Related papers: Exploring simplicity bias in 1D dynamical systems

Topological conjugateness of one dimensional unimodal dynamical systems, which are generated by interval [0, 1] into itself maps are studied. We study the smoothness and differentiability of the conjugacy of symmetrical and non-symmetrical…

This paper is a study of the dynamics of a new family of maps from the complex plane to itself, which we call twisted tent maps. A twisted tent map is a complex generalization of a real tent map. The action of this map can be visualized as…

A simple, intuitive approach to the assessment of probabilistic inferences is introduced. The Shannon information metrics are translated to the probability domain. The translation shows that the negative logarithmic score and the geometric…

The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We…

Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…

{\em Algorithms with predictions} incorporate machine learning predictions into algorithm design. A plethora of recent works incorporated predictions to improve on worst-case optimal bounds for online problems. In this paper, we initiate…

The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network's prediction, when confronted with a learning task. This iterative change can be naturally…

Entropy dimension is an entropy-type quantity which takes values in $[0,1]$ and classifies different levels of intermediate growth rate of complexity for dynamical systems. In this paper, we consider the complexity of skew products of…

State-of-the-art models often make use of superficial patterns in the data that do not generalize well to out-of-domain or adversarial settings. For example, textual entailment models often learn that particular key words imply entailment,…

In this paper we introduce a new model of random simplicial complexes depending on multiple probability parameters. This model includes the well-known Linial - Meshulam random simplicial complexes and random clique complexes as special…

Process flexibility is widely adopted as an effective strategy for responding to uncertain demand. Many algorithms for constructing sparse flexibility designs with good theoretical guarantees have been developed for balanced and symmetrical…

In a topological dynamical system the complexity of an orbit is a measure of the amount of information (algorithmic information content) that is necessary to describe the orbit. This indicator is invariant up to topological conjugation. We…

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…

We consider the use of Bayesian information criteria for selection of the graph underlying an Ising model. In an Ising model, the full conditional distributions of each variable form logistic regression models, and variable selection…

The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…

The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…

Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of…

Neural network design has utilized flexible nonlinear processes which can mimic biological systems, but has suffered from a lack of traceability in the resulting network. Graphical probabilistic models ground network design in probabilistic…

NLP models often rely on superficial cues known as dataset biases to achieve impressive performance, and can fail on examples where these biases do not hold. Recent work sought to develop robust, unbiased models by filtering biased examples…

We consider network models where information items flow %are sent from a source to a sink node. We start with a model where routing is constrained by energy available on nodes in finite supply (like in Smartdust) and efficiency is related…