THE HOPFIELD AND KOHONEN NETWORKS: AN IN VIVO TEST

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1 THE HOPFIELD AND KOHONEN NETWORKS: AN IN VIVO TEST Rita Pizzi 1, Andrea Fantasia 1, Danilo Rossetti 1, Giovanni Cino 1, Fabrizio Gelain 2 and Angelo Vescovi 2 1 Department of Information Technologies, University of Milan, via Bramante Crema (CR) Italy, pizzi@dti.unimi.it - 2 Stem Cells Research Institute DIBIT San Raffaele, via Olgettina Milano Italy Abstract: In the frame of a collaboration between Department of Information technology of the University of Milan and Stem Cells Research Institute of the DIBIT- San Raffaele, Milan, learning methods are under study following known models of the Artificial Neural Networks on human neural stem cells cultured on MEA (Multielectrode Arrays) support. The MEAs are constituted by a glass support where a set of tungsten electrodes are inserted to form a lattice structured by our group following the artificial Hopfield and Kohonen models. In such a way it is possible to electrically stimulate the neurons and to record their reaction, opening the possibility to verify in vivo learning models of the Artificial neural Networks. Neurons are stimulated with digital patterns constituted by bursts of different voltages at the input electrodes, and the electrical output generated by the neurons is analyzed with advanced methods in order to highlight organized answers by the natural neural network. The experiments performed up to now show how neurons react selectively to different patterns and show similar reactions in front of the presentation of identical or similar patterns. These results suggest the possibility of using the learning capabilities of these hybrid networks in different application fields, in particular in bionic applications. Keywords: Neural Networks, Stem Cells, Learning, Microelectrode Arrays.

2 The Hopfield and Kohonen Networks: an in vivo test Introduction During the last decade several experiments have been performed on the interfacing between electronic devices and biological neurons, in order to develop useful tools for the neurophysiological research and to build the technological bases for future bioelectronic prostheses, bionic robots and biological computers. As microelectrodes implanted directly into brain give rise to infections, scientist are experimenting the direct attachment of neurons to conductive material. Important results have been achieved by groups of the Max Planck Institute [Fromherz et al., 1991], the Georgia Tech [Lindner and Ditto, 1996], the Northwestern and Genoa University [Reger et al., 2000] and the Caltech [DeMarse et al., 2002]. Aim of our group is to develop architectures based on Artificial Neural Networks (following in particular the Hopfield and Kohonen models) using human neurons adhering to a glass support endowed with microelectrodes (MEA). The MEAs are connected to a PC by means of a standard acquisition card and custom hardware that allow both to stimulate the neurons and to record the voltages generated by the neurons, allowing to monitorize the electrical activity of the neural network after the pattern stimulation. In such a way we are able to investigate the learning capabilities of networks of biological neurons and the possible technological applications of such hybrid architectures. 2. Materials and Methods The problem of the adhesion between neurons and electrodes is crucial: materials have to be biocompatible and neurons must adhere firmly to the MEA electrodes in order to obtain the maximum local conductivity. Our MEAs are glass disks with 90 nickel-tungsten electrodes whose diameter is around 10 µ. The mean distance between electrodes is 70 µ (Fig. 1). In such a way we should have approximately one neuron for each electrode. The MEA is connected to the PC via an USB acquisition card (IOTech Personal DAQ/56).

