# Monarch-MoE: Structured Experts for Multimodal Continual Instruction Tuning

arXiv: https://arxiv.org/abs/2610.13215 · HTML: https://mlsanity.com/paper/2610.13215/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mixture of LoRA experts, one of 12 directions in Mixture-of-experts.
- Builds on 13 of its 13 references that are in the map.
- First posted on arXiv 9 Oct 2026.

## Placed in

- Mixture-of-experts / [Mixture of LoRA experts](https://mlsanity.com/moe/mixture-of-lora-experts/)

## Builds on (most cited first, 13 of 13)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Improved Baselines with Visual Instruction Tuning](https://mlsanity.com/paper/2310.03744/) (2023)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [Orthogonal Subspace Learning for Language Model Continual Learning](https://mlsanity.com/paper/2310.14152/) (2023)
- [Monarch: Expressive Structured Matrices for Efficient and Accurate Training](https://mlsanity.com/paper/2204.00595/) (2022)
- [CoIN: A Benchmark of Continual Instruction tuNing for Multimodel Large Language Model](https://mlsanity.com/paper/2403.08350/) (2024)
- [CL-MoE: Enhancing Multimodal Large Language Model with Dual Momentum Mixture-of-Experts for Continual Visual Question Answering](https://mlsanity.com/paper/2503.00413/) (2025)
- [HiDe-LLaVA: Hierarchical Decoupling for Continual Instruction Tuning of Multimodal Large Language Model](https://mlsanity.com/paper/2503.12941/) (2025)
- [MCITlib: Multimodal Continual Instruction Tuning Library and Benchmark](https://mlsanity.com/paper/2508.07307/) (2025)
- [Federated Continual Instruction Tuning](https://mlsanity.com/paper/2503.12897/) (2025)
- [MoRe Fine-Tuning with 10x Fewer Parameters](https://mlsanity.com/paper/2408.17383/) (2024)

## Abstract (arXiv)

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.