# Functional Neural Networks: Shift invariant models for functional data with applications to EEG classification

arXiv: https://arxiv.org/abs/2301.05869 · HTML: https://mlsanity.com/paper/2301.05869/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 47 references that are in the map.
- First posted on arXiv 14 Jan 2023.

## Builds on (most cited first, 11 of 11)

- [EEGNet: A Compact Convolutional Network for EEG-based Brain-Computer Interfaces](https://mlsanity.com/paper/1611.08024/) (2016)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline](https://mlsanity.com/paper/1611.06455/) (2016)
- [Deep learning-based electroencephalography analysis: a systematic review](https://mlsanity.com/paper/1901.05498/) (2019)
- [A review of feature extraction and performance evaluation in epileptic seizure detection using EEG](https://mlsanity.com/paper/1908.00492/) (2019)
- [Towards a universal neural network encoder for time series](https://mlsanity.com/paper/1805.03908/) (2018)
- [Modern Non-Linear Function-on-Function Regression](https://mlsanity.com/paper/2107.14151/) (2021)
- [A Non-linear Function-on-Function Model for Regression with Time Series Data](https://mlsanity.com/paper/2011.12378/) (2020)
- [Remaining Useful Life Estimation Using Functional Data Analysis](https://mlsanity.com/paper/1904.06442/) (2019)
- [The mRMR variable selection method: a comparative study for functional data](https://mlsanity.com/paper/1507.03496/) (2015)
- [A Portmanteau-type test for detecting serial correlation in locally stationary functional time series](https://mlsanity.com/paper/2009.07312/) (2020)

## Built on by (most cited first, 9 of 9)

- [Shape-Informed Clustering of Multi-Dimensional Functional Data via Deep Functional Autoencoders](https://mlsanity.com/paper/2509.22969/) (2025)
- [GT-PCA: Effective and Interpretable Dimensionality Reduction with General Transform-Invariant Principal Component Analysis](https://mlsanity.com/paper/2401.15623/) (2024)
- [EEG-MACS: Manifold Attention and Confidence Stratification for EEG-based Cross-Center Brain Disease Diagnosis under Unreliable Annotations](https://mlsanity.com/paper/2405.00734/) (2024)
- [Functional relevance based on the continuous Shapley value](https://mlsanity.com/paper/2411.18575/) (2024)
- [Consumer-grade EEG-based Eye Tracking](https://mlsanity.com/paper/2503.14322/) (2025)
- [EEG-EyeTrack: A Benchmark for Time Series and Functional Data Analysis with Open Challenges and Baselines](https://mlsanity.com/paper/2504.03760/) (2025)
- [A Composable Channel-Adaptive Architecture for Seizure Classification](https://mlsanity.com/paper/2512.19123/) (2025)
- [Self-Guidance: Enhancing Neural Codecs via Decoder Manifold Alignment](https://mlsanity.com/paper/2606.12940/) (2026)
- [Geometric Feature Learning for Functional Data Valued on the Symmetric Positive Definite Manifold](https://mlsanity.com/paper/2609.30487/) (2026)

## Abstract (arXiv)

It is desirable for statistical models to detect signals of interest independently of their position. If the data is generated by some smooth process, this additional structure should be taken into account. We introduce a new class of neural networks that are shift invariant and preserve smoothness of the data: functional neural networks (FNNs). For this, we use methods from functional data analysis (FDA) to extend multi-layer perceptrons and convolutional neural networks to functional data. We propose different model architectures, show that the models outperform a benchmark model from FDA in terms of accuracy and successfully use FNNs to classify electroencephalography (EEG) data.