Hi! I'm Riccardo

I study the geometric, algebraic, and information-theoretic structure of neural networks. I'm interested in how mathematical ideas can help us understand what models learn and how they make decisions.

My research spans symmetry and equivariance, representation learning, and interpretability in language models.

Education

PhD in Computer ScienceUniversity of Cambridge Ongoing
MPhil in Advanced Computer ScienceUniversity of Cambridge
BSc in Mathematics and Computer ScienceUniversity of Manchester

ResearchQuestions, methods, discoveries TeachingCourses & shared understanding TalksSeminars, workshops & ideas

Publications

All publications ↗

Three graph diagrams compare convolutional scalar weights, diagonal multi-head attention, and cross-head transport in Topological Attention.

arXiv preprint2026

Let the Heads Talk: Beyond Diagonal Graph Attention

Riccardo Ali*, Alessio Borgi*, Mario Severino*, Alessio Gravina, Davide Bacciu, Pietro Liò, Christopher Irwin*

* Equal contribution

TL;DR We connect matrix-valued transport in sheaf networks to communication between attention heads, motivating a graph attention mechanism that learns how heads interact along each edge.

Paper PDF Overview

GAPE diagram showing how a query gate contracts the effective context while a landmark gate protects a distant token from suppression.

arXiv preprint2026

Remember to Forget: Gated Adaptive Positional Encoding

Riccardo Ali*, Alessio Borgi*, Mario Severino*, Pietro Liò, Christopher Irwin*

* Equal contribution

TL;DR We introduce GAPE, a mask that augments positional encodings with two mechanisms: one suppresses irrelevant distant context, while the other protects important tokens from that suppression.

Paper PDF Overview

Running Lyapunov estimates across recurrent steps: Ouro remains above zero while Huginn converges to a negative exponent.

ICML Mechanistic Interpretability workshop2026

Lyapunov Spectral Analysis of Loop Transformer Dynamics

Fynn Kiwitt, Christopher Irwin, Riccardo Ali, Pietro Liò

TL;DR Lyapunov spectra distinguish mildly chaotic dynamics in Ouro from contracting dynamics in Huginn, tracing the difference to opposing layer contributions.

Paper PDF Poster Overview

Two digit orbits under horizontal flips are encoded into separate copies of the regular representation in latent space.

ICLR GRaM workshop2026

Algebraic Priors for Approximately Equivariant Networks

Riccardo Ali, Pietro Liò, Jamie Vicary

TL;DR We prove that, for finite groups, equivariant latent spaces almost surely contain copies of the regular representation, then use this structure as a parameter-free algebraic prior for approximate equivariance.

Paper PDF Code Overview

arXiv preprint2025

Entropy-Lens: Uncovering Decision Strategies in LLMs

Riccardo Ali*, Francesco Caso*, Christopher Irwin*, Pietro Liò

* Equal contribution

TL;DR Layer-by-layer entropy of token predictions reveals how LLMs expand and prune candidate continuations, with patterns specific to model families and tasks.

Paper PDF Code Overview

Algorithm 1: eigendecompose the learned metric, embed and change basis, apply a Clifford network, then transform the output back.

ICML GRaM workshop2024

Metric Learning for Clifford Group Equivariant Neural Networks

Riccardo Ali*, Paulina Kulytė*, Haitz Sáez de Ocáriz Borde, Pietro Liò

* Equal contribution

TL;DR We extend Clifford group equivariant networks to learn their latent metric from data, allowing the geometry of their representations to adapt to the task.

Paper PDF Code Overview

Diagram connecting expected risk to optimisation, estimation, approximation, and Bayes error, and relating these to variance, bias, and noise.

TMLR2024

Bias/Variance is not the same as Approximation/Estimation

Gavin Brown, Riccardo Ali

TL;DR Two classical explanations of prediction error are often conflated. We establish precisely how bias–variance and approximation–estimation differ and how they connect.

Paper PDF Overview