HPformer: Low-Parameter Transformer With Temporal Dependency Hierarchical Propagation for Health Informatics

Transformers based on Self-Attention (SA) mechanism have demonstrated unrivaled superiority in numerous areas. Compared to RNN-based networks, Transformers can learn the temporal dependency representation of an entire sequence in parallel, while efficiently dealing with long-range dependencies. However, the $\mathcal {O}(L^{2})$O(L2) ($L$L denotes the length of the sequence) computational complexity of the SA mechanism and the high memory usage make the construction cost of the Transformer-based model prohibitively expensive. To address these challenges, we propose a Transformer-like model, HPformer: Low-Parameter Transformer with Temporal Dependency Hierarchical Propagation. HPformer first chunks the sequence into $K$K ($K = \left\lceil \log {L} \right\rceil + 1$K=logL+1, $\left\lceil \cdot \right\rceil$· denotes ceiling operation) sequence segments, then leverages the hierarchical propagation mechanism with $\mathcal {O}(L)$O(L) computational complexity to learn the temporal dependencies between the segments and within the segments, and ultimately generates $K$K vectors as $Key$Key matrices. This reduces the complexity of the SA mechanism from $\mathcal {O}(L^{2})$O(L2) to $\mathcal {O}(L\log {L})$O(LlogL). In addition, we employ a strategy of sharing $Key$Key and $Value$Value matrices between layers to build the HPformer, thus reducing memory usage. Extensive experiments based on public health informatics benchmark and Long-Range Arena (LRA) benchmark have demonstrated that HPformer has advantages over Transformer-based models in terms of memory usage and efficiency.