Related papers: Characterizing information loss in a chaotic doubl…

Discovering governing equations that describe complex chaotic systems remains a fundamental challenge in physics and neuroscience. Here, we introduce the PEM-UDE method, which combines the prediction-error method with universal differential…

It has long been suggested that the biological brain operates at some critical point between two different phases, possibly order and chaos. Despite many indirect empirical evidence from the brain and analytical indication on simple neural…

Feed-forward neural networks (FNNs) work as standard building blocks in applying artificial intelligence (AI) to the physical world. They allow learning the dynamics of unknown physical systems (e.g., biological and chemical) {to predict…

Deep neural networks (DNNs) have achieved significant success in various applications with large-scale and balanced data. However, data in real-world visual recognition are usually long-tailed, bringing challenges to efficient training and…

Deterministic chaos is phenomenon from nonlinear dynamics and it belongs to greatest advances of twentieth-century science. Chaotic behavior appears apart of mathematical equations also in wide range in observable nature, so as in there…

Highly non-linear, chaotic or near chaotic, dynamic models are important in fields such as ecology and epidemiology: for example, pest species and diseases often display highly non-linear dynamics. However, such models are problematic from…

We introduce a model of randomly connected neural populations and study its dynamics by means of the dynamical mean-field theory and simulations. Our analysis uncovers a rich phase diagram, featuring high- and low-dimensional chaotic…

Although deep learning models have achieved state-of-the-art performance on a number of vision tasks, generalization over high dimensional multi-modal data, and reliable predictive uncertainty estimation are still active areas of research.…

Deep neural networks (DNNs) have garnered significant attention in financial asset pricing, due to their strong capacity for modeling complex nonlinear relationships within financial data. However, sophisticated models are prone to…

The Information Bottleneck (IB) method is an information theoretical framework to design a parsimonious and tunable feature-extraction mechanism, such that the extracted features are maximally relevant to a specific learning or inference…

Math Word Problems (MWP) aims to automatically solve mathematical questions given in texts. Previous studies tend to design complex models to capture additional information in the original text so as to enable the model to gain more…

We consider model social networks in which information propagates directionally across layers of rational agents. Each agent makes a locally optimal estimate of the state of the world, and communicates this estimate to agents downstream.…

We analyze the loss of information and the loss of learning capability inside an arrangement of neural networks. Our method is new and based on the formulation of non-unitary Bogoliubov transformations in order to connect the information…

This tutorial paper focuses on the variants of the bottleneck problem taking an information theoretic perspective and discusses practical methods to solve it, as well as its connection to coding and learning aspects. The intimate…

Scrambling in interacting quantum systems out of equilibrium is particularly effective in the chaotic regime. Under time evolution, initially localized information is said to be scrambled as it spreads throughout the entire system. This…

Many research works deal with chaotic neural networks for various fields of application. Unfortunately, up to now these networks are usually claimed to be chaotic without any mathematical proof. The purpose of this paper is to establish,…

Multi-task learning (MTL) is an important subject in machine learning and artificial intelligence. Its applications to computer vision, signal processing, and speech recognition are ubiquitous. Although this subject has attracted…

The hierarchical nature of corporate information processing is a topic of great interest in economic and management literature. Firms are characterised by a need to make complex decisions, often aggregating partial and uncertain…

The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of…

We present the information-ordered bottleneck (IOB), a neural layer designed to adaptively compress data into latent variables ordered by likelihood maximization. Without retraining, IOB nodes can be truncated at any bottleneck width,…