIT["s2 inhibition"]
+ layers = set(layer for layer, head in s2_inhibition_heads)
+
+ names_filter = lambda name: name in [utils.get_act_name("z", layer) for layer in layers]
+
+ def patching_hook_fn(z: Float[Tensor, "batch seq head d_head"], hook: HookPoint, cache: ActivationCache):
+ heads_to_patch = [head for layer, head in s2_inhibition_heads if layer == hook.layer()]
+ z[:, :, heads_to_patch] = cache[hook.name][:, :, heads_to_patch]
+ return z
+
+ for (row, col), desc, dataset in datasets:
+ # Get cache of values from the modified dataset
+ _, cache_for_patching = model.run_with_cache(dataset.toks, names_filter=names_filter, return_type=None)
+
+ # Run model on IOI dataset, but patch S-inhibition heads with signals from modified dataset
+ patched_logits = model.run_with_hooks(
+ ioi_dataset.toks, fwd_hooks=[(names_filter, partial(patching_hook_fn, cache=cache_for_patching))]
+ )
+
+ # Get logit diff for patched results
+ # Note, we still use IOI dataset for our "correct answers" reference point
+ results[row, col] = logits_to_ave_logit_diff_2(patched_logits, ioi_dataset)
+
+ imshow(
+ results,
+ labels={"x": "Positional signal", "y": "Token signal"},
+ x=["Original", "Inverted"],
+ y=["Original", "Random", "Inverted"],
+ title="Logit diff after changing all S2 inhibition heads' output signals via patching",
+ text_auto=".2f",
+ width=700,
+ )
+
+# %%
+
+results = t.zeros(len(CIRCUIT["s2 inhibition"]), 3, 2).to(device)
+
+
+def patching_hook_fn(z: Float[Tensor, "batch seq head d_head"], hook: HookPoint, cache: ActivationCache, head: int):
+ z[:, :, head] = cache[hook.name][:, :, head]
+ return z
+
+
+if MAIN:
+ for i, (layer, head) in enumerate(CIRCUIT["s2 inhibition"]):
+ model.reset_hooks(including_permanent=True)
+
+ hook_name = utils.get_act_name("z", layer)
+
+ for (row, col), desc, dataset in datasets:
+ # Get cache of values from the modified dataset
+ _, cache_for_patching = model.run_with_cache(
+ dataset.toks, names_filter=lambda name: name == hook_name, return_type=None
+ )
+
+ # Run model on IOI dataset, but patch S-inhibition heads with signals from modified dataset
+ patched_logits = model.run_with_hooks(
+ ioi_dataset.toks,
+ fwd_hooks=[(hook_name, partial(patching_hook_fn, cache=cache_for_patching, head=head))],
+ )
+
+ # Get logit diff for patched results
+ # Note, we still use IOI dataset for our "correct answers" reference point
+ results[i, row, col] = logits_to_ave_logit_diff_2(patched_logits, ioi_dataset)
+
+ imshow(
+ (results - results[0, 0, 0]) / results[0, 0, 0],
+ labels={"x": "Positional signal", "y": "Token signal"},
+ x=["Original", "Inverted"],
+ y=["Original", "Random", "Inverted"],
+ title="Logit diff after patching individual S2 inhibition heads (as proportion of clean logit diff)",
+ facet_col=0,
+ facet_labels=[f"{layer}.{head}" for (layer, head) in CIRCUIT["s2 inhibition"]],
+ facet_col_spacing=0.08,
+ width=1100,
+ text_auto=".2f",
+ )
+
+# %%
diff --git a/ARENA_files/__pycache__/arena_balanced_bracket_classifier_datasets.cpython-310.pyc b/ARENA_files/__pycache__/arena_balanced_bracket_classifier_datasets.cpython-310.pyc
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diff --git a/ARENA_files/arena_balanced_bracket_classifier_datasets.py b/ARENA_files/arena_balanced_bracket_classifier_datasets.py
new file mode 100644
index 0000000..ae40e95
--- /dev/null
+++ b/ARENA_files/arena_balanced_bracket_classifier_datasets.py
@@ -0,0 +1,115 @@
+# %%
+
+from typing import Union
+
+import torch as t
+from jaxtyping import Int
+from torch import Tensor
+
+device = t.device("cpu")
+
+MAIN = __name__ == "__main__"
+# %%
+
+
+class SimpleTokenizer:
+ START_TOKEN = 0
+ PAD_TOKEN = 1
+ END_TOKEN = 2
+ base_d = {"[start]": START_TOKEN, "[pad]": PAD_TOKEN, "[end]": END_TOKEN}
+
+ def __init__(self, alphabet: str):
+ self.alphabet = alphabet
+ # the 3 is because there are 3 special tokens (defined just above)
+ self.t_to_i = {**{c: i + 3 for i, c in enumerate(alphabet)}, **self.base_d}
+ self.i_to_t = {i: c for c, i in self.t_to_i.items()}
+
+ def tokenize(self, strs: list[str], max_len=None) -> Int[Tensor, "batch seq"]:
+ def c_to_int(c: str) -> int:
+ if c in self.t_to_i:
+ return self.t_to_i[c]
+ else:
+ raise ValueError(c)
+
+ if isinstance(strs, str):
+ strs = [strs]
+
+ if max_len is None:
+ max_len = max((max(len(s) for s in strs), 1))
+
+ ints = [
+ [self.START_TOKEN]
+ + [c_to_int(c) for c in s]
+ + [self.END_TOKEN]
+ + [self.PAD_TOKEN] * (max_len - len(s))
+ for s in strs
+ ]
+ return t.tensor(ints)
+
+ def decode(self, tokens) -> list[str]:
+ assert tokens.ndim >= 2, "Need to have a batch dimension"
+
+ def int_to_c(c: int) -> str:
+ if c < len(self.i_to_t):
+ return self.i_to_t[c]
+ else:
+ raise ValueError(c)
+
+ return [
+ "".join(
+ int_to_c(i.item()) for i in seq[1:] if i != self.PAD_TOKEN and i != self.END_TOKEN
+ )
+ for seq in tokens
+ ]
+
+ def __repr__(self) -> str:
+ return f"SimpleTokenizer({self.alphabet!r})"
+
+# %%
+
+tokenizer = SimpleTokenizer("()")
+
+class BracketsDataset:
+ """A dataset containing sequences, is_balanced labels, and tokenized sequences"""
+
+ def __init__(self, data_tuples: list):
+ """
+ data_tuples is list[tuple[str, bool]] signifying sequence and label
+ """
+ self.tokenizer = SimpleTokenizer("()")
+ self.strs = [x[0] for x in data_tuples]
+ self.isbal = t.tensor([x[1] for x in data_tuples])
+ self.toks = self.tokenizer.tokenize(self.strs)
+ self.open_proportion = t.tensor([s.count("(") / len(s) for s in self.strs])
+ self.starts_open = t.tensor([s[0] == "(" for s in self.strs]).bool()
+
+ def __len__(self) -> int:
+ return len(self.strs)
+
+ def __getitem__(self, idx) -> "BracketsDataset | tuple[str, t.Tensor, t.Tensor]":
+ if isinstance(idx, slice):
+ return self.__class__(list(zip(self.strs[idx], self.isbal[idx])))
+ return (self.strs[idx], self.isbal[idx], self.toks[idx])
+
+ def to(self, device) -> "BracketsDataset":
+ self.isbal = self.isbal.to(device)
+ self.toks = self.toks.to(device)
+ self.open_proportion = self.open_proportion.to(device)
+ self.starts_open = self.starts_open.to(device)
+ return self
+
+ @property
+ def seq_length(self) -> int:
+ return self.toks.size(-1)
+
+ @classmethod
+ def with_length(
+ cls, data_tuples: list[tuple[str, bool]], selected_len: int
+ ) -> "BracketsDataset":
+ return cls([(s, b) for (s, b) in data_tuples if len(s) == selected_len])
+
+ @classmethod
+ def with_start_char(
+ cls, data_tuples: list[tuple[str, bool]], start_char: str
+ ) -> "BracketsDataset":
+ return cls([(s, b) for (s, b) in data_tuples if s[0] == start_char])
diff --git a/ARENA_files/arena_part41_ioi_tests.py b/ARENA_files/arena_part41_ioi_tests.py
new file mode 100644
index 0000000..9abfe42
--- /dev/null
+++ b/ARENA_files/arena_part41_ioi_tests.py
@@ -0,0 +1,32 @@
+
+import sys
+from pathlib import Path
+from typing import Callable
+
+import torch as t
+
+# Make sure exercises are in the path
+if str(exercises_dir := Path(__file__).parent.parent) not in sys.path:
+ sys.path.append(str(exercises_dir))
+
+
+def test_logits_to_ave_logit_diff(logits_to_ave_logit_diff: Callable):
+ batch = 4
+ seq = 5
+ d_vocab = 6
+ logits = t.randn(batch, seq, d_vocab)
+ answer_tokens = t.randint(0, d_vocab, (batch, 2))
+
+ actual = logits_to_ave_logit_diff(logits, answer_tokens, per_prompt=True)
+ # expected = solutions.logits_to_ave_logit_diff(logits, answer_tokens, per_prompt=True)
+ final_logits = logits[:, -1, :]
+ answer_logits = final_logits.gather(dim=-1, index=answer_tokens)
+ correct_logits, incorrect_logits = answer_logits.unbind(dim=-1)
+ expected = correct_logits - incorrect_logits
+ t.testing.assert_close(actual, expected)
+
+ actual = logits_to_ave_logit_diff(logits, answer_tokens)
+ # expected = solutions.logits_to_ave_logit_diff(logits, answer_tokens)
+ t.testing.assert_close(actual, expected.mean())
+
+ print("All tests in `test_logits_to_ave_logit_diff` passed!")
diff --git a/ARENA_files/arena_plotly_utils.py b/ARENA_files/arena_plotly_utils.py
new file mode 100644
index 0000000..346e6bc
--- /dev/null
+++ b/ARENA_files/arena_plotly_utils.py
@@ -0,0 +1,652 @@
+import re
+
+import einops
+import numpy as np
+import pandas as pd
+import plotly.express as px
+import plotly.graph_objects as go
+import torch as t
+from jaxtyping import Float
+from plotly.subplots import make_subplots
+from torch import Tensor
+
+
+def to_numpy(tensor):
+ """
+ Helper function to convert a tensor to a numpy array. Also works on lists, tuples, and numpy arrays.
