Related papers: Generalized Composition via Nerves: Models and Alg…

The purpose of this dissertation is to set up a theory of generalized operads and multicategories, and to use it as a language in which to propose a definition of weak n-category. Included is a full explanation of why the proposed…

We consider compositions of natural numbers when there are different types of each natural number. Several recursions as well as some closed formulas for the number of compositions is derived. We also find its relationships with some known…

Consider the general linear group, which is not connected but rather has two connected components, the matrices with positive determinant and the ones with negative determinant. Consider the Iwasawa decomposition of its special linear…

In physics we often use very simple models to describe systems with many degrees of freedom, but it is not clear why or how this success can be transferred to the more complex biological context. We consider models for the joint…

Compositionality has traditionally been understood as a major factor in productivity of language and, more broadly, human cognition. Yet, recently, some research started to question its status, showing that artificial neural networks are…

Let M be a filtered module. Some properties of elements of M are "generic" in the following sense: (being open/stable) if an element z of M has a property P then any approximation of z has P; (being dense) any element of M is approximated…

In the context of general rough sets, the act of combining two things to form another is not straightforward. The situation is similar for other theories that concern uncertainty and vagueness. Such acts can be endowed with additional…

In recent years, artificial neural networks (ANNs) have become a universal tool for tackling real-world problems. ANNs have also shown great success in music-related tasks including music summarization and classification, similarity…

Simplicity is held by many to be the key to general intelligence. Simpler models tend to "generalise", identifying the cause or generator of data with greater sample efficiency. The implications of the correlation between simplicity and…

Deep tabular modelling increasingly relies on in-context learning where, during inference, a model receives a set of $(x,y)$ pairs as context and predicts labels for new inputs without weight updates. We challenge the prevailing view that…

We define the notion of a multi-sorted algebraic theory, which is a generalization of an algebraic theory in which the objects are of different "sorts." We prove a rigidification result for simplicial algebras over these theories, showing…

Machine learning models of music typically break up the task of composition into a chronological process, composing a piece of music in a single pass from beginning to end. On the contrary, human composers write music in a nonlinear…

Generalization is at the core of machine learning models. However, the definition of generalization is not entirely clear. We employ set theory to introduce the concepts of algorithms, hypotheses, and dataset generalization. We analyze the…

We provide a categorical framework for mathematical objects for which there is both a sort of "independent" and "dependent" composition. Namely we model them as duoidal categories in which both monoidal structures share a unit and the first…

We develop a compositional framework for generalized reversible computing using copy-discard categories and resource theories. We introduce partitioned matrices between partitioned sets as subdistribution matrices which preserve the…

Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…

Interventional causal models describe several joint distributions over some variables used to describe a system, one for each intervention setting. They provide a formal recipe for how to move between the different joint distributions and…

We propose a general class of sample based explanations of machine learning models, which we term generalized representers. To measure the effect of a training sample on a model's test prediction, generalized representers use two…

Communication is compositional if complex signals can be represented as a combination of simpler subparts. In this paper, we theoretically show that inductive biases on both the training framework and the data are needed to develop a…

Calibration is a fundamental property of a good predictive model: it requires that the model predicts correctly in proportion to its confidence. Modern neural networks, however, provide no strong guarantees on their calibration -- and can…