arXiv AI
Consistent Geometric Deep Learning via Hilbert Bundles and Cellular Sheaves
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Consistency of augmentation graph and network approximability in contrastive learning
arXiv:2502.04312v3 Announce Type: replace Abstract: Contrastive learning leverages data augmentation to develop feature representation without relying on large labeled datasets. However, despite its...
arXiv Machine Learning
Sep 7
Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learning
The paper introduces Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based training that turns hierarchical feature learning into an explicit iterative spectral procedure. In this framework, each layer independently selects directions with maximal low-degree correlation to the label, providing a tractable surrogate for deep learning and a kernel-space interpretation. Experiments on fully connected and convolutional networks show that Neural LoFi outperforms lazy random-feature baselines, recovers meaningful structured filters, and aligns with early gradient-descent feature discovery on real datasets.
arXiv Machine Learning
Jun 2
Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning
arXiv:2604. 20308v2 Announce Type: replace Abstract: Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued representations that capture relationships between directions-such as how atomic orientations covary in a molecule.
arXiv Machine Learning
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Riemannian Metric Matching for Scalable Geometric Modeling of Distributions
arXiv:2606. 14334v1 Announce Type: new Abstract: High-dimensional datasets often concentrate near low-dimensional structures, but estimating their geometry from samples typically relies on graphs and kernels that scale poorly with dataset size and dimension.
arXiv Machine Learning
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Sheaf-theoretic Signal Processing on Graphs: Spectral Theory, Filtering, and Sampling
arXiv:2608. 01318v1 Announce Type: cross Abstract: Modern sensing, communication, and learning systems generate heterogeneous network signals, with local data differing in dimension, modality, and geometric structure.
arXiv Machine Learning
Oct 21
LocaLeJEPA: Maximum Entropy Representations under Geometric Priors
LocaLeJEPA extends Joint-Embedding Predictive Architectures (JEPA) by introducing a manifold-theoretic reformulation that aligns representation learning with non‑Euclidean geometric priors. It incorporates a locally Euclidean distribution‑matching regularizer, LocaLeReg, to stabilize training and scale to large models. Experiments on ImageNet‑1K show that LocaLeJEPA outperforms the original LeJEPA across both hyperbolic and Euclidean backbones, improving linear and k‑NN classification as well as downstream tasks.