+ """
+ if isinstance(tensor, np.ndarray):
+ return tensor
+ elif isinstance(tensor, (list, tuple)):
+ array = np.array(tensor)
+ return array
+ elif isinstance(tensor, (t.Tensor, t.nn.parameter.Parameter)):
+ return tensor.detach().cpu().numpy()
+ elif isinstance(tensor, (int, float, bool, str)):
+ return np.array(tensor)
+ else:
+ raise ValueError(f"Input to to_numpy has invalid type: {type(tensor)}")
+
+
+# ! GENERIC PLOTTING FUNCTIONS
+
+update_layout_set = {
+ "xaxis_range",
+ "yaxis_range",
+ "hovermode",
+ "xaxis_title",
+ "yaxis_title",
+ "colorbar",
+ "colorscale",
+ "coloraxis",
+ "title_x",
+ "bargap",
+ "bargroupgap",
+ "xaxis_tickformat",
+ "yaxis_tickformat",
+ "title_y",
+ "legend_title_text",
+ "xaxis_showgrid",
+ "xaxis_gridwidth",
+ "xaxis_gridcolor",
+ "yaxis_showgrid",
+ "yaxis_gridwidth",
+ "yaxis_gridcolor",
+ "showlegend",
+ "xaxis_tickmode",
+ "yaxis_tickmode",
+ "margin",
+ "xaxis_visible",
+ "yaxis_visible",
+ "bargap",
+ "bargroupgap",
+ "coloraxis_showscale",
+ "xaxis_tickangle",
+ "yaxis_scaleanchor",
+ "xaxis_tickfont",
+ "yaxis_tickfont",
+}
+
+update_traces_set = {"textposition"}
+
+
+def imshow(tensor: t.Tensor, renderer=None, **kwargs):
+ kwargs_post = {k: v for k, v in kwargs.items() if k in update_layout_set}
+ kwargs_pre = {k: v for k, v in kwargs.items() if k not in update_layout_set}
+ if ("size" in kwargs_pre) or ("shape" in kwargs_pre):
+ size = kwargs_pre.pop("size", None) or kwargs_pre.pop("shape", None)
+ kwargs_pre["height"], kwargs_pre["width"] = size # type: ignore
+ facet_labels = kwargs_pre.pop("facet_labels", None)
+ border = kwargs_pre.pop("border", False)
+ return_fig = kwargs_pre.pop("return_fig", False)
+ text = kwargs_pre.pop("text", None)
+ xaxis_tickangle = kwargs_post.pop("xaxis_tickangle", None)
+ # xaxis_tickfont = kwargs_post.pop("xaxis_tickangle", None)
+ static = kwargs_pre.pop("static", False)
+ if "color_continuous_scale" not in kwargs_pre:
+ kwargs_pre["color_continuous_scale"] = "RdBu"
+ if "color_continuous_midpoint" not in kwargs_pre:
+ kwargs_pre["color_continuous_midpoint"] = 0.0
+ if "margin" in kwargs_post and isinstance(kwargs_post["margin"], int):
+ kwargs_post["margin"] = dict.fromkeys(list("tblr"), kwargs_post["margin"])
+ fig = px.imshow(to_numpy(tensor), **kwargs_pre).update_layout(**kwargs_post)
+ if facet_labels:
+ # Weird thing where facet col wrap means labels are in wrong order
+ if "facet_col_wrap" in kwargs_pre:
+ facet_labels = reorder_list_in_plotly_way(facet_labels, kwargs_pre["facet_col_wrap"])
+ for i, label in enumerate(facet_labels):
+ fig.layout.annotations[i]["text"] = label # type: ignore
+ if border:
+ fig.update_xaxes(showline=True, linewidth=1, linecolor="black", mirror=True)
+ fig.update_yaxes(showline=True, linewidth=1, linecolor="black", mirror=True)
+ if text:
+ if tensor.ndim == 2:
+ # if 2D, then we assume text is a list of lists of strings
+ assert isinstance(text[0], list)
+ assert isinstance(text[0][0], str)
+ text = [text]
+ else:
+ # if 3D, then text is either repeated for each facet, or different
+ assert isinstance(text[0], list)
+ if isinstance(text[0][0], str):
+ text = [text for _ in range(len(fig.data))]
+ for i, _text in enumerate(text):
+ fig.data[i].update(text=_text, texttemplate="%{text}", textfont={"size": 12})
+ # Very hacky way of fixing the fact that updating layout with xaxis_* only applies to first facet by default
+ if xaxis_tickangle is not None:
+ n_facets = 1 if tensor.ndim == 2 else tensor.shape[0]
+ for i in range(1, 1 + n_facets):
+ xaxis_name = "xaxis" if i == 1 else f"xaxis{i}"
+ fig.layout[xaxis_name]["tickangle"] = xaxis_tickangle # type: ignore
+ return fig if return_fig else fig.show(renderer=renderer, config={"staticPlot": static})
+
+
+def reorder_list_in_plotly_way(L: list, col_wrap: int):
+ """
+ Helper function, because Plotly orders figures in an annoying way when there's column wrap.
+ """
+ L_new = []
+ while len(L) > 0:
+ L_new.extend(L[-col_wrap:])
+ L = L[:-col_wrap]
+ return L_new
+
+
+def line(y: t.Tensor | list, renderer=None, **kwargs):
+ """
+ Edit to this helper function, allowing it to take args in update_layout (e.g. yaxis_range).
+ """
+ kwargs_post = {k: v for k, v in kwargs.items() if k in update_layout_set}
+ kwargs_pre = {k: v for k, v in kwargs.items() if k not in update_layout_set}
+ if ("size" in kwargs_pre) or ("shape" in kwargs_pre):
+ size = kwargs_pre.pop("size", None) or kwargs_pre.pop("shape", None)
+ kwargs_pre["height"], kwargs_pre["width"] = size # type: ignore
+ return_fig = kwargs_pre.pop("return_fig", False)
+ if "margin" in kwargs_post and isinstance(kwargs_post["margin"], int):
+ kwargs_post["margin"] = dict.fromkeys(list("tblr"), kwargs_post["margin"])
+ if "xaxis_tickvals" in kwargs_pre:
+ tickvals = kwargs_pre.pop("xaxis_tickvals")
+ kwargs_post["xaxis"] = dict(
+ tickmode="array",
+ tickvals=kwargs_pre.get("x", np.arange(len(tickvals))),
+ ticktext=tickvals,
+ )
+ if "hovermode" not in kwargs_post:
+ kwargs_post["hovermode"] = "x unified"
+ hovertext = kwargs_pre.pop("hovertext", None)
+ if "use_secondary_yaxis" in kwargs_pre and kwargs_pre["use_secondary_yaxis"]:
+ del kwargs_pre["use_secondary_yaxis"]
+ if "labels" in kwargs_pre:
+ labels: dict = kwargs_pre.pop("labels")
+ kwargs_post["yaxis_title_text"] = labels.get("y1", None)
+ kwargs_post["yaxis2_title_text"] = labels.get("y2", None)
+ kwargs_post["xaxis_title_text"] = labels.get("x", None)
+ for k in ["title", "template", "width", "height"]:
+ if k in kwargs_pre:
+ kwargs_post[k] = kwargs_pre.pop(k)
+ fig = make_subplots(specs=[[{"secondary_y": True}]]).update_layout(**kwargs_post)
+ y0 = to_numpy(y[0])
+ y1 = to_numpy(y[1])
+ x0, x1 = kwargs_pre.pop("x", [np.arange(len(y0)), np.arange(len(y1))])
+ name0, name1 = kwargs_pre.pop("names", ["yaxis1", "yaxis2"])
+ fig.add_trace(go.Scatter(y=y0, x=x0, name=name0), secondary_y=False)
+ fig.add_trace(go.Scatter(y=y1, x=x1, name=name1), secondary_y=True)
+ else:
+ y = (
+ list(map(to_numpy, y))
+ if isinstance(y, list) and not (isinstance(y[0], int) or isinstance(y[0], float))
+ else to_numpy(y)
+ ) # type: ignore
+ names = kwargs_pre.pop("names", None)
+ fig = px.line(y=y, **kwargs_pre).update_layout(**kwargs_post)
+ if names is not None:
+ fig.for_each_trace(lambda trace: trace.update(name=names.pop(0)))
+ if hovertext is not None:
+ ht = fig.data[0].hovertemplate
+ fig.for_each_trace(lambda trace: trace.update(hovertext=hovertext, hovertemplate="%{hovertext}
" + ht))
+
+ return fig if return_fig else fig.show(renderer=renderer)
+
+
+def scatter(x, y, renderer=None, **kwargs):
+ x = to_numpy(x)
+ y = to_numpy(y)
+ add_line = None
+ if "add_line" in kwargs:
+ add_line = kwargs.pop("add_line")
+ kwargs_post = {k: v for k, v in kwargs.items() if k in update_layout_set}
+ kwargs_traces = {k: v for k, v in kwargs.items() if k in update_traces_set}
+ kwargs_pre = {k: v for k, v in kwargs.items() if k not in (update_layout_set | update_traces_set)}
+ if ("size" in kwargs_pre) or ("shape" in kwargs_pre):
+ size = kwargs_pre.pop("size", None) or kwargs_pre.pop("shape", None)
+ kwargs_pre["height"], kwargs_pre["width"] = size # type: ignore
+ return_fig = kwargs_pre.pop("return_fig", False)
+ facet_labels = kwargs_pre.pop("facet_labels", None)
+ if "margin" in kwargs_post and isinstance(kwargs_post["margin"], int):
+ kwargs_post["margin"] = dict.fromkeys(list("tblr"), kwargs_post["margin"])
+ fig = px.scatter(y=y, x=x, **kwargs_pre).update_layout(**kwargs_post)
+ if add_line is not None:
+ xrange = fig.layout.xaxis.range or [x.min(), x.max()] # type: ignore
+ yrange = fig.layout.yaxis.range or [y.min(), y.max()] # type: ignore
+ add_line = add_line.replace(" ", "")
+ if add_line in ["x=y", "y=x"]:
+ fig.add_trace(go.Scatter(mode="lines", x=xrange, y=xrange, showlegend=False))
+ elif re.match("(x|y)=", add_line):
+ try:
+ c = float(add_line.split("=")[1])
+ except:
+ raise ValueError(
+ f"Unrecognized add_line: {add_line}. Please use either 'x=y' or 'x=c' or 'y=c' for some float c."
+ )
+ x, y = ([c, c], yrange) if add_line[0] == "x" else (xrange, [c, c])
+ fig.add_trace(go.Scatter(mode="lines", x=x, y=y, showlegend=False))
+ else:
+ raise ValueError(
+ f"Unrecognized add_line: {add_line}. Please use either 'x=y' or 'x=c' or 'y=c' for some float c."
