Related papers: On functors enumerating structures
We study the degree spectra and reverse-mathematical applications of computably enumerable and co-computably enumerable partial orders. We formulate versions of the chain/antichain principle and ascending/descending sequence principle for…
Coskey, Hamkins, and Miller [CHM12] proposed two possible analogues of the class of countable Borel equivalence relations in the setting of computable reducibility of equivalence relations on the computably enumerable (c.e.) sets. The first…
We have recently begun a project to develop a more effective and efficient way to marshal inferences from background knowledge to facilitate deep natural language understanding. The meaning of a word is taken to be the entities,…
The term {\em meta-programming} refers to the ability of writing programs that have other programs as data and exploit their semantics. The aim of this paper is presenting a methodology allowing us to perform a correct termination analysis…
We introduce spaces of exponential constructible functions in the motivic setting for which we construct direct image functors in the absolute and relative cases. This allows us to define a motivic Fourier transformation for which we get…
Recent research has recognized interpretability and robustness as essential properties of trustworthy classification. Curiously, a connection between robustness and interpretability was empirically observed, but the theoretical reasoning…
Logically constrained term rewriting is a rewriting framework that supports built-in data structures such as integers and bit vectors. Recently, constrained terms play a key role in various analyses and applications of logically constrained…
There exist applications of reinforcement learning like medicine where policies need to be ''interpretable'' by humans. User studies have shown that some policy classes might be more interpretable than others. However, it is costly to…
We prove that in an arbitrary o-minimal structure, every interpretable group is definably isomorphic to a definable one. We also prove that every definable group lives in a cartesian product of one-dimensional definable group-intervals (or…
Interpretations are a fundamental tool in mathematical logic, allowing structures to be encoded within other structures via logical definitions. We study $\MSO$ \emph{multidimensional point interpretations}, where elements of an interpreted…
This paper proves a homomorphism between extensional formal semantics and distributional vector space semantics, demonstrating structural compatibility. Formal semantics models meaning as reference, using logical structures to map…
We extend de Finetti's [Ann. Inst. H. Poincar\'{e} 7 (1937) 1--68] notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than…
Several researchers have argued that a machine learning system's interpretability should be defined in relation to a specific agent or task: we should not ask if the system is interpretable, but to whom is it interpretable. We describe a…
In complex inferential tasks like question answering, machine learning models must confront two challenges: the need to implement a compositional reasoning process, and, in many applications, the need for this reasoning process to be…
In this article, we introduce a notion of reducibility for partial functions on the natural numbers, which we call subTuring reducibility. One important aspect is that the subTuring degrees correspond to the structure of the realizability…
We explore functors between operator space categories, some properties of these functors, and establish relations between objects in these categories and their images under these functors, in particular regarding injectivity and injective…
For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians…
This paper introduces a new simplified version of the countable branching recurrence of Computability Logic, proves its equivalence to the old one, and shows that the basic logic induced by it is a proper superset of the basic logic induced…
Mechanistic interpretability aims to break models into meaningful parts; verifying that two such parts implement the same computation is a prerequisite. Existing similarity measures evaluate either empirical behaviour, leaving them blind to…
This article is first in a series of papers where we reprove the statements in constructing the Enhanced Operation Map and the abstract six-functor formalism developed by Liu-Zheng. In this paper, we prove a theorem regarding constructing…