Learnable Multi-Scale Wavelet Transformer: A Novel Alternative to Self-Attention

Abstract: Transformer architectures, underpinned by the self-attention mechanism, have achieved state-of-the-art results across numerous NLP tasks by effectively modeling long-range dependencies. However, the computational complexity of self-attention, scaling quadratically with input sequence length, presents significant challenges for processing very long sequences or operating under resource constraints. This paper introduces the Learnable Multi-Scale Wavelet Transformer (LMWT), a novel architecture that replaces the standard dot-product self-attention with a learnable multi-scale Haar wavelet transform module. Leveraging the intrinsic multi-resolution properties of wavelets, the LMWT efficiently captures both local details and global context. Crucially, the parameters of the wavelet transform, including scale-specific coefficients, are learned end-to-end during training, allowing the model to adapt its decomposition strategy to the data and task. We present the detailed mathematical formulation of the learnable Haar wavelet module and its integration into the transformer framework, supplemented by an architectural diagram. We conduct a comprehensive experimental evaluation on a standard machine translation benchmark (WMT16 En-De), comparing the LMWT against a baseline self-attention transformer using metrics like BLEU score, perplexity, and token accuracy. Furthermore, we analyze the computational complexity, highlighting the linear scaling of our approach, discuss its novelty in the context of related work, and explore the interpretability offered by visualizing the learned Haar coefficients. Our results indicate that the LMWT achieves competitive performance while offering substantial computational advantages, positioning it as a promising and novel alternative for efficient sequence modeling.