用小波变换统一大模型转小模型和小模型转大模型的知识迁移。

Transferring pre-trained knowledge from a source model to a target model of a different architectural size is a key challenge for flexible and efficient model scaling. However, current parameter-space methods treat Small-to-Large (S2L) and Large-to-Small (L2S) scaling as separate, incompatible problems, focusing on parameter synthesis and selection, respectively. This fragmented perspective has resulted in specialized tools, hindering a unified, bidirectional framework. In this paper, we propose BoT (Bidirectional knowledge Transfer), the first size-agnostic framework to unify S2L and L2S scaling. Our core insight is to treat model weights as continuous signals, where models of different sizes represent distinct discretizations of the transferable knowledge. This multi-resolution perspective directly casts S2L and L2S scaling as the signal processing operations of upsampling and downsampling, naturally leading to the adoption of the Discrete Wavelet Transform (DWT) and its Inverse (IDWT). BoT leverages the recursive nature of wavelets, using the decomposition level as a dynamic scaling factor to bridge disparate model sizes in a parameter-free and computationally efficient manner. Extensive experiments on DeiT, BERT, and GPT demonstrate significant pre-training FLOPs savings (up to 67.1% for S2L, 52.8% for L2S) and state-of-the-art performance on benchmarks like GLUE and SQuAD.