Related papers: Understanding and Designing Complex Systems: Respo…

Numerical climate model simulations run at high spatial and temporal resolutions generate massive quantities of data. As our computing capabilities continue to increase, storing all of the data is not sustainable, and thus it is important…

To reduce model size during post-training, compression methods, including knowledge distillation, low-rank approximation, and pruning, are often applied after fine-tuning the model. However, sequential fine-tuning and compression sacrifices…

Small random perturbations may have a dramatic impact on the long time evolution of dynamical systems, and large deviation theory is often the right theoretical framework to understand these effects. At the core of the theory lies the…

Labor market institutions are central for modern economies, and their polices can directly affect unemployment rates and economic growth. At the individual level, unemployment often has a detrimental impact on people's well-being and…

Predicting the future motion of vehicles has been studied using various techniques, including stochastic policies, generative models, and regression. Recent work has shown that classification over a trajectory set, which approximates…

Understanding generalization in modern machine learning settings has been one of the major challenges in statistical learning theory. In this context, recent years have witnessed the development of various generalization bounds suggesting…

Linear computation coding is concerned with the compression of multidimensional linear functions, i.e. with reducing the computational effort of multiplying an arbitrary vector to an arbitrary, but known, constant matrix. This paper…

The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…

In 'An asymptotic result on compressed sensing matrices', a new construction for compressed sensing matrices using combinatorial design theory was introduced. In this paper, we use deterministic and probabilistic methods to analyse the…

Even simply-defined, finite-state generators produce stochastic processes that require tracking an uncountable infinity of probabilistic features for optimal prediction. For processes generated by hidden Markov chains the consequences are…

Optimization in engineering requires appropriate models. In this article, a regression method for enhancing the predictive power of a model by exploiting expert knowledge in the form of shape constraints, or more specifically, monotonicity…

We apply category theory to extract multimodal document structure which leads us to develop information theoretic measures, content summarization and extension, and self-supervised improvement of large pretrained models. We first develop a…

Approximate inference in dynamic systems is the problem of estimating the state of the system given a sequence of actions and partial observations. High precision estimation is fundamental in many applications like diagnosis, natural…

Despite the growing availability of sensing and data in general, we remain unable to fully characterise many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture…

Linear models are used in online decision making, such as in machine learning, policy algorithms, and experimentation platforms. Many engineering systems that use linear models achieve computational efficiency through distributed systems…

Statistical sufficiency formalizes the notion of data reduction. In the decision theoretic interpretation, once a model is chosen all inferences should be based on a sufficient statistic. However, suppose we start with a set of procedures…

Chaitin's work, in its depth and breadth, encompasses many areas of scientific and philosophical interest. It helped establish the accepted mathematical concept of randomness, which in turn is the basis of tools that I have developed to…

This paper is concerned with the lossy compression of general random variables, specifically with rate-distortion theory and quantization of random variables taking values in general measurable spaces such as, e.g., manifolds and fractal…

With the increasing interplay between experimental and computational approaches at multiple length scales, new research directions are emerging in materials science and computational mechanics. Such cooperative interactions find many…

In this document, we present key findings in structured matrix approximation theory, with applications to the regressive representation of dynamic financial processes. Initially, we explore a comprehensive approach involving generic…