Learning Manifold
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Related Articles from SNS
Learning Manifold and It\^o Dynamics with Branched Neural Rough Differential Equations
arXiv:2606.05272v1 Announce Type: new Abstract: Neural rough differential equations (NRDEs) stay accurate under irregular sampling while taking far fewer integration steps than standard neural differential equations, summarising a finely sampled driver by its log-signature and advancing the hidden state over coarse intervals using the log-ODE method. This efficiency rests on the shuffle algebra, the algebraic counterpart of Stratonovich calculus. This reliance means NRDEs cannot expose the...
Revisiting Prototype Rehearsal for Exemplar-Free Continual Learning: Manifold-Aware Boundary Sampling with Adaptive Class-Balanced Loss
Announce Type: new Abstract: Exemplar-free class-incremental learning (EFCIL) aims to acquire new classes over time without storing raw data. Historically, prototype rehearsal, which samples around stored class prototypes and mixes them with current-task data, has been a popular strategy to reduce catastrophic forgetting. However, recent drift-compensation methods that explicitly realign prototypes in the evolving feature space consistently outperform prototype-based rehearsal, raising the...
MaCo-GAN: Manifold-Contrastive Adversarial Learning for Single Image Super-Resolution
new Abstract: Conventional Generative Adversarial Networks (GANs) for Single Image Super-Resolution (SISR) often struggle with hallucinated artifacts, largely because standard discriminators evaluate overall image naturalness rather than strict conditional realism. To address this, we propose MaCo-GAN, a novel manifold-contrastive GAN framework that replaces the conventional adversarial loss with a supervised contrastive objective. A core component of our method is a dynamic fake sample...
Learning from Demonstrations over Riemannian Manifolds using Neural ODEs: An Extended Abstract
Announce Type: new Abstract: Learning from demonstratins (LfD) is usually performed over Euclidean spaces, while the robot state, e.g. orientation, naturally evolves over curved spaces. Therefore, to ensure natural, complex motion generation, we investigate learning from demonstrations over Riemannian manifolds that are capable of encoding both position and orientation data.
Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning
arXiv:2604.20308v2 Announce Type: replace Abstract: Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued representations that capture relationships between directions-such as how atomic orientations covary in a molecule. These second-order representations are naturally captured by points on the symmetric...
IRIS: time-structured manifold projections
Announce Type: new Abstract: High-dimensional biomedical data, such as cell-by-gene matrices, are increasingly generated temporally. However, Manifold Learning algorithms, like t-SNE and UMAP, cannot incorporate time-ordering in their layouts, obfuscating the dynamics of cell types or other classes. As a solution, we present IRIS, a new Manifold Learning algorithm that structures layouts both chronologically and by manifold topology.
A Geometric Theory of Cognition for Machine Intelligence
Announce Type: replace Abstract: Developing artificial agents that unify representation, memory, adaptation, and prediction remains a fundamental challenge in artificial intelligence. Here we introduce a geometric framework in which cognitive computation emerges from Riemannian gradient flow on a learned latent manifold. The learned metric encodes representational constraints and computational preferences, while anisotropies in the geometry naturally generate multiple timescales of...
Flexible Online Representation Learning Based on Similarity Matching
Announce Type: replace Abstract: Sparse high-dimensional representations are conducive to uncovering nontrivial structures in unsupervised exploration of data. Such a representation can deal with the dense connectivity in graphs relevant to community detection problems. However, sparse high-dimensional representations are capable of doing more, including manifold tiling and feature learning.
Flexible Online Representation Learning Based on Similarity Matching
arXiv:2606.01546v1 Announce Type: new Abstract: Sparse high-dimensional representations are conducive to uncovering nontrivial structures in unsupervised exploration of data. Such a representation can deal with the dense connectivity in graphs relevant to community detection problems. However, sparse high-dimensional representations are capable of doing more, including manifold tiling and feature learning.
Riemannian-Manifold Steering: Geometry-Aware Generative Autoencoders for Label-Free Steering
arXiv:2605.24942v2 Announce Type: replace Abstract: Steering a language model - intervening on its internal activations to change downstream behaviour - has recently expanded beyond linear interpolation to nonlinear methods such as angular and kernelized steering, which define intervention transformations without learning an explicit geometry over paths in activation space. Freshly introduced geometry-aware manifold methods do learn such a geometry, but require labelled class centroids...