Related papers: Understanding Latent Diffusability via Fisher Geom…
Distributed algorithms, particularly Diffusion Least Mean Square, are widely favored for their reliability, robustness, and fast convergence in various industries. However, limited observability of the target can compromise the integrity of…
The study of continuous-time information diffusion has been an important area of research for many applications in recent years. When only the diffusion traces (cascades) are accessible, cascade-based network inference and influence…
Estimating subsurface dielectric properties is essential for applications ranging from environmental surveys of soils to nondestructive evaluation of concrete in infrastructure. Conventional wave inversion methods typically assume few…
Diffusion models (DMs) have revolutionized generative learning. They utilize a diffusion process to encode data into a simple Gaussian distribution. However, encoding a complex, potentially multimodal data distribution into a single…
Hierarchical parametric models consisting of observable and latent variables are widely used for unsupervised learning tasks. For example, a mixture model is a representative hierarchical model for clustering. From the statistical point of…
The rapid advancement of diffusion models has significantly improved high-quality image generation, making generated content increasingly challenging to distinguish from real images and raising concerns about potential misuse. In this…
In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process which…
Federated Learning (FL) is a promising framework for performing privacy-preserving, distributed learning with a set of clients. However, the data distribution among clients often exhibits non-IID, i.e., distribution shift, which makes…
The steep computational cost of diffusion models at inference hinders their use as fast physics emulators. In the context of image and video generation, this computational drawback has been addressed by generating in the latent space of an…
Expert specialization is fundamental to Mixture-of-Experts (MoE) model success, yet existing metrics (cosine similarity, routing entropy) lack theoretical grounding and yield inconsistent conclusions under reparameterization. We present an…
In the realm of deep learning, the Fisher information matrix (FIM) gives novel insights and useful tools to characterize the loss landscape, perform second-order optimization, and build geometric learning theories. The exact FIM is either…
Stochastic dynamical systems with slow or metastable behavior evolve, on long time scales, on an unknown low-dimensional manifold in high-dimensional ambient space. Building a reduced simulator from short-burst ambient ensembles is a…
Practical diffusion sampling is a numerical approximation problem: under a fixed inference budget, one must simulate a reverse-time ODE or SDE using only a limited number of denoising steps, so discretization error is often the dominant…
Using the transport-of-intensity approach for free-space optical propagation in the paraxial regime, we show that diffraction is fundamentally related to the Fisher information associated with models of the transverse intensity…
Generative modeling aims to generate new data samples that resemble a given dataset, with diffusion models recently becoming the most popular generative model. One of the main challenges of diffusion models is solving the problem in the…
As synthetic data proliferates across the Internet, it is often reused to train successive generations of generative models. This creates a ``self-consuming loop" that can lead to training instability or \textit{model collapse}. Common…
Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…
Random fields are useful mathematical objects in the characterization of non-deterministic complex systems. A fundamental issue in the evolution of dynamical systems is how intrinsic properties of such structures change in time. In this…
We study the effect of fading in the communication channels between nodes on the performance of the incremental least mean square (ILMS) algorithm. We derive steady-state performance metrics, including the mean-square deviation (MSD),…
Medical image segmentation is crucial for clinical diagnosis and treatment planning. Traditional methods typically produce a single segmentation mask, failing to capture inherent uncertainty. Recent generative models enable the creation of…