Projection

Overview

In the context of AI and specifically in modifying model behavior, projection is a mathematical technique used to remove unwanted components from a [vector] representing the model's activity, particularly to change how a model processes harmful prompts. It involves calculating the component of a vector (representing model activations) that is parallel to a specified [refusal direction] and subtracting this component, such that the resulting vector no longer has any component pointing in the refusal direction.

What is Projection?

Mathematically removing the [refusal direction] to modify AI behavior

• A technique to eliminate a specific component of a vector
• Used to modify how AI models behave and respond to harmful prompts
• Identifies and subtracts the part of a vector aligned with an undesirable direction

How Does it Work?

• The activation vector is treated as an arrow in a multi-dimensional space, representing how the model is processing
• A [refusal direction] vector indicates the model's unwanted response
• Projection calculates how much the activation aligns with the refusal direction, by finding its "shadow" onto the vector
• By subtracting that "shadow", we remove the response, and it allows for the model to respond in a new way

Mathematical Formula

The projection of an activation vector h onto a refusal direction d_refusal is calculated as:

proj_(d_refusal)(h) = (h · d_refusal) d_refusal

Related Concepts

• Parameters
• Model Architecture
• Vectors
• Refusal Direction
• Abliteration
• Orthogonalization
• Neural Networks