GAIN: Multiplicative Modulation for Domain Adaptation
Adapting LLMs to new domains causes forgetting because standard methods (e.g., full fine-tuning, LoRA) inject new directions into the weight space. We show that forgetting is governed by one algebraic property: whether the update preserves the column span of the pretrained weight matrix (Proposition 1). We propose GAIN, the simplest multiplicative alternative (W_new = S * W), which satisfies this by construction and can be absorbed into existing weights for zero inference cost. Across five models (774M to 70B) adapted sequentially over eight domains, GAIN improves earlier-domain perplexity by 7-13%, while LoRA degrades it by 18-36%. GAIN matches replay-augmented LoRA without storing prior...
| Authors | Hengshuai Yao, Xing Chen, Ahmed Murtadha et al. |
|---|---|
| Primary category | cs.LG |
| Published | 6 April 2026 |
| Last updated at source | 21 April 2026 |
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