DeepFRC: An End-to-End Deep Learning Model for Functional Registration and Classification
Siyuan Jiang, Yihan Hu, Wenjie Li, Pengcheng Zeng
TL;DR
DeepFRC is an innovative end-to-end deep learning framework that jointly performs functional data registration and classification, improving alignment accuracy and classification performance through a unified model with theoretical guarantees.
Contribution
It introduces the first joint model for functional registration and classification with theoretical guarantees and demonstrates superior empirical performance.
Findings
Outperforms state-of-the-art methods in alignment and classification.
Provides theoretical guarantees for registration approximation and generalization.
Shows robustness to noise, missing data, and dataset scale variations.
Abstract
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…
Peer Reviews
Decision·ICLR 2026 Poster
1. The paper presents a well-motivated problem by targeting the joint challenge of phase variability and classification in functional data analysis (FDA). 2. Empirical results are consistent: DeepFRC outperforms alternatives across several datasets, enhancing both alignment and classification and confirming the effectiveness of joint optimization. 3. Theoretical discussions and included proofs, effectively situate the model within the mathematical landscape of FDA.
1. The neural components (1D CNN, MLP, Fourier basis) are standard. The main contribution is integrating known elements instead of developing a new architecture or loss function. 2. The baseline models are too few and outdated; it would be better to include more recent baseline models for comparison.
The authors provide theoretical guarantees, proving that the model can approximate optimal warping functions and establishing a data-dependent generalization bound that links registration fidelity to classification performance.
1. The authors claim “but rarely addressing both simultaneously”, however, there are several works addressing registration and classification simultaneously, for example, [1] Zhang, Y. and Telesca, D., 2014. Joint clustering and registration of functional data. arXiv preprint arXiv:1403.7134. 2. Why transform the latent features into a monotone cumulative sum can guarantee diffeomorphism? 3. Novelty is limited, for registration, only introduce neural deformation operator for alignment 4. The cla
The paper demonstrates good originality by proposing the first end-to-end unified framework for joint functional data learning. The research quality is solid, well-supported by comprehensive theoretical analysis and systematic experimental validation.
1. It is not clear about the network architecture choices. 2. Current computational complexity analysis is not sufficient. 3. Lack of a detailed description of the datasets, which helps to understand the possible applications of the proposed method.
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Taxonomy
TopicsMachine Learning in Healthcare · Image Processing and 3D Reconstruction · Machine Learning and Data Classification