Task-Adaptive Wavelet Decomposition with Quadrature Mirror Filters for Time Series Classification
Resumo
Deep models for time series classification (TSC) are usually fed raw signal windows, and fixed wavelet families such as Daubechies-4 (Db4) target generic smoothness rather than the discriminative frequency content of a given task; it is unclear which architectures benefit from replacing fixed filters with trainable ones. We investigate a Learnable Wavelet Transform (LWT): a differentiable front-end that learns per-channel low-pass filter coefficients end-to-end with the classifier, derives the high-pass filter structurally through the Quadrature Mirror Filter (QMF) relationship, and can be warm-started from the Db4 basis by a closed-form least-squares fit. Crossing four input conditions (Raw, fixed Db4, LWT, LWT-Warm) with five backbones (MLP, CNN, LSTM, CNN-LSTM, Transformer) on three benchmarks (Ford-A, SCP1, UWaveGesture), we test the hypothesis that the value of a wavelet front-end is backbone-dependent. The results confirm it: globally expressive backbones are largely insensitive to the front-end, whereas a fixed Db4 decomposition repeatedly collapses convolutional and recurrent backbones to the majority class, and making the filter learnable reverses every collapse, peaking at +56.4 accuracy points over Db4 on the low-data UWaveGesture.
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