Episodic Memory and Information Recognition Using Solitonic Neural Networks Based on Photorefractive Plasticity

Round 1

Reviewer 1 Report

The idea to ‘attempt to replicate the fundamental blocks of the biological   

nervous system and their way of communicating’ is interesting, but significant modeling would be needed to use soliton collisions for this. The wish is for a medium for ‘processing data and 

simultaneously retaining its memory’. So this would mimic biological systems, where information produces a strengthening or weakening of the synapses’.

What is meant by ‘a single solitonic neuron’? The pulses in a neurons are not solitons. With an ’ X-Junction structure’ that is ‘ created by the propagation of photorefractive solitons’, the interaction depends on the material and the amplitudes and relative phases of the incoming solitons. It is stated that the photorefractive networks ‘learn by changing their structure according to the incoming information’ .

The ‘Mathematical Model’ of sect.3 does not seem to include material characteristics or even the geometry being modelled. Is this a fiber or flat waveguide or other?What are the phases? There is no actual nonlinearity mentioned.

What is the characteristic of the ‘photorefractive’ material? This would be critical.

Thus the modelling seems too simplistic to relate to any real device. There is mention of a ‘virgin medium’ without saying what crystal or element is being considered.

After a spatial soliton collision, forming an X-junction, there is always an ‘offset’ between the (parallel) output and input beams. This is given in many papers/sites, e.g. Figure 2  of http://www.scholarpedia.org/article/Soliton;  also YAW-DONG WU (2004) Nonlinear All-Optical Switching Device

by Using the Spatial Soliton Collision, Fiber and Integrated Optics, 23:5, 387-404; also chap.1 of‘ Soliton-Guided Quantum Information Processing’, 2017, DOI:10.1007/978-3-319-33921-4_13

In book:  Advances in Unconventional Computing (pp.297-307),

Author:Kenneth Steiglitz.

 But this is not apparent in fig.8, and no reason is given. How is the permanent change of refractive index made?

The conclusion  states that ‘The study carried out effectively demonstrates that an SNN is able to reproduce the   

functionality of an episodic memory, learning numbers’,etc, but actually it  only shows some features of a simplistic model.

Overall,  as other papers have pointed out, the theme could be of use for the future, but the modeling of the desired  physical system given here  is too vague and is insufficient to validate the idea. I recommend rejection of this submission.

 

Author Response

Q1: What is meant by ‘a single solitonic neuron’? The pulses in a neurons are not solitons. With an ’ X-Junction structure’ that is ‘ created by the propagation of photorefractive solitons’, the interaction depends on the material and the amplitudes and relative phases of the incoming solitons. It is stated that the photorefractive networks ‘learn by changing their structure according to the incoming information’.

A1: We think that the referee misunderstood this point. By single solitonic neuron we means a single X-junction formed by solitonic waveguides, as reported everywhere and also in references 19. We never spoke about pulses and we are not arguing that signals in the neurons are solitons: we used photorefractive solitons as waveguides for signals: being nonlinear, such waveguides can be furthermore modified also by the signals that propagate inside, making such structures fully addressable.

 

Q2.1: The ‘Mathematical Model’ of sect.3 does not seem to include material characteristics…..

A2.1: We have included in the new text the name of the used material (lithium niobate) as well as all the numerical parameters used (tab.5). The mathematical model describes a saturable nonlinearity which is typical for the photorefractive media and we believe it is fully appropriate.

 

Q2.2: …… or even the geometry being modelled. Is this a fiber or flat waveguide or other? What are the phases? There is no actual nonlinearity mentioned.

A2.2: There is no special geometry here: photorefractive spatial solitons are fully 3D-solutions and do not require a specific material geometry. As it is well known, Kerr solitons are only stable in 1D and, consequently, require a waveguide. Similar for solitons in fibres, even if in fibres we consider more temporal solitons instead of spatial ones.

Only using saturable nonlinearity, as the photorefractive one, stable 3D solitons can be created at ultralow powers (uW, nW). References on this can be found in many papers or textbook: for example the referee might see Trillo-Torruellas, Spatial Solitons, Springer Optical Sciences series v 82 (2002).

 

Q3: What is the characteristic of the ‘photorefractive’ material? This would be critical.

A3: We have included in the new text the name of the used material (lithium niobate) as well as all the numerical parameters used (tab.5).

 

Q4: Thus the modelling seems too simplistic to relate to any real device. There is mention of a ‘virgin medium’ without saying what crystal or element is being considered.

A4: We have modified this phrase: in fact we were not referring this to a “virgin” material but to a “virgin” network. The modified phrase says now: < The result is a perfectly balanced network, which  means that if any further signal propagating inside a waveguide reaches the crossing, it will be split 50-50 to the output channels. Thus, it represents a virgin network from the point of view of learning.> (lines 309-312).

