Octopus: History-Free Gradient Orthogonalization for Continual Learning in Multimodal Large Language Models

Catastrophic forgetting remains a major obstacle to continual learning in large language models (LLMs) and vision--language models (VLMs). Although Mixture-of-Experts (MoE) architectures offer an efficient path to scaling, existing LoRA-based MoE continual learning methods still face a fundamental trade-off: they either isolate experts too aggressively, limiting knowledge transfer across tasks, or allow task-specific updates to overwrite important existing parameters, leading to severe forgetting. To address this, we propose CP-MoE, a continual learning framework built around a transient expert that captures early task-specific updates and guides their integration into stable experts. CP-MoE introduces a consistency-preserving routing bias, which uses the transient expert to estimate representation similarity with stable experts and steer routing towards more compatible expert selection, and a transient expert-guided regularisation mechanism, which selectively protects important historical parameters during merging. Together, these components reduce parameter interference and forgetting while preserving cross-task knowledge transfer. We validate CP-MoE on both unimodal and multimodal continual learning benchmarks with LLM-based and VLM-based MoE models. On SuperNI benchmark, spanning diverse sequential language tasks, CP-MoE achieves state-of-the-art performance and stronger zero-shot transfer to unseen tasks. On VQA v2 dataset, it scales effectively to multimodal visual reasoning, consistently reduces forgetting, and outperforms strong MoE baselines.

A central challenge in continual learning for large language models (LLMs) is catastrophic forgetting, where adapting to new tasks can substantially degrade performance on previously learned ones. Existing projection-based methods mitigate such interference by restricting parameter updates to subspaces that are orthogonal to directions associated with past tasks. However, these methods are typically formulated under Euclidean parameter geometry, with update magnitudes and projections governed by the Frobenius norm. The recent empirical success of the Muon optimizer, which applies orthogonalized matrix updates and admits a spectral-norm interpretation, suggests that Frobenius geometry may not be the most effective choice for matrix-valued LLM parameters. Motivated by this observation, we propose Muon-OGD, a spectral-norm-aware continual learning framework that integrates Muon-style operator-norm geometry with orthogonal projection constraints. Our method formulates each update as a spectral-norm-constrained optimization problem with linear non-interference constraints, and solves it efficiently through dual iterations and Newton--Schulz matrix-sign approximations. By applying orthogonalized momentum updates that avoid protected directions associated with prior tasks, Muon-OGD aims to improve the stability--plasticity trade-off in sequential LLM adaptation. We evaluate the proposed method on standard continual learning benchmarks, TRACE, and domain-specific Coding--Math--Medical curricula using both encoder--decoder and decoder-only architectures. Empirically, Muon-OGD consistently improves over sequential fine-tuning and competitive orthogonal-gradient baselines, while remaining computationally scalable. These results suggest that spectral-norm-aware update geometry provides a practical and effective alternative to Frobenius-norm projection for continual learning in LLMs.

Continual adaptation is essential for multimodal large language models (MLLMs) deployed across evolving domains, but the state-of-the-art MR-LoRA method highly relies on the assumption that a MLLM-based router is necessary to process complex multimodal inputs. This paper revisits this claim on the MLLM-CL benchmark and argues for two claims. \textbf{First}, routing does not require an MLLM: a simple training-free, replay-free ptotypical routing method (\textsc{RePRo}), uses frozen pretrained features and task prototypes to match the MLLM-based router of MR-LoRA at far lower computational cost. \textbf{Second}, shared experts do not improve continual learning for MLLMs, despite their theoretical appeal. We show that these findings arise from two structural limitations of MLLM-CL: (1) its tasks are \textbf{highly separable} in representation space, and (2) its fixed task order makes conclusions \textbf{sensitive to a single curriculum} rather than robust across diverse continual-learning trajectories. As a result, the benchmark primarily rewards learning in isolation rather than genuine continual transfer. This motivates a new design for future benchmarks of continual MLLM learning, with overlapping task manifolds, multiple task orders, fine-grained domain shifts, and evaluation protocols that reward forward transfer as well as retention.