Finance and Stochastics Seminar – Tom Hadfield

Tom Hadfield is speaking at the Huxley Building on Tuesday 20 October, as part of the Finance & Stochastics seminar series. His talk is titled Patnaik-Pearson intrinsic dimension for internal representations of neural networks, and it's a deep dive into how we measure the complexity of the data a neural network is processing.

At its heart, Hadfield is introducing a new way to measure the intrinsic dimension of a data manifold — the Patnaik-Pearson dimension — and applying it to the internal representations of neural networks like transformers. The idea of intrinsic dimension is about figuring out the true number of degrees of freedom in a dataset, rather than just counting the number of dimensions it's embedded in. By treating the weight matrices of a neural network as data manifolds, Hadfield relates this new dimension to the HTSR and SETOL analysis of Martin, Mahoney and Hinrichs, and the TwoNN intrinsic dimension estimator of Facco et al. He shows that the critical values of the tail exponent coincide for the two approaches, and he gets there using both theoretical and numerical techniques, including Voiculescu's free probability.

The seminar is run by the Imperial College Mathematical Finance Group, which hosts a weekly series open to everyone. The organisers say they aim for a diverse range of speakers that reflects the UK's professional probability community in terms of gender, ethnicity, geography and career stage, and they invite speakers from across the UK, Europe and the world. Hadfield's talk sits right in that mix, bringing together probability, geometry and the inner workings of modern AI.

It runs from 14:00 to 15:00 in Room 140 of the Huxley Building on the South Kensington Campus, SW7 2AZ. Entry is free and it's a drop-in, so there's no registration needed — you can just turn up.