PolaFormer: Polarity-aware Linear Attention for Vision Transformers

Linear attention has emerged as a promising alternative to softmax-based attention, leveraging kernelized feature maps to reduce complexity from quadratic to linear in sequence length. However, the non-negative constraint on feature maps and the relaxed exponential function used in approximation lead to significant information loss compared to the original query-key dot products, resulting in less discriminative attention maps with higher entropy. To address the missing interactions driven by negative values in query-key pairs, we propose a polarity-aware linear attention mechanism that explicitly models both same-signed and opposite-signed query-key interactions, ensuring comprehensive coverage of relational information. Furthermore, to restore the spiky properties of attention maps, we provide a theoretical analysis proving the existence of a class of element-wise functions (with positive first and second derivatives) that can reduce entropy in the attention distribution. For simplicity, and recognizing the distinct contributions of each dimension, we employ a learnable power function for rescaling, allowing strong and weak attention signals to be effectively separated. Extensive experiments demonstrate that the proposed PolaFormer improves performance on various vision tasks, enhancing both expressiveness and efficiency by up to 4.6%. Code is available at https://github.com/ZacharyMeng/PolaFormer . Figure 1: Attention weight visualization. Unlike prior linear attention approaches ((Katharopoulos et al., 2020) the 3rd and (Han et al., 2023a) 4th plots) that generate uniform responses, the proposed PolaFormer captures a more accurate query-key interaction with lower entropy, closely resembling softmax while maintaining linear complexity.