Related papers: Categorical semantics of a simple differential pro…
We show how (well-established) type systems based on non-idempotent intersection types can be extended to characterize termination properties of functional programming languages with pattern matching features. To model such programming…
Automatic differentiation (AD) has been a topic of interest for researchers in many disciplines, with increased popularity since its application to machine learning and neural networks. Although many researchers appreciate and know how to…
A differential category is an additive symmetric monoidal category, that is, a symmetric monoidal category enriched over commutative monoids, with an algebra modality, axiomatizing smooth functions, and a deriving transformation on this…
Modal automata are a classic formal model for component-based systems that comes equipped with a rich specification theory supporting abstraction, refinement and compositional reasoning. In recent years, quantitative variants of modal…
Deep neural networks have enabled major progresses in semantic segmentation. However, even the most advanced neural architectures suffer from important limitations. First, they are vulnerable to catastrophic forgetting, i.e. they perform…
Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the…
Logic programming with fixed-point definitions is a useful extension of traditional logic programming. Fixed-point definitions can capture simple model checking problems and closed-world assumptions. Its operational semantics is typically…
"Natural languages are programming languages for minds." Can we or should we take this slogan seriously? If so, how? Can answers be found by looking at the various "dynamic" treatments of natural language developed over the last decade or…
Compact closed categories have found applications in modeling quantum information protocols by Abramsky-Coecke. They also provide semantics for Lambek's pregroup algebras, applied to formalizing the grammatical structure of natural…
A new categorical setting is defined in order to characterize the subrecursive classes belonging to complexity hierarchies. This is achieved by means of coercion functors over a symmetric monoidal category endowed with certain recursion…
In this work we present a theoretical model for differentiable programming. We construct an algebraic language that encapsulates formal semantics of differentiable programs by way of Operational Calculus. The algebraic nature of Operational…
We describe a mathematical structure that can give extensional denotational semantics to higher-order probabilistic programs. It is not limited to discrete probabilities, and it is compatible with integration in a way the models that have…
Many techniques in computer vision, machine learning, and statistics rely on the fact that a signal of interest admits a sparse representation over some dictionary. Dictionaries are either available analytically, or can be learned from a…
Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we…
Operational semantics have been enormously successful, in large part due to its flexibility and simplicity, but they are not compositional. Denotational semantics, on the other hand, are compositional but the lattice-theoretic models are…
In this paper we propose a general approach to define a many-valued preferential interpretation of gradual argumentation semantics. The approach allows for conditional reasoning over arguments and boolean combination of arguments, with…
It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, i.e. to divide such a program into a number of different "levels", such that the models of the entire program can be…
We propose a new modeling approach that is a generalization of generative and discriminative models. The core idea is to use an implicit parameterization of a joint probability distribution by specifying only the conditional distributions.…
Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful…
Natural language processing has greatly benefited from the introduction of the attention mechanism. However, standard attention models are of limited interpretability for tasks that involve a series of inference steps. We describe an…