BRIDGE: BRANCH-GUIDED RESIDUAL INTERVENTIONS VIA DYNAMIC GEOMETRY

Representation intervention controls the behavior of large language models (LLMs) at inference time without updating parameters. Existing methods typically choose intermediate or late layers empirically as the source of intervention signals. However, we find that early-layer signals in fact achieve higher coverage of correct answers, but many irrelevant signals hinder direct use for effective intervention. To address this challenge, we propose BRIDGE (Branch-guided Residual Interventions via Dynamic GEometry). Unlike prior methods, BRIDGE extracts intervention signals by identifying the useful early branches and preserves general capabilities through a minimal, norm-preserving edit. Specifically, Early Branch Identification (EBI) projects an early-layer hidden state through the output head to select first-token anchors, extends them into short natural branches, and learns coverage-based utilities to identify the branches worth strengthening. Dynamics-aware Geometric Editing (DGE) then specifies a target utility gain, solves for the smallest norm-preserving residual edit that achieves it, and keeps the edit only when a forward pass confirms a positive realized gain. Across five Llama and Qwen models from 3B to 32B, BRIDGE consistently improves truthfulness, fairness, and safety alignment while preserving general capabilities, showing that properly identified early branches provide effective intervention signals for controllable LLM generation. Our code is available at https://anonymous.4open.science/r/Bridge-1FC8.