LaplacianFormer:Rethinking Linear Attention with Laplacian Kernel

• URL: http://arxiv.org/abs/2604.20368v1
• Date: Wed, 22 Apr 2026 09:04:54 GMT
• Title: LaplacianFormer:Rethinking Linear Attention with Laplacian Kernel
• Abstract summary: quadratic complexity of softmax attention presents a major obstacle for scaling Transformers to high-resolution vision tasks.<n>We propose LaplacianFormer, a Transformer variant that employs a Laplacian kernel as a principled alternative to softmax.<n>Experiments on ImageNet show LaplacianFormer achieves strong performance-efficiency trade-offs while improving attention.
• Score: 27.87296519831803
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The quadratic complexity of softmax attention presents a major obstacle for scaling Transformers to high-resolution vision tasks. Existing linear attention variants often replace the softmax with Gaussian kernels to reduce complexity, but such approximations lack theoretical grounding and tend to oversuppress mid-range token interactions. We propose LaplacianFormer, a Transformer variant that employs a Laplacian kernel as a principled alternative to softmax, motivated by empirical observations and theoretical analysis. To address expressiveness degradation under low-rank approximations, we introduce a provably injective feature map that retains fine-grained token information. For efficient computation, we adopt a Nyström approximation of the kernel matrix and solve the resulting system using Newton--Schulz iteration, avoiding costly matrix inversion and SVD. We further develop custom CUDA implementations for both the kernel and solver, enabling high-throughput forward and backward passes suitable for edge deployment. Experiments on ImageNet show that LaplacianFormer achieves strong performance-efficiency trade-offs while improving attention expressiveness.

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