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  • Christoph Walter Senn 1,2,*,† and
  • Itsuo Kumazawa 2,†

Reviewer 1: Anonymous Reviewer 2: Anonymous

Round 1

Reviewer 1 Report

In the manuscript “Abstract Reservoir Computing”, the authors proposed the abstractly regularized Mass-Spring networks and obtained a closed-form updating rule for weight matrix by solving a constrained optimization problem to predict the time series signals with noises. Based on simulation experiments, the authors showed that in contrast to the classical approach with L2-regularization, the training approach developed in their work performs better for predicting time series signals with more noise. 

Major concerns:

  1. In Equation (1), the dimension of matrix B should be ℜd×f if xt∈ ℜd and all the vectors are column vectors. However, in the authors’ manuscript, B ∈ ℜf×d. The vector and matrix dimensions in other equations are also confusing. For instance, in Equation (2), I cannot deduce the dimension of the weight matrix w. Is xτ a column vector or row vector?
  2. Equation (9): Is this closed-form solution contributed by this work? If so, please provide rigorous mathematical proof. If not, please give citations. I ask for proof because this formula was claimed by the authors as a major contribution of this paper and supports the simulation results.

Minor comments:

  1. Equation (15): How many samples are used to evaluate errors in your simulation experiments?
  2. Page 1: The author affiliations are not properly formatted. Affiliation associated with superscript 2 was produced twice. The "current address" affiliation is a duplicate of the one associated with superscript 1.
  3. Figures 5-7: x labels and y labels are missing.
  4. Figures 8-11: Font size is a little small.

Author Response

Dear Reviewer,

Thank you for your time and comments.

Regarding the major concerns:

In Equation (1), the dimension of matrix B should be ℜd×f if xt∈ ℜd and all the vectors are column vectors. However, in the authors’ manuscript, B ∈ ℜf×d. The vector and matrix dimensions in other equations are also confusing. For instance, in Equation (2), I cannot deduce the dimension of the weight matrix w. Is xτ a column vector or row vector?

Matrix B in Equation (1) was indeed supposed to be ℜd×f, and we corrected it accordingly. The weights w are stored in a column vector ∈ℜd. We understand the difficulties regarding the dimension/shape of the vectors and adjusted the manuscript to state if they are a column or row vector.

Equation (9): Is this closed-form solution contributed by this work? If so, please provide rigorous mathematical proof. If not, please give citations. I ask for proof because this formula was claimed by the authors as a major contribution of this paper and supports the simulation results.

We added the derivation of the closed form solution to the manuscript.

Regarding the minor concerns:

Equation (15): How many samples are used to evaluate errors in your simulation experiments?

Each test set for the three datasets consists of 5000 samples. And we averaged the results over 10 experiment runs.

Page 1: The author affiliations are not properly formatted. Affiliation associated with superscript 2 was produced twice. The "current address" affiliation is a duplicate of the one associated with superscript 1.

That was caused due to having multiple e-mail addresses for the same affiliation. We corrected this issue by only listing the e-mail address of the corresponding author.

Figures 5-7: x labels and y labels are missing.

We added the x label "timesteps" and named the y-axis "y" as it is dimensionless.

Figures 8-11: Font size is a little small.

We increased the size of the figures to make them more readable.

 

Thank you again for your time and valuable input.

Reviewer 2 Report

The research carried out by authors is of great significance and application value, especially in the field of physical reservoir computing. By establishing the physical model and using the improved mass spring networks for training, and used to solve the problem of multi parameter modeling.

My suggestions are as follows:

1) The abstract does not highlight the core technology, innovation and technical level of this paper, so it is suggested to rewrite it.

2) For the evaluation of experimental results, only MSE is used. I suggest to consider increasing the evaluation indexes of stability and anti-noise ability.

Author Response

Dear Reviewer,

Thank you for your time and comments.

Regarding your raised points:

The abstract does not highlight the core technology, innovation and technical level of this paper, so it is suggested to rewrite it.

We updated the abstract with the following text:

Noise of any kind can be an issue when translating results from simulations to the real world. We suddenly have to deal with building tolerances, faulty sensors or just noisy sensor readings. This is especially evident in systems with many free parameters, such as the ones used in physical reservoir computing. By abstracting away these kinds of noise sources using intervals, we derive a regularized training regime for reservoir computing using sets of possible reservoir states. Numerical simulations are used to show the effectiveness of our approach against different sources of errors that can appear in real-world scenarios and compare them with standard approaches. Our results support the application of interval arithmetic to improve the robustness of mass-spring networks trained in simulations.

For the evaluation of experimental results, only MSE is used. I suggest to consider increasing the evaluation indexes of stability and anti-noise ability.

We are not sure if we understand evaluation indexes correctly. Do you mean to increase the noise levels, or would it be possible to elaborate on it?

Thank you very much for your time and valuable feedback.

 

Round 2

Reviewer 1 Report

Dear authors,

I just found some format errors in your reference list (e.g., Reference 5, Reference 7, etc.). Please consider formatting your reference list correctly.

FYI, 

5.Vandoorne, K.; Dambre, J.; Verstraeten, D.; Schrauwen, B.; Bienstman, P. Parallel Reservoir Computing Using Optical Amplifiers.Neural Networks, IEEE Transactions on2011,22, 1469 – 1481. doi:10.1109/TNN.2011.2161771.

7.Hauser, H.; Füchslin, R.; Nakajima, K., Morphological Computation - The Body as a Computational Resource; 2014; pp. 226–. 

Author Response

Dear Reviewer,

Thank you for your feedback.

We updated the references accordingly.