Related papers: A Weakly Initial Algebra for Higher-Order Abstract…
We describe a derivational approach to abstract interpretation that yields novel and transparently sound static analyses when applied to well-established abstract machines for higher-order and imperative programming languages. To…
Higher inductive types are inductive types that include nontrivial higher-dimensional structure, represented as identifications that are not reflexivity. While work proceeds on type theories with a computational interpretation of univalence…
We introduce the notion of a template for discrete Morse theory. Templates provide a memory efficient approach to the computation of homological invariants (e.g., homology, persistent homology, Conley complexes) of cell complexes. We…
We derive a CUR-type factorization for tensors in the Tucker format based on interpolatory decomposition, which we will denote as Higher Order Interpolatory Decomposition (HOID). Given a tensor $\mathcal{X}$, the algorithm provides a set of…
We introduce the notion of identity coercions between non-indexed and indexed variants of inductive datatypes, such as lists and vectors. An identity coercion translates one type to another such that the coercion function definitionally…
We present the first definition of strictly associative and unital $\infty$-category. Our proposal takes the form of a type theory whose terms describe the operations of such structures, and whose definitional equality relation enforces…
Compositionality proofs in higher-order languages are notoriously involved, and general semantic frameworks guaranteeing compositionality are hard to come by. In particular, Turi and Plotkin's bialgebraic abstract GSOS framework, which…
Higher-order unification (HOU) concerns unification of (extensions of) $\lambda$-calculus and can be seen as an instance of equational unification ($E$-unification) modulo $\beta\eta$-equivalence of $\lambda$-terms. We study equational…
Deep learning models have achieved remarkable success across various domains, yet their learned representations and decision-making processes remain largely opaque and hard to interpret. This work introduces HOLE (Homological Observation of…
In this short paper, we present a simple variant of the recursive path ordering, specified for Logically Constrained Simply Typed Rewriting Systems (LCSTRSs). This is a method for curried systems, without lambda but with partially applied…
Abstract interpretation, Hoare logic, and incorrectness (or reverse Hoare) logic are powerful techniques for static analysis of computer programs. All of them have been successfully extended to the quantum setting, but largely developed in…
In this paper, we study a practical yet challenging task, On-the-fly Category Discovery (OCD), aiming to online discover the newly-coming stream data that belong to both known and unknown classes, by leveraging only known category knowledge…
In deep learning, the recently introduced state space models utilize HiPPO (High-order Polynomial Projection Operators) memory units to approximate continuous-time trajectories of input functions using ordinary differential equations…
In this report, we introduce observation algebras, constructed by considering the downclosed subsets of a coherence space ordered by reverse inclusion. These may be interpreted as specifications of sets of events via some predicates with…
The Andr\'e-Quillen cohomology of an algebra with coefficients in a module is defined by deriving a functor based on K\"ahler differential forms. It can be computed using a cofibrant resolution of the algebra in a model category structure…
Cross-lingual information extraction (CLIE) is an important and challenging task, especially in low resource scenarios. To tackle this challenge, we propose a training method, called Halo, which enforces the local region of each hidden…
These notes survey and explore an emerging method, which we call the low-degree method, for predicting and understanding statistical-versus-computational tradeoffs in high-dimensional inference problems. In short, the method posits that a…
Taking an algebraic perspective on the basic structures of Rough Concept Analysis as the starting point, in this paper we introduce some varieties of lattices expanded with normal modal operators which can be regarded as the natural rough…
We present an environment, benchmark, and deep learning driven automated theorem prover for higher-order logic. Higher-order interactive theorem provers enable the formalization of arbitrary mathematical theories and thereby present an…
The calculus of Dependent Object Types (DOT) has enabled a more principled and robust implementation of Scala, but its support for type-level computation has proven insufficient. As a remedy, we propose $F^\omega_{..}$, a rigorous…