相关论文: From Layers to Networks: Comparing Neural Represen…

We propose a geometry-to-flow diffusion model that utilizes obstacle shape as input to predict a flow field around an obstacle. The model is based on a learnable Markov transition kernel to recover the data distribution from the Gaussian…

The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…

Learning the distribution of data on Riemannian manifolds is crucial for modeling data from non-Euclidean space, which is required by many applications in diverse scientific fields. Yet, existing generative models on manifolds suffer from…

Diffusion-based models have achieved notable empirical successes in reinforcement learning (RL) due to their expressiveness in modeling complex distributions. Despite existing methods being promising, the key challenge of extending existing…

Diffusion models have emerged as a powerful framework for generative tasks in deep learning. They decompose generative modeling into two computational primitives: deterministic neural-network evaluation and stochastic sampling. Current…

Diffusion Generative Models (DGM) have rapidly surfaced as emerging topics in the field of computer vision, garnering significant interest across a wide array of deep learning applications. Despite their high computational demand, these…

Diffusion models have become a leading framework in generative modeling, yet their theoretical understanding -- especially for high-dimensional data concentrated on low-dimensional structures -- remains incomplete. This paper investigates…

We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…

Water diffusion gives rise to micron-scale sensitivity of diffusion MRI (dMRI) to cellular-level tissue structure. Precision medicine and quantitative imaging depend on uncovering the information content of dMRI and establishing its…

Quantifying similarity between neural representations -- e.g. hidden layer activation vectors -- is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks…

Understanding the deep representations of complex networks is an important step of building interpretable and trustworthy machine learning applications in the age of internet. Global surrogate models that approximate the predictions of a…

Diffusion, a fundamental internal mechanism emerging in many physical processes, describes the interaction among different objects. In many learning tasks with limited training samples, the diffusion connects the labeled and unlabeled data…

We introduce the diffusion and superposition distances as two metrics to compare signals supported in the nodes of a network. Both metrics consider the given vectors as initial temperature distributions and diffuse heat trough the edges of…

An unsupervised learning algorithm to cluster hyperspectral image (HSI) data is proposed that exploits spatially-regularized random walks. Markov diffusions are defined on the space of HSI spectra with transitions constrained to near…

Far from equilibrium, neural systems self-organize across multiple scales. Exploiting multiscale self-organization in neuroscience and artificial intelligence requires a computational framework for modeling the effective non-equilibrium…

Geological parameterization entails the representation of a geomodel using a small set of latent variables and a mapping from these variables to grid-block properties such as porosity and permeability. Parameterization is useful for data…

While the manifold hypothesis is widely adopted in modern machine learning, complex data is often better modeled as stratified spaces -- unions of manifolds (strata) of varying dimensions. Stratified learning is challenging due to varying…

Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…

Shape information is crucial for human perception and cognition, and should therefore also play a role in cognitive AI systems. We employ the interdisciplinary framework of conceptual spaces, which proposes a geometric representation of…

Comparison of data representations is a complex multi-aspect problem that has not enjoyed a complete solution yet. We propose a method for comparing two data representations. We introduce the Representation Topology Divergence (RTD),…