Related papers: Growth Functions, Rates and Classes of String-Base…
We briefly review the properties of radially growing interfaces and their connection to biological growth. We focus on simplified models which result from the abstraction of only considering domain growth and not the interface curvature.…
The implications of string theory for understanding the dimension of uncompactified spacetime are investigated. Using recent ideas in string cosmology, a new model is proposed to explain why three spatial dimensions grew large. Unlike the…
This work introduces a growable and modular neural network architecture that naturally avoids catastrophic forgetting and interference in continual reinforcement learning. The structure of each module allows the selective combination of…
Dominant sequence models like the Transformer represent structure implicitly through dense attention weights, incurring quadratic complexity. We propose RewriteNets, a novel neural architecture built on an alternative paradigm: explicit,…
We review a series of forthcoming results leading to the construction of a natural evolution on the space of loops with values in a Riemannian manifold. In particular, this clarifies the algebraic structure of the renormalisation procedures…
The aim of this paper is to undertake an experimental investigation of the trade-offs between program-size and time computational complexity. The investigation includes an exhaustive exploration and systematic study of the functions…
In this work, a new model for macroscopic plant tissue growth based on dynamical Riemannian geometry is presented. We treat 1D and 2D tissues as continuous, deformable, growing geometries for sizes larger than 1mm. The dynamics of the…
Physical growth traits can be naturally represented by continuous functions. In a large dataset of infancy growth patterns, we develop a practical approach to infer statistical associations between growth-trajectories and IQ performance in…
We consider a sequence of related multivariate time series learning tasks, such as predicting failures for different instances of a machine from time series of multi-sensor data, or activity recognition tasks over different individuals from…
Curriculum Learning for Reinforcement Learning is an increasingly popular technique that involves training an agent on a sequence of intermediate tasks, called a Curriculum, to increase the agent's performance and learning speed. This paper…
For years, astrophysicists, plasma fusion and fluid physicists have puzzled over Rayleigh-Taylor turbulent mixing layers. In particular, strong discrepancies in the growth rates have been observed between experiments and numerical…
Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (1) not naturally amenable to gradient-based optimization, and (2) incompatible…
In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the…
We consider directed weighted graphs and define various families of path counting functions. Our main results are explicit formulas for the main term of the asymptotic growth rate of these counting functions, under some irrationality…
This thesis is a study of two dimensional noncritical string theory. The main tool which is used, is the matrix model. Introductions to both the Liouville model and its matrix model formulation are included. In particular the special states…
Learning a policy capable of moving an agent between any two states in the environment is important for many robotics problems involving navigation and manipulation. Due to the sparsity of rewards in such tasks, applying reinforcement…
We study Turing pattern formation in a system undergoing radial growth in two dimensions. The Lengyel-Epstein two variable model is implemented in COMSOL Multiphysics and solved on domains growing at different speeds while sweeping other…
We study the relative growth of finitely generated subgroups in finitely generated groups, and the corresponding distortion function of the embeddings. We explore which functions are equivalent to the relative growth functions and…
Given an $\mathbb{N}$-weighted tree automaton, we give a decision procedure for exponential vs polynomial growth (with respect to the input size) in quadratic time, and an algorithm that computes the exact polynomial degree of growth in…
Reasoning has substantially improved the performance of large language models (LLMs) on complicated tasks. Central to the current reasoning studies, Process Reward Models (PRMs) offer a fine-grained evaluation of intermediate reasoning…