arXiv research

A new diffusion sampling method combines Krylov subspace and diffusion models for faster and more efficient inverse problems.

Study on reliability of latent reuse in diffusion models under distribution shift.

This paper improves diffusion models for low-dimensional data.

GDMaps reduces high-dimensional data to lower dimensions for better classification.

Diffusion models' sampling paths lie in a low-dimensional subspace, resembling boomerangs.

New algorithm improves multitask learning across diverse agents.

Diffusion models improve creativity by smoothing the score function, leading to interpolated data.

GEOMANCER learns manifold factors without supervision.

Fairness-aware diffusion for graph neural networks

Diffusion models learn multi-modal distributions with optimal efficiency.

Gradient-based framework for optimizing text prompts in diffusion models.

SBMs learn manifold-like structures by mixing samples with a non-conservative field.

LOL method simplifies forming linear combinations of latent variables.

IntroVAC learns interpretable latent subspaces for better image quality.

Two adaptive kernel selection methods improve the accuracy of Kernelized Diffusion Maps.

New method aligns diffusion models for inference-time properties without retraining.

The paper analyzes reflected diffusion models on hypercube data.

Survey of Laplacian-based methods for data dimensionality reduction and embedding.

Studying SGD on deep neural networks using diffusion maps.

Proposes a new method for efficient manifold denoising robust to high dimensional noise.

Study on DiTs' rates of approximation and estimation under various data assumptions.

Proposes a model to generate high-dimensional financial returns using latent factor structure.

Motivated by marginals-mimicking results for Itô processes via SDEs and by their applications to volatility modeling in finance, we discuss the weak convergence of the law of a hypoelliptic diffusions conditioned to belong to a target affine subspace at final time, namely $\mathcal{L}(Z_t|Y_t = y)$ if $X_{\cdot}=(Y_\cd…

New method designs joint initial noises for diffusion models to improve diversity and alignment.

This study explains how adversarial interaction creates non-homogeneous patterns using a pseudo-Reaction-Diffusion model.

Paper uses autoencoders for efficient reduced-order modeling of eigenvalue problems.

A new method for SVGD reduces variance in high dimensions.

Diagonal Frog: High-order positivity-preserving FD schemes for anisotropic Fokker-Planck equations

State-of-the-art computer codes for simulating real physical systems are often characterized by a vast number of input parameters. Performing uncertainty quantification (UQ) tasks with Monte Carlo (MC) methods is almost always infeasible because of the need to perform hundreds of thousands or even millions of forward m…

Paper bounds subspace estimator error from noisy projections.

PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The problem of subspace learning or PCA in the presence of outliers is called robust su…

Union of Subspaces (UoS) is a popular model to describe the underlying low-dimensional structure of data. The fine details of UoS structure can be described in terms of canonical angles (also known as principal angles) between subspaces, which is a well-known characterization for relative subspace positions. In this pa…

Study $Sp(n)$-orbits in complex and $Σ$-complex subspaces of Hermitian quaternionic vector spaces.

In subspace clustering, a group of data points belonging to a union of subspaces are assigned membership to their respective subspaces. This paper presents a new approach dubbed Innovation Pursuit (iPursuit) to the problem of subspace clustering using a new geometrical idea whereby subspaces are identified based on the…

We consider the problem of detecting whether a tensor signal having many missing entities lies within a given low dimensional Kronecker-Structured (KS) subspace. This is a matched subspace detection problem. Tensor matched subspace detection problem is more challenging because of the intertwined signal dimensions. We s…

Paper shows affine constraint is unnecessary for high-dimensional data.

New method reduces PDE model parameters by 30% with sparsity.

A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The corresponding subspace clustering problem has been extensively studied in the lit…

Latent DiTs improve data distribution recovery and inference efficiency under low-dimensional latent space.

This paper investigates the generalization of Principal Component Analysis (PCA) to Riemannian manifolds. We first propose a new and general type of family of subspaces in manifolds that we call barycentric subspaces. They are implicitly defined as the locus of points which are weighted means of $k+1$ reference points.…

Flow Matching models help generative models stay within the subspace of real data.

In this letter, we consider two sets of observations defined as subspace signals embedded in noise and we wish to analyze the distance between these two subspaces. The latter entails evaluating the angles between the subspaces, an issue reminiscent of the well-known Procrustes problem. A Bayesian approach is investigat…

Give deterministic necessary and sufficient conditions to guarantee that if a subspace fits certain partially observed data from a union of subspaces, it is because such data really lies in a subspace. Furthermore, Give deterministic necessary and sufficient conditions to guarantee that if a subspace fits certain parti…

In this paper, we exhibit the tradeoffs between the (training) sample, computation and storage complexity for the problem of supervised classification using signal subspace estimation. Our main tool is the use of tensor subspaces, i.e. subspaces with a Kronecker structure, for embedding the data into lower dimensions. …

A new method for faster optimization in high dimensions.

We assume data sampled from a mixture of d-dimensional linear subspaces with spherically symmetric distributions within each subspace and an additional outlier component with spherically symmetric distribution within the ambient space (for simplicity we may assume that all distributions are uniform on their correspondi…

An elliptic theory is constructed for operators acting in subspaces defined via odd pseudodifferential projections. Subspaces of this type arise as Calderon subspaces for first order elliptic differential operators on manifolds with boundary, or as spectral subspaces for self-adjoint elliptic differential operators of …

WPCA improves subspace recovery robustness to outliers.