Related papers: How long does it take for Internal DLA to forget i…
We consider the dynamics of the simplest chain of large number $N$ of particles. We find, in the double scaling limit, the partition of the parameter space onto two domains, where for one domain the supremum (over all time interval…
Directed acyclic graphs (DAGs) are fundamental structures used across many scientific fields. A key concept in DAGs is the least common ancestor (LCA), which plays a crucial role in understanding hierarchical relationships. Surprisingly…
Latent Dirichlet allocation (LDA) is widely used for unsupervised topic modelling on sets of documents. No temporal information is used in the model. However, there is often a relationship between the corresponding topics of consecutive…
We consider simple random walk on a discrete cylinder with base a large d-dimensional torus of side-length N, when d is two or more. We develop a stochastic domination control on the local picture left by the random walk in boxes of…
We consider a model of a discrete time "interacting particle system" on the integer line where infinitely many changes are allowed at each instance of time. We describe the model using chameleons of two different colours, {\it viz}., red…
Machine learning (ML) can process large sets of data generated from complex systems, which is ideal for classification tasks as often appeared in critical phenomena. Meanwhile ML techniques have been found effective in detecting critical…
The Internal Diffusion Limited Aggregation has been introduced by Diaconis and Fulton in 1991. It is a growth model defined on an infinite set and associated to a Markov chain on this set. We focus here on sets which are finitely generated…
When gas molecules bind to a surface they may do so in such a way that the adsorption of one molecule inhibits the arrival of others. We consider random sequential adsorption in which the empty sites of a graph are irreversibly occupied in…
We introduce a two-type internal DLA model which is an example of a non-unary abelian network. Starting with n "oil" and n "water" particles at the origin, the particles diffuse in Z according to the following rule: whenever some site x has…
Disobeying the classical wisdom of statistical learning theory, modern deep neural networks generalize well even though they typically contain millions of parameters. Recently, it has been shown that the trajectories of iterative…
We provide an end-to-end differentially private spectral algorithm for learning LDA, based on matrix/tensor decompositions, and establish theoretical guarantees on utility/consistency of the estimated model parameters. The spectral…
A central challenge in continual learning is forgetting, the loss of performance on previously learned tasks induced by sequential adaptation to new ones. While forgetting has been extensively studied empirically, rigorous theoretical…
In-context learning (ICL) derives its power from enabling Large Language Models to adapt to new tasks via prompt-based reasoning alone, entirely bypassing the need for parameter updates. Existing theories primarily study ICL in single-task…
The ability to separate and analyze chemical species with high resolution, sensitivity, and throughput is central to the development of microfluidics systems. Deterministic lateral displacement (DLD) is a continuous separation method based…
A dynamical system, called a binary closed chain of contours, is studied. The dynamica system belongs to the class of Buslaev networks. The system contains $N$ {\it contours.} There two cells and a particle in each contour. There two…
Motivated by robotic surveillance applications, this paper studies the novel problem of maximizing the return time entropy of a Markov chain, subject to a graph topology with travel times and stationary distribution. The return time entropy…
Systems of interacting continuous-time Markov chains are a powerful model class, but inference is typically intractable in high dimensional settings. Auxiliary information, such as noisy observations, is typically only available at discrete…
The paper is devoted to the relationship between the continuous Markovian description of Levy flights developed previously and their equivalent representation in terms of discrete steps of a wandering particle, a certain generalization of…
Continual learning is a process that involves training learning agents to sequentially master a stream of tasks or classes without revisiting past data. The challenge lies in leveraging previously acquired knowledge to learn new tasks…
The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous to internal DLA. We show that the set of occupied sites for this model on an infinite regular tree is a…