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An important goal in studying the relations between unitary VOAs and conformal nets is to prove the equivalence of their ribbon categories. In this article, we prove this conjecture for many familiar examples. Our main idea is to construct…
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…
Recursive Neural Network (RecNN), a type of models which compose words or phrases recursively over syntactic tree structures, has been proven to have superior ability to obtain sentence representation for a variety of NLP tasks. However,…
Functional reactive programming (FRP) makes it possible to express temporal aspects of computations in a declarative way. Recently we developed two kinds of categorical models of FRP: abstract process categories (APCs) and concrete process…
Throughout the history of functional programming, recursion has emerged as a natural method for describing loops in programs. However, there does often exist a substantial cognitive distance between the recursive definition and the simplest…
Combining component & connector architecture descriptionlanguageswithcomponentbehaviormodelinglanguages enables modeling great parts of software architectures platformindependently. Nontrivial systems typically contain components with…
In this paper, we apply the machinery developed in arXiv:2401.06641(2) to study the behavior of computable categoricity relativized to non-c.e. degrees. In particular, we show that we can build a computable structure which is not computably…
Protein inverse folding-that is, predicting an amino acid sequence that will fold into the desired 3D structure-is an important problem for structure-based protein design. Machine learning based methods for inverse folding typically use…
We show how security type systems from the literature of language-based noninterference can be represented more directly as predicates defined by structural recursion on the programs. In this context, we show how our uniform syntactic…
Refinement types are types equipped with predicates that specify preconditions and postconditions of underlying functional languages. We propose a general semantic construction of dependent refinement type systems from underlying type…
Martin-L\"of's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of well-founded relations is presented. Using primitive…
Despite ample evidence that our concepts, our cognitive architecture, and mathematics itself are all deeply compositional, few models take advantage of this structure. We therefore propose a radically compositional approach to computational…
How should we compare the capabilities of language models (LMs) and humans? I draw inspiration from comparative psychology to highlight some challenges. In particular, I consider a case study: processing of recursively nested grammatical…
Human language understanding operates at multiple levels of granularity (e.g., words, phrases, and sentences) with increasing levels of abstraction that can be hierarchically combined. However, existing deep models with stacked layers do…
This survey paper examines the effective model theory obtained with the BSS model of real number computation. It treats the following topics: computable ordinals, satisfaction of computable infinitary formulas, forcing as a construction…
Can recurrent neural nets, inspired by human sequential data processing, learn to understand language? We construct simplified datasets reflecting core properties of natural language as modeled in formal syntax and semantics: recursive…
In this paper, we give an overview of some recent work on applying tools from category theory in finite model theory, descriptive complexity, constraint satisfaction, and combinatorics. The motivations for this work come from Computer…
In recent years, there has been an increased interest in tools that establish \emph{incorrectness} rather than correctness of program properties. In this work we build on this approach by developing a novel methodology to prove…
This paper proposes bimorphic recursion, which is restricted polymorphic recursion such that every recursive call in the body of a function definition has the same type. Bimorphic recursion allows us to assign two different types to a…
We propose a generalized version of context-sensitivity in term rewriting based on the notion of "forbidden patterns". The basic idea is that a rewrite step should be forbidden if the redex to be contracted has a certain shape and appears…