3 The Hopfield and Kohonen Networks: an in vivo test 3 Figure 1. MEA s structure Our neurons are adult cells cultured by indifferentiated stem cells [Vescovi et al., 1999]. In our experiments the electrodes have been connected following two theoretical models: - A Kohonen Self-organizing Map [Kohonen, 1990], composed by an input layer and a competitive layer connected following the standard architecture. In the Kohonen models, as known, the classification capability is carried out by means a competition between neurons. - A Hopfield Network [Hopfield, 1984], where the set of input electrodes coincides with the set of output electrodes. In the theoretical model, learning takes place when the network stabilizes in an equilibrium configuration and memories are placed in the local minima of the energy landscape. The choice of these models is due both to their architecture, easy to implement on MEAs, and to their resemblance to neurophisiological structures, often highlighted by their authors [Kohonen, 1990], [Hopfield, 1984]. The next step was to realize two hybrid networks able to discriminate simple patterns. A software simulation showed that the minimum configurations able to recognize two different patterns, "zero" and "one", pure or affected by noise, formed each one by 8 bits, were 1) a Kohonen networks with 8 input neurons and 3 output neurons and 2) a Hopfield networks with 8 input/output neurons. These networks have been implemented on the MEAs, culturing the stem cells on the connection sites and structuring the networks correctly by means of hardware connections (Fig.2). The input patterns are converted into suitable electrical stimuli (similar to the biological action potentials at 40 Hz ) by a custom hardware device. The output signals are also sampled at 40 Hz. These choices have been made on the basis of neurophysiological considerations. In fact several studies seem

4 The Hopfield and Kohonen Networks: an in vivo test 10 to confirm that signals related to the most advanced CNS activities (perception, cognition, conscience) synchronize around 40 Hz [Menon and Freeman, 1996]. Figure 2. Kohonen (left) and Hopfield (right) architecture on MEA In order to be sure that the recorded signals were actually coming from the electrical neural activity, we compared the reaction of a MEA containing only culture liquid with the electrical activities of the MEA with living cells (Fig. 3). It is evident that the neurons reply to a zero pattern, formed by the highest voltage (all the 8 electrodes on ), emitting the lowest voltage (green circles in figure), whereas the culture liquid, as expected by a conductive medium, answers to the zero pattern with a high voltage (Fig. 4). Figure 3. Electrical signals from neurons

5 The Hopfield and Kohonen Networks: an in vivo test 5 Figure 4. Electrical signals from the culture liquid Fig. 5 shows the reaction of the Kohonen network after the stimulation with zero patterns pure or affected by noise (green circles) and with one patterns pure or affected by noise (red circles). Similar effects have been shown even by the Hopfield network. Figure 5. Electrical signals from neurons stimulated with different patterns: zero (green circles) and one (red circles) A training phase has been carried out on the networks by stimulating them repeatedly with all the patterns, pure and affected by noise. At the end of the experiments we recorded the neural activities in order to ascertain the presence of permanent learning. Differently from the culture liquid, that shows the same kind of behavior before and after the stimulations, the MEAs with neurons show significant differences in their electrical activities.

6 The Hopfield and Kohonen Networks: an in vivo test 10 The recorded activities have been analyzed by means of Recurrence Quantification Analysis (RQA) [Zbilut and Webber, 1992]. Such non-linear analysis tool elaborates the signal time series in a multidimensional space, that is the phase space of the dynamical system represented by the neural network signals. Recurrent Plots show how the vectors in the phase space are near or distant each others. All the distances between the vector pairs are calculated and translated into colour bands. Hot colours (yellow, red, orange) are associated to short distances, cold colours (blue, black) show long distances. Signals repeating fixed distances between vectors are organized, signals with random distances are not. In this way we obtain uniform colour distribution of random signals, whereas deterministic and self-similar signals show structured plots with wide colour bands. Our RQA analysis of the neural activity lead to interesting results: after the training, signals coming from the reply to similar patterns form similar Recurrent Plots. In the following figures we can see the self-organization of a single output channel (corresponding to a specific electrode/neuron) before stimulation, during training and after training as a reply of a specific pattern. Fig. 6a shows a Kohonen output channel before stimulation. The plot is not structured and show lack of self-organization. Figure 6a. RQA plot of a Kohonen output channel before stimulation The training phase generates a change in the plots structure. The plot of the same channel after the training phase (fig. 6b) shows wide uniform colour bands corresponding to high self-organization. The band width grows in time during the training.

