# DeepFRC: An End-to-End Deep Learning Model for Functional Registration and Classification

arXiv: https://arxiv.org/abs/2501.18116 · HTML: https://mlsanity.com/paper/2501.18116/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 49 references that are in the map.
- First posted on arXiv 30 Jan 2025.

## Builds on (most cited first, 14 of 14)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [1D Convolutional Neural Networks and Applications: A Survey](https://mlsanity.com/paper/1905.03554/) (2019)
- [Universal approximations of invariant maps by neural networks](https://mlsanity.com/paper/1804.10306/) (2018)
- [TSLANet: Rethinking Transformers for Time Series Representation Learning](https://mlsanity.com/paper/2404.08472/) (2024)
- [Mobile Sensor Data Anonymization](https://mlsanity.com/paper/1810.11546/) (2018)
- [Temporal Transformer Networks: Joint Learning of Invariant and Discriminative Time Warping](https://mlsanity.com/paper/1906.05947/) (2019)
- [Deep Learning for Functional Data Analysis with Adaptive Basis Layers](https://mlsanity.com/paper/2106.10414/) (2021)
- [Functional Data Analysis of Amplitude and Phase Variation](https://mlsanity.com/paper/1512.03216/) (2015)
- [Deep Neural Network Classifier for Multi-dimensional Functional Data](https://mlsanity.com/paper/2205.08592/) (2022)
- [Bayesian Framework for Simultaneous Registration and Estimation of Noisy, Sparse and Fragmented Functional Data](https://mlsanity.com/paper/1912.05125/) (2019)
- [Review of Functional Data Analysis](https://mlsanity.com/paper/1507.05135/) (2015)
- [Neural Networks as Functional Classifiers](https://mlsanity.com/paper/2010.04305/) (2020)
- [Multiclass classification for multidimensional functional data through deep neural networks](https://mlsanity.com/paper/2305.13349/) (2023)

## Built on by (most cited first, 3 of 3)

- [NeuralFLoC: Neural Flow-Based Joint Registration and Clustering of Functional Data](https://mlsanity.com/paper/2602.03169/) (2026)
- [Neural Optimal Transport in Hilbert Spaces: Characterizing Spurious Solutions and Gaussian Smoothing](https://mlsanity.com/paper/2602.14086/) (2026)
- [Functional Autoencoders for Amplitude-Phase Representation Learning](https://mlsanity.com/paper/2609.34207/) (2026)

## Abstract (arXiv)

Functional data, representing curves or trajectories, are ubiquitous in fields like biomedicine and motion analysis. A fundamental challenge is phase variability -- temporal misalignments that obscure underlying patterns and degrade model performance. Current methods often address registration (alignment) and classification as separate, sequential tasks. This paper introduces DeepFRC, an end-to-end deep learning framework that jointly learns diffeomorphic warping functions and a classifier within a unified architecture. DeepFRC combines a neural deformation operator for elastic alignment, a spectral representation using Fourier basis for smooth functional embedding, and a class-aware contrastive loss that promotes both intra-class coherence and inter-class separation. We provide the first theoretical guarantees for such a joint model, proving its ability to approximate optimal warpings and establishing a data-dependent generalization bound that formally links registration fidelity to classification performance. Extensive experiments on synthetic and real-world datasets demonstrate that DeepFRC consistently outperforms state-of-the-art methods in both alignment quality and classification accuracy, while ablation studies validate the synergy of its components. DeepFRC also shows notable robustness to noise, missing data, and varying dataset scales. Code is available at https://github.com/Drivergo-93589/DeepFRC.