相关论文: Classifying topoi in synthetic guarded domain theo…

A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines…

Some basic notions and results in Topological Dynamics are extended to continuous groupoid actions in topological spaces. We focus mainly on recurrence properties. Besides results that are analogous to the classical case of group actions,…

This paper introduces a new mathematical framework for analysis and optimization of tensor expressions within an enclosing loop. Tensors are multi-dimensional arrays of values. They are common in high performance computing (HPC) and machine…

As collaborative learning allows joint training of a model using multiple sources of data, the security problem has been a central concern. Malicious users can upload poisoned data to prevent the model's convergence or inject hidden…

Abstract interpretation-based static analyses rely on abstract domains of program properties, such as intervals or congruences for integer variables. Galois connections (GCs) between posets provide the most widespread and useful formal tool…

Structured recursion schemes have been widely used in constructing, optimising, and reasoning about programs over inductive and coinductive datatypes. Their plain forms, catamorphisms and anamorphisms, are restricted in expressiveness. Thus…

Different fields in applied machine learning such as computer vision, speech or natural language processing have been building domain-specialised solutions. Currently, we are witnessing an opposing trend towards developing more generalist…

Time, data and memory trade off attack is one of the most important threats against pseudo- random generators and resisting against it, is considered as a main criteria of designing such generators. In this research, the pseudo-random GMGK…

We present simple lattice realizations of symmetry-protected topological (SPT) phases with $q$-form global symmetries where charged excitations have $q$ spatial dimensions. Specifically, we construct $d$ space-dimensional models supported…

This paper lays the foundations of an approach to applying Gromov's ideas on quantitative topology to topological data analysis. We introduce the "contiguity complex", a simplicial complex of maps between simplicial complexes defined in…

We introduce a temporal logic to reason on global applications in an asynchronous setting. First, we define the Distributed States Logic (DSL), a modal logic for localities that embeds the local theories of each component into a theory of…

Term unification plays an important role in many areas of computer science, especially in those related to logic. The universal mechanism of grammar-based compression for terms, in particular the so-called Singleton Tree Grammars (STG),…

A non-empty subset of a topological space is irreducible if whenever it is covered by the union of two closed sets, then already it is covered by one of them. Irreducible sets occur in proliferation: (1) every singleton set is irreducible,…

Symmetry Protected Topological (SPT) phases describe trivially-acting symmetries. We argue that a symmetry-based description of SPT phases ought to include the topological twist fields associated to the symmetry. Doing so allows us to…

Recent work has proposed a promising approach to improving scalability of program synthesis by allowing the user to supply a syntactic template that constrains the space of potential programs. Unfortunately, creating templates often…

We regard a geometric theory classified by a topos as a syntactic presentation for the topos and develop tools for finding such presentations. Extensions of geometric theories, which can add axioms, symbols and sorts, are treated as objects…

A convenient bicategory of topological stacks is constructed which is both complete and Cartesian closed. This bicategory, called the bicategory of compactly generated stacks, is the analogue of classical topological stacks, but for a…

One of the most common methods to train machine learning algorithms today is the stochastic gradient descent (SGD). In a distributed setting, SGD-based algorithms have been shown to converge theoretically under specific circumstances. A…

This work addresses the general problem of control synthesis for continuous-space, discrete-time stochastic systems with probabilistic guarantees via finite abstractions. While established methods exist, they often trade off accuracy for…

We use a categorical topological semantics to examine the Deutsch-Jozsa, hidden subgroup and single-shot Grover algorithms. This reveals important structures hidden by conventional algebraic presentations, and allows novel proofs of…