Induction Heads

An induction head operates via a two-step mechanism. First, a previous token head attends to the immediately preceding token and copies its embedding into the residual stream. Second, the induction head itself uses a K-composition pattern: its query vector is computed from the current token, but its key vector is computed from the previous token head's output. This causes it to attend to tokens that followed a similar prefix in the past, effectively implementing the rule: 'If I see token A now, look for the last time A appeared and predict what came after it.'

The defining architectural signature of an induction head is K-composition with a previous token head. The attention score is computed as softmax(Q_current · K_previous), where the key vector is derived from the output of an earlier attention head that attended to the prior position. This compositional structure creates a prefix-matching mechanism: the head searches for positions where the key vector (representing the token after a prefix) matches the query vector (representing the current token). This is distinct from simple copying because it generalizes across different occurrences of the same token.

Induction heads are the primary circuit responsible for in-context learning in transformer models. When a model exhibits the ability to complete a pattern like A B -> A B after seeing a few examples, induction heads are performing the underlying computation. They explain why models can copy novel sequences, repeat patterns, and perform simple algorithmic tasks without weight updates. The strength of induction heads correlates directly with a model's few-shot learning capability, and their formation during training coincides with the phase change where in-context learning emerges.

Induction heads do not exist at initialization; they form abruptly during training in a phase change event. Research shows that models first develop bigram statistics (attending to the immediately previous token), and then suddenly restructure to form induction heads. This transition is visible in loss curves as a sharp drop and corresponds to the model transitioning from memorization to acquiring a general in-context copying algorithm. Once formed, induction heads rapidly strengthen and become the dominant mechanism for sequence completion tasks.

In larger models, induction heads often exhibit polysemanticity: a single head may implement multiple induction-like behaviors across different token positions or contexts. This is related to the phenomenon of superposition, where the model compresses more features than it has dimensions. Sparse autoencoders can be used to decompose an induction head's activations into distinct, monosemantic features, revealing that what appears as one head may actually be several superimposed induction circuits operating in parallel across different token types or positional offsets.

The functional role of induction heads is confirmed through activation patching experiments. By replacing the output of a candidate induction head with activations from a corrupted forward pass (where the prefix context is altered) and observing the resulting logit changes, researchers can causally verify that the head is responsible for copying behavior. Path patching further isolates the specific K-composition pathway, demonstrating that ablating the connection between the previous token head and the induction head's key computation destroys the copying capability while leaving other functions intact.

The fundamental unit of mechanistic analysis. A circuit is a sparse, interpretable subgraph of a neural network—consisting of connected attention heads and MLP neurons—that implements a specific, human-understandable algorithm.

• Induction heads form a core circuit for in-context learning
• Circuits are discovered through causal interventions, not just correlation
• The goal is to decompose the full model into a collection of composable circuits

A causal intervention technique used to isolate the function of a specific model component. To test if a head is an induction head, researchers replace its activation at a specific layer and position with a value from a corrupted forward pass and measure the change in loss.

• Clean vs. corrupted runs: Compare model behavior with and without the patched activation
• Used to prove that induction heads are causally necessary for in-context copying
• Localizes function to specific attention heads rather than entire layers

The specific attention pattern that defines induction heads. In K-composition, the key vectors computed by an earlier attention head are read by the query vectors of a later head in a subsequent token position.

• The previous token head writes into the key subspace
• The induction head reads from that subspace via its query
• This creates a chain: 'Token B' attends to 'Token A' because a previous occurrence of 'A' was followed by 'B'

A hypothesized phenomenon where a neural network represents more independent features than it has dimensions in a given layer. Induction heads rely on the model's ability to compress token identity and positional context into overlapping representations.

• The residual stream carries both the 'current token' and 'previous token' signals
• Induction heads must disentangle these superimposed features
• Sparse autoencoders are used to decompose these polysemantic representations into monosemantic features

A linear decomposition technique that attributes the final logit output for a token directly to the individual contributions of each attention head and MLP layer. This method provides a mathematical proof of an induction head's effect.

• Decomposes the residual stream into additive paths
• Shows how the induction head's output directly increases the logit of the correct next token
• Validates that the circuit's function matches the hypothesized algorithm

The broader research program that induction heads emerged from. This field seeks to reverse-engineer the specific functional roles of every attention head and MLP layer in transformer architectures.

• Induction heads were discovered in 2022 by Olsson et al. while analyzing in-context learning
• Found to be a universal emergent circuit in models of sufficient size
• Related to function vectors and task vectors that encode specific behaviors