Hi all,
This week, our visitor Gemma de les Coves will talk about “The scope of universality and unreachability”. See below for the abstract.
The talk will take place on Wednesday at 11:15 in HIT K52.
It may also be of interest to some of you that Tobias Reinhart, who is working with Gemma, is giving a talk about “Universal Spin Models are Universal Approximators in Machine Learning” on Tuesday at 10:00 in HIT F32.
Best, Ladina
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Title: The scope of universality and unreachability
Abstract: I will share our attempts to understand the scope of some forms of universality, such as those of Turing machines or spin models (arxiv: 2406.16607 https://arxiv.org/abs/2406.16607, 2407.13428 https://www.arxiv.org/abs/2407.13428, 2006.03529 https://arxiv.org/abs/2006.03529 ), as well as their relation to forms of unreachability such as uncomputability or undecidability.
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Title:
Universal Spin Models are Universal Approximators in Machine Learning
Abstract:
One of the theoretical pillars that sustain certain machine learning models are universal approximation theorems, which prove that they can approximate all functions from a function class to arbitrary precision. Independently, classical spin models are termed universal if they can reproduce the behavior of any other spin model in their low energy sector. Universal spin models have been characterized via sufficient and necessary conditions, showing that simple models such as the 2d Ising with fields are universal. In this work, we prove that universal spin models are universal approximators of probability distributions. As a consequence, the characterization of the former gives rise to universal approximation theorems for the latter. This allows us to derive new proofs of universal approximation theorems for restricted and deep Boltzmann machines, as well as deep belief networks. This work illustrates that independently discovered universality statements may be intimately related, enabling the transfer of results.