manifold-learning

The paper proposes Smooth Rank t-SNE (SR-tSNE), a t-SNE variant with a differentiable sigmoid rank term that preserves the ordering of neighbors, plus an Ordinal DLP metric; it outperforms 12 baselines across eight benchmarks and improves downstream tasks like label transfer, single-cell clustering, and algorithmic trading.

论文提出 Geodesic-SVDD 框架，通过球面原型学习和测地线潜在空间 Mixup 实现单轮通信的分布式表格数据学习，在多个联邦基准上超越现有方法和联邦树集成。

The paper introduces Variational Atlas Autoencoders, a mixture-of-charts framework that learns multiple local latent representations over a data manifold, using latent-evidence routing to treat chart assignment as self-supervised posterior inference, achieving better-structured latent spaces and higher sample quality on datasets like CelebA.

FlashDiffusion is a matrix-free method that evaluates dense Gaussian kernel blocks in fused GPU tiles and couples the eigensolver to an empirical beta-flow that selects the finite-sample resolution scale, avoiding O(N^2) memory costs in diffusion-map spectral decompositions.

This paper develops intrinsic dense associative memories on Riemannian manifolds by casting memory as Epanechnikov kernel-density mode seeking, showing that curvature—via Ricci curvature thresholds and geodesic capacity scalings—determines what such a memory retains, creates, and forgets, with demonstrations on WordNet noun hierarchy.

This paper proposes an adaptive spectral bandwidth control method for kernelized graph construction to align kernel spectral properties with intrinsic manifold dimensions, showing improvements in self-supervised learning embedding tasks on CIFAR-100.

This paper proposes a manifold-aware encoding strategy for general coded computing that exploits the intrinsic low-dimensional geometry of high-dimensional data to improve straggler resilience in distributed systems. Experiments show reduced mean squared recovery error in neural network inference and polynomial evaluation tasks.

This paper proposes an unsupervised framework combining manifold learning and interpretable graph embeddings to address geometric and interpretability gaps in visual representations, enhancing performance in image retrieval and GCN classification tasks.

This paper proposes LA-ReduNet, a lightweight adaptive architecture that uses hyperspherical manifold learning and adaptive step sizes to significantly reduce the number of layers needed for the MCR2 objective in neural networks, achieving comparable classification accuracy with far fewer parameters.

This paper introduces a data-driven framework combining supervised classification and generative modeling to reconstruct separatrices in multistable dynamical systems, using neural networks and score-based generative models to approximate boundaries of basins of attraction.

An essay critiquing the common conflation of optimization and learning in neural network research, arguing that training should be understood as inverse reconstruction and studied through the evolving homology of weight-defined piecewise manifolds.

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.