+ )
+ if facet_labels:
+ for i, label in enumerate(facet_labels):
+ fig.layout.annotations[i]["text"] = label # type: ignore
+ fig.update_traces(**kwargs_traces)
+ return fig if return_fig else fig.show(renderer=renderer)
+
+
+def bar(tensor, renderer=None, **kwargs):
+ """ """
+ if isinstance(tensor, list):
+ if isinstance(tensor[0], t.Tensor):
+ arr = [to_numpy(tn) for tn in tensor]
+ elif isinstance(tensor[0], list):
+ arr = [np.array(tn) for tn in tensor]
+ else:
+ arr = np.array(tensor)
+ else:
+ arr = to_numpy(tensor)
+ kwargs_post = {k: v for k, v in kwargs.items() if k in update_layout_set}
+ kwargs_pre = {k: v for k, v in kwargs.items() if k not in update_layout_set}
+ return_fig = kwargs_pre.pop("return_fig", False)
+ names = kwargs_pre.pop("names", None)
+ if "hovermode" not in kwargs_post:
+ kwargs_post["hovermode"] = "x unified"
+ if "margin" in kwargs_post and isinstance(kwargs_post["margin"], int):
+ kwargs_post["margin"] = dict.fromkeys(list("tblr"), kwargs_post["margin"])
+ fig = px.bar(y=arr, **kwargs_pre).update_layout(**kwargs_post)
+ if names is not None:
+ for i in range(len(fig.data)):
+ fig.data[i]["name"] = names[i // 2 if "marginal" in kwargs_pre else i]
+ return fig if return_fig else fig.show(renderer=renderer)
+
+
+def hist(tensor, renderer=None, **kwargs):
+ kwargs_post = {k: v for k, v in kwargs.items() if k in update_layout_set}
+ kwargs_pre = {k: v for k, v in kwargs.items() if k not in update_layout_set}
+ # draw = kwargs_pre.pop("draw", True)
+ # static = kwargs_pre.pop("static", False)
+ return_fig = kwargs_pre.pop("return_fig", False)
+ if isinstance(tensor, list):
+ if isinstance(tensor[0], t.Tensor):
+ arr = [to_numpy(tn) for tn in tensor]
+ elif isinstance(tensor[0], list):
+ arr = [np.array(tn) for tn in tensor]
+ else:
+ arr = np.array(tensor)
+ else:
+ arr = to_numpy(tensor)
+ if "modebar_add" not in kwargs_post:
+ kwargs_post["modebar_add"] = [
+ "drawline",
+ "drawopenpath",
+ "drawclosedpath",
+ "drawcircle",
+ "drawrect",
+ "eraseshape",
+ ]
+ add_mean_line = kwargs_pre.pop("add_mean_line", False)
+ names = kwargs_pre.pop("names", None)
+ if "barmode" not in kwargs_post:
+ kwargs_post["barmode"] = "overlay"
+ if "bargap" not in kwargs_post:
+ kwargs_post["bargap"] = 0.0
+ if "margin" in kwargs_post and isinstance(kwargs_post["margin"], int):
+ kwargs_post["margin"] = dict.fromkeys(list("tblr"), kwargs_post["margin"])
+ if "hovermode" not in kwargs_post:
+ kwargs_post["hovermode"] = "x unified"
+ if "autosize" not in kwargs_post:
+ kwargs_post["autosize"] = False
+
+ # If `arr` has a list of arrays, then just doing px.histogram doesn't work annoyingly enough
+ # This is janky, even for my functions!
+ if isinstance(arr, list) and isinstance(arr[0], np.ndarray):
+ assert "marginal" not in kwargs_pre, "Can't use `marginal` with a list of arrays"
+ for thing_to_move_from_pre_to_post in ["title", "template", "height", "width", "labels"]:
+ if thing_to_move_from_pre_to_post in kwargs_pre:
+ kwargs_post[thing_to_move_from_pre_to_post] = kwargs_pre.pop(thing_to_move_from_pre_to_post)
+ if "labels" in kwargs_post:
+ kwargs_post["xaxis_title_text"] = kwargs_post["labels"].get("x", "")
+ kwargs_post["yaxis_title_text"] = kwargs_post["labels"].get("y", "")
+ del kwargs_post["labels"]
+ fig = go.Figure(layout=go.Layout(**kwargs_post))
+ if "nbins" in kwargs_pre:
+ kwargs_pre["nbinsx"] = int(kwargs_pre.pop("nbins"))
+ for x in arr:
+ fig.add_trace(go.Histogram(x=x, name=names.pop(0) if names is not None else None, **kwargs_pre))
+ else:
+ fig = px.histogram(x=arr, **kwargs_pre).update_layout(**kwargs_post)
+ if names is not None:
+ for i in range(len(fig.data)):
+ fig.data[i]["name"] = names[i // 2 if "marginal" in kwargs_pre else i]
+
+ assert isinstance(arr, (np.ndarray, Tensor))
+
+ if add_mean_line:
+ if arr.ndim == 1:
+ fig.add_vline(
+ x=arr.mean(),
+ line_width=3,
+ line_dash="dash",
+ line_color="black",
+ annotation_text=f"Mean = {arr.mean():.3f}",
+ annotation_position="top",
+ )
+ elif arr.ndim == 2:
+ for i in range(arr.shape[0]):
+ fig.add_vline(
+ x=arr[i].mean(),
+ line_width=3,
+ line_dash="dash",
+ line_color="black",
+ annotation_text=f"Mean = {arr.mean():.3f}",
+ annotation_position="top",
+ )
+ return fig if return_fig else fig.show(renderer=renderer)
+
+
+# ! PLOTTING FUNCTIONS FOR PART 2: INTRO TO MECH INTERP
+
+
+def plot_comp_scores(
+ model, comp_scores, title: str = "", baseline: t.Tensor | None = None, filename: str | None = None
+):
+ fig = px.imshow(
+ to_numpy(comp_scores),
+ y=[f"L0H{h}" for h in range(model.cfg.n_heads)],
+ x=[f"L1H{h}" for h in range(model.cfg.n_heads)],
+ labels={"x": "Layer 1", "y": "Layer 0"},
+ title=title,
+ color_continuous_scale="RdBu" if baseline is not None else "Blues",
+ color_continuous_midpoint=baseline if baseline is not None else None,
+ zmin=None if baseline is not None else 0.0,
+ width=550,
+ height=450,
+ )
+ fig.show()
+ if filename is not None:
+ fig.write_html(filename)
+
+
+def convert_tokens_to_string(model, tokens, batch_index=0):
+ """
+ Helper function to convert tokens into a list of strings, for printing.
+ """
+ if len(tokens.shape) == 2:
+ tokens = tokens[batch_index]
+ return [f"|{model.tokenizer.decode(tok)}|_{c}" for (c, tok) in enumerate(tokens)]
+
+
+def plot_logit_attribution(model, logit_attr: t.Tensor, tokens: t.Tensor, title: str = "", filename: str | None = None):
+ tokens = tokens.squeeze()
+ y_labels = convert_tokens_to_string(model, tokens[:-1])
+ x_labels = ["Direct"] + [f"L{l}H{h}" for l in range(model.cfg.n_layers) for h in range(model.cfg.n_heads)]
+ fig = imshow(
+ to_numpy(logit_attr), # type: ignore
+ x=x_labels,
+ y=y_labels,
+ labels={"x": "Term", "y": "Position", "color": "logit"},
+ title=title if title else None,
+ height=100 + (30 if title else 0) + 15 * len(y_labels),
+ width=24 * len(x_labels),
+ return_fig=True,
+ )
+ fig.show()
+ if filename is not None:
+ fig.write_html(filename)
+
+
+# ! PLOTTING FUNCTIONS FOR PART 4: BALANCED BRACKET CLASSIFICATION
+
+color_discrete_map = dict(
+ zip(
+ ["both failures", "just neg failure", "balanced", "just total elevation failure"],
+ px.colors.qualitative.D3,
+ )
+)
+# names = ["balanced", "just total elevation failure", "just neg failure", "both failures"]
+# colors = ['#2CA02C', '#1c96eb', '#b300ff', '#ff4800']
+# color_discrete_map = dict(zip(names, colors))
+
+
+def plot_failure_types_scatter(
+ unbalanced_component_1: Float[Tensor, "batch"],
+ unbalanced_component_2: Float[Tensor, "batch"],
+ failure_types_dict: dict[str, Float[Tensor, "batch"]],
+ data,
+ filename: str | None = None,
+):
+ failure_types = np.full(len(unbalanced_component_1), "", dtype=np.dtype("U32"))
+ for name, mask in failure_types_dict.items():
+ failure_types = np.where(to_numpy(mask), name, failure_types)
+ failures_df = pd.DataFrame(
+ {
+ "Head 2.0 contribution": to_numpy(unbalanced_component_1),
+ "Head 2.1 contribution": to_numpy(unbalanced_component_2),
+ "Failure type": to_numpy(failure_types),
+ }
+ )[data.starts_open.tolist()]
+ fig = px.scatter(
+ failures_df,
+ color_discrete_map=color_discrete_map,
+ x="Head 2.0 contribution",
+ y="Head 2.1 contribution",
+ color="Failure type",
+ title="h20 vs h21 for different failure types",
+ template="simple_white",
+ height=600,
+ width=800,
+ # category_orders={"color": failure_types_dict.keys()},
+ ).update_traces(marker_size=4)
+ fig.show()
+ if filename is not None:
+ fig.write_html(filename)
+
+
+def plot_contribution_vs_open_proportion(
+ unbalanced_component: Float[Tensor, "batch"],
+ title: str,
+ failure_types_dict: dict,
+ data,
+ filename: str | None = None,
+):
+ failure_types = np.full(len(unbalanced_component), "", dtype=np.dtype("U32"))
+ for name, mask in failure_types_dict.items():
+ failure_types = np.where(to_numpy(mask), name, failure_types)
+ fig = (
+ px.scatter(
+ x=to_numpy(data.open_proportion),
+ y=to_numpy(unbalanced_component),
+ color=failure_types,
+ color_discrete_map=color_discrete_map,
+ title=title,
+ template="simple_white",
+ height=500,
+ width=800,
+ labels={"x": "Open-proportion", "y": "Head contribution"},
+ )
+ .update_traces(marker_size=4, opacity=0.5)
+ .update_layout(legend_title_text="Failure type")
+ )
+ fig.show()
+ if filename is not None:
+ fig.write_html(filename)
+
+
+def mlp_attribution_scatter(
+ out_by_component_in_pre_20_unbalanced_dir: Float[Tensor, "comp batch"],
+ data,
+ failure_types_dict: dict,
+ filenames: list[str] | None = None,
+) -> None:
+ failure_types = np.full(out_by_component_in_pre_20_unbalanced_dir.shape[-1], "", dtype=np.dtype("U32"))
+ for name, mask in failure_types_dict.items():
+ failure_types = np.where(to_numpy(mask), name, failure_types)
+ for layer in range(2):
+ mlp_output = out_by_component_in_pre_20_unbalanced_dir[3 + layer * 3]
+ fig = (
+ px.scatter(
+ x=to_numpy(data.open_proportion[data.starts_open]),
+ y=to_numpy(mlp_output[data.starts_open]),
+ color_discrete_map=color_discrete_map,
+ color=to_numpy(failure_types)[to_numpy(data.starts_open)],
+ title=f"Amount MLP {layer} writes in unbalanced direction for Head 2.0",
+ template="simple_white",
+ height=500,
+ width=800,
+ labels={"x": "Open-proportion", "y": "Head 2.0 contribution"},
+ )
+ .update_traces(marker_size=4, opacity=0.5)
+ .update_layout(legend_title_text="Failure type")
+ )
+ fig.show()
+ if filenames is not None:
+ assert len(filenames) == 2
+ fig.write_html(filenames[layer])
+
+
+def plot_neurons(
+ neurons_in_unbalanced_dir: Float[Tensor, "batch neurons"],
+ model,
+ data,
+ failure_types_dict: dict,
+ layer: int,
+ renderer=None,
+ filename: str | None = None,
+):
+ failure_types = np.full(neurons_in_unbalanced_dir.shape[0], "", dtype=np.dtype("U32"))
+ for name, mask in failure_types_dict.items():
+ failure_types = np.where(to_numpy(mask[to_numpy(data.starts_open)]), name, failure_types)
+
+ # Get data that can be turned into a dataframe (plotly express is sometimes easier to use with a dataframe)
+ # Plot a scatter plot of all the neuron contributions, color-coded according to failure type, with slider to view neurons
+ neuron_numbers = einops.repeat(t.arange(model.cfg.d_model), "n -> (s n)", s=data.starts_open.sum())
+ failure_types = einops.repeat(failure_types, "s -> (s n)", n=model.cfg.d_model)
+ data_open_proportion = einops.repeat(data.open_proportion[data.starts_open], "s -> (s n)", n=model.cfg.d_model)
+ df = pd.DataFrame(
+ {
+ "Output in 2.0 direction": to_numpy(neurons_in_unbalanced_dir.flatten()),
+ "Neuron number": to_numpy(neuron_numbers),
+ "Open-proportion": to_numpy(data_open_proportion),
+ "Failure type": failure_types,
+ }
+ )
+ fig = (
+ px.scatter(
+ df,
+ x="Open-proportion",
+ y="Output in 2.0 direction",
+ color="Failure type",
+ animation_frame="Neuron number",
+ title=f"Neuron contributions from layer {layer}",
+ template="simple_white",
+ height=800,
+ width=1100,
+ )
+ .update_traces(marker_size=3)
+ .update_layout(xaxis_range=[0, 1], yaxis_range=[-5, 5])
+ )
+ fig.show(renderer=renderer)
+ if filename is not None:
+ fig.write_html(filename)
+
+
+def plot_attn_pattern(pattern: Float[Tensor, "batch head_idx seqQ seqK"], filename: str | None = None):
+ fig = px.imshow(
+ pattern,
+ title="Estimate for avg attn probabilities when query is from '('",
+ labels={
+ "x": "Key tokens (avg of left & right parens)",
+ "y": "Query tokens (all left parens)",
+ },
+ height=900,
+ width=900,
+ color_continuous_scale="RdBu_r",
+ range_color=[0, pattern.max().item()],
+ ).update_layout(
+ xaxis=dict(
+ tickmode="array",
+ ticktext=["[start]", *[f"{i+1}" for i in range(40)], "[end]"],
+ tickvals=list(range(42)),
+ tickangle=0,
+ ),
+ yaxis=dict(
+ tickmode="array",
+ ticktext=["[start]", *[f"{i+1}" for i in range(40)], "[end]"],
+ tickvals=list(range(42)),
+ ),
+ )
+ fig.show()
+ if filename is not None:
+ fig.write_html(filename)
+
+
+def hists_per_comp(
+ out_by_component_in_unbalanced_dir: Float[Tensor, "component batch"],
+ data,
+ xaxis_range=(-1, 1),
+ filename: str | None = None,
+):
+ """
+ Plots the contributions in the unbalanced direction, as supplied by the `out_by_component_in_unbalanced_dir` tensor.
