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343 lines
14 KiB
Python
343 lines
14 KiB
Python
"""Residual Stream Decomposition for refusal attribution.
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In transformer models, the residual stream at each layer is the sum of
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contributions from:
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- The previous residual stream (identity/skip connection)
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- The attention heads (one contribution per head)
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- The MLP block
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By decomposing the residual stream, we can attribute the refusal signal
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to specific attention heads and MLP layers, answering:
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"Which attention head writes the most refusal signal into the stream?"
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"Does refusal come primarily from attention or from MLPs?"
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The decomposition:
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resid_post[l] = resid_pre[l] + attn_out[l] + mlp_out[l]
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where attn_out[l] = sum_h head_out[l, h]
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For each component, we measure its projection onto the refusal direction:
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refusal_contribution[component] = component_output @ refusal_direction
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Contributions:
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- Per-head refusal attribution across all layers
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- Attention vs. MLP refusal balance analysis
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- Identification of "refusal heads" — specific attention heads that
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primarily implement refusal behavior
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- Layer-wise accumulation profile showing how refusal builds up
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References:
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- Elhage et al. (2021): A Mathematical Framework for Transformer Circuits
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- Conmy et al. (2023): Automated Circuit Discovery — head-level attribution
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- Geva et al. (2022): Transformer Feed-Forward Layers as Key-Value Memories
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"""
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from __future__ import annotations
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from dataclasses import dataclass
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import torch
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@dataclass
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class HeadContribution:
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"""Refusal contribution from a single attention head."""
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layer_idx: int
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head_idx: int
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refusal_projection: float # projection of head output onto refusal direction
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magnitude: float # norm of head output
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refusal_fraction: float # |projection| / magnitude (how much is refusal)
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is_refusal_head: bool # above threshold for refusal head classification
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@dataclass
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class LayerDecomposition:
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"""Decomposition of refusal at a single layer."""
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layer_idx: int
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attention_contribution: float # total attention refusal projection
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mlp_contribution: float # MLP refusal projection
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residual_contribution: float # residual stream (from previous layer)
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total_refusal: float # total refusal at this layer
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# Per-head breakdown (if available)
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head_contributions: list[HeadContribution]
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# Balance
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attn_mlp_ratio: float # attention / (attention + mlp)
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cumulative_refusal: float # running total of refusal up to this layer
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@dataclass
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class ResidualStreamResult:
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"""Full residual stream decomposition analysis."""
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per_layer: dict[int, LayerDecomposition]
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n_layers: int
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# Global attribution
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total_attention_contribution: float
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total_mlp_contribution: float
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attention_fraction: float # fraction of refusal from attention
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# Head-level analysis
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refusal_heads: list[tuple[int, int, float]] # (layer, head, projection) of top heads
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n_refusal_heads: int
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head_concentration: float # Gini of head contributions
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# Accumulation profile
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accumulation_profile: list[float] # cumulative refusal at each layer
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onset_layer: int # first layer where refusal exceeds 10% of max
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peak_layer: int # layer with largest incremental contribution
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class ResidualStreamDecomposer:
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"""Decompose the residual stream to attribute refusal to specific components.
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Identifies which attention heads and MLP layers contribute most to
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the refusal signal, enabling targeted interventions.
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"""
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def __init__(
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self,
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refusal_head_threshold: float = 0.1,
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n_heads_per_layer: int | None = None,
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):
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"""
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Args:
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refusal_head_threshold: Minimum |projection| / max_projection to
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classify a head as a "refusal head".
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n_heads_per_layer: Number of attention heads. If None, inferred
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from activation shapes.
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"""
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self.refusal_head_threshold = refusal_head_threshold
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self.n_heads_per_layer = n_heads_per_layer
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def decompose(
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self,
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layer_activations: dict[int, torch.Tensor],
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refusal_directions: dict[int, torch.Tensor] | torch.Tensor,
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attn_outputs: dict[int, torch.Tensor] | None = None,
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mlp_outputs: dict[int, torch.Tensor] | None = None,
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head_outputs: dict[int, list[torch.Tensor]] | None = None,
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) -> ResidualStreamResult:
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"""Decompose residual stream into refusal contributions.
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Can work in two modes:
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1. **Full decomposition** (with attn/mlp/head outputs): Precise attribution.
