Related papers: A Mathematical Framework for Superintelligent Mach…
Recursive coalgebras provide an elegant categorical tool for modelling recursive algorithms and analysing their termination and correctness. By considering coalgebras over categories of suitably indexed families, the correctness of the…
Class-Incremental Learning aims to update a deep classifier to learn new categories while maintaining or improving its accuracy on previously observed classes. Common methods to prevent forgetting previously learned classes include…
To enhance group robustness to spurious correlations, prior work often relies on auxiliary group annotations and assumes identical sets of groups across training and test domains. To overcome these limitations, we propose to leverage…
We introduce a term algebra as a new formal specification language for the coordinating architectures of distributed systems consisting of a finite yet unbounded number of components. The language allows to describe infinite sets of systems…
We obtain a Galois correspondence between the lattice of intermediate C*-discrete subalgebras intermediate to a given irreducible C*-discrete inclusion, and characterize these as targets of compatible expectations under a traciality…
We introduce "synchronous algebras", an algebraic structure tailored to recognize automatic relations (aka. synchronous relations, or regular relations). They are the equivalent of monoids for regular languages, however they conceptually…
We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, for which we rely on the algebra of Pregroups, introduced by…
Deep learning has revolutionized the field of artificial intelligence. Based on the statistical correlations uncovered by deep learning-based methods, computer vision has contributed to tremendous growth in areas like autonomous driving and…
A class of languages C is perfect if it is closed under Boolean operations and the emptiness problem is decidable. Perfect language classes are the basis for the automata-theoretic approach to model checking: a system is correct if the…
Many computer vision tasks address the problem of scene understanding and are naturally interrelated e.g. object classification, detection, scene segmentation, depth estimation, etc. We show that we can leverage the inherent relationships…
A period is a complex number arising as the integral of a rational function with algebraic number coefficients over a rationally-defined region. Although periods are typically transcendental numbers, there is a conjectural Galois theory of…
The class of Basic Feasible Functionals BFF$_2$ is the type-2 counterpart of the class FP of type-1 functions computable in polynomial time. Several characterizations have been suggested in the literature, but none of these present a…
We consider an orbit category of the bounded derived category of a path algebra of type A_n which can be viewed as a -(m+1)-cluster category, for m >= 1. In particular, we give a characterisation of those maximal m-rigid objects whose…
This paper discusses the application of L1-regularized maximum entropy modeling or SL1-Max [9] to multiclass categorization problems. A new modification to the SL1-Max fast sequential learning algorithm is proposed to handle conditional…
Large language models (LLMs) have shown impressive few-shot generalization on many tasks via in-context learning (ICL). Despite their success in showing such emergent abilities, the scale and complexity of larger models also lead to…
We present a two-stage framework for deep one-class classification. We first learn self-supervised representations from one-class data, and then build one-class classifiers on learned representations. The framework not only allows to learn…
We present a comprehensive language theoretic causality analysis framework for explaining safety property violations in the setting of concurrent reactive systems. Our framework allows us to uniformly express a number of causality notions…
This paper introduces a Fuzzy Logic framework for scene learning, recognition and similarity detection, where scenes are taught via human examples. The framework allows a robot to: (i) deal with the intrinsic vagueness associated with…
We present an algebraic characterization of the complexity classes Logspace and Nlogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is rooted in proof theory…
We introduce and characterize a particularly tractable class of unital type 1 C*-algebras with bounded dimension of irreducible representations. Algebras in this class are called recursive subhomogeneous algebras, and they have an inductive…