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[2602.15128] PolyNODE: Variable-dimension Neural ODEs on M-polyfolds
Summary
The paper introduces PolyNODE, a novel variable-dimensional Neural ODE model that extends traditional NODEs to M-polyfolds, enabling dynamic flow-based modeling in geometric deep learning.
Why It Matters
This research addresses the limitations of existing Neural ODEs, which are confined to fixed dimensions. By introducing variable-dimensional modeling, PolyNODE opens new avenues for complex data representation and processing, particularly in tasks requiring flexibility in dimensionality.
Key Takeaways
- PolyNODE extends Neural ODEs to variable dimensions using M-polyfolds.
- The model can effectively handle dimensional bottlenecks in data.
- PolyNODE autoencoders can be trained for reconstruction and classification tasks.
- The research includes publicly available code for further experimentation.
- This innovation could enhance applications in geometric deep learning.
Computer Science > Machine Learning arXiv:2602.15128 (cs) [Submitted on 16 Feb 2026] Title:PolyNODE: Variable-dimension Neural ODEs on M-polyfolds Authors:Per Åhag, Alexander Friedrich, Fredrik Ohlsson, Viktor Vigren Näslund View a PDF of the paper titled PolyNODE: Variable-dimension Neural ODEs on M-polyfolds, by Per {\AA}hag and Alexander Friedrich and Fredrik Ohlsson and Viktor Vigren N\"aslund View PDF HTML (experimental) Abstract:Neural ordinary differential equations (NODEs) are geometric deep learning models based on dynamical systems and flows generated by vector fields on manifolds. Despite numerous successful applications, particularly within the flow matching paradigm, all existing NODE models are fundamentally constrained to fixed-dimensional dynamics by the intrinsic nature of the manifold's dimension. In this paper, we extend NODEs to M-polyfolds (spaces that can simultaneously accommodate varying dimensions and a notion of differentiability) and introduce PolyNODEs, the first variable-dimensional flow-based model in geometric deep learning. As an example application, we construct explicit M-polyfolds featuring dimensional bottlenecks and PolyNODE autoencoders based on parametrised vector fields that traverse these bottlenecks. We demonstrate experimentally that our PolyNODE models can be trained to solve reconstruction tasks in these spaces, and that latent representations of the input can be extracted and used to solve downstream classification tasks. The c...
