Induction Heads

What they are

Induction heads are the canonical interpretable circuit in transformers. They implement a simple but powerful algorithm:

"Find the previous occurrence of the current token. Predict that what came after it last time will come after it this time."

Given the sequence [A][B]...[A], an induction head at the second [A] attends to [B] (the token that followed the first [A]) and boosts its probability.

This is the mechanism underlying in-context learning: the ability to follow patterns from the context without any weight updates.

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The two-head circuit

Induction is a two-component circuit:

Layer 0: "Previous token" head
    At position t: attends to position t-1
    Copies token[t-1] into the residual stream at position t

Layer 1+: "Induction" head
    At position t: uses the "what came before me?" information
    to attend back to the previous occurrence of token[t]
    Boosts the probability of whatever followed it

The two heads must work together — neither alone produces induction behaviour. This is the first documented circuit in transformers.

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Detection

from kamui.mechinterp import InductionHeadDetector

detector = InductionHeadDetector(model)

# Score all (layer, head) pairs
scores = detector.score_all_heads()
# Returns: {(0,0): 0.04, (0,1): 0.07, (1,2): 0.83, (1,5): 0.71, ...}

# Visualise
detector.plot_scores(scores)
# Heatmap: rows=layers, cols=heads, cell=induction score

# Find heads above threshold
induction_heads = [(l, h) for (l, h), s in scores.items() if s > 0.5]

The scoring method

Construct sequences of the form [random × 50][same random × 50]. At each position t in the second half, measure the attention weight on position t - prefix_length (the "induction position").

A high average weight on the induction position = induction head.

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Causal verification

Detection alone is correlation. Verify causally with ablation:

# How much does removing induction heads hurt in-context learning?
baseline_icl = measure_icl(model)

ablated_icl = detector.ablate_and_measure(
    heads=induction_heads,
    task="repeat_pattern",
)

print(f"ICL degradation: {(baseline_icl - ablated_icl) / baseline_icl:.1%}")
# Expected: significant drop (30-70%) — induction heads drive ICL

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Expected findings in KAMUI small model

Based on Olsson et al. (2022) and replications in similar-scale models:

• Layer 0: contains "previous token" heads (low induction score, high attention to position t-1)
• Layer 1: contains induction heads (high induction score, > 0.5)
• Layers 2+: may contain weaker induction heads or other circuits

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References

Olsson et al. (2022). In-context Learning and Induction Heads. Transformer Circuits Thread. https://transformer-circuits.pub/2022/in-context-learning-and-induction-heads/