Related papers: Plane-Walking Automata
Nonuniform families of polynomial-size finite automata and pushdown automata respectively have strong connections to nonuniform-NL and nonuniform-LOGCFL. We examine the behaviors of unambiguous and co-nondeterministic computations produced…
Multi-index models - functions which only depend on the covariates through a non-linear transformation of their projection on a subspace - are a useful benchmark for investigating feature learning with neural nets. This paper examines the…
We overcome the barrier of constructing N=4 superconformal models in one space dimension for more than three particles. The D(2,1;alpha) superalgebra of our systems is realized on the coordinates and momenta of the particles, their…
Manipulation tasks can often be decomposed into multiple subtasks performed in parallel, e.g., sliding an object to a goal pose while maintaining contact with a table. Individual subtasks can be achieved by task-axis controllers defined…
We study weighted residual dynamics associated with a rank-one projection in finite dimension. The iteration reduces, after finitely many steps, to a nonlinear recursion on a stabilized active subspace. We prove that this recursion can be…
At present, object recognition studies are mostly conducted in a closed lab setting with classes in test phase typically in training phase. However, real-world problem is far more challenging because: i) new classes unseen in the training…
We investigate here the hardness of conjugacy and factorization of subshifts of finite type (SFTs) in dimension $d>1$. In particular, we prove that the factorization problem is $\Sigma^0_3$-complete and the conjugacy problem…
We argue that hierarchical methods can become the key for modular robots achieving reconfigurability. We present a hierarchical approach for modular robots that allows a robot to simultaneously learn multiple tasks. Our evaluation results…
We introduce a new problem formulation, Double-Deck Multi-Agent Pickup and Delivery (DD-MAPD), which models the multi-robot shelf rearrangement problem in automated warehouses. DD-MAPD extends both Multi-Agent Pickup and Delivery (MAPD) and…
We provide a unifying framework where artificial neural networks and their architectures can be formally described as particular cases of a general mathematical construction--machines of finite depth. Unlike neural networks, machines have a…
We investigate multi-field multicritical scalar theories using CFT constraints on two- and three-point functions combined with the Schwinger-Dyson equation. This is done in general and without assuming any symmetry for the models, which we…
It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n> 1. Recently the physical meaning of these higher categorical…
We study the problem of distributed multi-task learning with shared representation, where each machine aims to learn a separate, but related, task in an unknown shared low-dimensional subspaces, i.e. when the predictor matrix has low rank.…
In this paper we try to organize machine teaching as a coherent set of ideas. Each idea is presented as varying along a dimension. The collection of dimensions then form the problem space of machine teaching, such that existing teaching…
Given a nondeterministic finite-state automaton (NFA), we aim to estimate the size of an equivalent deterministic finite-state automaton (DFA). We demonstrate that computing the state complexity of an NFA within polynomial precision is…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
We initiate the classification of unitary superconformal defects in unitary superconformal field theories (SCFT) of diverse spacetime dimensions $3\leq d \leq 6$. Our method explores general constraints from the defect superconformal…
Convolutional Neural Networks (CNNs) currently achieve state-of-the-art accuracy in image classification. With a growing number of classes, the accuracy usually drops as the possibilities of confusion increase. Interestingly, the class…
In this paper we present a new approach to decentralized supervisory control of large automata with communicating supervisors. We first generalize the recently developed top-down architecture of multilevel coordination control with a…
We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automata…