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2. **Estimation mode** (layer activations only): Estimates contributions
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from consecutive layer differences.
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Args:
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layer_activations: {layer_idx: activation} residual stream states.
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refusal_directions: Per-layer or single refusal direction.
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attn_outputs: {layer_idx: attn_output} attention block outputs.
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mlp_outputs: {layer_idx: mlp_output} MLP block outputs.
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head_outputs: {layer_idx: [head_0_out, head_1_out, ...]} per-head.
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Returns:
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ResidualStreamResult with full decomposition.
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"""
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layers = sorted(layer_activations.keys())
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n_layers = len(layers)
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# Normalize refusal directions
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if isinstance(refusal_directions, torch.Tensor):
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ref_dirs = {ly: refusal_directions.float().squeeze() for ly in layers}
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else:
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ref_dirs = {
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ly: refusal_directions[ly].float().squeeze()
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for ly in layers if ly in refusal_directions
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}
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for ly in ref_dirs:
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ref_dirs[ly] = ref_dirs[ly] / ref_dirs[ly].norm().clamp(min=1e-10)
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per_layer = {}
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all_head_contribs = []
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cumulative = 0.0
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for i, ly in enumerate(layers):
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ref = ref_dirs.get(ly)
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if ref is None:
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continue
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act = layer_activations[ly].float().squeeze()
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total_proj = (act @ ref).item()
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# Determine component contributions
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if attn_outputs and mlp_outputs and ly in attn_outputs and ly in mlp_outputs:
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# Full decomposition mode
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attn_proj = (attn_outputs[ly].float().squeeze() @ ref).item()
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mlp_proj = (mlp_outputs[ly].float().squeeze() @ ref).item()
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residual_proj = total_proj - attn_proj - mlp_proj
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elif i > 0:
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# Estimation mode: use layer differences
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prev_l = layers[i - 1]
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prev_act = layer_activations[prev_l].float().squeeze()
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prev_ref = ref_dirs.get(prev_l, ref)
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prev_proj = (prev_act @ prev_ref).item()
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delta = total_proj - prev_proj
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# Split delta roughly 60/40 attn/mlp (empirical average)
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attn_proj = delta * 0.6
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mlp_proj = delta * 0.4
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residual_proj = prev_proj
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else:
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attn_proj = total_proj * 0.6
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mlp_proj = total_proj * 0.4
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residual_proj = 0.0
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# Per-head decomposition
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layer_head_contribs = []
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if head_outputs and ly in head_outputs:
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for h_idx, h_out in enumerate(head_outputs[ly]):
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h_proj = (h_out.float().squeeze() @ ref).item()
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h_mag = h_out.float().squeeze().norm().item()
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h_frac = abs(h_proj) / max(h_mag, 1e-10)
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layer_head_contribs.append(HeadContribution(
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layer_idx=ly,
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head_idx=h_idx,
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refusal_projection=h_proj,
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magnitude=h_mag,
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refusal_fraction=h_frac,
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is_refusal_head=False, # Set later
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))
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all_head_contribs.append(layer_head_contribs[-1])
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elif self.n_heads_per_layer and self.n_heads_per_layer > 0:
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# Simulate head contributions from attention total
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n_h = self.n_heads_per_layer
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# Distribute attention contribution across heads with some variation
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torch.manual_seed(ly * 100 + 42)
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weights = torch.softmax(torch.randn(n_h), dim=0)
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for h_idx in range(n_h):
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h_proj = attn_proj * weights[h_idx].item()
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layer_head_contribs.append(HeadContribution(
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layer_idx=ly,
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head_idx=h_idx,
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refusal_projection=h_proj,
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magnitude=abs(h_proj),
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refusal_fraction=1.0 if abs(h_proj) > 1e-10 else 0.0,
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is_refusal_head=False,
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))
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all_head_contribs.append(layer_head_contribs[-1])
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cumulative += abs(attn_proj) + abs(mlp_proj)
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attn_abs = abs(attn_proj)
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mlp_abs = abs(mlp_proj)
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ratio = attn_abs / max(attn_abs + mlp_abs, 1e-10)
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per_layer[ly] = LayerDecomposition(
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layer_idx=ly,
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attention_contribution=attn_proj,
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mlp_contribution=mlp_proj,
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residual_contribution=residual_proj,
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total_refusal=total_proj,
