Related papers: Sinkhorn Based Associative Memory Retrieval Using …
In this work, we use a tempering-based adaptive particle filter to infer from a partially observed stochastic rotating shallow water (SRSW) model which has been derived using the Stochastic Advection by Lie Transport (SALT) approach. The…
We develop a semi-analytic deterministic framework for charged-particle transport with continuous slowing-down in energy and angular scattering. Directed transport and energy advection are treated by method-of-characteristics integration,…
Presented is a novel way to combine snapshot compressive imaging and lateral shearing interferometry in order to capture the spatio-spectral phase of an ultrashort laser pulse in a single shot. A deep unrolling algorithm is utilised for the…
Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by…
Autoregressive generative PDE solvers can be accurate one step ahead yet drift over long rollouts, especially in coarse-to-fine regimes where each step must regenerate unresolved fine scales. This is the regime of diffusion and…
The shear shallow water model provides an approximation for shallow water flows by including the effect of vertical shear in the model. This model can be derived from the depth averaging process by including the second order velocity…
We present and explore a new shock-capturing particle hydrodynamics approach. Our starting point is a commonly used discretization of smoothed particle hydrodynamics. We enhance this discretization with Roe's approximate Riemann solver, we…
Nearest-neighbor search in large vector databases is crucial for various machine learning applications. This paper introduces a novel method using tensor-train (TT) low-rank tensor decomposition to efficiently represent point clouds and…
Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space. Existing discrete methods are not scalable as they assume access to the complete set of…
Wasserstein Gradient Flows (WGF) with respect to specific functionals have been widely used in the machine learning literature. Recently, neural networks have been adopted to approximate certain intractable parts of the underlying…
In state estimation tasks, the usual assumption of exactly known disturbance distribution is often unrealistic and renders the estimator fragile in practice. The recently emerging Wasserstein distributionally robust state estimation (DRSE)…
The ability to compare two degenerate probability distributions (i.e. two probability distributions supported on two distinct low-dimensional manifolds living in a much higher-dimensional space) is a crucial problem arising in the…
Deploying continual object detection on microcontrollers (MCUs) with under 100KB memory requires efficient feature compression that can adapt to evolving task distributions. Existing approaches rely on fixed compression strategies (e.g.,…
We study stability of optimizers and convergence of Sinkhorn's algorithm for the entropic optimal transport problem. In the special case of the quadratic cost, our stability bounds imply that if one of the two entropic potentials is…
Developing deterministic neighborhood-informed point-particle closure models using machine learning has garnered interest in recent times from dispersed multiphase flow community. The robustness of neural models for this complex multi-body…
Recent advances in variational inference enable the modelling of highly structured joint distributions, but are limited in their capacity to scale to the high-dimensional setting of stochastic neural networks. This limitation motivates a…
Associative memory models, such as Hopfield networks and their modern variants, have garnered renewed interest due to advancements in memory capacity and connections with self-attention in transformers. In this work, we introduce a unified…
This study leverages the basic insight that the gradient-flow equation associated with the relative Boltzmann entropy, in relation to a Gaussian reference measure within the Hellinger-Kantorovich (HK) geometry, preserves the class of…
Numerous point-cloud understanding techniques focus on whole entities and have succeeded in obtaining satisfactory results and limited sparsity tolerance. However, these methods are generally sensitive to incomplete point clouds that are…
We study analytically and numerically a Hopfield fully-connected network with $d$-dimensional vector spins. These networks are models of associative memory that generalize the standard Hopfield with Ising spins, where $P$ examples are…