Related papers: Sinkhorn Based Associative Memory Retrieval Using …
As the complexity of modern control systems increases, it becomes challenging to derive an accurate model of the uncertainty that affects their dynamics. Wasserstein Distributionally Robust Optimization (DRO) provides a powerful framework…
Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…
Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data…
Predictive states for stochastic processes are a nonparametric and interpretable construct with relevance across a multitude of modeling paradigms. Recent progress on the self-supervised reconstruction of predictive states from time-series…
Approximate Nearest Neighbor (ANN) search has become fundamental to modern AI infrastructure, powering recommendation systems, search engines, and large language models across industry leaders from Google to OpenAI. Hierarchical Navigable…
We propose a mathematical methodology to derive a stochastic parameterization of bulk warm cloud micro-physics properties. Unlike previous bulk parameterizations, the stochastic parameterization does not assume any particular droplet size…
Time-varying mixture densities occur in many scenarios, for example, the distributions of keywords that appear in publications may evolve from year to year, video frame features associated with multiple targets may evolve in a sequence. Any…
We give an explicit stochastic Hamiltonian model of discontinuous unitary evolution for quantum spontaneous jumps like in a system of atoms in quantum optics, or in a system of quantum particles that interacts singularly with "bubbles"…
Restricted Boltzmann Machines are described by the Gibbs measure of a bipartite spin glass, which in turn corresponds to the one of a generalised Hopfield network. This equivalence allows us to characterise the state of these systems in…
We propose and analyze a solution to the problem of recovering a block sparse signal with sparse blocks from linear measurements. Such problems naturally emerge inter alia in the context of mobile communication, in order to meet the…
This paper addresses distributed parameter estimation in stochastic dynamic systems with quantized measurements, constrained by quantized communication and Markovian switching directed topologies. To enable accurate recovery of the original…
Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different…
We present a new perspective on the celebrated Sinkhorn algorithm by showing that is a special case of incremental/stochastic mirror descent. In order to see this, one should simply plug Kullback-Leibler divergence in both mirror map and…
Quantum coherence and entanglement are fundamental resources in quantum technologies, yet their efficient estimation for unknown states by employing minimal resources in experimental settings remains challenging, particularly in…
As computers approach the physical limits of information storable in memory, new methods will be needed to further improve information storage and retrieval. We propose a quantum inspired vector based approach, which offers a contextually…
We study properties of the Petz recovery map in chaotic systems, such as the Hayden-Preskill setup for evaporating black holes and the SYK model. Since these systems exhibit the phenomenon called scrambling, we expect that the expression of…
We study the data selection problem, whose aim is to select a small representative subset of data that can be used to efficiently train a machine learning model. We present a new data selection approach based on $k$-means clustering and…
We examine a previouly introduced attractor neural network model that explains the persistent activities of neurons in the anterior ventral temporal cortex of the brain. In this model, the coexistence of several attractors including…
Stochastic gradient descent (SGD) is a popular algorithm for minimizing objective functions that arise in machine learning. For constant step-sized SGD, the iterates form a Markov chain on a general state space. Focusing on a class of…
Distributionally robust optimization (DRO) has emerged as a powerful paradigm for reliable decision-making under uncertainty. This paper focuses on DRO with ambiguity sets defined via the Sinkhorn discrepancy: an entropy-regularized…