Related papers: Fluctuation-dissipation theorem and models of lear…
Enquiries concerning the underlying mechanisms and the emergent properties of a biological brain have a long history of theoretical postulates and experimental findings. Today, the scientific community tends to converge to a single…
In this work, we study the dynamics of a single active Brownian particle, as well as the collective behavior of interacting active Brownian particles, in a fluctuating heterogeneous environment. We employ a variant of the diffusing…
We analyse large deviations of time-averaged quantities in stochastic processes with long-range memory, where the dynamics at time t depends itself on the value q_t of the time-averaged quantity. First we consider the elephant random walk…
In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…
Use of machine learning to perform database operations, such as indexing, cardinality estimation, and sorting, is shown to provide substantial performance benefits. However, when datasets change and data distribution shifts, empirical…
The Bayesian brain hypothesis postulates that the brain accurately operates on statistical distributions according to Bayes' theorem. The random failure of presynaptic vesicles to release neurotransmitters may allow the brain to sample from…
Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory.…
We apply macroscopic fluctuation theory to study the diffusion of a tracer in a one-dimensional interacting particle system with excluded mutual passage, known as single-file diffusion. In the case of Brownian point particles with hard-core…
In this work, we have studied simple models that can be solved analytically to illustrate various fluctuation theorems. These fluctuation theorems provide symmetries individually to the distributions of physical quantities like the…
The fluctuation-dissipation theorem is a cornerstone result in statistical mechanics that can be used to translate the statistics of the free natural variability of a system into information on its forced response to perturbations. By…
Deep learning algorithms have made incredible strides in the past decade, yet due to their complexity, the science of deep learning remains in its early stages. Being an experimentally driven field, it is natural to seek a theory of deep…
Learning to transfer considers learning solutions to tasks in a such way that relevant knowledge can be transferred from known task solutions to new, related tasks. This is important for general learning, as well as for improving the…
Living organisms survive and multiply even though they have uncertain and incomplete information about their environment and imperfect models to predict the consequences of their actions. Bayesian models have been proposed to face this…
The fundamental insight into Brownian motion by Einstein is that all substances exhibit continual fluctuations due to thermal agitation balancing with the frictional resistance. However, even at thermal equilibrium, biological activity can…
Entropy and the fluctuation-dissipation theorem are at the heart of statistical mechanics near equilibrium. Driving a system beyond the linear response regime leads to (i) the breakdown of the fluctuation-dissipation theorem and (ii) a…
General results from statistical learning theory suggest to understand not only brain computations, but also brain plasticity as probabilistic inference. But a model for that has been missing. We propose that inherently stochastic features…
We consider a model of Bayesian observational learning in which a sequence of agents receives a private signal about an underlying binary state of the world. Each agent makes a decision based on its own signal and its observations of…
We study learning algorithms when there is a mismatch between the distributions of the training and test datasets of a learning algorithm. The effect of this mismatch on the generalization error and model misspecification are quantified.…
The classical Luria-Delbr\"uck model for fluctuation analysis is extended to the case where cells can either divide or die at the end of their generation time. This leads to a family of probability distributions generalizing the…
Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…