Training Deep Neural Networks Using Conjugate Gradient-like Methods

Round 1

Reviewer 1 Report

The article is a very pertinent and, despite being a rather well-known topic, the Authors have developed a very thorough theoretical part, full of interesting ideas.

Despite this, some integration and clarification are needed: for these reasons it is proposed a "major revision".

Some comments:

1. Lines 32-51 the general description is too concise: a slightly broader description could be useful for the reader
2. Lines 234-236: please explain better the results (too concise)
3. Section 6: the conclusions are presented in an unclear way: please explain better

Minor comments:

1. Figure 1 is too little and not clear: please improve dimension and resolution
2. Figure 2 is too little and not clear: please improve dimension and resolution
3. Figure 3 is too little and not clear: please improve dimension and resolution
4. Figure 4 is too little and not clear: please improve dimension and resolution
5. Figure 5 is too little and not clear: please improve dimension and resolution
6. Figure 6 is too little and not clear: please improve dimension and resolution
7. Figure 7 is too little and not clear: please improve dimension and resolution
8. Figure 8 is too little and not clear: please improve dimension and resolution
9. Figure 9 is too little and not clear: please improve dimension and resolution
10. Figure 10 is too little and not clear: please improve dimension and resolution
11. Figure 11 is too little and not clear: please improve dimension and resolution
12. Figure 12 is too little and not clear: please improve dimension and resolution
13. The expression between lines 92/93 has no identification number
14. The expressions between lines 141/142 have no identification numbers
15. The expression top page 7 has no identification number
16. Some expressions of “Lemma A1” have no identification numbers
17. Some expressions of “Lemma A2” have no identification numbers
18. Some expressions of “Theorem A1” have no identification numbers
19. Expression (9): please arrange the two members on different lines and assign each one an identification number
20. Expression (10): please arrange the 3 members on different lines and assign each one an identification number
21. It is recommended an extensive reading to correct some sentences and typo errors.

I also suggest integrating the References with at least these three papers:

• Caciotta, M., Giarnetti, S., Leccese, F.”Hybrid neural network system for electric load forecasting of telecomunication station” (2009) 19th IMEKO World Congress 2009, 1, pp. 586-590.
• Caciotta, M., Giarnetti, S., Leccese, F., Orioni, B., Oreggia, M., Pucci, C., Rametta, S. “Flavors mapping by Kohonen network classification of Panel Tests of Extra Virgin Olive Oil” (2016) Measurement: Journal of the International Measurement Confederation, 78, pp. 366-372. DOI: 10.1016/j.measurement.2015.09.051
• Proietti, A., Liparulo, L., Leccese, F., Panella, M. “Shapes classification of dust deposition using fuzzy kernel-based approaches” (2016) Measurement: Journal of the International Measurement Confederation, 77, pp. 344-350. DOI: 10.1016/j.measurement.2015.09.025

Author Response

Please see the attachment. 

Author Response File: Author Response.pdf

Reviewer 2 Report

A statistical test should be used for the comparison of the examined methods.
The authors should better explain why the proposed methodology seems to work well and present some information about the time efficiency of their method.

Author Response

Please see the attachment. 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Accepted in present form

Reviewer 2 Report

The paper could be accepted in the current form