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Supervised learning of few dirty bosons with variable particle number
by Pere Mujal, Àlex Martínez Miguel, Artur Polls, Bruno Juliá-Díaz, Sebastiano Pilati
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|Authors (as registered SciPost users):||Pere Mujal · Sebastiano Pilati|
|Preprint Link:||https://arxiv.org/abs/2010.03875v2 (pdf)|
|Date submitted:||2021-01-22 11:31|
|Submitted by:||Mujal, Pere|
|Submitted to:||SciPost Physics|
We investigate the supervised machine learning of few interacting bosons in optical speckle disorder via artificial neural networks. The learning curve shows an approximately universal power-law scaling for different particle numbers and for different interaction strengths. We introduce a network architecture that can be trained and tested on heterogeneous datasets including different particle numbers. This network provides accurate predictions for all system sizes included in the training set and, by design, is suitable to attempt extrapolations to (computationally challenging) larger sizes. Notably, a novel transfer-learning strategy is implemented, whereby the learning of the larger systems is substantially accelerated and made consistently accurate by including in the training set many small-size instances.
List of changes
1. We have reformulated the abstract, following the second Referee’s comment about the accuracy of the extrapolations to larger system sizes.
2. In the introduction, we have added citations to new Refs.  and , which were mentioned by the second Referee in his/her report.
3. We have modified the introduction according to the second Referee’s report comments on the extrapolations. The claim on the extrapolation accuracy is substantially scaled down.
4. At the end of Sec. 2.3, we have extended the discussion on the use of regularization techniques and on the procedure we adopted to inspect for the possible occurrence of overfitting (see comment by the second Referee).
5. In Secs. 4.1, 4.2, and 4.3, we have modified the claims and discussion about the extrapolations, emphasising the specific conditions where reasonable accuracy is obtained, and mentioning the need for further analysis on larger systems.
6. We have added the right panels in Figs. 3 and 4 to better visualize the discrepancies in the extrapolations and in the outcomes of accelerated learning (see comment by the second Referee).
7. In the conclusions, we have added a sentence about the approximately universal behaviour of the learning curve, speculating that different neural network architecture might provide a faster learning (see comment by the second Referee).
8. In the conclusions, we have mentioned the possibility of computing other physical quantities (see comment by the second Referee).
9. In the conclusions, we expand the discussion on cold-atom quantum simulators and on three-body recombinations (see comment by the first Referee). We cite new Refs. and , which report cold-atom experiments on the deterministic preparation of few-body systems with controlled atom numbers.
10. In the conclusions, we have pointed out the possibility of using quantum machine learning, citing new Refs. [48-52], following a comment by the first Referee.
Submission & Refereeing History
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Reports on this Submission
- Cite as: Anonymous, Report on arXiv:2010.03875v2, delivered 2021-02-15, doi: 10.21468/SciPost.Report.2558
Although the authors have addressed all of my comments, their response is rather disappointing. Most of the changes made are in more careful wording of the claims. Of course, this is welcome, but my suggestions, most of which declined politely by the authors, were meant to provide the reader with a better understanding of the result. For example, point 1 in my original review could have shown the limitations of extrapolation and could easily have been done with their already existing data. Unfortunately, the authors did not accept my suggestion. The same goes for points 2,3 and 4. In point 5, the authors again do not take my suggestion, but instead, present a histogram of the absolute error. This addition is not helpful, in my opinion. My original proposal was to subtract the linear term and still plot the data as a function of E. That way, one could see the systematic deviation with the energy. The authors choose not to do that; I suspect because the result is not favorable. My overall feeling is that the authors decided to make only small "cosmetic" changes. However, as already noted in my first review, the paper's two established claims justify its publication, and since in this version the authors softened the third claim, I can recommend its acceptance.