# Causal Convolutional Neural Networks as Finite Impulse Response Filters

arXiv: https://arxiv.org/abs/2510.24125 · HTML: https://mlsanity.com/paper/2510.24125/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 67 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## Builds on (most cited first, 17 of 17)

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- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [VideoMamba: State Space Model for Efficient Video Understanding](https://mlsanity.com/paper/2403.06977/) (2024)
- [Implicit Bias of Gradient Descent on Linear Convolutional Networks](https://mlsanity.com/paper/1806.00468/) (2018)
- [On the approximation of functions by tanh neural networks](https://mlsanity.com/paper/2104.08938/) (2021)
- [TFAD: A Decomposition Time Series Anomaly Detection Architecture with Time-Frequency Analysis](https://mlsanity.com/paper/2210.09693/) (2022)
- [Deep Convolutional Networks in System Identification](https://mlsanity.com/paper/1909.01730/) (2019)
- [Convolutional Neural Networks Demystified: A Matched Filtering Perspective Based Tutorial](https://mlsanity.com/paper/2108.11663/) (2021)
- [Using Graph Neural Networks and Frequency Domain Data for Automated Operational Modal Analysis of Populations of Structures](https://mlsanity.com/paper/2407.06492/) (2024)
- [Deep learning with transfer functions: new applications in system identification](https://mlsanity.com/paper/2104.09839/) (2021)

## Abstract (arXiv)

This study investigates the behavior of Causal Convolutional Neural Networks (CNNs) with quasi-linear activation functions when applied to time-series data characterized by multimodal frequency content. We demonstrate that, once trained, such networks exhibit properties analogous to Finite Impulse Response (FIR) filters, particularly when the convolutional kernels are of extended length exceeding those typically employed in standard CNN architectures. Causal CNNs are shown to capture spectral features both implicitly and explicitly, offering enhanced interpretability for tasks involving dynamic systems. Leveraging the associative property of convolution, we further show that the entire network can be reduced to an equivalent single-layer filter resembling an FIR filter optimized via least-squares criteria. This equivalence yields new insights into the spectral learning behavior of CNNs trained on signals with sparse frequency content. The approach is validated on both simulated beam dynamics and real-world bridge vibration datasets, underlining its relevance for modeling and identifying physical systems governed by dynamic responses.