manifold-learning

Proposes HDE-Net, a manifold-constrained deep neural network that uses hyperbolic space to better model rule-based structures in tabular data, achieving state-of-the-art performance on the TALENT-tiny-core benchmark while maintaining efficiency.

This paper proposes incorporating symmetries into affinity kernels for spectral embedding, proving convergence of invariant graph Laplacians on quotient manifolds with improved sample complexity.

Proposes LieBN, a framework for batch normalization over Lie groups, applicable to SPD, rotation, and correlation manifolds, with theoretical guarantees and extensive experiments.

Proposes a reinforcement learning framework that uses locally linear embeddings to capture environment dynamics and an attention mechanism to adaptively fuse dynamics-specific and reward-specific features, inspired by neural principles, improving learning efficiency.

This paper proposes a Finslerian graph neural network that estimates the Finsler Laplacian on point clouds, proving convergence and demonstrating its use in recovering Finsler metrics from heat diffusion.

This paper rethinks structural anomaly detection by shifting from decision boundaries to projection operators onto the low-dimensional manifold of normal data, showing that projection-aligned methods outperform existing boundary-based and reconstruction-based approaches.

This paper argues that for large enough models, unfiltered data can improve generalization by providing weak perturbations, contrary to the common assumption that only high-quality filtered data is beneficial. The authors caution that harmful conditional shifts can still damage models, but over-curation may remove useful perturbations.

This paper introduces MGAP, a training-free decoding method that reduces hallucinations in Multimodal Large Language Models by adaptively suppressing only the harmful parts of language priors while preserving the model's semantic manifold. The method outperforms prior baselines on POPE and CHAIR benchmarks.

This paper introduces Branched Neural Rough Differential Equations, a method for learning manifold and Itô dynamics by combining rough path theory with neural networks, enabling the modeling of complex stochastic and geometric structures.

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.