Related papers: NoBLE for lattice trees and lattice animals
Lorentz lattice gases (LLGs) are discrete-time transport models in which a point particle moves ballistically between lattice sites and is scattered by randomly placed, quenched local scatterers such as ``rotators'' or ``mirrors.'' Despite…
Self-avoiding walks are studied on the 3-simplex fractal lattice as a model of linear polymer conformations in a dilute, non-homogeneous solution. A model is supplemented with bending energies and attractive-interaction energies between…
We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40…
Aligned large language models (LLMs) demonstrate exceptional capabilities in task-solving, following instructions, and ensuring safety. However, the continual learning aspect of these aligned LLMs has been largely overlooked. Existing…
Test-time Scaling (TTS) has been demonstrated to significantly enhance the reasoning capabilities of Large Language Models (LLMs) during the inference phase without altering model parameters. However, existing TTS methods are largely…
We compare our upper bounds on the exponential growth constant $\phi(\Lambda)$ characterizing the asymptotic behavior of spanning forests on Archimedean lattices $\Lambda$ with recently derived upper bounds. Our upper bounds on…
Biggins [Uniform convergence of martingales in the branching random walk. {\em Ann. Probab.}, 20(1):137--151, 1992] proved local uniform convergence of additive martingales in $d$-dimensional supercritical branching random walks at complex…
Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection…
We introduce Random Latent Exploration (RLE), a simple yet effective exploration strategy in reinforcement learning (RL). On average, RLE outperforms noise-based methods, which perturb the agent's actions, and bonus-based exploration, which…
Longitudinal imaging studies are essential to understanding the neural development of neuropsychiatric disorders, substance use disorders, and the normal brain. The main objective of this paper is to develop a two-stage adjusted…
We present general algorithms (fully implemented in Maple) for calculations of various quantities related to constrained directed walks for a general set of steps on the square lattice in two dimensions. As a special case, we rederive…
Learning adaptable policies is crucial for robots to operate autonomously in our complex and quickly changing world. In this work, we present a new meta-learning method that allows robots to quickly adapt to changes in dynamics. In contrast…
In the mean field (or random link) model there are $n$ points and inter-point distances are independent random variables. For $0 < \ell < \infty$ and in the $n \to \infty$ limit, let $\delta(\ell) = 1/n \times$ (maximum number of steps in a…
Training Large Language Models (LLMs) from scratch requires immense computational resources, making it prohibitively expensive. Model scaling-up offers a promising solution by leveraging the parameters of smaller models to create larger…
Asymptotic efficiency of targeted maximum likelihood estimators (TMLE) of target features of the data distribution relies on a a second order remainder being asymptotically negligible. In previous work we proposed a nonparametric MLE termed…
We study in detail the postselection problem in a specific model: bosons hopping on a lattice subjected to continuous local measurements of quadrature observables. We solve the model analytically and show that the postselection overhead can…
We study three different random walk models on several two-dimensional lattices by Monte Carlo simulations. One is the usual nearest neighbor random walk. Another is the nearest neighbor random walk which is not allowed to backtrack. The…
The asymptotic expansion of the massive scalar field propagator on a n-dimensional lattice is derived. The method used is based on the evaluation of the asymptotic expansion of the modified Bessel function $I_{\nu}(\nu^{2} \beta)$ as the…
Legged robots are able to navigate complex terrains by continuously interacting with the environment through careful selection of contact sequences and timings. However, the combinatorial nature behind contact planning hinders the…
We study sampling from a target distribution ${\nu_* = e^{-f}}$ using the unadjusted Langevin Monte Carlo (LMC) algorithm. For any potential function $f$ whose tails behave like ${\|x\|^\alpha}$ for ${\alpha \in [1,2]}$, and has…