Related papers: Central Limit Theorems for Classical Multidimensio…
After having introduced the notion of universality in statistical mechanics and its importance for our comprehension of the macroscopic behavior of interacting systems, I review recent progress in the understanding of the scaling limit of…
The classical limit of quantum mechanics is discussed for closed quantum systems in terms of observational aspects. Initially, the failure of the limit h->0 is explicitly demonstrated in a model of two quantum mechanically interacting…
The notion of neural collapse refers to several emergent phenomena that have been empirically observed across various canonical classification problems. During the terminal phase of training a deep neural network, the feature embedding of…
We present MMbeddings, a probabilistic embedding approach that reinterprets categorical embeddings through the lens of nonlinear mixed models, effectively bridging classical statistical theory with modern deep learning. By treating…
Classical physics is approached from quantum mechanics in the macroscopic limit. The technical device to achieve this goal is the quantum version of the central limit theorem, derived for an observable at a given time and for the…
Metric embeddings are a widely used method in algorithm design, where generally a ``complex'' metric is embedded into a simpler, lower-dimensional one. Historically, the theoretical computer science community has focused on bi-Lipschitz…
In the present contribution we discuss the role of experimental limitations in the classical limit problem. We studied some simple models and found that Quantum Mechanics does not re-produce classical mechanical predictions, unless we…
Despite their remarkable ability to capture linguistic nuances across diverse languages, questions persist regarding the degree of alignment between languages in multilingual embeddings. Drawing inspiration from research on high-dimensional…
Representation learning is currently a very hot topic in modern machine learning, mostly due to the great success of the deep learning methods. In particular low-dimensional representation which discriminates classes can not only enhance…
We study detection methods for multivariable signals under dependent noise. The main focus is on three-dimensional signals, i.e. on signals in the space-time domain. Examples for such signals are multifaceted. They include geographic and…
We find the asymptotic distribution of the multi-dimensional multi-scale and kernel estimators for high-frequency financial data with microstructure. Sampling times are allowed to be asynchronous and endogenous. In the process, we show that…
In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical…
An essential part of monitoring machine learning models in production is measuring input and output data drift. In this paper, we present a system for measuring distributional shifts in natural language data and highlight and investigate…
Decentralized state estimation in a communication-constrained sensor network is considered. The exchanged estimates are dimension-reduced to reduce the communication load using a linear mapping to a lower-dimensional space. The mean squared…
Multimodal representation learning produces high-dimensional embeddings that align diverse modalities in a shared latent space. While this enables strong generalization, it also introduces scalability challenges, both in terms of storage…
Typical deep clustering methods, while achieving notable progress, can only provide one clustering result per dataset. This limitation arises from their assumption of a fixed underlying data distribution, which may fail to meet user needs…
A well motivated method for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here formulate this problem as a linear program and provide an…
Though deep learning has pushed the boundaries of classification forward, in recent years hints of the limits of standard classification have begun to emerge. Problems such as fooling, adding new classes over time, and the need to retrain…
This paper describes one objective function for learning semantically coherent feature embeddings in multi-output classification problems, i.e., when the response variables have dimension higher than one. In particular, we consider the…
Robust control design is mainly devoted to guarantee closed-loop stability of a model-based control law in presence of parametric and structural uncertainties. The control law is usually a complex feedback law which is derived from a…