Learnable Weighted Superposition in HDC and its Application to Multi-channel Time Series Classification

The vector superposition operation plays a central role in Hyperdimensional Computing (HDC), enabling compositionality of hypervectors without expanding the dimensionality, unlike concatenation. However, a problem arises when the quantity of superimposed vectors surpasses a certain threshold, which is determined by the hypervector’s information capacity relative to its dimensionality. Beyond this point, cross-talk noise incrementally obscures the distinctiveness of individual hypervectors and information is lost. To solve this challenge, we introduce a novel method for weighting individual hypervectors within the superposition, ensuring that only those hypervectors crucial for a given task are prioritized. The weights are learned end-to-end using the backpropagation algorithm in a neural network. Our method is characterized by two key features: (1) The resultant weighting model is exceptionally compact, as the number of trainable weights is equal to the total number of hypervectors in the superposition; (2) The model offers enhanced explainability due to the compositional nature of its encoding. These features collectively contribute to the efficiency and effectiveness of our proposed classification approach using hyperdimensional computing. We illustrate our approach through the multi-channel time series classification task. In this framework, each channel is encoded as a hypervector-descriptor, and those are subsequently composed into a single hypervector via superposition. This superimposed vector forms the basis for training the classification model based on the neural network. Applying our approach of weighted superposition on this task improved the classification performance compared to standard superposition or concatenation of feature vectors, especially for larger numbers of channels.