+ """
+ titles = {
+ (1, 1): "embeddings",
+ (2, 1): "head 0.0",
+ (2, 2): "head 0.1",
+ (2, 3): "mlp 0",
+ (3, 1): "head `1.0`",
+ (3, 2): "head `1.1`",
+ (3, 3): "mlp 1",
+ (4, 1): "head 2.0",
+ (4, 2): "head 2.1",
+ (4, 3): "mlp 2",
+ }
+ n_layers = out_by_component_in_unbalanced_dir.shape[0] // 3
+ fig = make_subplots(rows=n_layers + 1, cols=3)
+ for ((row, col), title), in_dir in zip(titles.items(), out_by_component_in_unbalanced_dir):
+ fig.add_trace(
+ go.Histogram(
+ x=to_numpy(in_dir[data.isbal]),
+ name="Balanced",
+ marker_color="blue",
+ opacity=0.5,
+ legendgroup="1",
+ showlegend=title == "embeddings",
+ ),
+ row=row,
+ col=col,
+ )
+ fig.add_trace(
+ go.Histogram(
+ x=to_numpy(in_dir[~data.isbal]),
+ name="Unbalanced",
+ marker_color="red",
+ opacity=0.5,
+ legendgroup="2",
+ showlegend=title == "embeddings",
+ ),
+ row=row,
+ col=col,
+ )
+ fig.update_xaxes(title_text=title, row=row, col=col, range=xaxis_range)
+ fig.update_layout(
+ width=1200,
+ height=250 * (n_layers + 1),
+ barmode="overlay",
+ legend=dict(yanchor="top", y=0.92, xanchor="left", x=0.4),
+ title="Histograms of component significance",
+ )
+ fig.show()
+ if filename is not None:
+ fig.write_html(filename)
+
+
+def plot_loss_difference(log_probs, rep_str, seq_len, filename: str | None = None):
+ fig = px.line(
+ to_numpy(log_probs),
+ hover_name=rep_str[1:],
+ title=f"Per token log prob on correct token, for sequence of length {seq_len}*2 (repeated twice)",
+ labels={"index": "Sequence position", "value": "Log prob"},
+ ).update_layout(showlegend=False, hovermode="x unified")
+ fig.add_vrect(x0=0, x1=seq_len - 0.5, fillcolor="red", opacity=0.2, line_width=0)
+ fig.add_vrect(x0=seq_len - 0.5, x1=2 * seq_len - 1, fillcolor="green", opacity=0.2, line_width=0)
+ fig.show()
+ if filename is not None:
+ fig.write_html(filename)
diff --git a/ARENA_files/brackets_data.json b/ARENA_files/brackets_data.json
new file mode 100644
index 0000000..a467945
--- /dev/null
+++ b/ARENA_files/brackets_data.json
@@ -0,0 +1 @@
+[["(()((())()(((())()))((", false], ["))(()()(", false], ["(())(())", true], [")())())()(())()))(((())())", false], [")(()(())(()))()))())))", false], ["(()(()()())())", true], ["(())()()))))", false], ["(()((()(()))))", true], ["()", true], ["()", true], ["(()(()())(()()())(((())((()))())))", true], ["))()", false], ["()(((()(())()()())))", true], ["()()", true], ["())((())(()())(())()(())((()()()(())))", false], ["()(())", true], [")())()())(", false], ["()())(()((()())()())))", false], ["((((())))(())())((((()))))()", true], [")((()()(((", false], ["()", true], ["((()((())()())())())", true], ["()((((", false], ["()", true], ["()(((())))", true], ["()()((((()))()(())))()", true], ["((((((((((())(()()()", false], [")(()())))()((())))()(()(()", false], [")))())())))()(((())()(())(())))))()())()", false], ["(()((()()))()())()", true], ["()", true], ["()()()()))))()()((()))(())", false], ["((", false], ["()", true], ["(())()((((()))))((((())(", false], ["(((())(())()()))(()()))(()", false], [")((((())((())))(()((", false], [")((()())((((())()(", false], ["))()()()()())))()))(()))(()(())(()))))", false], ["()", true], ["((()((()((())()))((())))(((())(())))()))", true], ["()(())()", true], [")(((()(((((((()())(()(((()()((", false], ["((()()((()(()())())((()))())()()))", true], ["(())((()))))(())(((()))())(()(", false], ["(())()", true], ["(((())()))", true], [")()()()()(())((())(((())(()))()((()())", false], ["()(())()", true], [")(())(", false], [")())))()()(())())(((", false], [")))((())(()))))))(()()))()((()", false], ["(())", true], ["(()))(()((", false], [")()(()(()))()(((()()", false], ["((()(())()))())(()", false], ["((()))", true], [")(())()))(()(()(", false], ["(()())()()))()", false], ["((", false], [")(()(()())))())()()))))))(((", false], ["()(())", true], ["(())))(())((()()()))()(())())()())))(())", false], ["(())())(()((((", false], [")))))(())(((()()))()()(()))())))((", false], ["()()(())())()()())(()))()()(()()(())))))", false], ["()", true], ["(())", true], ["()()((())())()))((())(()", false], ["())(", false], [")))()()((()(()))()(((()((()(((()((()())(", false], ["((((((()((())(", false], ["(()()())(())))(((())", false], ["))(()())))(())))))))))((((", false], [")(((()(()()((())))((())))((()((()(()", false], ["(()())()", true], ["()", true], [")(((()()(((())((())))(())(()()", false], [")())))(())((", false], [")))()(", false], ["()", true], ["(()))(()((()))(((((()())))()()((()))(())", false], ["()))(()(()(()()(", false], ["((()(()(()))(()((()()))()(()())(", false], [")))(()))))())((((())((", false], ["()((()()()(()())(((()())()((", false], ["))", false], ["()", true], ["()", true], ["()()(()())", true], [")())()((())((()(", false], ["(()())", true], [")()((()()))(()(())(()))((()())()", false], ["()((()(()())()()()((()))))", true], ["((()))", true], [")(", false], [")(())()())((", false], ["))()(()()()(", false], ["))))))(()))(()", false], [")())(((()()(()", false], ["()()()", true], ["()(()())", true], 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\ No newline at end of file
diff --git a/ARENA_files/brackets_model_state_dict.pt b/ARENA_files/brackets_model_state_dict.pt
new file mode 100644
index 0000000..af292ab
Binary files /dev/null and b/ARENA_files/brackets_model_state_dict.pt differ
diff --git a/ARENA_files/ioi_circuit_extraction.py b/ARENA_files/ioi_circuit_extraction.py
new file mode 100644
index 0000000..266ecc8
--- /dev/null
+++ b/ARENA_files/ioi_circuit_extraction.py
@@ -0,0 +1,180 @@
+from functools import partial
+
+import einops
+import torch as t
+from jaxtyping import Bool, Float
+from torch import Tensor
+from transformer_lens import HookedTransformer, utils
+from transformer_lens.hook_points import HookPoint
+
+from .ioi_dataset import IOIDataset
+
+CIRCUIT = {
+ "name mover": [(9, 9), (10, 0), (9, 6)],
+ "backup name mover": [(10, 10), (10, 6), (10, 2), (10, 1), (11, 2), (9, 7), (9, 0), (11, 9)],
+ "negative name mover": [(10, 7), (11, 10)],
+ "s2 inhibition": [(7, 3), (7, 9), (8, 6), (8, 10)],
+ "induction": [(5, 5), (5, 8), (5, 9), (6, 9)],
+ "duplicate token": [(0, 1), (0, 10), (3, 0)],
+ "previous token": [(2, 2), (4, 11)],
+}
+
+SEQ_POS_TO_KEEP = {
+ "name mover": "end",
+ "backup name mover": "end",
+ "negative name mover": "end",
+ "s2 inhibition": "end",
+ "induction": "S2",
+ "duplicate token": "S2",
+ "previous token": "S1+1",
+}
+
+
+# # Simple test: do the indices for head 9.9 (which is a name mover head) match the positions of the "end" tokens?
+
+# heads_circuit = get_heads_circuit(ioi_dataset)
+# assert (heads_circuit[(9, 9)] == ioi_dataset.word_idx["end"]).all()
+
+
+def get_heads_and_posns_to_keep(
+ means_dataset: IOIDataset,
+ model: HookedTransformer,
+ circuit: dict[str, list[tuple[int, int]]],
+ seq_pos_to_keep: dict[str, str],
+) -> dict[int, Bool[Tensor, "batch seq head"]]:
+ """
+ Returns a dictionary mapping layers to a boolean mask giving the indices of the
+ z output which *shouldn't* be mean-ablated.
