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Symbolic regression aims to recover closed-form expressions from numerical data, but in differentiable symbolic regression the recovered expression depends not only on the grammar but also on the fixed architecture through which variables…
This paper develops a systematic framework for integrating local categories that model logical connectives using higher category theory. By extending these local categories into a unified two-category enriched with natural isomorphisms, the…
Let $\mathcal{S}$ be a small category admitting binary products. We show that the whole theory of monoidal $\mathcal{S}$-fibered categories, which is customarily formulated in terms of the usual internal tensor product, can be rephrased…
A subunit in a monoidal category is a subobject of the monoidal unit for which a canonical morphism is invertible. They correspond to open subsets of a base topological space in categories such as those of sheaves or Hilbert modules. We…
Neural networks have become an increasingly popular tool for solving many real-world problems. They are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this…
We study the problem of learning probabilistic first-order logical rules for knowledge base reasoning. This learning problem is difficult because it requires learning the parameters in a continuous space as well as the structure in a…
Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…
This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic…
In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…
With the wide range of quantum programming languages on offer now, efficient program verification and type checking for these languages presents a challenge -- especially when classical debugging techniques may affect the states in a…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
We propose a layered hierarchical architecture called UCLA (Universal Causality Layered Architecture), which combines multiple levels of categorical abstraction for causal inference. At the top-most level, causal interventions are modeled…
Most deep neural networks are considered to be black boxes, meaning their output is hard to interpret. In contrast, logical expressions are considered to be more comprehensible since they use symbols that are semantically close to natural…
We propose a graphical language that accommodates two monoidal structures: a multiplicative one for pairing and an additional one for branching. In this colored PROP, whether wires in parallel are linked through the multiplicative structure…
Explainable artificial intelligence has rapidly emerged since lawmakers have started requiring interpretable models for safety-critical domains. Concept-based neural networks have arisen as explainable-by-design methods as they leverage…
Coherence theorems for covariant structures carried by a category have traditionally relied on the underlying term rewriting system of the structure being terminating and confluent. While this holds in a variety of cases, it is not a…
Monads govern computational side-effects in programming semantics. They can be combined in a ''bottom-up'' way to handle several instances of such effects. Indexed monads and graded monads do this in a modular way. Here, instead, we equip…
Metatheorems about type theories are often proven by interpreting the syntax into models constructed using categorical gluing. We propose to use only sconing (gluing along a global section functor) instead of general gluing. The sconing is…
The cut-elimination procedure for the provability logic is known to be problematic: a L\"ob-like rule keeps cut-formulae intact on reduction, even in the principal case, thereby complicating the proof of termination. In this paper, we…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…