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Frequency Selective Neural Networks as a Foundation Architecture for Time Series Learning
Hui Huang, Ye Sun, Shiyan Hu
TL;DR
Time-series learning lacks representations that respect complex, non-stationary oscillatory modes while remaining adaptable through deep optimization. FSNN addresses this gap with a differentiable Wiener-like learnable filter bank, and reports state-of-the-art performance across general and clinical benchmarks while producing physically meaningful frequency-selective representations.
Problem
Existing deep-learning architectures map oscillatory time series into abstract spatial or token representations, causing spectral entanglement and limiting physical interpretability.
Method
FSNN represents time series as compositions of oscillatory modes using a dynamic learnable filter bank with a differentiable Wiener-like prior.
Results
FSNN reports state-of-the-art accuracy on general time-series benchmarks and highly imbalanced clinical PTB-XL tasks, including 77.0% average accuracy on standard multivariate UEA datasets.
Takeaways & Limitations
FSNN produces frequency-selective filters with physical meaning, connecting interpretable signal processing with end-to-end deep representation learning.
Takeaways & Limitations
The Wiener filter prior assumes distinct, stable oscillatory modes and may be too restrictive for highly chaotic, impulsive, or strictly non-periodic signals.
Abstract
from arXiv · showhide
Time-series data across physical and biological domains are fundamentally driven by complex, non-stationary oscillatory modes. While deep learning models, such as Convolutional Neural Networks (CNNs), Recurrent Neural Networks, and Transformers, have dominated sequential analysis, they remain fundamentally "spectral-blind". By mapping continuous physical waves into unconstrained spatial or discrete token spaces, these architectures suffer from severe spectral entanglement, acting as opaque black boxes that decouple predictive accuracy from physical reality. In this paper, we introduce the Frequency Selective Neural Network (FSNN), pioneering a foundation architecture guaranteeing physical interpretability without sacrificing expressive power of deep learning. FSNN addresses spectral entanglement by explicitly embedding the rigorous mathematics of advanced signal processing into its neural topology. Through a fully differentiable Wiener-like filter bank optimized via complex-domain backpropagation, FSNN autonomously discovers and isolates the precise physical modes of a given task. Extensive evaluations demonstrate that FSNN establishes state-of-the-art predictive performance, achieving $77.0\%$ average accuracy on the standard 10 multivariate UEA datasets and leading across all major metrics on the highly imbalanced PTB-XL clinical ECG benchmark. Crucially, in contrast to yielding abstract feature maps, FSNN converges directly on physically meaningful frequency bands, such as isolating the cardiac QRS complex, providing a highly scalable, interpretable paradigm for robust pattern recognition in complex temporal domains. Our code is available at: https://github.com/ad6174hhhh/FSNN.
1 INTRODUCTION
FSNN addresses the mismatch between oscillatory, non-stationary time-series signals and spectrally unconstrained deep-learning representations by combining learnable signal-processing structure with deep optimization. The paper presents physical interpretability and benchmark performance as its central outcomes.
- Motivation: Time-series signals comprise evolving frequency, amplitude, and phase components organized into recurring physical or biological modes.These non-stationary oscillatory modes underlie applications including healthcare monitoring, predictive maintenance, and anomaly detection.
- Motivation: CNNs, Transformers, and related architectures represent signals through abstract spatial or discrete-token structures that produce spectral entanglement or obscure continuous frequency modes.InceptionTime is described as having chaotic, overlapping frequency responses, while TimesNet’s 2D convolutional formulation obscures the continuous spectrum.
- Prior approaches: Classical filter banks provide physically interpretable band-limited decompositions, but fixed heuristics cannot adapt dynamically to massive datasets.Filter parameters such as center frequency and bandwidth correspond directly to tangible physical properties.
- FSNN: FSNN embeds a fully differentiable, mathematically smooth Wiener-like prior into an adaptable neural architecture to isolate distinct real-world frequencies.The stated design aims to prevent chaotic, entangled noise while retaining end-to-end optimization and forcing learned parameters toward physical frequencies.
- Results: 77.0% average accuracy is reported for FSNN on standard multivariate UEA datasets, alongside outperformance of existing temporal and frequency-domain models on the highly imbalanced PTB-XL ECG benchmark.The introduction identifies these evaluations as evidence for predictive efficacy and representational capabilities.
- Interpretability: FSNN learns distinct frequency-selective filters with clear physical meaning, providing interpretable representations rather than abstract feature maps.The paper frames this as a step toward physical interpretability in time-series learning.
2 RELATED WORK
Related work spans recurrent, convolutional, Transformer, and self-supervised sequence models, alongside classical and neuralized signal-processing approaches. The paper identifies a continuing gap between temporal modeling flexibility and spectrally disciplined, physically interpretable representations.
- Deep sequence models: Recurrent architectures such as LSTNet model temporal dependencies by maintaining hidden-state representations over time.The passage presents recurrent modeling as an earlier foundation for sequence analysis.
- Convolutional models: InceptionTime uses multi-scale receptive fields, but unconstrained spatial convolutions can yield chaotic, overlapping frequency responses.The passage characterizes these convolutions as arbitrary finite impulse response filters without structural or spectral constraints.
- Self-supervised models: Self-supervised frameworks improve representations for forecasting, anomaly detection, and clustering, but their standard convolutional or attention backbones retain spectral vulnerabilities.The stated limitation concerns the underlying backbone mechanisms rather than the self-supervised objective itself.
