Related papers: Algebraic Machine Learning: Learning as computing …

Standard meta-learning for representation learning aims to find a common representation to be shared across multiple tasks. The effectiveness of these methods is often limited when the nuances of the tasks' distribution cannot be captured…

Machine learning often aims to produce latent embeddings of inputs which lie in a larger, abstract mathematical space. For example, in the field of 3D modeling, subsets of Euclidean space can be embedded as vectors using implicit neural…

Analogical reasoning is a hallmark of human intelligence, enabling us to solve new problems by transferring knowledge from one situation to another. Yet, developing artificial intelligence systems capable of robust human-like analogical…

In the last years there has been a growing interest in the study of learning problems associated with algebraic structures. The framework we use models the scenario in which a learner is given larger and larger fragments of a structure from…

We consider the problem of learning the semantics of composite algebraic expressions from examples. The outcome is a versatile framework for studying learning tasks that can be put into the following abstract form: The input is a partial…

This paper introduces a novel measure-theoretic theory for machine learning that does not require statistical assumptions. Based on this theory, a new regularization method in deep learning is derived and shown to outperform previous…

We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an iterated rewriting system defines a formal class of models into which all the main architectures…

Despite the wide variety of input types in machine learning, this diversity is often not fully reflected in their representations or model architectures, leading to inefficiencies throughout a model's lifecycle. This paper introduces an…

Statistical learning algorithms are finding more and more applications in science and technology. Atomic-scale modeling is no exception, with machine learning becoming commonplace as a tool to predict energy, forces and properties of…

This research started with an algebra for reasoning about rely/guarantee concurrency for a shared memory model. The approach taken led to a more abstract algebra of atomic steps, in which atomic steps synchronise (rather than interleave)…

Providing machine learning (ML) over relational data is a mainstream requirement for data analytics systems. While almost all the ML tools require the input data to be presented as a single table, many datasets are multi-table, which forces…

Recent work in deep learning has opened new possibilities for solving classical algorithmic tasks using end-to-end learned models. In this work, we investigate the fundamental task of solving linear systems, particularly those that are…

Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…

The goal of machine learning is to find models that minimize prediction error on data that has not yet been seen. Its operational paradigm assumes access to a dataset $S$ and articulates a scheme for evaluating how well a given model…

A central goal of unsupervised learning is to acquire representations from unlabeled data or experience that can be used for more effective learning of downstream tasks from modest amounts of labeled data. Many prior unsupervised learning…

Many combinatorial optimisation problems hide algebraic structures that, once exposed, shrink the search space and improve the chance of finding the global optimal solution. We present a general framework that (i) identifies algebraic…

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…

There is a wide gap between symbolic reasoning and deep learning. In this research, we explore the possibility of using deep learning to improve symbolic reasoning. Briefly, in a reasoning system, a deep feedforward neural network is used…

We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms governing intra-layer and inter-layer interactions, study their…

In this paper, we introduce a discrete variant of the meta-learning framework. Meta-learning aims at exploiting prior experience and data to improve performance on future tasks. By now, there exist numerous formulations for meta-learning in…