OV Circuit

The OV circuit's primary function is to transform the source token's residual stream into a format suitable for addition to the destination token. It dictates the semantic content of the information transfer.

• W_V projects the source token's representation into a value vector.
• W_O projects the weighted sum of value vectors back into the residual stream dimension.
• The composition W_O W_V defines the head's vocabulary of writable outputs.

Performing Singular Value Decomposition (SVD) on the OV circuit matrix reveals the principal directions of information transfer. The top singular vectors often correspond to interpretable semantic transformations.

• High singular values indicate dominant copying behaviors.
• Low singular values suppress irrelevant information.
• This decomposition is central to identifying induction heads and their copying patterns.

The attention head's behavior is fully described by the interaction of two independent circuits:

• QK Circuit: Determines where to attend. It computes the attention pattern using query and key projections.
• OV Circuit: Determines what to write. It computes the content to be moved from source to destination.

A head can attend broadly (QK) but write a very specific token (OV), or vice versa.

The direct effect of an attention head on the output logits can be computed by applying the unembedding matrix directly to the OV output. This is called direct logit attribution.

• Formula: logit_effect = W_U @ W_O @ v
• This isolates the head's contribution to the final token prediction.
• It reveals if a head promotes or suppresses specific tokens, such as copying the next token in an induction head.

Activation patching isolates the OV circuit's causal role. By replacing the value vectors from a corrupted run with clean values, researchers can measure the circuit's specific contribution.

• Patching only the OV output proves sufficiency.
• This technique validates that the OV circuit is the minimal pathway for a specific behavior.
• It distinguishes the OV circuit's role from the MLP layers' contributions.

The OV circuit writes its output directly into the residual stream of the destination token. This additive update is the mechanism by which information is moved between token positions.

• The residual stream accumulates OV outputs from all heads.
• Each head's OV circuit operates independently in a sum of components.
• The dimensionality of W_O matches the residual stream, ensuring seamless addition.

The computational pathway formed by the query and key projection matrices that determines which previous tokens an attention head attends to. While the OV circuit dictates what information is copied, the QK circuit computes the attention pattern—a probability distribution over source positions—that decides where the information comes from. Together, the QK and OV circuits form the complete functional unit of an attention head.

A specialized computational subunit within a transformer layer that computes a weighted sum of past token representations. Each head contains its own QK circuit for routing attention and OV circuit for determining the content to write into the residual stream. Mechanistic interpretability often decomposes heads into these two independent circuits to isolate their distinct functional roles in information movement.

The primary information highway in a transformer where each layer reads from and writes to a shared accumulating state. The OV circuit's output is added directly into the residual stream at the destination token position. This additive nature means the OV circuit's contribution is a vector that modifies the destination token's representation, enabling the model to compose information from multiple source tokens across different heads and layers.

A specific type of attention head discovered through mechanistic analysis that performs in-context copying. Its OV circuit is configured to copy the value of the token immediately following a previous occurrence of the current token. This mechanism is fundamental to in-context learning, enabling the model to recognize and continue patterns like [A][B] ... [A] → [B] without weight updates.

A matrix factorization technique used to decompose the OV weight matrix into interpretable rank-one components. By factorizing W_O W_V into its principal singular vectors, researchers can identify the dominant directions along which the OV circuit reads from the source token and writes to the destination token. This reveals the semantic subspaces that the head copies, such as attribute-value pairs or syntactic relationships.

A causal intervention technique that replaces a model's internal activation at a specific layer and token position with a cached activation from a different forward pass. By patching the output of the OV circuit and measuring the change in the model's final prediction, researchers can isolate the precise contribution of a specific head's information-copying operation to downstream behavior.