 

Q5: After a spatial soliton collision, forming an X-junction, there is always an ‘offset’ between the (parallel) output and input beams. This is given in many papers/sites, e.g. Figure 2  of http://www.scholarpedia.org/article/Soliton;  also YAW-DONG WU (2004) Nonlinear All-Optical Switching Device. But this is not apparent in fig.8, and no reason is given. How is the permanent change of refractive index made?

A5: we do not understand the question. We have already theoretically and experimentally observed solitonic X-junctions using photorefractive solitons and no offsets were present. The already published papers are:

• Alonzo M., Moscatelli D., Bastiani L., Belardini A., Soci C. and Fazio E., All-Optical Reinforcement Learning In Solitonic X-Junctions. Scientific Reports 8, 5716 1-7, (2018)
• Bile A., Moratti F., Tari H., Fazio E., Supervised and Unsupervised learning using a fully-plastic all-optical unit of artificial intelligence based on solitonic waveguides, Neural Computing & Applications 2021. https://doi.org/10.1007/ s00521-021-06299-7s.

In the first one you can find theory and experiment, while in the second just theory. Two more experimental papers are now submitted where no offset was observed:

• Bile A., Chauvet M., Tari H., Fazio E., Addressable photonic neuron using solitonic X-junctions in Lithium Niobate thin films, submitted
• Bile A., Chauvet M., Tari H., Fazio E., All-optical erasing of photorefractive solitonic channels in Lithium Niobate thin films, submitted

For this reason, we did not mention any offset which indeed was and is not present in photorefractive solitonic X-junctions.

 

Q6: The conclusion  states that ‘The study carried out effectively demonstrates that an SNN is able to reproduce the functionality of an episodic memory, learning numbers’,etc, but actually it  only shows some features of a simplistic model.

A6: In the paper we demonstrate that the proposed network is able to memorize 4-bit numbers and further to recognize them. This is what an episodic memory should do, and this is what it does. We are now investigating different kinds of memories (both procedural and semantic ones) which are not topics of the present paper and that will be published in future ones.

Reviewer 2 Report

This article describes a technique for photonic implementation of trainable neural networks. The optical architecture proposed by the authors is very simple, but is likely to be of considerable technological interest for future neural network development, since it easily implemented from an engineering point of view, and is inherently very scalable. The article is very well written and well presented, and I am pleased to recommend it for publication in Applied Sciences.

The manuscript contains a few very minor English-language grammatical errors and typographical errors that need to be corrected before publication, but these can easily be addressed at the subediting stage.

The authors write 'Van Neumann's circuit geometries' on line 455 of the manuscript, and the journal subeditors should confirm whether the authors intended to write 'Von Neumann's circuit geometries'.

 

Author Response

Q1: The manuscript contains a few very minor English-language grammatical errors and typographical errors that need to be corrected before publication, but these can easily be addressed at the subediting stage.

A1: The manuscript has been checked and some grammar and typing errors corrected.

 

Q2: The authors write 'Van Neumann's circuit geometries' on line 455 of the manuscript, and the journal subeditors should confirm whether the authors intended to write 'Von Neumann's circuit geometries'.

A2: The name has been corrected.

Reviewer 3 Report

This manuscript addresses networks based on spatial-soliton-waveguide X-junctions, it draws the analogy with neuron networks, and shows that such junctions can perform various tasks, such as information memorization and recognition. The authors demonstrate theoretically that corresponding networks can be applied for 4-bit information processing. The manuscript is interesting and interdisciplinary. The authors utilize memory effect of photorefractive medium, since beams propagating in it can induce relatively long-living waveguides that can be modified by successively propagating excitations, the fact that is used for training of the induced network. I will be inclined to recommend publication provided that the authors adequately address the following concerns:

1. I think that the statement about photorefractive plasticity in the abstract is unclear and may appear misleading without additional explanation. I understand that the ability of structure to readjust under the action of signal that it receives is meant, but there is in general no such phenomenon as “photorefractive plasticity”. Please reformulate or extend this part of the abstract.
2. Complex networks and X-junctions optically induced in photorefractive materials were studied in the following papers: Optics Express 13, 1774 (2005); Optics Letters 30, 1180 (2005) and some other works. I suggest to extend discussion of this aspect in the introduction.
3. Line 98. Reference is missing.
4. It is necessary to discuss how operation and information encoding in the solitonic network is affected by unavoidable material losses, especially taking into account that the authors suggest to use crystals with edges, where total internal reflection occurs and part of the signal may be lost.
5. Please provide all parameters used in the model (10), including electro-optic coefficient, intensities, characteristic beam scales. One should also discuss how viable is the model for very narrow crystals (width of only 150 µm) considered here. Is the crystal biased?
6. The authors have to specify how exactly single or several input signal beams “train” the network and modify it. This apparently should include considerations based on the buildup of the field E_e in the crystal. Is nonlinearity involved in the buildup process, i.e. how exactly signal interacts with each junction? Does it propagate in linear or in nonlinear regime?
7. Photorefractive system has memory effect. This means that induced refractive index profile builds up during some time (several seconds?) and then gradually disappears (i.e. recorded structure is not permanent). In this respect, the information on how exactly training of the network was performed is needed (i.e. on which time scales the presented results remain valid).

