Monarch-MoE: Structured Experts for Multimodal Continual Instruction Tuning

Learning new tasks in multimodal continual instruction tuning can cause catastrophic forgetting of previously acquired knowledge. Although multi-expert LoRA distributes learning across experts, updates to a dense low-rank expert can still affect many output features. We introduce Monarch-MoE, which replaces the dense factors in LoRA experts with block-diagonal factors connected by a fixed permutation. This structure provides blockwise gradient isolation: individual block-pair updates affect only one output block, while connections between all input and output blocks are maintained. To make these compact experts practical on memory-limited hardware, we combine batched computation, fused forward operators, and an optimized backward pass. Across three continual-learning methods evaluated on MLLM-DCL and UCIT with LLaVA-1.5-7B, Monarch-MoE improves first-task retention while reducing adapter parameters by approximately 75% and 50%, respectively. In the main comparison, first-task forgetting is as low as 0.52 percentage points on MLLM-DCL and 0.10 on UCIT, with method-dependent trade-offs in final performance. Our implementation supports fine-tuning and inference on a single 24 GB RTX 4090, with lower measured memory use and competitive runtime in the evaluated settings. Together, these algorithmic and systems improvements make structured experts a practical option for continual adaptation on memory-limited hardware.