Related papers: An Algebraic Approach to Learning and Grounding
The purpose of a program analysis is to compute an abstract meaning for a program which approximates its dynamic behaviour. A compositional program analysis accomplishes this task with a divide-and-conquer strategy: the meaning of a program…
This work revisits operator learning from a spectral perspective by introducing Polar Linear Algebra, a structured framework based on polar geometry that combines a linear radial component with a periodic angular component. Starting from…
Key to tasks that require reasoning about natural language in visual contexts is grounding words and phrases to image regions. However, observing this grounding in contemporary models is complex, even if it is generally expected to take…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
Logic is the main formal language to perform automated reasoning, and it is further a human-interpretable language, at least for small formulae. Learning and optimising logic requirements and rules has always been an important problem in…
The notion of concept has been studied for centuries, by philosophers, linguists, cognitive scientists, and researchers in artificial intelligence (Margolis & Laurence, 1999). There is a large literature on formal, mathematical models of…
Analysis of (partial) groundness is an important application of abstract interpretation. There are several proposals for improving the precision of such an analysis by exploiting type information, icluding our own work with Hill and King,…
We are often interested in decomposing complex, structured data into simple components that explain the data. The linear version of this problem is well-studied as dictionary learning and factor analysis. In this work, we propose a…
Notions of computation can be modelled by monads. Algebraic effects offer a characterization of monads in terms of algebraic operations and equational axioms, where operations are basic programming features, such as reading or updating the…
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…
We investigate grounded language learning through real-world data, by modelling a teacher-learner dynamics through the natural interactions occurring between users and search engines; in particular, we explore the emergence of semantic…
I present a formal connection between algebraic effects and game semantics, two important lines of work in programming languages semantics with applications in compositional software verification. Specifically, the algebraic signature…
This paper examines the characterization and learning of grammars defined with enriched representational models. Model-theoretic approaches to formal language theory traditionally assume that each position in a string belongs to exactly one…
To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the…
We introduce a new application for inductive logic programming: learning the semantics of programming languages from example evaluations. In this short paper, we explored a simplified task in this domain using the Metagol meta-interpretive…
In this paper we present a formal computational framework for modeling manipulation actions. The introduced formalism leads to semantics of manipulation action and has applications to both observing and understanding human manipulation…
We propose a novel algebraic framework for treating probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on…
Embeddings are a fundamental component of many modern machine learning and natural language processing models. Understanding them and visualizing them is essential for gathering insights about the information they capture and the behavior…
The interpretation of spatial references is highly contextual, requiring joint inference over both language and the environment. We consider the task of spatial reasoning in a simulated environment, where an agent can act and receive…
Occupancy prediction tasks focus on the inference of both geometry and semantic labels for each voxel, which is an important perception mission. However, it is still a semantic segmentation task without distinguishing various instances.…