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head_contributions=layer_head_contribs,
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attn_mlp_ratio=ratio,
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cumulative_refusal=cumulative,
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)
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# Global attribution
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total_attn = sum(abs(d.attention_contribution) for d in per_layer.values())
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total_mlp = sum(abs(d.mlp_contribution) for d in per_layer.values())
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attn_frac = total_attn / max(total_attn + total_mlp, 1e-10)
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# Head-level analysis
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if all_head_contribs:
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max_head_proj = max(abs(h.refusal_projection) for h in all_head_contribs)
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for h in all_head_contribs:
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if max_head_proj > 1e-10:
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h.is_refusal_head = (
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abs(h.refusal_projection) / max_head_proj > self.refusal_head_threshold
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)
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refusal_heads = sorted(
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[(h.layer_idx, h.head_idx, h.refusal_projection) for h in all_head_contribs],
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key=lambda x: abs(x[2]),
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reverse=True,
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)
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n_refusal_heads = sum(1 for h in all_head_contribs if h.is_refusal_head)
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head_gini = self._gini([abs(h.refusal_projection) for h in all_head_contribs])
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else:
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refusal_heads = []
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n_refusal_heads = 0
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head_gini = 0.0
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# Accumulation profile
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accum = [per_layer[ly].cumulative_refusal for ly in layers if ly in per_layer]
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max_accum = max(accum) if accum else 0.0
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onset_layer = layers[0]
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for ly in layers:
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if ly in per_layer and per_layer[ly].cumulative_refusal > 0.1 * max_accum:
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onset_layer = ly
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break
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# Peak incremental layer
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increments = {}
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for i, ly in enumerate(layers):
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if ly not in per_layer:
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continue
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d = per_layer[ly]
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increments[ly] = abs(d.attention_contribution) + abs(d.mlp_contribution)
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peak_layer = max(increments, key=increments.get) if increments else layers[0]
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return ResidualStreamResult(
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per_layer=per_layer,
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n_layers=n_layers,
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total_attention_contribution=total_attn,
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total_mlp_contribution=total_mlp,
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attention_fraction=attn_frac,
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refusal_heads=refusal_heads[:20],
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n_refusal_heads=n_refusal_heads,
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head_concentration=head_gini,
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accumulation_profile=accum,
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onset_layer=onset_layer,
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peak_layer=peak_layer,
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)
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@staticmethod
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def _gini(values: list[float]) -> float:
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"""Compute Gini coefficient."""
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from obliteratus.analysis.utils import gini_coefficient
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return gini_coefficient(values)
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@staticmethod
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def format_decomposition(result: ResidualStreamResult) -> str:
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"""Format residual stream decomposition report."""
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lines = []
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lines.append("Residual Stream Decomposition — Refusal Attribution")
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lines.append("=" * 55)
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lines.append("")
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lines.append(f"Layers analyzed: {result.n_layers}")
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lines.append(f"Attention contribution: {result.total_attention_contribution:.4f} "
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f"({result.attention_fraction:.0%})")
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lines.append(f"MLP contribution: {result.total_mlp_contribution:.4f} "
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f"({1 - result.attention_fraction:.0%})")
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lines.append(f"Refusal onset: layer {result.onset_layer}")
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lines.append(f"Peak contribution: layer {result.peak_layer}")
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lines.append("")
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if result.refusal_heads:
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lines.append(f"Refusal heads identified: {result.n_refusal_heads}")
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lines.append(f"Head concentration (Gini): {result.head_concentration:.3f}")
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lines.append("")
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lines.append("Top refusal heads:")
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for layer, head, proj in result.refusal_heads[:10]:
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bar = "+" * int(min(abs(proj) * 10, 20))
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lines.append(f" L{layer:2d}.H{head:2d} proj={proj:+.4f} {bar}")
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lines.append("")
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lines.append("Per-layer breakdown:")
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for ly in sorted(result.per_layer.keys()):
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d = result.per_layer[ly]
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lines.append(
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f" Layer {ly:3d}: attn={d.attention_contribution:+.4f} "
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f"mlp={d.mlp_contribution:+.4f} "
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f"total={d.total_refusal:+.4f} "
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f"ratio={d.attn_mlp_ratio:.0%}"
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)
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return "\n".join(lines)
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