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That shared features between train and test data are required for generalisation in artificial neural networks has been a common assumption of both proponents and critics of these models. Here, we show that convolutional architectures avoid…
Generic sentences express generalisations about the world without explicit quantification. Although generics are central to everyday communication, building a precise semantic framework has proven difficult, in part because speakers use…
A framework and method are proposed for the study of constituent composition in fMRI. The method produces estimates of neural patterns encoding complex linguistic structures, under the assumption that the contributions of individual…
In this dissertation we develop a new formal graphical framework for causal reasoning. Starting with a review of monoidal categories and their associated graphical languages, we then revisit probability theory from a categorical perspective…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
The sets used to construct other mathematical objects are pure sets, which means that all of their elements are sets, which are themselves pure. One set may therefore be within another, not as an element, but as an element of an element, or…
This paper describes a computational framework for a grammar architecture in which different linguistic domains such as morphology, syntax, and semantics are treated not as separate components but compositional domains. Word and phrase…
Deep learning has led researchers to rethink the relationship between memorization and generalization. In many settings, memorization does not hurt generalization due to implicit regularization and may help by memorizing long-tailed…
Symbolic Music Generation relies on the contextual representation capabilities of the generative model, where the most prevalent approach is the Transformer-based model. The learning of musical context is also related to the structural…
Given a simplicial complex and a collection of subcomplexes covering it, the nerve theorem, a fundamental tool in topological combinatorics, guarantees a certain connectivity of the simplicial complex when connectivity conditions on the…
Out-of-distribution generalization capabilities of sequence-to-sequence models can be studied from the lens of two crucial forms of generalization: length generalization -- the ability to generalize to longer sequences than ones seen during…
We employ projective Fra\"iss\'e theory to define the "generic combinatorial $n$-simplex" as the pro-finite, simplicial complex that is canonically associated with a family of simply defined selection maps between finite triangulations of…
Humans can reason compositionally whilst grounding language utterances to the real world. Recent benchmarks like ReaSCAN use navigation tasks grounded in a grid world to assess whether neural models exhibit similar capabilities. In this…
Modelling musical structure is vital yet challenging for artificial intelligence systems that generate symbolic music compositions. This literature review dissects the evolution of techniques for incorporating coherent structure, from…
This paper reviews concepts, modeling approaches, and recent findings along a spectrum of different levels of abstraction of neural network models including generalization across (1) Samples, (2) Distributions, (3) Domains, (4) Tasks, (5)…
Wiltshire-Gordon has introduced a homotopy model for ordered configuration spaces on a given simplicial complex. That author asserts that, after a suitable subdivision, his model also works for unordered configuration spaces. We supply…
Compositional generalization-the systematic combination of known components into novel structures-remains a core challenge in cognitive science and machine learning. Although transformer-based large language models can exhibit strong…
We compute two parametric determinants in which rows and columns are indexed by compositions, where in one determinant the entries are products of binomial coefficients, while in the other the entries are products of powers. These results…
A composition of $n\in\NN$ is an ordered collection of one or more positive integers whose sum is $n$. The number of summands is called the number of parts of the composition. A palindromic composition of $n$ is a composition of $n$ in…
Providing a human-understandable explanation of classifiers' decisions has become imperative to generate trust in their use for day-to-day tasks. Although many works have addressed this problem by generating visual explanation maps, they…