3️⃣ White-box Methods

# TODO: Extract attention patterns
def extract_attention_patterns(model, tokenizer, cot_trace: str, sentences: list[str]) -> dict:
    """
    Extract attention weights and aggregate to sentence-sentence matrices.

    Returns:
        Dictionary with:
        - token_attention: (num_layers, num_heads, seq_len, seq_len)
        - sentence_attention: (num_layers, num_heads, num_sentences, num_sentences)
        - vertical_attention: (num_layers, num_heads, num_sentences)
          [how much each sentence receives from all downstream]
    """
    pass

# TODO: Identify receiver heads
# from scipy.stats import kurtosis  # Will import when needed


def identify_receiver_heads(
    vertical_attention: np.ndarray,
    min_distance: int = 4,  # Ignore nearby sentences
) -> dict:
    """
    Identify receiver heads by computing kurtosis of attention distributions.

    Args:
        vertical_attention: (num_layers, num_heads, num_sentences)
        min_distance: Minimum sentence distance to consider

    Returns:
        Dictionary with kurtosis scores, top receiver heads, etc.
    """
    pass

# TODO: Compare receiver head attention to resampling importance
def compare_receiver_heads_to_importance(
    receiver_head_scores: np.ndarray,
    importance_scores: list[dict],
    sentences: list[str],
    categories: list[str],
):
    """
    Validate that receiver heads attend to high-importance sentences.

    Expected: Plan Generation and Uncertainty Management receive most attention
    """
    pass

# TODO: Implement sentence masking
def compute_sentence_sentence_causality(
    model, tokenizer, cot_trace: str, sentences: list[str], source_idx: int, target_idx: int
) -> float:
    """
    Measure causal effect of source sentence on target sentence.

    Process:
    1. Forward pass with full trace → get logits for target sentence
    2. Mask attention to source sentence → get logits for target sentence
    3. Compute average log-KL divergence across target tokens
    4. Normalize by average effect from all prior sentences

    Returns:
        Normalized causal importance score
    """
    pass

# TODO: Build full causal matrix
def compute_causal_matrix(model, tokenizer, cot_trace: str, sentences: list[str]) -> np.ndarray:
    """
    Compute full sentence-to-sentence causal importance matrix.

    Returns:
        Matrix of shape (num_sentences, num_sentences)
        where matrix[i, j] = causal importance of sentence i on sentence j
        (only defined for j > i)
    """
    pass

# TODO: Visualize causal matrix


def plot_causal_matrix(
    causal_matrix: np.ndarray,
    sentences: list[str],
    categories: list[str] = None,
    top_n: int = None,  # Show only top N most important sentences
):
    """
    Plot sentence-to-sentence causal importance as heatmap.

    Darker colors = stronger causal dependencies
    """
    pass

TODO: Case study analysis
Identify strong dependencies in causal matrix
Trace paths from planning → computation → answer
Show how backtracking creates loops in the graph

# TODO: Find backtracking sentences
def find_backtracking_moments(
    sentences: list[dict],
    keywords: list[str] = ["wait", "let me", "double check", "hmm", "actually"],
) -> list[int]:
    """
    Find sentences that indicate backtracking or uncertainty.

    Returns:
        List of sentence indices where backtracking occurs
    """
    pass

TODO: Measure backtracking impact
Use resampling to see how removing backtracking sentences affects final answer
Show that backtracking sentences have high counterfactual importance

TODO: Intervention experiment
Option 1: Use activation steering to suppress "Wait" token
Option 2: Mask attention at backtracking position
Option 3: Directly modify logits to reduce probability of "Wait"

Hypothesis: Without "Wait", model proceeds with incorrect reasoning
This proves backtracking has causal role, not just correlation