+
+ The output of this function will be used for the hook function that does ablation.
+ """
+ heads_and_posns_to_keep = {}
+ batch, seq, n_heads = len(means_dataset), means_dataset.max_len, model.cfg.n_heads
+
+ for layer in range(model.cfg.n_layers):
+ mask = t.zeros(size=(batch, seq, n_heads))
+
+ for head_type, head_list in circuit.items():
+ seq_pos = seq_pos_to_keep[head_type]
+ indices = means_dataset.word_idx[seq_pos]
+ for layer_idx, head_idx in head_list:
+ if layer_idx == layer:
+ mask[:, indices, head_idx] = 1
+
+ heads_and_posns_to_keep[layer] = mask.bool()
+
+ return heads_and_posns_to_keep
+
+
+# # Simple test: check the correct mask is produced when the heads circuit is "just keep layer 0, head 0, sequence position 0"
+
+# heads_circuit_test = {(0, 0): t.full(size=(len(ioi_dataset),), fill_value=0)}
+# heads_and_posns_to_keep = get_heads_and_posns_to_keep(heads_circuit_test, ioi_dataset, model)
+
+# # Check all masks for layers after the first one are zero
+# for layer in range(1, model.cfg.n_layers):
+# assert (~heads_and_posns_to_keep[layer]).all()
+
+# # Check mask for first layer is one at sequence position 0 for head 0, and zero everywhere else
+# layer0_mask = heads_and_posns_to_keep[0]
+# assert layer0_mask.shape == (len(ioi_dataset), ioi_dataset.max_len, model.cfg.n_heads)
+# assert (~layer0_mask[:, 1:, :]).all()
+# assert (~layer0_mask[:, 0, 1:]).all()
+# assert (layer0_mask[:, 0, 0] == True).all()
+
+
+def hook_fn_mask_z(
+ z: Float[Tensor, "batch seq head d_head"],
+ hook: HookPoint,
+ heads_and_posns_to_keep: dict[int, Bool[Tensor, "batch seq head"]],
+ means: Float[Tensor, "layer batch seq head d_head"],
+) -> Float[Tensor, "batch seq head d_head"]:
+ """
+ Hook function which masks the z output of a transformer head.
+
+ heads_and_posns_to_keep
+ dict created with the get_heads_and_posns_to_keep function. This tells
+ us where to mask.
+
+ means
+ Tensor of mean z values of the means_dataset over each group of prompts
+ with the same template. This tells us what values to mask with.
+ """
+ # Get the mask for this layer, and add d_head=1 dimension so it broadcasts correctly
+ mask_for_this_layer = heads_and_posns_to_keep[hook.layer()].unsqueeze(-1).to(z.device)
+
+ # Set z values to the mean
+ z = t.where(mask_for_this_layer, z, means[hook.layer()])
+
+ return z
+
+
+def compute_means_by_template(
+ means_dataset: IOIDataset, model: HookedTransformer
+) -> Float[Tensor, "layer batch seq head_idx d_head"]:
+ """
+ Returns the mean of each head's output over the means dataset. This mean is
+ computed separately for each group of prompts with the same template (these
+ are given by means_dataset.groups).
+ """
+ # Cache the outputs of every head
+ _, means_cache = model.run_with_cache(
+ means_dataset.toks.long(),
+ return_type=None,
+ names_filter=lambda name: name.endswith("z"),
+ )
+ # Create tensor to store means
+ n_layers, n_heads, d_head = model.cfg.n_layers, model.cfg.n_heads, model.cfg.d_head
+ batch, seq_len = len(means_dataset), means_dataset.max_len
+ means = t.zeros(size=(n_layers, batch, seq_len, n_heads, d_head), device=model.cfg.device)
+
+ # Get set of different templates for this data
+ for layer in range(model.cfg.n_layers):
+ z_for_this_layer: Float[Tensor, "batch seq head d_head"] = means_cache[
+ utils.get_act_name("z", layer)
+ ]
+ for template_group in means_dataset.groups:
+ z_for_this_template = z_for_this_layer[template_group]
+ z_means_for_this_template = einops.reduce(
+ z_for_this_template, "batch seq head d_head -> seq head d_head", "mean"
+ )
+ means[layer, template_group] = z_means_for_this_template
+
+ return means
+
+
+def add_mean_ablation_hook(
+ model: HookedTransformer,
+ means_dataset: IOIDataset,
+ circuit: dict[str, list[tuple[int, int]]] = CIRCUIT,
+ seq_pos_to_keep: dict[str, str] = SEQ_POS_TO_KEEP,
+ is_permanent: bool = True,
+) -> HookedTransformer:
+ """
+ Adds a permanent hook to the model, which ablates according to the circuit and
+ seq_pos_to_keep dictionaries.
+
+ In other words, when the model is run on ioi_dataset, every head's output will
+ be replaced with the mean over means_dataset for sequences with the same template,
+ except for a subset of heads and sequence positions as specified by the circuit
+ and seq_pos_to_keep dicts.
+ """
+
+ model.reset_hooks(including_permanent=True)
+
+ # Compute the mean of each head's output on the ABC dataset, grouped by template
+ means = compute_means_by_template(means_dataset, model)
+
+ # Convert this into a boolean map
+ heads_and_posns_to_keep = get_heads_and_posns_to_keep(
+ means_dataset, model, circuit, seq_pos_to_keep
+ )
+
+ # Get a hook function which will patch in the mean z values for each head, at
+ # all positions which aren't important for the circuit
+ hook_fn = partial(hook_fn_mask_z, heads_and_posns_to_keep=heads_and_posns_to_keep, means=means)
+
+ # Apply hook
+ model.add_hook(lambda name: name.endswith("z"), hook_fn, is_permanent=is_permanent) # type: ignore
+
+ return model
diff --git a/ARENA_files/ioi_dataset.py b/ARENA_files/ioi_dataset.py
new file mode 100644
index 0000000..a4c9ed5
--- /dev/null
+++ b/ARENA_files/ioi_dataset.py
@@ -0,0 +1,692 @@
+import copy
+import random
+import warnings
+
+import numpy as np
+import torch as t
+from transformers import AutoTokenizer
+
+NAMES = [
+ "Aaron",
+ "Adam",
+ "Alan",
+ "Alex",
+ "Alice",
+ "Amy",
+ "Anderson",
+ "Andre",
+ "Andrew",
+ "Andy",
+ "Anna",
+ "Anthony",
+ "Arthur",
+ "Austin",
+ "Blake",
+ "Brandon",
+ "Brian",
+ "Carter",
+ "Charles",
+ "Charlie",
+ "Christian",
+ "Christopher",
+ "Clark",
+ "Cole",
+ "Collins",
+ "Connor",
+ "Crew",
+ "Crystal",
+ "Daniel",
+ "David",
+ "Dean",
+ "Edward",
+ "Elizabeth",
+ "Emily",
+ "Eric",
+ "Eva",
+ "Ford",
+ "Frank",
+ "George",
+ "Georgia",
+ "Graham",
+ "Grant",
+ "Henry",
+ "Ian",
+ "Jack",
+ "Jacob",
+ "Jake",
+ "James",
+ "Jamie",
+ "Jane",
+ "Jason",
+ "Jay",
+ "Jennifer",
+ "Jeremy",
+ "Jessica",
+ "John",
+ "Jonathan",
+ "Jordan",
+ "Joseph",
+ "Joshua",
+ "Justin",
+ "Kate",
+ "Kelly",
+ "Kevin",
+ "Kyle",
+ "Laura",
+ "Leon",
+ "Lewis",
+ "Lisa",
+ "Louis",
+ "Luke",
+ "Madison",
+ "Marco",
+ "Marcus",
+ "Maria",
+ "Mark",
+ "Martin",
+ "Mary",
+ "Matthew",
+ "Max",
+ "Michael",
+ "Michelle",
+ "Morgan",
+ "Patrick",
+ "Paul",
+ "Peter",
+ "Prince",
+ "Rachel",
+ "Richard",
+ "River",
+ "Robert",
+ "Roman",
+ "Rose",
+ "Ruby",
+ "Russell",
+ "Ryan",
+ "Sarah",
+ "Scott",
+ "Sean",
+ "Simon",
+ "Stephen",
+ "Steven",
+ "Sullivan",
+ "Taylor",
+ "Thomas",
+ "Tyler",
+ "Victoria",
+ "Warren",
+ "William",
+]
+
+ABC_TEMPLATES = [
+ "Then, [A], [B] and [C] went to the [PLACE]. [B] and [C] gave a [OBJECT] to [A]",
+ "Afterwards [A], [B] and [C] went to the [PLACE]. [B] and [C] gave a [OBJECT] to [A]",
+ "When [A], [B] and [C] arrived at the [PLACE], [B] and [C] gave a [OBJECT] to [A]",
+ "Friends [A], [B] and [C] went to the [PLACE]. [B] and [C] gave a [OBJECT] to [A]",
+]
+
+BAC_TEMPLATES = [
+ template.replace("[B]", "[A]", 1).replace("[A]", "[B]", 1) for template in ABC_TEMPLATES
+]
+
+BABA_TEMPLATES = [
+ "Then, [B] and [A] went to the [PLACE]. [B] gave a [OBJECT] to [A]",
+ "Then, [B] and [A] had a lot of fun at the [PLACE]. [B] gave a [OBJECT] to [A]",
+ "Then, [B] and [A] were working at the [PLACE]. [B] decided to give a [OBJECT] to [A]",
+ "Then, [B] and [A] were thinking about going to the [PLACE]. [B] wanted to give a [OBJECT] to [A]",
+ "Then, [B] and [A] had a long argument, and afterwards [B] said to [A]",
+ "After [B] and [A] went to the [PLACE], [B] gave a [OBJECT] to [A]",
+ "When [B] and [A] got a [OBJECT] at the [PLACE], [B] decided to give it to [A]",
+ "When [B] and [A] got a [OBJECT] at the [PLACE], [B] decided to give the [OBJECT] to [A]",
+ "While [B] and [A] were working at the [PLACE], [B] gave a [OBJECT] to [A]",
+ "While [B] and [A] were commuting to the [PLACE], [B] gave a [OBJECT] to [A]",
+ "After the lunch, [B] and [A] went to the [PLACE]. [B] gave a [OBJECT] to [A]",
+ "Afterwards, [B] and [A] went to the [PLACE]. [B] gave a [OBJECT] to [A]",
+ "Then, [B] and [A] had a long argument. Afterwards [B] said to [A]",
+ "The [PLACE] [B] and [A] went to had a [OBJECT]. [B] gave it to [A]",
+ "Friends [B] and [A] found a [OBJECT] at the [PLACE]. [B] gave it to [A]",
+]
+
+BABA_LONG_TEMPLATES = [
+ "Then in the morning, [B] and [A] went to the [PLACE]. [B] gave a [OBJECT] to [A]",
