ResMerge: Residual-based Spectral Merging of Large Language Models

Model merging offers a training-free way to combine multiple post-trained expert models, but merging experts obtained through reinforcement learning (RL) remains challenging. Existing spectral merging methods often assume that leading singular directions contain the main task signal, while lower-energy residual components can be compressed, selected, or attenuated to reduce interference. We find that this assumption does not hold for RL task vectors: after decomposing each task vector into a leading spectral head and a residual component, both parts can independently recover substantial behavior knowledge, while exhibiting different merging properties. The head is highly concentrated and informative but more prone to sharp cross-expert conflicts, whereas the residual component is more dispersed and provides a more stable basis for aggregation. Based on this observation, we propose ResMerge, a residual-based spectral merging framework for RL experts. ResMerge first constructs a stable residual backbone with Spherical Residual Consensus Adaptation, which estimates a reliability-weighted consensus direction on the Frobenius sphere. It then reintroduces leading-head information through a Lightweight Head Correction module gated by positive cross-expert agreement. Experiments across multiple RL expert groups and capability domains show that ResMerge better preserves expert capabilities than representative task-vector and spectral merging baselines. The implementation of ResMerge is publicly available at https://github.com/sunyd0303-cpu/ResMerge-release.

PASs-MoE: Mitigating Misaligned Co-drift among Router and Experts via Pathway Activation Subspaces for Continual Learning

Continual instruction tuning (CIT) requires multimodal large language models (MLLMs) to adapt to a stream of tasks without forgetting prior capabilities. A common strategy is to isolate updates by routing inputs to different LoRA experts. However, existing LoRA-based Mixture-of-Experts (MoE) methods often jointly update the router and experts in an indiscriminate way, causing the router's preferences to co-drift with experts' adaptation pathways and gradually deviate from early-stage input-expert specialization. We term this phenomenon Misaligned Co-drift, which blurs expert responsibilities and exacerbates forgetting.To address this, we introduce the pathway activation subspace (PASs), a LoRA-induced subspace that reflects which low-rank pathway directions an input activates in each expert, providing a capability-aligned coordinate system for routing and preservation. Based on PASs, we propose a fixed-capacity PASs-based MoE-LoRA method with two components: PAS-guided Reweighting, which calibrates routing using each expert's pathway activation signals, and PAS-aware Rank Stabilization, which selectively stabilizes rank directions important to previous tasks. Experiments on a CIT benchmark show that our approach consistently outperforms a range of conventional continual learning baselines and MoE-LoRA variants in both accuracy and anti-forgetting without adding parameters. Our code will be released upon acceptance.