Journal Club for Quantum Physics and Machine Learning



Next Journal Club Meeting: Tuesday, 20th April 2021, 4:30pm CET.

Rui Lin (ETH Zürich) will present the following paper: Minimal model of permutation symmetry in unsupervised learning

Abstract: Permutation of any two hidden units yields invariant properties in typical deep generative neural networks. This permutation symmetry plays an important role in understanding the computation performance of a broad class of neural networks with two or more hidden units. However, a theoretical study of the permutation symmetry is still lacking. Here, we propose a minimal model with only two hidden units in a restricted Boltzmann machine, which aims to address how the permutation symmetry affects the critical learning data size at which the concept-formation (or spontaneous symmetry breaking in physics language) starts, and moreover semi-rigorously prove a conjecture that the critical data size is independent of the number of hidden units once this number is finite. Remarkably, we find that the embedded correlation between two receptive fields of hidden units reduces the critical data size. In particular, the weakly-correlated receptive fields have the benefit of significantly reducing the minimal data size that triggers the transition, given less noisy data. Inspired by the theory, we also propose an efficient fully-distributed algorithm to infer the receptive fields of hidden units. Furthermore, our minimal model reveals that the permutation symmetry can also be spontaneously broken following the spontaneous symmetry breaking. Overall, our results demonstrate that the unsupervised learning is a progressive combination of spontaneous symmetry breaking and permutation symmetry breaking which are both spontaneous processes driven by data streams (observations). All these effects can be analytically probed based on the minimal model, providing theoretical insights towards understanding unsupervised learning in a more general context.

Upcoming Journal Club meetings:

Date Time Speaker Affiliation Reference
20th April 2021 4:30pm CET  Rui Lin  ETH Zürich Minimal model of permutation symmetry in unsupervised learning
4th May 2021 4:30pm CET  Agnes Valenti  ETH Zürich Scalable Hamiltonian learning for large-scale out-of-equilibrium quantum dynamics
18th May 2021 4:30 CET  TBA  TBA  TBA
1st June 2021 4:30 CET  TBA  TBA  TBA


Past Journal Club Meetings:

Date Time Speaker Affiliation Reference
6th April 2021 4:30pm CET  Miriam Büttner  University of Freiburg

Learning Potentials of Quantum Systems using Deep Neural Networks


 23rd March 2021 4:30pm CET Luuk Coopmans  Trinity College Dublin/Dublin Institute for Advanced Studies Protocol Discovery for the Quantum Control of Majoranas by Differential Programming and Natural Evolution Strategies
 9th March 2021 4:30pm CET  Axel Lode University of Freiburg

Interpretable Phase Detection and Classification with Persistent Homology


 23rd February 2021  4:30pm CET  Evert van Nieuwenburg  University of Copenhagen A NEAT Quantum Error Decoder
 9th February 2021  3pm CET  Shahnawaz Ahmed  Chalmers University of  Technology Classification and reconstruction of optical quantum states with deep neural networks 
 26th January 2021  3pm CET  Julian Arnold  University of Basel Interpretable and unsupervised phase classification
 12th January 2021  3pm CET  Paolo Molignini  University of Cambridge

Scientific intuition inspired by machine learning generated hypotheses


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