Author Response

Before all, we would like to thank reviewer 3 because her/his comments were all appropriate and helped us to make the text clearer. Thank you.

 

Here the answers to the questions:

Q1: I think that the statement about photorefractive plasticity in the abstract is unclear and may appear misleading without additional explanation. I understand that the ability of structure to readjust under the action of signal that it receives is meant, but there is in general no such phenomenon as “photorefractive plasticity”. Please reformulate or extend this part of the abstract.

A1: It is true that the expression “photorefractive plasticity” does not exist but with this paper we intended to introduce such new concept. It is indeed also true that the abstract was somehow unclear: we thanks the reviewer for pointing out it. In the text we substitute the term “plasticity” with “nonlinearity” but we did introduce “photorefractive plasticity” at the end of the whole phare in brackets as explanation: < By exploiting photorefractive nonlinearity as if it were a biological neuroplasticity, the network modifies and adapts to the incoming signals, memorizing and recognizing them (photorefractive plasticity).>

 

Q2: Complex networks and X-junctions optically induced in photorefractive materials were studied in the following papers: Optics Express 13, 1774 (2005); Optics Letters 30, 1180 (2005) and some other works. I suggest to extend discussion of this aspect in the introduction.

A2: In the introduction section we added and contextualized some new references [12-16], those proposed by the reviewer and others (lines 60-61).

 

Q3: Line 98. Reference is missing.

A3: Reference has been added.

 

Q4: It is necessary to discuss how operation and information encoding in the solitonic network is affected by unavoidable material losses, especially taking into account that the authors suggest to use crystals with edges, where total internal reflection occurs and part of the signal may be lost.

A4: On this point we do not fully agree with the reviewer. Total reflection, contrarily to mirrors, gives perfectly 100% reflectivity. Thus, from the theoretical point of view, no losses should be considered, as we did. In practice, losses in solitonic total reflection are very low and usually only related to the surface roughness. This can be seen in the following papers:

• Jäger, S.P. Gorza, C. Cambournac, M. Haelterman, M. Chauvet, Sharp waveguide bends induced by spatial solitons, Appl. Phys. Lett. 88, 061117 (2006)
• Alonzo, C. Soci, M. Chauvet, E. Fazio, Solitonic waveguide reflection at an electric interface, Opt. Expr. 27(15), 20273-20281 (2019)
• Fazio, M. Alonzo and A. Belardini, Addressable Refraction and Curved Soliton Waveguides Using Electric Interfaces, Appl. Sci. 9, 347-1/10 (2019)

For this reason, total-reflection losses were not introduced in the text. We did introduce these references (23-25].

 

Q5: Please provide all parameters used in the model (10), including electro-optic coefficient, intensities, characteristic beam scales. One should also discuss how viable is the model for very narrow crystals (width of only 150 µm) considered here. Is the crystal biased?

A5:   We introduce the name of the nonlinear material as well as tab.5 with all the used parameters (lines 330-306). We also introduce further references where photorefractive solitons in 8 micron thick films are generated [27-29]. The crystal is indeed biased as in all photorefractive-soliton expt’s: it might occur with an external electric bias or applying a temperature gradient (pyroelectric bias) as in many recent papers.

 

Q6: The authors have to specify how exactly single or several input signal beams “train” the network and modify it. This apparently should include considerations based on the buildup of the field E_e in the crystal. Is nonlinearity involved in the buildup process, i.e. how exactly signal interacts with each junction? Does it propagate in linear or in nonlinear regime?

A6: To answer this questions we introduced new part in the text:< Signal beams are at a wavelength longer than the writing ones but still absorbed: as a consequence, signal beams are able to excite charges and to induce nonlinearity too, with lower efficiency due to the longer wavelength. Their propagation inside the soliton channels is indeed nonlinear in nature, reinforcing the nonlinear refractive index contrast of the used channel by means of an increasing of the local screening electric field. > (lines 355-360)

 

Q7: Photorefractive system has memory effect. This means that induced refractive index profile builds up during some time (several seconds?) and then gradually disappears (i.e. recorded structure is not permanent). In this respect, the information on how exactly training of the network was performed is needed (i.e. on which time scales the presented results remain valid).

A7: to explain such point, we have added a new brief paragraph in the text: paragraph 5.2 Materials and memorization, lines 462-479. In this paragraph we explain that different photorefractive media with different dielectric response time might have different kinds of application according to the needs: fast media for RAM purposes, slow media for ROM purposes. Moreover we introduce that with very thin films of photorefractive crystals, the written channels can be totally erased by light, a novelty that is now submitted for publication somewhere else.