Related papers: How to explain grokking
Learning and inference movement is a very challenging problem due to its high dimensionality and dependency to varied environments or tasks. In this paper, we propose an effective probabilistic method for learning and inference of basic…
This thesis is dedicated to the study of stochastic processes; non-deterministic physical phenomena that can be well described by classical physics. The stochastic processes we are interested in are akin to Brownian Motion and can be…
Recent rapid advances in single particle tracking and supercomputing techniques resulted in an unprecedented abundance of diffusion data exhibiting complex behaviours, such the presence of power law tails of the msd and memory functions,…
We identify an issue in recent approaches to learning-based control that reformulate systems with uncertain dynamics using a stochastic differential equation. Specifically, we discuss the approximation that replaces a model with fixed but…
A machine learning method is proposed using two agents that simulate the biological behavior of a predator and a prey. In this method, the predator and the prey interact with each other - the predator chases the prey while the prey runs…
Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized.…
World models have recently emerged as a promising approach to reinforcement learning (RL), achieving state-of-the-art performance across a wide range of visual control tasks. This work aims to obtain a deep understanding of the robustness…
Deep neural networks exhibit a fascinating spectrum of phenomena ranging from predictable scaling laws to the unpredictable emergence of new capabilities as a function of training time, dataset size and network size. Analysis of these…
The generalized Langevin equation with an exponential kernel is used to analyze memory effects on the optimal work done by a Brownian particle in a heat bath and subjected to a harmonic moving potential. The generalized overdamping scenario…
We solve a Langevin equation, first studied by de Gennes, in which there is a solid-solid or dry friction force acting on a Brownian particle in addition to the viscous friction usually considered in the study of Brownian motion. We obtain…
The relativistic generalization of a free Brownian motion theory is presented. The global characteristics of the relaxation are {\it explicitly} found for the velocity and momentum (stochastic) kinetics. It is shown that the thermal…
Gyroscopic motion explanation in texts is relatively long and requires reasonable level of comfort with the mathematical tools used. On the other hand, popular explanation outside academic courses does not explain the phenomenon and only…
The present article deals with general mechanics in an unconventional manner. At first, Newtonian mechanics for a point particle has been described in vectorial picture, considering Cartesian, polar and tangent-normal formulations in a…
In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external…
The generalized Langevin equation is a model for the motion of coarse-grained particles where dissipative forces are represented by a memory term. The numerical realization of such a model requires the implementation of a stochastic…
The study of Deep Network (DN) training dynamics has largely focused on the evolution of the loss function, evaluated on or around train and test set data points. In fact, many DN phenomenon were first introduced in literature with that…
We study the coarse-graining approach to derive a generator for the evolution of an open quantum system over a finite time interval. The approach does not require a secular approximation but nevertheless generally leads to a…
We derive the delay in travel time of photons due to the spin of a body both inside a rotating shell and outside a rotating body. We then show that this time delay by the spin of an astrophysical object might be detected in different images…
In this paper, we study the mean reflected stochastic differential equations driven by G-Brownian motion, where the constraint depends on the expectation of the solution rather than on its paths. Well-posedness is achieved by first…
A leading hypothesis for the surprising generalization of neural networks is that the dynamics of gradient descent bias the model towards simple solutions, by searching through the solution space in an incremental order of complexity. We…