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Bibliographic Details
Main Author:	Liu, Dong
Format:	Preprint
Published:	2025
Subjects:	Machine Learning Differential Geometry
Online Access:	https://arxiv.org/abs/2512.01151
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Geometric and Spectral Alignment for Deep Neural Network I
by: Liu, Ziran, et al.
Published: (2026)

Geometric and Spectral Alignment for Deep Neural Network II
by: Liu, Ziran, et al.
Published: (2026)

Geometric Learning with Positively Decomposable Kernels
by: Da Costa, Nathael, et al.
Published: (2023)

GeoHNNs: Geometric Hamiltonian Neural Networks
by: Aboussalah, Amine Mohamed, et al.
Published: (2025)

Riemannian Integrated Gradients: A Geometric View of Explainable AI
by: Costanza, Federico, et al.
Published: (2025)

Jet Functors and Weil Algebras in Automatic Differentiation: A Geometric Analysis
by: Sangha, Amandip
Published: (2025)

Hardness of Learning Neural Networks under the Manifold Hypothesis
by: Kiani, Bobak T., et al.
Published: (2024)

Geometric Contact Flows: Contactomorphisms for Dynamics and Control
by: Testa, Andrea, et al.
Published: (2025)

Learning Beyond Euclid: Curvature-Adaptive Generalization for Neural Networks on Manifolds
by: Sarkar, Krisanu
Published: (2025)

Conformal Transformation of Kernels: A Geometric Perspective on Text Classification
by: Rădulescu, Ioana, et al.
Published: (2024)

On Higher-Order Geometric Refinements of Classical Covariance Asymptotics: An Approach via Intrinsic and Extrinsic Information Geometry
by: Amir, Malik, et al.
Published: (2026)

Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifolds
by: Sun, Xingzhi, et al.
Published: (2024)

A singular Riemannian Geometry Approach to Deep Neural Networks III. Piecewise Differentiable Layers and Random Walks on $n$-dimensional Classes
by: Benfenati, Alessandro, et al.
Published: (2024)

Machine Learned Calabi-Yau Metrics and Curvature
by: Berglund, Per, et al.
Published: (2022)

TopoGeoScore: A Self-Supervised Source-Only Geometric Framework for OOD Checkpoint Selection
by: Hazratian, Farid, et al.
Published: (2026)

Deep Learning as Ricci Flow
by: Baptista, Anthony, et al.
Published: (2024)

The Geometric Wall: Manifold Structure Predicts Layerwise Sparse Autoencoder Scaling Laws
by: Zaher, Eslam, et al.
Published: (2026)

Geometric Gaussian Approximations of Probability Distributions
by: Da Costa, Nathaël, et al.
Published: (2025)

Man, Machine, and Mathematics
by: Dogra, Akshunna S.
Published: (2026)

Discretized Gradient Flow for Manifold Learning in the Space of Embeddings
by: Gold, Dara, et al.
Published: (2019)

Manifold Learning with Normalizing Flows: Towards Regularity, Expressivity and Iso-Riemannian Geometry
by: Diepeveen, Willem, et al.
Published: (2025)

Geometric statistics with subspace structure preservation for SPD matrices
by: Mostajeran, Cyrus, et al.
Published: (2024)

Riemannian Variational Flow Matching for Material and Protein Design
by: Zaghen, Olga, et al.
Published: (2025)

Cross-Layer Subspace Coupling for LLM Compression: A Unifying Framework and Its Empirical Limits
by: Khilar, Snigdha Chandan
Published: (2026)

Geodesics in the Deep Linear Network
by: Chen, Alan
Published: (2025)

Barycentric subspace analysis of network-valued data
by: Maignant, Elodie, et al.
Published: (2025)

Universal Collection of Euclidean Invariants between Pairs of Position-Orientations
by: Bellaard, Gijs, et al.
Published: (2025)

Roto-Translation Invariant Metrics on Position-Orientation Space
by: Bellaard, Gijs, et al.
Published: (2025)

Flow Matching on Lie Groups
by: Sherry, Finn M., et al.
Published: (2025)

Robust Tangent Space Estimation via Laplacian Eigenvector Gradient Orthogonalization
by: Kohli, Dhruv, et al.
Published: (2025)

Deep Generative Models: Complexity, Dimensionality, and Approximation
by: Wang, Kevin, et al.
Published: (2025)

Distance Measure Based on an Embedding of the Manifold of K-Component Gaussian Mixture Models into the Manifold of Symmetric Positive Definite Matrices
by: Vishwakarma, Amit, et al.
Published: (2025)

Universal kernels via harmonic analysis on Riemannian symmetric spaces
by: Steinert, Franziskus, et al.
Published: (2025)

Tangentially Aligned Integrated Gradients for User-Friendly Explanations
by: Simpson, Lachlan, et al.
Published: (2025)

Simultaneous Optimization of Geodesics and Fréchet Means
by: Rygaard, Frederik Möbius, et al.
Published: (2025)

Staying on the Manifold: Geometry-Aware Noise Injection
by: Jacobsen, Albert Kjøller, et al.
Published: (2025)

Learning with Confidence
by: Richardson, Oliver Ethan
Published: (2025)

Cartan moving frames and the data manifolds
by: Tron, Eliot, et al.
Published: (2024)

Kernel-Gradient Drifting Models
by: Esteban-Casadevall, Maria, et al.
Published: (2026)

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