7 The Hopfield and Kohonen Networks: an in vivo test 7 Figure 6b. RQA plot of a Kohonen output channel after training Fig. 7a shows the answer after stimulation with zero pattern and Fig. 7b shows the same output after stimulation with one pattern. The plots show that the network behaves differently depending on the stimulation pattern. Figure 7a.RQA plot after stimulation with zero pattern

8 The Hopfield and Kohonen Networks: an in vivo test 10 Figure7b. RQA plot after stimulation with one pattern We applied the same procedure to the output signals coming from the Hopfield network, obtaining the same kind of reactions. 3. Discussion and Conclusions After a qualitative analysis of the output signals we can reasonably affirm that stimulation with organized electrical patterns modifies the system and improves the system information suggesting a kind of learning and memorization. The neural networks show, after a training stage constituted by iterated stimulation with different patterns, an organized behavior and the capability of reacting selectively to different patterns. Besides, similar patterns make the neurons react in similar manner. Thus the neurons show a form of selective coding, highlighting a strong and lasting self-organization as a reply of stimulation. In the future we will improve both the cell culture on MEA and the measuring and interfacing tools and the analysis methods. We will also increase the connections between MEAs and PC in order to implement more complex networks. At the moment we are carrying on experiments with more complex patterns and new kinds of analysis of the output signals. In particular, we are using the ITSOM Artificial neural network [Pizzi et al., 2002] in order to codify the output and to discriminate the neural response. Our first results are encouraging, confirming the possibility of discriminating different patterns by means of different binary strings, coming out from the artificial network that elaborates the biological signal output. In this way it will be possible to use the neural replies in several ways, from robotics to biological computation to neuro-electronic prostheses.

9 The Hopfield and Kohonen Networks: an in vivo test 9 Our new experiment, with a much faster acquisition card and a more advanced custom hardware, is designed to implement a real actuator. We will stimulate with simple commands the hybrid network system, the biological network will reply with a train of signals that the artificial network will codify in binary string that will pilot a minirobot. Acknowledgements We are indebted to Prof. Degli Antoni (University of Milan) for his precious suggestions and encouragement, and with ST Microelectronics for the financial support. References Fromherz, P., Schaden, H., Vetter, T. (1991), Neuroscience,129: Lindner, J. F., Ditto, W. (1996), Exploring the nonlinear dynamics of a physiologically viable model neuron, AIP Conf. Proc. 375(1): 709. Reger, B., Fleming, K.M., Sanguineti, V., Simon Alford, S., Mussa Ivaldi, F.A. (2000), Connecting Brains to Robots: The Development of a Hybrid System for the Study of Learning in Neural Tissues, Artificial Life VII, Portland, Oregon. DeMarse, T.B., Wagenaar, D.A., Potter, S.M. (2002), The neurallycontrolled artificial animal: a neural-computer interface between cultured neural networks and a robotic body, SFN 2002, Orlando, Florida. Vescovi., A.L., Parati, E.A., Gritti, A., Poulin, P., Ferrario, M., Wanke, E., Frölichsthal-Schoeller, P., Cova, L., Arcellana-Panlilio, M., Colombo, A., and Galli, R. (1999), Isolation and cloning of multipotential stem cells from the embryonic human CNS and establishment of transplantable human neural stem cell lines by epigenetic stimulation., Exp. Neurol. 156: Kohonen, T. (1990), Self-Organisation and Association Memory, Springer Verlag. Hopfield, J.J. (1984), Neural Networks and Physical Systems with Emergent Collective Computational Abilities, Proc. Nat. Acad. Sci USA, 81. Menon, V., Freeman, W.J. (1996), Spatio-temporal Correlations in Human Gamma Band Electrocorticograms, Electroenc. and Clin.. Neurophys. 98, Zbilut, J.P., Webber, C.L. (1992), Embeddings and delays as derived from quantification of recurrent plots, Phys. Lett. 171.

10 The Hopfield and Kohonen Networks: an in vivo test 10 Pizzi, R., de Curtis, M., Dickson, C. (2002), Evidence of Chaotic Attractors in Cortical Fast Oscillations Tested by an Artificial Neural Network, in: Advances in Soft Computing, J. Kacprzyk ed., Physica Verlag.