Related papers: Category Theoretic Analysis of Photon-based Decisi…

A growing number of approaches exist to generate explanations for image classification. However, few of these approaches are subjected to human-subject evaluations, partly because it is challenging to design controlled experiments with…

Lenses, optics and dependent lenses (or equivalently morphisms of containers, or equivalently natural transformations of polynomial functors) are all widely used in applied category theory as models of bidirectional processes. From the…

In machine learning, the notion of multi-armed bandits refers to a class of online learning problems, in which an agent is supposed to simultaneously explore and exploit a given set of choice alternatives in the course of a sequential…

Lenses are a well-established structure for modelling bidirectional transformations, such as the interactions between a database and a view of it. Lenses may be symmetric or asymmetric, and may be composed, forming the morphisms of a…

A population of neurons typically exhibits a broad diversity of responses to sensory inputs. The intuitive notion of functional classification is that cells can be clustered so that most of the diversity is captured in the identity of the…

We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by a mode theory which specifies a collection of modes, modalities, and transformations between them. We show that different choices of mode…

This paper presents an approach to the design of autonomous, real-time systems operating in uncertain environments. We address issues of problem solving and reflective control of reasoning under uncertainty in terms of two fundamental…

Taking advantage of contextual information can potentially boost the performance of recommender systems. In the era of big data, such side information often has several dimensions. Thus, developing decision-making algorithms to cope with…

Many structured prediction tasks in machine vision have a collection of acceptable answers, instead of one definitive ground truth answer. Segmentation of images, for example, is subject to human labeling bias. Similarly, there are multiple…

Single image-level annotations only correctly describe an often small subset of an image's content, particularly when complex real-world scenes are depicted. While this might be acceptable in many classification scenarios, it poses a…

As AI systems evolve from static tools to dynamic agents, traditional categorical governance frameworks -- based on fixed risk tiers, levels of autonomy, or human oversight models -- are increasingly insufficient on their own. Systems built…

The question of selecting the "best" amongst different choices is a common problem in statistics. In drug development, our motivating setting, the question becomes, for example: what is the dose that gives me a pre-specified risk of…

This dissertation reports some first steps towards a compositional account of active inference and the Bayesian brain. Specifically, we use the tools of contemporary applied category theory to supply functorial semantics for approximate…

Quantum techniques are expected to revolutionize how information is acquired, exchanged, and processed. Yet it has been a challenge to realize and measure their values in practical settings. We present first photon machine learning as a new…

Classification of datasets into two or more distinct classes is an important machine learning task. Many methods are able to classify binary classification tasks with a very high accuracy on test data, but cannot provide any easily…

Each year, numerous segmentation and classification algorithms are invented or reused to solve problems where machine vision is needed. Generally, the efficiency of these algorithms is compared against the results given by one or many human…

Scientists, engineers, biologists, and technology specialists universally leverage image segmentation to extract shape ensembles containing many thousands of curves representing patterns in observations and measurements. These large curve…

One of the major challenges in biology concerns the integration of data across length and time scales into a consistent framework: how do macroscopic properties and functionalities arise from the molecular regulatory networks - and how can…

Simple optics are defined using actions of monoidal categories. Compound optics arise, for instance, as natural transformations between polynomial functors. Since a monoidal category is a special case of a bicategory, we formulate complex…

Photon subtraction is useful to produce nonclassical states of light addressed to applications in photonic quantum technologies. After a very accelerated development, this technique makes possible obtaining either single photons or optical…