+ "Then in the morning, [B] and [A] had a lot of fun at the [PLACE]. [B] gave a [OBJECT] to [A]",
+ "Then in the morning, [B] and [A] were working at the [PLACE]. [B] decided to give a [OBJECT] to [A]",
+ "Then in the morning, [B] and [A] were thinking about going to the [PLACE]. [B] wanted to give a [OBJECT] to [A]",
+ "Then in the morning, [B] and [A] had a long argument, and afterwards [B] said to [A]",
+ "After taking a long break [B] and [A] went to the [PLACE], [B] gave a [OBJECT] to [A]",
+ "When soon afterwards [B] and [A] got a [OBJECT] at the [PLACE], [B] decided to give it to [A]",
+ "When soon afterwards [B] and [A] got a [OBJECT] at the [PLACE], [B] decided to give the [OBJECT] to [A]",
+ "While spending time together [B] and [A] were working at the [PLACE], [B] gave a [OBJECT] to [A]",
+ "While spending time together [B] and [A] were commuting to the [PLACE], [B] gave a [OBJECT] to [A]",
+ "After the lunch in the afternoon, [B] and [A] went to the [PLACE]. [B] gave a [OBJECT] to [A]",
+ "Afterwards, while spending time together [B] and [A] went to the [PLACE]. [B] gave a [OBJECT] to [A]",
+ "Then in the morning afterwards, [B] and [A] had a long argument. Afterwards [B] said to [A]",
+ "The local big [PLACE] [B] and [A] went to had a [OBJECT]. [B] gave it to [A]",
+ "Friends separated at birth [B] and [A] found a [OBJECT] at the [PLACE]. [B] gave it to [A]",
+]
+
+BABA_LATE_IOS = [
+ "Then, [B] and [A] went to the [PLACE]. [B] gave a [OBJECT] to [A]",
+ "Then, [B] and [A] had a lot of fun at the [PLACE]. [B] gave a [OBJECT] to [A]",
+ "Then, [B] and [A] were working at the [PLACE]. [B] decided to give a [OBJECT] to [A]",
+ "Then, [B] and [A] were thinking about going to the [PLACE]. [B] wanted to give a [OBJECT] to [A]",
+ "Then, [B] and [A] had a long argument and after that [B] said to [A]",
+ "After the lunch, [B] and [A] went to the [PLACE]. [B] gave a [OBJECT] to [A]",
+ "Afterwards, [B] and [A] went to the [PLACE]. [B] gave a [OBJECT] to [A]",
+ "Then, [B] and [A] had a long argument. Afterwards [B] said to [A]",
+]
+
+BABA_EARLY_IOS = [
+ "Then [B] and [A] went to the [PLACE], and [B] gave a [OBJECT] to [A]",
+ "Then [B] and [A] had a lot of fun at the [PLACE], and [B] gave a [OBJECT] to [A]",
+ "Then [B] and [A] were working at the [PLACE], and [B] decided to give a [OBJECT] to [A]",
+ "Then [B] and [A] were thinking about going to the [PLACE], and [B] wanted to give a [OBJECT] to [A]",
+ "Then [B] and [A] had a long argument, and after that [B] said to [A]",
+ "After the lunch [B] and [A] went to the [PLACE], and [B] gave a [OBJECT] to [A]",
+ "Afterwards [B] and [A] went to the [PLACE], and [B] gave a [OBJECT] to [A]",
+ "Then [B] and [A] had a long argument, and afterwards [B] said to [A]",
+]
+
+ABBA_TEMPLATES = BABA_TEMPLATES[:]
+ABBA_LATE_IOS = BABA_LATE_IOS[:]
+ABBA_EARLY_IOS = BABA_EARLY_IOS[:]
+
+for TEMPLATES in [ABBA_TEMPLATES, ABBA_LATE_IOS, ABBA_EARLY_IOS]:
+ for i in range(len(TEMPLATES)):
+ first_clause = True
+ for j in range(1, len(TEMPLATES[i]) - 1):
+ if TEMPLATES[i][j - 1 : j + 2] == "[B]" and first_clause:
+ TEMPLATES[i] = TEMPLATES[i][:j] + "A" + TEMPLATES[i][j + 1 :]
+ elif TEMPLATES[i][j - 1 : j + 2] == "[A]" and first_clause:
+ first_clause = False
+ TEMPLATES[i] = TEMPLATES[i][:j] + "B" + TEMPLATES[i][j + 1 :]
+
+VERBS = [" tried", " said", " decided", " wanted", " gave"]
+
+PLACES = [
+ "store",
+ "garden",
+ "restaurant",
+ "school",
+ "hospital",
+ "office",
+ "house",
+ "station",
+]
+
+OBJECTS = [
+ "ring",
+ "kiss",
+ "bone",
+ "basketball",
+ "computer",
+ "necklace",
+ "drink",
+ "snack",
+]
+
+
+def gen_prompt_uniform(
+ templates: list[str], names, nouns_dict, N, symmetric, prefixes=None, abc=False
+):
+ nb_gen = 0
+ ioi_prompts = []
+ while nb_gen < N:
+ temp = random.choice(templates)
+ temp_id = templates.index(temp)
+ name_1 = ""
+ name_2 = ""
+ name_3 = ""
+ while len(set([name_1, name_2, name_3])) < 3:
+ name_1 = random.choice(names)
+ name_2 = random.choice(names)
+ name_3 = random.choice(names)
+
+ nouns = {}
+ ioi_prompt = {}
+ for k in nouns_dict:
+ nouns[k] = random.choice(nouns_dict[k])
+ ioi_prompt[k] = nouns[k]
+ prompt = temp
+ for k in nouns_dict:
+ prompt = prompt.replace(k, nouns[k])
+
+ if prefixes is not None:
+ L = random.randint(30, 40)
+ pref = ".".join(random.choice(prefixes).split(".")[:L])
+ pref += "<|endoftext|>"
+ else:
+ pref = ""
+
+ prompt1 = prompt.replace("[A]", name_1)
+ prompt1 = prompt1.replace("[B]", name_2)
+ if abc:
+ prompt1 = prompt1.replace("[C]", name_3)
+ prompt1 = pref + prompt1
+ ioi_prompt["text"] = prompt1
+ ioi_prompt["IO"] = name_1
+ ioi_prompt["S"] = name_2
+ ioi_prompt["TEMPLATE_IDX"] = temp_id
+ ioi_prompts.append(ioi_prompt)
+ if abc:
+ ioi_prompts[-1]["C"] = name_3
+
+ nb_gen += 1
+
+ if symmetric and nb_gen < N:
+ prompt2 = prompt.replace("[A]", name_2)
+ prompt2 = prompt2.replace("[B]", name_1)
+ prompt2 = pref + prompt2
+ ioi_prompts.append(
+ {"text": prompt2, "IO": name_2, "S": name_1, "TEMPLATE_IDX": temp_id}
+ )
+ nb_gen += 1
+ return ioi_prompts
+
+
+def gen_flipped_prompts(
+ prompts: list[dict], templates_by_prompt: list[str], flip: str, names: list[str], seed: int
+) -> list[dict]:
+ """
+ Flip prompts in a way described by the flip argument. Returns new prompts.
+
+ prompts: list[dict]
+ list of prompts, each prompt is a dict with keys "S", "IO", "text", etc
+
+ templates_by_prompt: list[str]
+ each element is "ABBA" or "BABA"
+
+ flip: str
+ "ABB -> XYZ, BAB -> XYZ" means that the prompt "A and B went to [place], B gave [object] to A" becomes "X and Y went to [place], Z gave [object] to A" (and equivalent for the BABA case)
+
+ names: list[str]
+ list of names, for when flip involves random tokens
+
+ seed: int
+ provides reproducibility
+
+ Note that we don't bother flipping the last token in the prompt (IO2), since
+ we don't use it for anything (intuitively, we use this function to create
+ datasets to provide us with corrupted signals, but we still use the IO2 from
+ the original uncorrupted IOI database as our "correct answer", so we don't
+ care about what the correct answer (IO2) for the corrupted set is).
+ """
+ random.seed(seed)
+ np.random.seed(seed)
+ abba_flip, baba_flip = flip.split(",")
+ flip_dict = {
+ "ABB": [flip.strip() for flip in abba_flip.split("->")],
+ "BAB": [flip.strip() for flip in baba_flip.split("->")],
+ }
+
+ new_prompts = []
+
+ for idx, (prompt, template) in enumerate(zip(prompts, templates_by_prompt)):
+ flip_orig, flip_new = flip_dict[template[:-1]]
+
+ prompt = copy.copy(prompt)
+
+ # Get indices and original values of first three names int the prompt
+ prompt_split = prompt["text"].split(" ")
+ orig_names_and_posns = [(i, s) for i, s in enumerate(prompt_split) if s in names][:3]
+ orig_names = list(zip(*orig_names_and_posns))[1]
+
+ # Get a dictionary of the correspondence between orig names and letters in flip_orig
+ # (and get a subdict for those names which are kept in flip_new)
+ orig_names_key = {letter: s for s, letter in zip(orig_names, flip_orig)}
+ kept_names_key = {k: v for k, v in orig_names_key.items() if k in flip_new}
+ # This line will throw an error if flip_orig is wrong (e.g. if it says "SOS" but the
+ # S1 and S2 tokens don't actually match
+ assert len(orig_names_key) == len(set(flip_orig))
+
+ # Get all random names we'll need, in the form of a dictionary
+ sorted_names = sorted(set(names) - set(orig_names), key=names.index) # type: ignore
+ sorted_flips = sorted(set(flip_new) - set(flip_orig), key=flip_new.index)
+ rand_names = {letter: np.random.choice(sorted_names) for letter in sorted_flips}
+
+ # Get a "full dictionary" which maps letters in flip_new to the new values they will have
+ name_replacement_dict = {**kept_names_key, **rand_names}
+ assert len(name_replacement_dict) == len(set(flip_new)), (name_replacement_dict, flip_new)
+
+ # Populate the new names, with either random names or with the corresponding orig names
+ for (i, s), letter in zip(orig_names_and_posns, flip_new):
+ prompt_split[i] = name_replacement_dict[letter]
+
+ # Join the prompt back together
+ prompt["text"] = " ".join(prompt_split)
+
+ # Change the identity of the S and IO tokens.
+ # S token is just same as S2, but IO is a bit messier because it might not be
+ # well-defined (it's defined as the unique non-duplicated name of the first
+ # two). If it's ill-defined, WLOG set it to be the second name.