- Transformer models: Transformer variants target long-range dependencies and address self-attention’s quadratic sequence-length complexity through linearization, sparsity, or frequency-domain decomposition.The passage names Autoformer, FEDformer, and Flowformer as examples of this direction.
- Classical signal processing: Classical filter banks decompose complex non-stationary signals into distinct band-limited modes for targeted analysis of oscillatory and transient components.They map one-dimensional time-domain signals into two-dimensional time-frequency representations.
- Classical signal processing: The Wiener filter provides an optimal, computationally efficient closed-form solution for reconstructing signals corrupted by interference, distortion, or noise.Its frequency-domain formulation minimizes mean square error and balances inverse filtering against noise amplification using power spectra.
- Physics-informed neural models: Scattering convolution networks embed fixed wavelet transforms and nonlinearities to compute representations stable to local deformations and invariant to translation.They represent an earlier effort to incorporate physical inductive biases into neural architectures.
3 PROPOSED METHODOLOGY
FSNN embeds differentiable Wiener-like filter banks into a spectral-domain neural layer, learning physically interpretable frequency modes while retaining scalable deep-learning computation.
- Signal-processing foundation: Filter banks decompose complex signals into distinct band-limited modes, but classical center frequencies and bandwidths are fixed and require domain-specific tuning for non-stationary signals.The analysis bank applies K filters as X_k(ω) = X(ω)H_k(ω).
- Interpretability and robustness: The Wiener-like structural prior produces smooth, effectively band-limited filters that resist spectral leakage and wideband noise.This constraint restricts the network toward localized, bell-shaped spectral envelopes rather than chaotic frequency responses.
- FSNN architecture: FSNN converts classical signal processing into a dynamic, end-to-end differentiable neural layer rather than using fixed or unconstrained frequency-domain processing.The architecture combines deep-learning adaptability with a noise-resistant structural constraint.
- Forward pass: Input signals are transformed by RFFT, modulated with Wiener-like filters and complex cross-channel weights, then mapped to output modes through the spectral-domain layer.For X ∈ R^(B×C_in×L), the layer produces Y ∈ R^(B×C_out×L), where C_out is the number of extracted modes or output channels.
- Adaptive spectral selection: Learnable center frequencies are adjusted toward discriminative spectral bands, while learnable bandwidth penalties zoom filters toward narrow or broad class-relevant frequency ranges.The bandwidth penalty uses |α_k| to remain strictly positive, and backpropagation updates the center frequencies during training.
- Computational complexity: O(L log L) sequence-length time complexity makes FSNN more efficient than quadratic self-attention for exceptionally long time-series sequences.The complexity assumes C_in and C_out are typically small constants representing channel or mode dimensions.
4 EXPERIMENTS
FSNN is evaluated across multivariate UEA datasets and the imbalanced PTB-XL ECG benchmark, where it combines strong classification performance with physically interpretable frequency-selective representations. The experiments also identify scope boundaries for the Wiener-based architecture.
- Representational Superiority on Benchmark Datasets: FSNN outperforms Transformer-based models and TimesNet while operating through differentiable Wiener filtering in the 1D spectral domain.The learned filter bank isolates oscillatory modes rather than relying on token-based attention or 2D reshaping.
- Representational Superiority on Benchmark Datasets: 77.0% average accuracy establishes FSNN as the best overall performer on the 10 multivariate UEA datasets.It surpasses TimesNet at 73.6%, Flowformer at 73.0%, and Rocket at 72.5%.
- Physical Interpretability and Clinical ECG Classification: FSNN leads PTB-XL performance with Macro AUROC 0.9312, Macro AUPRC 0.8278, and Macro F1-score 0.7418.The evaluation compares FSNN variants with 1D-CNN, XceptionTime, and PaiFilter/FilterNet in a highly imbalanced clinical ECG setting.
- Physical Interpretability and Clinical ECG Classification: Learned FSNN filters form localized spectral envelopes that isolate cardiac bands associated with P/T-wave morphology and the QRS complex.FSNN emphasizes frequencies below 5 Hz for P- and T-wave morphology and 10–25 Hz modes for the high-energy QRS complex.
- Discussion: The Wiener prior provides interpretable, noise-resistant representations, but its band-limited assumption may restrict performance on chaotic, impulsive, or strictly non-periodic signals.The paper also notes that the complex weight tensor’s dimensionality is currently tied to sequence length.
5 CONCLUSION
FSNN brings advanced signal-processing structure into deep representation learning, using mode-adaptive filters to learn physically meaningful frequency bands. It reports strong performance across general time-series and imbalanced clinical tasks while retaining an interpretable, white-box formulation.
- FSNN integrates advanced signal processing into an end-to-end deep learning architecture.The architecture transitions classical static filter banks into optimized, differentiable components.
- FSNN achieves state-of-the-art accuracy on general time-series benchmarks and highly imbalanced clinical tasks such as PTB-XL.
- The network learns center frequencies, bandwidths, and oscillatory modes through continuous, mode-adaptive Wiener-like filters.
- FSNN can isolate physically meaningful frequency bands, including the ECG QRS complex, while rejecting high-frequency noise.
- The architecture is presented as a transparent and robust white-box alternative to unconstrained latent representations.