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Generic programming (GP) is an increasingly important trend in programming languages. Well-known GP mechanisms, such as type classes and the C++0x concepts proposal, usually combine two features: 1) a special type of interfaces; and 2)…

Undirected graphical models are a widely used class of probabilistic models in machine learning that capture prior knowledge or putative pairwise interactions between variables. Those interactions are encoded in a graph for pairwise…

Featherweight Generic Go (FGG) is a minimal core calculus modeling the essential features of the programming language Go. It includes support for overloaded methods, interface types, structural subtyping and generics. The most…

Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm's superiority over another. However, when it comes to inference algorithms for probabilistic logic programs,…

Grammatical inference is a classical problem in computational learning theory and a topic of wider influence in natural language processing. We treat grammars as a model of computation and propose a novel neural approach to induction of…

Forecasting time series on graphs is a fundamental problem in graph signal processing. When each entity of the network carries a vector of values for each time stamp instead of a scalar one, existing approaches resort to the use of product…

Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…

Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…

Message passing on a factor graph is a powerful paradigm for the coding of approximate inference algorithms for arbitrarily graphical large models. The notion of a factor graph fragment allows for compartmentalization of algebra and…

Predictive coding graphs (PCGs) are a recently introduced generalization to predictive coding networks, a neuroscience-inspired probabilistic latent variable model. Here, we prove how PCGs define a mathematical superset of feedforward…

Probabilistic programming languages are valuable because they allow domain experts to express probabilistic models and inference algorithms without worrying about irrelevant details. However, for decades there remained an important and…

We develop a nonstandard approach to exploring polynomials associated with peaks and runs of permutations. With the aid of a context-free grammar, or a set of substitution rules, one can perform a symbolic calculus, and the computation…

Discrete structures are currently second-class in differentiable programming. Since functions over discrete structures lack overt derivatives, differentiable programs do not differentiate through them and limit where they can be used. For…

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…

Ad hoc parsers are everywhere: they appear any time a string is split, looped over, interpreted, transformed, or otherwise processed. Every ad hoc parser gives rise to a language: the possibly infinite set of input strings that the program…

This paper investigates the usage of generating functions (GFs) encoding measures over the program variables for reasoning about discrete probabilistic programs. To that end, we define a denotational GF-transformer semantics for…

We consider a core language of graph queries. These queries are seen as formulas to be solved with respect to graph-oriented databases. For this purpose, we first define a graph query algebra where some operations over graphs and sets of…

Recent data-efficient molecular generation approaches exploit graph grammars to introduce interpretability into the generative models. However, grammar learning therein relies on expert annotation or unreliable heuristics for algorithmic…

Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…

Representing and exploiting multivariate signals requires capturing relations between variables, which we can represent by graphs. Graph dictionaries allow to describe complex relational information as a sparse sum of simpler structures,…