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This paper proposes Lie group embedded dynamical neural networks (LieEDNN) with learning algorithms based on gradient descent and metric projection on smooth manifolds, enabling stable dynamics on Lie groups like SO(3) and SE(3) for robotics and control applications.
This paper introduces geometry-aware flow matching for natural images by treating them as points on a hypersphere, proposing SOT-CFM and SFM methods that improve generative modeling by leveraging the spherical structure of image data.
This article explores how sparse autoencoders (SAEs) can capture curved neural geometry, revealing three distinct ways SAE features represent manifolds, and presents an unsupervised pipeline to uncover geometric structure in neural representations.
This paper investigates reasoning in LLMs as an intrinsic dynamical process, finding that inference-time representations self-organize into low-dimensional manifolds. It proposes a label-free diagnostic based on internal dynamics to assess reasoning quality, suggesting that effective reasoning is governed by geometric and informational constraints.
Neural networks appear to speak English on the surface, but internally organize information in geometric space (curves, loops, surfaces, manifolds). Understanding "neural geometry" may be the key to understanding, debugging, and controlling models.