I’m Riccardo, currently an MPhil student in Advanced Computer Science at the University of Cambridge.
My main research focus is on Artificial Intelligence, particularly in Geometric and Categorical Deep Learning.
My dissertation is titled “Towards Category-Theoretic Message Passing”, where I’m using category theory and abstract algebra to rethink message passing rigorously.
I’m also interested in the geometry of deep learning and natural gradients, as well as theoretical learning theory.
Generally, I’m interested in whatever can enhance our understanding of machine learning systems!
One of my favourite theorems :)
Riccardo Ali
PhD CS, Cambridge
MPhil CS, Cambridge
BSc Maths & CS, Manchester
Publications
Ali, R., Kulytė, P., de Ocáriz Borde, H. S., & Lio, P. (2024). Metric Learning for Clifford Group Equivariant Neural Networks. ICML 2024 Workshop on Geometry-Grounded Representation Learning and Generative Modeling. https://openreview.net/forum?id=4tw1U41t6Q
@inproceedings{ali2024metric,
title = {Metric Learning for Clifford Group Equivariant Neural Networks},
author = {Ali, Riccardo and Kulyt{\.{e}}, Paulina and de Oc{\'a}riz Borde, Haitz S{\'a}ez and Lio, Pietro},
booktitle = {ICML 2024 Workshop on Geometry-grounded Representation Learning and Generative Modeling},
year = {2024},
url = {https://openreview.net/forum?id=4tw1U41t6Q},
file = {metric_learning_cgenns.pdf}
}
Clifford Group Equivariant Neural Networks (CGENNs) leverage Clifford algebras and multivectors as an alternative approach to incorporating group equivariance to ensure symmetry constraints in neural representations. In principle, this formulation generalizes to orthogonal groups and preserves equivariance regardless of the metric signature. However, previous works have restricted internal network representations to Euclidean or Minkowski (pseudo-)metrics, handpicked depending on the problem at hand. In this work, we propose an alternative method that enables the metric to be learned in a data-driven fashion, allowing the CGENN network to learn more flexible representations. Specifically, we populate metric matrices fully, ensuring they are symmetric by construction, and leverage eigenvalue decomposition to integrate this additional learnable component into the original CGENN formulation in a principled manner. Additionally, we motivate our method using insights from category theory, which enables us to explain Clifford algebras as a categorical construction and guarantee the mathematical soundness of our approach. We validate our method in various tasks and showcase the advantages of learning more flexible latent metric representations. The code and data are available at https://github.com/rick-ali/Metric-Learning-for-CGENNs
Brown, G., & Ali, R. (2024). Bias/Variance is not the same as Approximation/Estimation. Transactions on Machine Learning Research. https://openreview.net/forum?id=4TnFbv16hK
@article{brown2024biasvariance,
title = {Bias/Variance is not the same as Approximation/Estimation},
author = {Brown, Gavin and Ali, Riccardo},
journal = {Transactions on Machine Learning Research},
issn = {2835-8856},
year = {2024},
url = {https://openreview.net/forum?id=4TnFbv16hK},
file = {bias_variance.pdf}
}
We study the relation between two classical results: the bias-variance decomposition, and the approximation-estimation decomposition. Both are important conceptual tools in Machine Learning, helping us describe the nature of model fitting. It is commonly stated that they are “closely related”, or “similar in spirit”. However, sometimes it is said they are equivalent. In fact they are different, but have subtle connections cutting across learning theory, classical statistics, and information geometry, that (very surprisingly) have not been previously observed. We present several results for losses expressible as Bregman divergences: a broad family with a known bias-variance decomposition. Discussion and future directions are presented for more general losses, including the 0/1 classification loss.
