PRISM

Using gradient optimization alongside imposing constraints on independent representation, PRISM discovers multiple distinct routes at different levels; in sharp contrast to CAA that derives one path by computing differences. While CAA calculates just one direction toward target performance independently of others, PRISM separately identifies k such directions and integrates them into a unified manifold without overlapping or excessive loss when supervised.

This method draws upon recent research such as "Geometry of Refusal in Large Language Models" by Wollschläger.

PRISM optimizes using a combined target function that consists of four key elements: separation loss (ensuring clear differentiation among positives and negatives), independent loss (preventing blending across different experimental factors), similarity bounds (maintaining distinctness among axes rather than orthogonality) and reduction of modification for negatives (minimizing alteration to negative instances). Consistency is maintained here. "PRISM utilizes optimization with respect to a composite

• Multi-directional Behaviors: When the behavior is mediated by multiple directions (like refusal)
• Manifold Structure: When you expect a cone or manifold geometry rather than linear
• Ablation Tasks: When you want to remove rather than add a behavior
• Minimal Side Effects: When preserving model behavior on non-target inputs is important
• CAA Insufficient: When a single direction doesn't capture the full behavior