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The unprecedented pace of machine learning research has lead to incredible advances, but also poses hard challenges. At present, the field lacks strong theoretical underpinnings, and many important achievements stem from ad hoc design…

This manuscript presents a novel framework that integrates higher-order symmetries and category theory into machine learning. We introduce new mathematical constructs, including hyper-symmetry categories and functorial representations, to…

We present a novel application of category theory for deep learning. We show how category theory can be used to understand and work with the linear layer functions of group equivariant neural networks whose layers are some tensor power…

Neural networks have become an increasingly popular tool for solving many real-world problems. They are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this…

The paper introduces a novel framework based on category theory to enhance the explainability of artificial intelligence systems, particularly focusing on word embeddings. Key topics include the construction of categories $\mathcal{L}_T$…

As AI systems advance and integrate into society, well-designed and transparent evaluations are becoming essential tools in AI governance, informing decisions by providing evidence about system capabilities and risks. Yet there remains a…

Deep learning, despite its remarkable achievements, is still a young field. Like the early stages of many scientific disciplines, it is marked by the discovery of new phenomena, ad-hoc design decisions, and the lack of a uniform and…

In this survey, we provide an overview of category theory-derived machine learning from four mainstream perspectives: gradient-based learning, probability-based learning, invariance and equivalence-based learning, and topos-based learning.…

Explainable AI (XAI) aims to address the human need for safe and reliable AI systems. However, numerous surveys emphasize the absence of a sound mathematical formalization of key XAI notions -- remarkably including the term "explanation"…

We introduce a new hierarchical deep learning framework for recursive higher-order meta-learning that enables neural networks (NNs) to construct, solve, and generalise across hierarchies of tasks. Central to this approach is a generative…

Harnessing the potential computational advantage of quantum computers for machine learning tasks relies on the uploading of classical data onto quantum computers through what are commonly referred to as quantum encodings. The choice of such…

In humans and other animals, category learning enhances discrimination between stimuli close to the category boundary. This phenomenon, called categorical perception, was also empirically observed in artificial neural networks trained on…

Fine-tuning a pre-trained deep neural network has become a successful paradigm in various machine learning tasks. However, such a paradigm becomes particularly challenging with tabular data when there are discrepancies between the feature…

We propose the design of novel categorical generative AI architectures (GAIAs) using topos theory, a type of category that is ``set-like": a topos has all (co)limits, is Cartesian closed, and has a subobject classifier. Previous theoretical…

At present, there are no easily understood explainable artificial intelligence (AI) methods for discrete token inputs, like text. Most explainable AI techniques do not extend well to token sequences, where both local and global features…

Unlike human-engineered systems such as aeroplanes, where each component's role and dependencies are well understood, the inner workings of AI models remain largely opaque, hindering verifiability and undermining trust. This paper…

Artificial intelligence (AI) is currently based largely on black-box machine learning models which lack interpretability. The field of eXplainable AI (XAI) strives to address this major concern, being critical in high-stakes areas such as…

Category theory has been successfully applied in various domains of science, shedding light on universal principles unifying diverse phenomena and thereby enabling knowledge transfer between them. Applications to machine learning have been…

Topological deep learning is a formalism that is aimed at introducing topological language to deep learning for the purpose of utilizing the minimal mathematical structures to formalize problems that arise in a generic deep learning…

Despite the growing use of transformer models in computer vision, a mechanistic understanding of these networks is still needed. This work introduces a method to reverse-engineer Vision Transformers trained to solve image classification…