CRMA：用于大语言模型模块化持续微调的谱约束骨干
CRMA: A Spectrally-Bounded Backbone for Modular Continual Fine-Tuning of LLMs
AI总结：
提出CRMA残差适配器，通过Sinkhorn归一化确保混合矩阵双随机，从而在结构上约束谱范数，实现共享基座的持续训练与跨任务正向迁移，无需回放或蒸馏。
摘要：
大语言模型的顺序微调面临两难选择：要么让共享基座持续学习并接受灾难性遗忘，要么在第一个任务后冻结它并放弃跨任务优化。每任务适配器方法（LoRAHub、AdapterFusion、PackNet、Progressive Networks）选择了后一条路径。我们提出CRMA（约束残差混合适配器），一种残差适配器，其内部混合矩阵M通过Sinkhorn归一化在每次前向传播时保持双随机，因此根据Birkhoff定理，||M||_2 <= 1由构造保证——这是一种结构约束，而非惩罚项。CRMA的谱约束骨干提供了一个持续训练的共享基座，这是早期模块化方法无法实现的，同时保留了它们的遗忘保证。在Mistral-7B上，跨越5个顺序领域和3个种子，基于CRMA骨干的模块化每任务LoRA将损失相对漂移从+42.96% ± 5.5（朴素顺序微调）降低到-0.17% ± 0.17，且每种子范围不重叠，并将先前任务的保留损失比匹配的冻结基座基线提高了1.99% ± 0.54。三个独立的实验设置（Mistral-7B 4领域受控消融、TinyLlama 3领域污染控制复现、Mistral-7B 7B跨领域探测）均显示出正向反向迁移——无需回放缓冲区、无需增加每任务内存、无需蒸馏。在Gemma-2-9B上的推理时消融证实CRMA介导了对顺序训练知识的访问：在相同权重和相同问题上，仅通过切换CRMA注入，结果从38/100提升到98/100。867次记录的训练步骤验证了||M||_2 = 1.0在float32精度内（最大偏差1.2×10^-7）。遗忘预防效果在1.1B-9.2B参数和四个架构系列中均成立。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
