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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,695 papers · 148 categories

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6 results for “PDE-G-CNNs”

Analysis of (sub-)Riemannian PDE-G-CNNscs.LG

New approximative kernels improve PDE-G-CNNs for geometric deep learning.

problem Inaccurate approximations of exact kernels in PDE-G-CNNs.

method Developed new approximative kernels that work regardless of spatial anisotropy.

result New kernels provide better error estimates and maintain reflectional symmetries.

PDE-G-CNNs sub-Riemannian approximative kernels geometric deep learning classification performance

2022-10-03abs ↗pdf ↗

Orientation Scores should be a Piece of Cakemath.DG

Cake wavelets minimize orientation score uncertainty.

problem Minimizing uncertainty in orientation scores.

method Axiomatically derived wavelets for orientation score lifting.

result Uncertainty gap of cake wavelets is less than 1.1.

wavelets orientation score cake wavelets uncertainty minimization fast reconstruction

2025-04-01abs ↗pdf ↗

PDE-based Group Equivariant Convolutional Neural Networkscs.LG

We present a PDE-based framework that generalizes Group equivariant Convolutional Neural Networks (G-CNNs). In this framework, a network layer is seen as a set of PDE-solvers where geometrically meaningful PDE-coefficients become the layer's trainable weights. Formulating our PDEs on homogeneous spaces allows these net…

2020-01-24abs ↗pdf ↗

Analysis and Computation of Geodesic Distances on Reductive Homogeneous Spacesmath.DG

Study on geodesic distances on SE(3)/SO(2) in machine learning.

problem Investigating the efficiency of computationally efficient sections in selecting geodesic distances.

method Analyzing geodesic distances on reductive homogeneous spaces, proving the efficiency of minimal distance sections.

result Minimal distance sections are not always geodesic minimizers, but minimal horizontal geodesics are.

geodesic distances equivariant neural networks PDE-based group CNNs reductive homogeneous spaces SO(2)-conjugation invariant

2025-04-07abs ↗pdf ↗

Geometric Generative Models based on Morphological Equivariant PDEs and GANscs.CV

Geometric models improve feature extraction and equivariance in image generation.

problem Improving feature extraction at multiscale levels and reducing network complexity.

method Proposes a geometric generative model based on morphological PDEs and GANs, incorporating equivariance for geometric interpretability.

result Preliminary results show GM-GAN outperforms classical GANs on MNIST data.

image generation feature extraction equivariance partial differential equations morphology

2024-03-22abs ↗pdf ↗

Diffusion-Shock PDEs for Deep Learning on Position-Orientation Spacemath.DG

Extends RDS filtering to position-orientation space for better image processing.

problem Enhancing and inpainting images with crossing structures.

method Created a version of RDS filtering using gauge frames, studying generalised diffusion.

result RDS filtering on position-orientation space improves denoising and inpainting of crossing structures.

image processing deep learning position-orientation space gauge frames diffusion

2025-09-08abs ↗pdf ↗