Related papers: Error threshold in simple landscapes

It is a long-standing question in origin-of-life research whether the information content of replicating molecules can be maintained in the presence of replication errors. Extending standard quasispecies models of non-enzymatic replication,…

For a class of stochastic restart algorithms we address the effect of a nonzero level of randomization in maximizing the convergence rate for general energy landscapes. The resulting characterization of the optimal level of randomization is…

Cross-entropy (CE) is the default training loss for supervised classification, but its sample efficiency is limited when labels are scarce. Existing remedies primarily act on the data side, via augmentation, synthesis, or transfer from…

Various recent experimental results show that large language models (LLM) exhibit emergent abilities that are not present in small models. System performance is greatly improved after passing a certain critical threshold of scale. In this…

Describing the evolution of a population of genomes evolving in a complex fitness landscape is generally very hard. We here introduce an approximate Gaussian closure scheme to characterize analytically the statistics of a genomic population…

We demonstrate that, for a range of state-of-the-art machine learning algorithms, the differences in generalisation performance obtained using default parameter settings and using parameters tuned via cross-validation can be similar in…

The fuel-driven process of replication in living systems generates distributions of copied entities with varying degrees of copying accuracy. Here we introduce a thermodynamically consistent ensemble for investigating universal population…

Motivated by empirical observations of prolonged plateaus and stage-wise progression during training, we investigate the loss landscape of transformer models trained on in-context next-token prediction tasks. In particular, we focus on…

When biological populations expand into new territory, the evolutionary outcomes can be strongly influenced by genetic drift, the random fluctuations in allele frequencies. Meanwhile, spatial variability in the environment can also…

We define a general class of network formation models, Statistical Exponential Random Graph Models (SERGMs), that nest standard exponential random graph models (ERGMs) as a special case. We provide the first general results on when these…

We consider the classical Wright-Fisher model with mutation and selection. Mutations occur independently in each locus, and selection is performed according to the sharp peak landscape. In the asymptotic regime studied in [3], a…

Maximum-entropy ensembles are key primitives in statistical mechanics from which thermodynamic properties can be derived. Over the decades, several approaches have been put forward in order to justify from minimal assumptions the use of…

We argue that in fully-connected networks a phase transition delimits the over- and under-parametrized regimes where fitting can or cannot be achieved. Under some general conditions, we show that this transition is sharp for the hinge loss.…

We study structural equation modeling (SEM) for diffusion processes with jumps. Based on high-frequency data, we consider the parameter estimation and the goodness-of-fit test in the SEM. Using a threshold method, we propose the…

We develop an empirical likelihood (EL) framework for random forests and related ensemble methods, providing a likelihood-based approach to quantify their statistical uncertainty. Exploiting the incomplete $U$-statistic structure inherent…

This work provides a theoretical framework for assessing the generalization error of graph neural networks in the over-parameterized regime, where the number of parameters surpasses the quantity of data points. We explore two widely…

Large sets of genotypes give rise to the same phenotype because phenotypic expression is highly redundant. Accordingly, a population can accept mutations without altering its phenotype, as long as thegenotype mutates into another one on the…

In many applications of evolutionary algorithms the computational cost of applying operators and storing populations is comparable to the cost of fitness evaluation. Furthermore, by knowing what exactly has changed in an individual by an…

We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…

Random forests are ensemble learning methods introduced by Breiman (2001) that operate by averaging several decision trees built on a randomly selected subspace of the data set. Despite their widespread use in practice, the respective roles…