提出CRMA结构，让大模型持续学习不遗忘，且无需额外存储或重放数据。
CRMA: A Spectrally-Bounded Backbone for Modular Continual Fine-Tuning of LLMs
- 用双随机矩阵约束残差适配器，从结构上保证谱范数不超过1
- 在5个任务序列上使损失漂移从+42.96%降至-0.17%，显著减少遗忘
- 适用于参数量1.1B到9.2B的多种模型架构，适合需要持续学习的场景
大语言模型顺序微调面临两难：共享主干持续学习会灾难性遗忘，冻结主干则无法跨任务优化。现有模块化方法（如LoRAHub、AdapterFusion）选择冻结主干。本文提出CRMA（受限残差混合适配器），其内部混合矩阵M通过Sinkhorn归一化始终保持双随机性，依据Birkhoff定理，||M||_2 ≤ 1 在每次前向传播中由结构保证——非惩罚项。该谱界主干支持持续训练，同时保留原有遗忘防护能力。在Mistral-7B上，5个连续领域任务下，模块化每任务LoRA配合CRMA主干将损失相对漂移从+42.96% ± 5.5降至-0.17% ± 0.17，且各种子实验结果独立；相较冻结主干基线，先序任务保持损失提升1.99% ± 0.54。三个独立实验（Mistral-7B四域控制消融、TinyLlama三域污染复制、Mistral-7B跨域探针）均显示正向迁移，无需重放缓冲区、无需增长每任务记忆、无需知识蒸馏。Gemma-2-9B推理阶段消融验证：仅开启CRMA注入时，正确率从38/100升至98/100。867步训练验证||M||_2 = 1.0（浮点精度内最大偏差1.2×10^-7）。遗忘抑制效果覆盖1.1B–9.2B参数量与四个架构族。
原文摘要 · Abstract (English)
Sequential fine-tuning of large language models forces a choice: let the shared substrate keep learning and accept catastrophic forgetting, or freeze it after task one and foreclose cross-task refinement. Per-task adapter methods (LoRAHub, AdapterFusion, PackNet, Progressive Networks) take the second path. We introduce CRMA (Constrained Residual Mixing Adapter), a residual adapter whose internal mixing matrix M is doubly-stochastic at every forward pass via Sinkhorn normalization, so by Birkhoff's theorem ||M||_2 <= 1 holds by construction -- a structural bound, not a penalty. CRMA's spectrally bounded backbone provides a continuously trained shared substrate that earlier modular methods could not, while preserving their forgetting guarantees. On Mistral-7B across 5 sequential domains and 3 seeds, modular per-task LoRA on a CRMA backbone reduces loss-relative drift from +42.96% +/- 5.5 (naive sequential fine-tuning) to -0.17% +/- 0.17, with disjoint per-seed ranges, and improves prior-task holdout loss by 1.99% +/- 0.54 over a matched frozen-substrate baseline. Three independent experimental setups (Mistral-7B 4-domain controlled ablation, TinyLlama 3-domain contamination-controlled replication, Mistral-7B cross-domain probes at 7B) all show positive backward transfer -- without replay buffers, without growing per-task memory, and without distillation. An inference-time ablation on Gemma-2-9B confirms CRMA mediates access to sequentially trained knowledge: 98/100 vs. 38/100 on the same weights and same questions with only CRMA injection toggled. 867 logged training steps verify ||M||_2 = 1.0 within float32 precision (max deviation 1.2 x 10^-7). The forgetting-prevention effect holds across 1.1B-9.2B parameters and four architecture families.
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