+ prompt["S"] = name_replacement_dict[flip_new[-1]]
+ possible_IOs = [
+ name_replacement_dict[letter]
+ for letter in flip_new[:2]
+ if list(flip_new).count(letter) == 1
+ ]
+ # Case where IO is well-defined
+ if len(possible_IOs) == 1:
+ prompt["IO"] = possible_IOs[0]
+ # Case where it isn't well-defined
+ else:
+ prompt["IO"] = name_replacement_dict[flip_new[1]]
+
+ new_prompts.append(prompt)
+
+ return new_prompts
+
+
+def get_name_idxs(prompts, tokenizer, idx_types=["IO", "S1", "S2"], prepend_bos=False):
+ name_idx_dict = dict((idx_type, []) for idx_type in idx_types)
+ for prompt in prompts:
+ text_split = prompt["text"].split(" ")
+ toks = tokenizer.tokenize(" ".join(text_split[:-1]))
+ # Get the first instance of IO token
+ name_idx_dict["IO"].append(toks.index(tokenizer.tokenize(" " + prompt["IO"])[0]))
+ # Get the first instance of S token
+ name_idx_dict["S1"].append(toks.index(tokenizer.tokenize(" " + prompt["S"])[0]))
+ # Get the last instance of S token
+ name_idx_dict["S2"].append(
+ len(toks) - toks[::-1].index(tokenizer.tokenize(" " + prompt["S"])[0]) - 1
+ )
+
+ return [int(prepend_bos) + t.tensor(name_idx_dict[idx_type]) for idx_type in idx_types]
+
+
+def get_word_idxs(prompts, word_list, tokenizer):
+ """Get the index of the words in word_list in the prompts. Exactly one of the word_list word has to be present in each prompt"""
+ idxs = []
+ tokenized_words = [tokenizer.decode(tokenizer(word)["input_ids"][0]) for word in word_list]
+ for prompt in prompts:
+ toks = [
+ tokenizer.decode(t)
+ for t in tokenizer(prompt["text"], return_tensors="pt", padding=True)["input_ids"][0]
+ ]
+ idx = None
+ for i, w_tok in enumerate(tokenized_words):
+ if word_list[i] in prompt["text"]:
+ try:
+ idx = toks.index(w_tok)
+ if toks.count(w_tok) > 1:
+ idx = len(toks) - toks[::-1].index(w_tok) - 1
+ except:
+ idx = toks.index(w_tok)
+ # raise ValueError(toks, w_tok, prompt["text"])
+ if idx is None:
+ raise ValueError(f"Word {word_list} and {i} not found {prompt}")
+ idxs.append(idx)
+ return t.tensor(idxs)
+
+
+def get_end_idxs(toks, tokenizer, name_tok_len=1, prepend_bos=False):
+ relevant_idx = int(prepend_bos)
+ # if the sentence begins with an end token
+ # AND the model pads at the end with the same end token,
+ # then we need make special arrangements
+
+ pad_token_id = tokenizer.pad_token_id
+
+ end_idxs_raw = []
+ for i in range(toks.shape[0]):
+ if pad_token_id not in toks[i][1:]:
+ end_idxs_raw.append(toks.shape[1])
+ continue
+ nonzers = (toks[i] == pad_token_id).nonzero()[relevant_idx][0].item()
+ end_idxs_raw.append(nonzers)
+ end_idxs = t.tensor(end_idxs_raw)
+ end_idxs = end_idxs - 1 - name_tok_len
+
+ for i in range(toks.shape[0]):
+ assert toks[i][end_idxs[i] + 1] != 0 and (
+ toks.shape[1] == end_idxs[i] + 2 or toks[i][end_idxs[i] + 2] == pad_token_id
+ ), (
+ toks[i],
+ end_idxs[i],
+ toks[i].shape,
+ "the END idxs aren't properly formatted",
+ )
+
+ return end_idxs
+
+
+def get_idx_dict(ioi_prompts, tokenizer, prepend_bos=False, toks=None):
+ (
+ IO_idxs,
+ S1_idxs,
+ S2_idxs,
+ ) = get_name_idxs(
+ ioi_prompts,
+ tokenizer,
+ idx_types=["IO", "S1", "S2"],
+ prepend_bos=prepend_bos,
+ )
+
+ end_idxs = get_end_idxs(
+ toks,
+ tokenizer,
+ name_tok_len=1,
+ prepend_bos=prepend_bos,
+ )
+
+ punct_idxs = get_word_idxs(ioi_prompts, [",", "."], tokenizer)
+
+ return {
+ "IO": IO_idxs,
+ "IO-1": IO_idxs - 1,
+ "IO+1": IO_idxs + 1,
+ "S1": S1_idxs,
+ "S1-1": S1_idxs - 1,
+ "S1+1": S1_idxs + 1,
+ "S2": S2_idxs,
+ "end": end_idxs,
+ "starts": t.zeros_like(end_idxs),
+ "punct": punct_idxs,
+ }
+
+
+class IOIDataset:
+ def __init__(
+ self,
+ prompt_type: str | list[str], # if list, then it will be a list of templates
+ N=500,
+ tokenizer=None,
+ prompts=None,
+ symmetric=False,
+ prefixes=None,
+ nb_templates=None,
+ prepend_bos=False,
+ manual_word_idx=None,
+ has_been_flipped: bool = False,
+ seed=0,
+ device="cuda",
+ ):
+ self.seed = seed
+ random.seed(self.seed)
+ np.random.seed(self.seed)
+ if not (
+ N == 1
+ or not prepend_bos
+ or (tokenizer is not None and tokenizer.bos_token_id == tokenizer.eos_token_id)
+ ):
+ warnings.warn("Probably word_idx will be calculated incorrectly due to this formatting")
+ self.has_been_flipped = has_been_flipped
+ assert not (symmetric and prompt_type == "ABC")
+ assert (prompts is not None) or (not symmetric) or (N % 2 == 0), f"{symmetric} {N}"
+ self.prompt_type = prompt_type
+
+ if nb_templates is None:
+ nb_templates = len(BABA_TEMPLATES)
+
+ if prompt_type == "ABBA":
+ self.templates = ABBA_TEMPLATES[:nb_templates].copy()
+ elif prompt_type == "BABA":
+ self.templates = BABA_TEMPLATES[:nb_templates].copy()
+ elif prompt_type == "mixed":
+ self.templates = (
+ BABA_TEMPLATES[: nb_templates // 2].copy()
+ + ABBA_TEMPLATES[: nb_templates // 2].copy()
+ )
+ random.shuffle(self.templates)
+ elif prompt_type == "ABC":
+ self.templates = ABC_TEMPLATES[:nb_templates].copy()
+ elif prompt_type == "BAC":
+ self.templates = BAC_TEMPLATES[:nb_templates].copy()
+ elif prompt_type == "ABC mixed":
+ self.templates = (
+ ABC_TEMPLATES[: nb_templates // 2].copy()
+ + BAC_TEMPLATES[: nb_templates // 2].copy()
+ )
+ random.shuffle(self.templates)
+ elif isinstance(prompt_type, list):
+ self.templates = prompt_type
+ else:
+ raise ValueError(prompt_type)
+
+ if tokenizer is None:
+ self.tokenizer = AutoTokenizer.from_pretrained("gpt2")
+ self.tokenizer.pad_token = self.tokenizer.eos_token
+ else:
+ self.tokenizer = tokenizer
+
+ self.prefixes = prefixes
+ self.prompt_type = prompt_type
+ if prompts is None:
+ self.ioi_prompts = gen_prompt_uniform( # list of dict of the form {"text": "Alice and Bob bla bla. Bob gave bla to Alice", "IO": "Alice", "S": "Bob"}
+ self.templates,
+ NAMES,
+ nouns_dict={"[PLACE]": PLACES, "[OBJECT]": OBJECTS},
+ N=N,
+ symmetric=symmetric,
+ prefixes=self.prefixes,
+ abc=(prompt_type in ["ABC", "ABC mixed", "BAC"]),
+ )
+ else:
+ assert N == len(prompts), f"{N} and {len(prompts)}"
+ self.ioi_prompts = prompts
+
+ all_ids = [prompt["TEMPLATE_IDX"] for prompt in self.ioi_prompts]
+ all_ids_ar = np.array(all_ids)
+ self.groups: list[list[int]] = []
+ for id in list(set(all_ids)):
+ self.groups.append(np.where(all_ids_ar == id)[0]) # type: ignore
+
+ small_groups = []
+ for group in self.groups:
+ if len(group) < 5:
+ small_groups.append(len(group))
+
+ self.sentences = [
+ prompt["text"] for prompt in self.ioi_prompts
+ ] # a list of strings. Renamed as this should NOT be forward passed
+
+ self.templates_by_prompt = [] # for each prompt if it's ABBA or BABA
+ for i in range(N):
+ if self.sentences[i].index(self.ioi_prompts[i]["IO"]) < self.sentences[i].index(
+ self.ioi_prompts[i]["S"]
+ ):
+ self.templates_by_prompt.append("ABBA")
+ else:
+ self.templates_by_prompt.append("BABA")
+
+ texts = [
+ (self.tokenizer.bos_token if prepend_bos else "") + prompt["text"]
+ for prompt in self.ioi_prompts
+ ]
+ self.toks = t.Tensor(self.tokenizer(texts, padding=True).input_ids).long()
+
+ self.word_idx = get_idx_dict(
+ self.ioi_prompts,
+ self.tokenizer,
+ prepend_bos=prepend_bos,
+ toks=self.toks,
+ )
+ self.prepend_bos = prepend_bos
+ if manual_word_idx is not None:
+ self.word_idx = manual_word_idx
+
+ self.N = N
+ self.max_len = max(
+ [len(self.tokenizer(prompt["text"]).input_ids) for prompt in self.ioi_prompts]
+ )
+
+ self.io_tokenIDs = [
+ self.tokenizer.encode(" " + prompt["IO"])[0] for prompt in self.ioi_prompts
+ ]
+ self.s_tokenIDs = [
+ self.tokenizer.encode(" " + prompt["S"])[0] for prompt in self.ioi_prompts
+ ]
+
+ self.tokenized_prompts = []
+
+ for i in range(self.N):
+ self.tokenized_prompts.append(
+ "|".join([self.tokenizer.decode(tok) for tok in self.toks[i]])
+ )
+
+ self.device = device
+ self.to(device)
+
+ def gen_flipped_prompts(self, flip):
+ # Check if it's already been flipped (shouldn't string 2 flips together)
+ if self.has_been_flipped:
+ warnings.warn(
+ "This dataset has already been flipped. Generally, you should try and apply flips in one step, because this can lead to errors."
