Behavior Quotient Learning for Low-Rank Adaptation of LLM Agents

Summary

The paper proposes BQ-LoRA, a single-adapter low-rank fine-tuning framework for LLM agents that addresses behavioral redundancy among training trajectories. It argues that multiple trajectories can induce equivalent changes in decision distributions, so uniform averaging over-represents redundant behaviors, and that aggregated updates can exceed the LoRA rank budget, so weight-space projection distorts intended decision changes. BQ-LoRA has two modules: behavior quotient balancing (BQB) defines a local quotient manifold over effective updates — identifying updates that agree in first-order effects on normalized decision representations at fixed reference histories — and reweights trajectory gradients by the local density (Gaussian affinities) of their quotient-tangent directions; decision preserving compression (DPC) projects the balanced direction onto the fixed-rank tangent space, forms an affine target, and refactorizes it back to rank r while jointly minimizing weight error and first-order decision distortion. On AppWorld and BrowseComp-Plus with Qwen3.5-4B/9B backbones, BQ-LoRA averages 2.14 (4B) and 2.12 (9B) percentage points above the strongest baseline across eight metrics and yields the lowest interaction counts, though MoRAgent still leads on AppWorld Test-N at both scales. Ablations attribute 3.57-3.83 point drops to removing either module. Main limitations: no variance for the main tables, no wall-clock analysis of the per-step pairwise Jacobian computations, no code release, and missing solver details for the rank-constrained refactorization.