Related papers: Concurrent Kleene Algebra with Observations: from …
We have implemented Kima, an automated error correction system for concurrent logic programs. Kima corrects near-misses such as wrong variable occurrences in the absence of explicit declarations of program properties. Strong moding/typing…
Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and…
Finding overcomplete latent representations of data has applications in data analysis, signal processing, machine learning, theoretical neuroscience and many other fields. In an overcomplete representation, the number of latent features…
Partial combinatory algebras are algebraic structures that serve as generalized models of computation. In this paper, we study embeddings of pcas. In particular, we systematize the embeddings between relativizations of Kleene's models, of…
To answer complex queries on knowledge graphs, logical reasoning over incomplete knowledge is required due to the open-world assumption. Learning-based methods are essential because they are capable of generalizing over unobserved…
This paper investigates the logical strength of completeness theorems for modal propositional logic within second-order arithmetic. We demonstrate that the weak completeness theorem for modal propositional logic is provable in…
Canonical Correlation Analysis (CCA) is a linear representation learning method that seeks maximally correlated variables in multi-view data. Non-linear CCA extends this notion to a broader family of transformations, which are more powerful…
A framework named Copula Component Analysis (CCA) for blind source separation is proposed as a generalization of Independent Component Analysis (ICA). It differs from ICA which assumes independence of sources that the underlying components…
Within the tensor product $K \mathop{\otimes_{\cal R}} C_2'$ of any ${}^*$-continuous Kleene algebra $K$ with the polycyclic ${}^*$-continuous Kleene algebra $C_2'$ over two bracket pairs there is a copy of the fixed-point closure of $K$:…
We consider algebras of languages over the signature of reversible Kleene lattices, that is the regular operations (empty and unit languages, union, concatenation and Kleene star) together with intersection and mirror image. We provide a…
State-space language models such as Mamba and gated linear attention (GLA) offer efficient alternatives to transformers due to their linear complexity and parallel training, but often lack the expressivity and robust state-tracking needed…
Tractability results for the model checking problem of logics yield powerful algorithmic meta theorems of the form: Every computational problem expressible in a logic $L$ can be solved efficiently on every class $\mathscr{C}$ of structures…
Automata learning is a popular technique for inferring minimal automata through membership and equivalence queries. In this paper, we generalise learning to the theory of coalgebras. The approach relies on the use of logical formulas as…
Knowledge amalgamation (KA) aims to learn a compact student model to handle the joint objective from multiple teacher models that are are specialized for their own tasks respectively. Current methods focus on coarsely aligning teachers and…
We define and study basic properties of *-continuous Kleene $\omega$-algebras that involve a *-continuous Kleene algebra with a *-continuous action on a semimodule and an infinite product operation that is also *-continuous. We show that…
Particle-based Bayesian deep learning often requires a similarity metric to compare two networks. However, naive similarity metrics lack permutation invariance and are inappropriate for comparing networks. Centered Kernel Alignment (CKA) on…
This paper introduces Concurrent Valuation Algebras (CVAs), a novel extension of ordered valuation algebras (OVAs). CVAs include two combine operators representing parallel and sequential products, adhering to a weak exchange law. This…
An operational probabilistic theory where all systems are classical, and all pure states of composite systems are entangled, is constructed. The theory is endowed with a rule for composing an arbitrary number of systems, and with a…
The Cylindrical Algebraic Decomposition (CAD) algorithm is a comprehensive tool to perform quantifier elimination over real closed fields. CAD has doubly exponential running time, making it infeasible for practical purposes. We propose to…
General Continual Learning (GCL) aims at learning from non independent and identically distributed stream data without catastrophic forgetting of the old tasks that don't rely on task boundaries during both training and testing stages. We…