Related papers: Geometric framework for biological evolution
We introduce a new model of evolution on a fitness landscape possessing a tunable degree of neutrality. The model allows us to study the general properties of molecular species undergoing neutral evolution. We find that a number of…
Understanding how deep neural networks learn representations remains a central challenge in machine learning theory. In this work, we propose a feature-centric framework for analyzing neural network training by relating weight updates to…
In this thesis we consider primarily the dynamics of quantum systems subjected to continuous observation. In the Schr\"{o}dinger picture the evolution of a continuously monitored quantum system, referred to as a `quantum trajectory', may be…
Genotypic fitness landscapes are constructed by assessing the fitness of all possible combinations of a given number of mutations. In the last years, several experimental fitness landscapes have been completely resolved. As fitness…
Fitness landscapes are a useful concept to study the dynamics of meta-heuristics. In the last two decades, they have been applied with success to estimate the optimization power of several types of evolutionary algorithms, including genetic…
Infinitely many distinct trait values may arise in populations bearing quantitative traits, and modeling their population dynamics is thus a formidable task. While classical models assume fixed or infinite population size, models in which…
The fitness landscape defines the relationship between genotypes and fitness in a given environment, and underlies fundamental quantities such as the distribution of selection coefficient, or the magnitude and type of epistasis. A better…
With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this…
Autonomous (noise-agnostic) generative models, such as Equilibrium Matching and blind diffusion, challenge the standard paradigm by learning a single, time-invariant vector field that operates without explicit noise-level conditioning.…
In the paper the memory effect in the system consisting from a trajectory of process and an environment is considered. The environment is presented by scalar potential and noise. The evolution of system is interpreted as process of the…
Random fields are useful mathematical objects in the characterization of non-deterministic complex systems. A fundamental issue in the evolution of dynamical systems is how intrinsic properties of such structures change in time. In this…
Fundamental properties of macroscopic gene-mating dynamic evolutionary systems are investigated. We focus on a single locus, any number of alleles in a two-gender dioecious population, for a large class of systems within population…
Deep learning models have seen significant successes in numerous applications, but their inner workings remain elusive. The purpose of this work is to quantify the learning process of deep neural networks through the lens of a novel…
Selection, mutation and random drift affect the dynamics of allele frequencies and consequently of quantitative traits. While the macroscopic dynamics of quantitative traits can be measured, the underlying allele frequencies are typically…
Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained…
Estimating the state of an environment from high-dimensional, multimodal, and noisy observations is a fundamental challenge in reinforcement learning (RL). Traditional approaches rely on probabilistic models to account for the uncertainty,…
A macroscopic theory for describing cellular states during steady-growth is presented, which is based on the consistency between cellular growth and molecular replication, as well as the robustness of phenotypes against perturbations.…
The magnitude of a metric space is a novel invariant that provides a measure of the 'effective size' of a space across multiple scales, while also capturing numerous geometrical properties, such as curvature, density, or entropy. We develop…
We explore the measurement problem in the entropic dynamics approach to quantum theory. The dual modes of quantum evolution---either continuous unitary evolution or abrupt wave function collapse during measurement---are unified by virtue of…
Biological and artificial neural systems form high-dimensional neural representations that underpin their computational capabilities. Methods for quantifying geometric similarity in neural representations have become a popular tool for…