+ )
+
+ # Redefine seed (so it's different depending on what the flip is, e.g. we don't want (IO, RAND) then (S, RAND) to give us the same rand names)
+ seed = self.seed + sum(map(ord, list("".join(flip))))
+
+ # Get flipped prompts
+ flipped_prompts = gen_flipped_prompts(
+ self.ioi_prompts, self.templates_by_prompt, flip, NAMES, seed
+ )
+
+ flipped_ioi_dataset = IOIDataset(
+ prompt_type=self.prompt_type,
+ N=self.N,
+ tokenizer=self.tokenizer,
+ prompts=flipped_prompts,
+ prefixes=self.prefixes,
+ prepend_bos=self.prepend_bos,
+ manual_word_idx=self.word_idx,
+ has_been_flipped=True,
+ seed=seed,
+ device=self.device,
+ )
+ return flipped_ioi_dataset
+
+ def copy(self):
+ copy_ioi_dataset = IOIDataset(
+ prompt_type=self.prompt_type,
+ N=self.N,
+ tokenizer=self.tokenizer,
+ prompts=self.ioi_prompts.copy(),
+ prefixes=self.prefixes.copy() if self.prefixes is not None else self.prefixes,
+ )
+ return copy_ioi_dataset
+
+ def __getitem__(self, key):
+ sliced_prompts = self.ioi_prompts[key]
+ sliced_dataset = IOIDataset(
+ prompt_type=self.prompt_type,
+ N=len(sliced_prompts),
+ tokenizer=self.tokenizer,
+ prompts=sliced_prompts,
+ prefixes=self.prefixes,
+ prepend_bos=self.prepend_bos,
+ )
+ return sliced_dataset
+
+ def __setitem__(self, key, value):
+ raise NotImplementedError()
+
+ def __delitem__(self, key):
+ raise NotImplementedError()
+
+ def __len__(self):
+ return self.N
+
+ def to(self, device):
+ self.toks = self.toks.to(device)
+ return self
diff --git a/ARENA_files/part51_balanced_bracket_classifier_tests.py b/ARENA_files/part51_balanced_bracket_classifier_tests.py
new file mode 100644
index 0000000..cb1d8af
--- /dev/null
+++ b/ARENA_files/part51_balanced_bracket_classifier_tests.py
@@ -0,0 +1,239 @@
+# %%
+from typing import Callable
+
+import einops
+import torch as t
+from jaxtyping import Float, Int
+from ARENA_files.arena_balanced_bracket_classifier_datasets import BracketsDataset
+from torch import Tensor
+from transformer_lens import ActivationCache, HookedTransformer
+
+# from IPython import get_ipython
+# ipython = get_ipython()
+# # Code to automatically update the HookedTransformer code as its edited without restarting the kernel
+# ipython.magic("load_ext autoreload")
+# ipython.magic("autoreload 2")
+
+MAIN = __name__ == "__main__"
+device = t.device("mps" if t.backends.mps.is_available() else "cuda" if t.cuda.is_available() else "cpu")
+
+t.set_grad_enabled(False)
+
+# %%
+
+
+def test_get_activations(get_activations: Callable, model: HookedTransformer, data: BracketsDataset):
+ import ARENA_Balanced_Brackets as solutions
+
+ embed_actual = get_activations(model, data.toks, "hook_embed")
+ embed_expected = solutions.get_activations(model, data.toks, "hook_embed")
+ t.testing.assert_close(embed_actual, embed_expected)
+
+ dict_actual = get_activations(model, data.toks, ["hook_embed", "hook_pos_embed"])
+ dict_expected = solutions.get_activations(model, data.toks, ["hook_embed", "hook_pos_embed"])
+ assert isinstance(dict_actual, ActivationCache)
+ t.testing.assert_close(dict_actual["hook_pos_embed"], dict_expected["hook_pos_embed"])
+
+ print("All tests in `test_get_activations` passed!")
+
+
+def test_get_ln_fit(get_ln_fit: Callable, model: HookedTransformer, data: BracketsDataset):
+ import ARENA_Balanced_Brackets as solutions
+
+ for seq_pos in [1, 0, None]:
+ fit_actual = get_ln_fit(model, data, model.ln_final, seq_pos)
+ fit_expected = solutions.get_ln_fit(model, data, model.ln_final, seq_pos)
+ t.testing.assert_close(fit_actual[0].coef_, fit_expected[0].coef_)
+
+ print("All tests in `test_get_ln_fit` passed!")
+
+
+# %%
+
+
+def test_get_pre_final_ln_dir(get_pre_final_ln_dir: Callable, model: HookedTransformer, data: BracketsDataset):
+ import ARENA_Balanced_Brackets as solutions
+
+ dir_actual = get_pre_final_ln_dir(model, data)
+ dir_expected = solutions.get_pre_final_ln_dir(model, data)
+ t.testing.assert_close(dir_actual, dir_expected)
+ print("All tests in `test_get_pre_final_ln_dir` passed!")
+
+
+# %%
+
+
+def test_get_out_by_components(get_out_by_components: Callable, model: HookedTransformer, data: BracketsDataset):
+ import ARENA_Balanced_Brackets as solutions
+
+ dir_actual = get_out_by_components(model, data)
+ dir_expected = solutions.get_out_by_components(model, data)
+ t.testing.assert_close(dir_actual.sum(1), dir_expected.sum(1))
+ print("All tests in `test_get_out_by_components` passed!")
+
+
+# %%
+
+
+def test_out_by_component_in_unbalanced_dir(
+ out_by_component_in_unbalanced_dir: Float[Tensor, "comp batch"],
+ model: HookedTransformer,
+ data: BracketsDataset,
+):
+ import ARENA_Balanced_Brackets as solutions
+
+ out_by_components_seq0 = solutions.get_out_by_components(model, data)[:, :, 0, :] # [component batch d_model]
+ pre_final_ln_dir = solutions.get_pre_final_ln_dir(model, data) # [d_model]
+
+ out_by_component_in_unbalanced_dir_expected = einops.einsum(
+ out_by_components_seq0,
+ pre_final_ln_dir,
+ "comp batch d_model, d_model -> comp batch",
+ ) # [component batch]
+ out_by_component_in_unbalanced_dir_expected -= (
+ out_by_component_in_unbalanced_dir_expected[:, data.isbal].mean(dim=1).unsqueeze(1)
+ )
+
+ t.testing.assert_close(out_by_component_in_unbalanced_dir, out_by_component_in_unbalanced_dir_expected)
+
+ print("All tests in `test_out_by_component_in_unbalanced_dir` passed!")
+
+
+# %%
+
+
+def test_out_by_component_in_pre_20_unbalanced_dir(
+ out_by_component_in_pre_20_unbalanced_dir: Float[Tensor, "comp batch"],
+ model: HookedTransformer,
+ data: BracketsDataset,
+):
+ import ARENA_Balanced_Brackets as solutions
+
+ out_by_components_seq1: Float[Tensor, "comp batch d_model"] = solutions.get_out_by_components(model, data)[
+ :, :, 1, :
+ ]
+ pre_layer2_outputs_seqpos1 = out_by_components_seq1[:-3]
+ out_by_component_in_pre_20_unbalanced_dir_expected = einops.einsum(
+ pre_layer2_outputs_seqpos1,
+ solutions.get_pre_20_dir(model, data),
+ "comp batch emb, emb -> comp batch",
+ )
+ out_by_component_in_pre_20_unbalanced_dir_expected -= out_by_component_in_pre_20_unbalanced_dir_expected[
+ :, data.isbal
+ ].mean(-1, keepdim=True)
+
+ t.testing.assert_close(
+ out_by_component_in_pre_20_unbalanced_dir,
+ out_by_component_in_pre_20_unbalanced_dir_expected,
+ rtol=0.0,
+ atol=1e-4,
+ )
+
+ print("All tests in `test_out_by_component_in_pre_20_unbalanced_dir` passed!")
+
+
+# %%
+
+
+def test_get_post_final_ln_dir(get_post_final_ln_dir, model: HookedTransformer):
+ import ARENA_Balanced_Brackets as solutions
+
+ actual = get_post_final_ln_dir(model)
+ expected = solutions.get_post_final_ln_dir(model)
+ t.testing.assert_close(actual, expected)
+ print("All tests in `test_get_post_final_ln_dir` passed!")
+
+
+def test_total_elevation_and_negative_failures(
+ data: BracketsDataset,
+ total_elevation_failure: Float[Tensor, "batch"],
+ negative_failure: Float[Tensor, "batch"],
+):
+ import ARENA_Balanced_Brackets as solutions
+
+ tef_expected, nf_expected = solutions.is_balanced_vectorized_return_both(data.toks)
+
+ t.testing.assert_close(negative_failure, nf_expected)
+ t.testing.assert_close(
+ total_elevation_failure,
+ tef_expected,
+ msg="total_elevation_failure is not correct. Did you remember to read the sequence from right to left?",
+ )
+
+ print("All tests in `test_total_elevation_and_negative_failures` passed!")
+
+
+# %%
+
+
+def test_get_attn_probs(get_attn_probs: Callable, model: HookedTransformer, data: BracketsDataset):
+ import ARENA_Balanced_Brackets as solutions
+
+ probs_actual = get_attn_probs(model, data, 2, 0)
+ probs_expected = solutions.get_attn_probs(model, data, 2, 0)
+ t.testing.assert_close(probs_actual, probs_expected)
+ print("All tests in `test_get_attn_probs` passed!")
+
+
+# %%
+
+
+def test_get_WOV(get_WOV: Callable, model: HookedTransformer):
+ W_OV_00 = get_WOV(model, 0, 0)
+ W_OV_00_expected = model.W_V[0, 0] @ model.W_O[0, 0]
+
+ t.testing.assert_close(W_OV_00, W_OV_00_expected)
+ print("All tests in `test_get_WOV` passed!")
+
+
+def test_get_pre_20_dir(get_pre_20_dir: Callable, model: HookedTransformer, data: BracketsDataset):
+ import ARENA_Balanced_Brackets as solutions
+
+ dir_actual = get_pre_20_dir(model, data)
+ dir_expected = solutions.get_pre_20_dir(model, data)
+ t.testing.assert_close(dir_actual, dir_expected)
+ print("All tests in `test_get_pre_20_dir` passed!")
+
+
+def test_get_out_by_neuron(get_out_by_neuron: Callable, model: HookedTransformer, data: BracketsDataset):
+ import ARENA_Balanced_Brackets as solutions
+
+ out = get_out_by_neuron(model, data, layer=0, seq=1)
+ out_expected = solutions.get_out_by_neuron(model, data, layer=0, seq=1)
+ t.testing.assert_close(out, out_expected)
+ print("All tests in `test_get_out_by_neuron` passed!")
+
+
+def test_get_out_by_neuron_in_20_dir(
+ get_out_by_neuron_in_20_dir: Callable, model: HookedTransformer, data: BracketsDataset
+):
+ import ARENA_Balanced_Brackets as solutions
+
+ out = get_out_by_neuron_in_20_dir(model, data, layer=0)
+ out_expected = solutions.get_out_by_neuron_in_20_dir(model, data, layer=0)
+ t.testing.assert_close(out, out_expected)
+ print("All tests in `test_get_out_by_neuron_in_20_dir` passed!")
+
+
+def test_get_out_by_neuron_in_20_dir_less_memory(
+ get_out_by_neuron_in_20_dir_less_memory: Callable,
+ model: HookedTransformer,
+ data: BracketsDataset,
+):
+ import ARENA_Balanced_Brackets as solutions
+
+ out = get_out_by_neuron_in_20_dir_less_memory(model, data, layer=0)
+ out_expected = solutions.get_out_by_neuron_in_20_dir_less_memory(model, data, layer=0)
+ t.testing.assert_close(out, out_expected)
+ print("All tests in `test_get_out_by_neuron_in_20_dir_less_memory` passed!")
+
+
+def test_get_q_and_k_for_given_input(get_q_and_k_for_given_input, model, tokenizer):
+ import ARENA_Balanced_Brackets as solutions
+
+ parens = "()"
+ q, k = get_q_and_k_for_given_input(model, tokenizer, parens, 0)
+ q_expected, k_expected = solutions.get_q_and_k_for_given_input(model, tokenizer, parens, 0)
+ t.testing.assert_close(q, q_expected)
+ t.testing.assert_close(k, k_expected)
+ print("All tests in `test_get_q_and_k_for_given_input` passed!")