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In recent years, model collapse has become a critical issue in language model training, making it essential to understand the underlying mechanisms driving this phenomenon. In this paper, we investigate recursive parametric model training…
Migration between different habitats is ubiquitous among biological populations. In this Letter, we study a simple quasispecies model for evolution in two different habitats, with different fitness landscapes, coupled through one-way…
A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…
The ability of organisms to accurately sense their environment and respond accordingly is critical for evolutionary success. However, exactly how the sensory ability influences fitness is a topic of active research, while the necessity of a…
Conventional population genetics considers the evolution of a limited number of genotypes corresponding to phenotypes with different fitness. As model phenotypes, in particular RNA secondary structure, have become computationally tractable,…
This Letter studies the quasispecies dynamics of a population capable of genetic repair evolving on a time-dependent fitness landscape. We develop a model that considers an asexual population of single-stranded, conservatively replicating…
We reconsider the Eigen's quasi-species model for competing self-reproductive macromolecules in populations characterized by a single-peaked fitness landscape. The use of ideas and tools borrowed from polymers theory and statistical…
Increasing the L2 regularization of Deep Neural Networks (DNNs) causes a first-order phase transition into the under-parametrized phase -- the so-called onset-of learning. We explain this transition via the scalar (Ricci) curvature of the…
Quasispecies theory predicts that there is a critical mutation probability above which a viral population will go extinct. Above this threshold the virus loses the ability to replicate the best adapted genotype, leading to a population…
A quasispecies is a set of interrelated genotypes that have reached a situation of equilibrium while evolving according to the usual Darwinian principles of selection and mutation. Quasispecies studies invariably assume that it is possible…
We study the phase transition from the persistence phase to the extinction phase for the SIRS (susceptible/ infected/ refractory/ susceptible) model of diseases spreading on small world network. We show the effects of all the parameters…
An elastic spring network is an example of evolvable matter. It can be pruned to couple separated pairs of nodes so that when a strain is applied to one of them, the other responds either in-phase or out-of-phase. This produces two pruned…
Muller's ratchet, in its prototype version, models a haploid, asexual population whose size~$N$ is constant over the generations. Slightly deleterious mutations are acquired along the lineages at a constant rate, and individuals carrying…
We find an advantage of recombination for a category of complex fitness landscapes. Recent studies of empirical fitness landscapes reveal complex gene interactions and multiple peaks, and recombination can be a powerful mechanism for…
In this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the…
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…
The adaptation rate in theoretical models of biological evolution increases with the mutation rate but only to a point when mutations into lethal states cause extinction. One would expect that removing such states should be beneficial for…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
We investigate the effect of quantum errors on a monitored Brownian Sachdev-Ye-Kitaev (SYK) model featuring a measurement-induced phase transition that can be understood as a symmetry-breaking transition of an effective $Z_4$ magnet in the…
The influence of time-dependent fitnesses on the infinite population dynamics of simple genetic algorithms (without crossover) is analyzed. Based on general arguments, a schematic phase diagram is constructed that allows one to characterize…