Self-Supervised Learning with Recursive Quadrature Filters for Neural Time Series

We develop self-supervised methods for training Recursive Quadrature Filter (RQF) encoders on unlabeled time series. RQFs are biologically motivated, complex-valued temporal filters that form a special class of diagonal state-space models (SSMs). Each RQF acts as a band-pass filter whose selectivity is determined by two learnable parameters: its tuning frequency and bandwidth. We separately introduce a self-supervised learning objective based on prediction error; the encoder is trained so that its current state predicts its own future activity. In the windowed mode, the summary of the current window predicts the summary of a later window; in the dense mode, the state at the current timestep predicts future log-power. Each RQF encoder is pretrained on a dataset and then a readout (e.g., a task-specific classifier) is trained on the output of the RQF encoder, with the encoder either frozen or fully fine-tuned. For multichannel EEG and intracranial recordings, a shared encoder processes each channel separately, and a spatial readout combines the channel representations using electrode locations. Across four neural benchmarks using scalp EEG or intracranial ECoG, the pretrained RQF system performs close to the state of the art while using a small fraction of the parameters of the competing models. For example, a 110k-parameter RQF system reaches 0.9130 ± 0.0036 test AUROC on TUAB, within the range achieved by state-of-the-art EEG foundation models with 1.0M--369M parameters.