Neuromazes: 3-Dimensional Spiketrain Processors

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1 Neuromazes: 3-Dimensional Spiketrain Processors ANDRZEJ BULLER, MICHAL JOACHIMCZAK, JUAN LIU & ADAM STEFANSKI 2 Human Information Science Laboratories Advanced Telecommunications Research Institute International (ATR) Hikaridai, Keihanna Science City, Kyoto JAPAN Abstract: - Neuromazes are pulsed neural networks synthesized in a 3-dimensional cellular space. They are being developed for the artificial brains of future generation robots. In neuromazes there are two processing elements: dendrite-cells that return a pulse at clock t if one and only one pulse entered it at clock t- and threshold-cells that return a pulse at clock t if its counter was 2 or more at clock t-. At every clock t the weighted sum of pulses that entered the threshold-cell at clock t- is added to the discharged or not discharged counter. The weights can be or or. Every cell receives pulses from k defined neighbors and sends pulses to up to 6-k defined neighbors (k 6). We present NeuroMaze TM 3. Pro a software tool for rapid prototyping of neuromaze-based modules for artificial brains. Some related designs are presented here. Key-Words: - Pulsed Neural Networks, Cellular Automata, Artificial Brain, Discrete Control Systems, Robots Introduction Neuromazes are pulsed para-neural networks synthesized in a 3-dimensional cellular space [][3]. We are developing them for the artificial brains of future generation robots. One day we may have to put an entire brain inside a robot s head. In this case, a general-purpose microprocessor and memories loaded with unnecessary libraries may be wasteful of space. Neuromazes will occupy less space since they employ only as many elements as truly necessary. Neuromazes employ two kinds of processing elemets: dendrite-cells (D-cells) and threshold-cells (T-cells). Every D-cell returns a pulse at clock t if and only if the weighted sum of pulses returned by the cell s neighbors at clock t- was equal to. The weights can be or. Every T-cell returns a pulse at clock t if its counter was 2 or more at clock t-. The value of the counter at clock t- is sum of a discharged or not discharged value of the counter at clock t-2 and the weighted sum of pulses returned by the cell s neighbors at clock t-2. The counter discharges at clock t if its value at clock t was beyond (-6; ). The weights can be or or. Every cell can receive pulses from k neighbors defined by its non-zero weights and send pulses to up to 6-k neighbors (k 6) defined by their non-zero cells. In 2-dimensional schemes we show the cells as squares, where transparent or black-filled triangle symbolizes a weight equal to or, respectively. T-cells on the schematics contain a number indicating the state of the counter (Figure ). The simplest neuromazes can be built of D-cells only (Figures 2 and 3). a. b. Figure. Examples of neuromaze processing cells. (a) D-cell with weights related to its Western neighbor and Northern neighbor equal to. (b) T-cell with weights related to its Western neighbor and Southern neighbor equal to and the weight related to its Eastern neighbor equal to. Practical neuromazes may consist of millions of D- cells and T-cells. The data they process is represented by spike-trains. Since the pulses in neuromazes have always the same amplitude, the information can be processed via frequency modulation, phase modulation, or special manipulations on spike sequences. On leave from Gdansk University of Technology, Poland 2 On leave from Simon Fraser University, Vancouver, Canada

2 t= t=2 t=4 t= t=3 t=5 much time to meet assumed requirements. Second, the geometrical constraints may cause difficulties in organization of desired interconnections between sub-structures. The solution currently investigated is based on the idea that the desired neuromaze consists of modules of cells and appropriate inputs/outputs of the modules are connected using ordinary wires. t= Figure 2. Neuromaze-style oscillator 2 Simple neuromazes Simple neuromazes are devices built using only a few processing cells and performing elementary operations on spikes or spiketrains. As illustrating examples we provide: an Eeckhaut gate (Figure 3), a frequency divider (Figure 4), and a phase shifter (Figure 5). t= t=2 t=4 2 x u t=5 t=6 y Figure 3. Eeckhaut gate. Let us assume that if a cell at a given clock returns a pulse, it is in the state, while a cell that at a given clock does not returns a pulse is in the state. Let the states of cells labeled x, y and u at clock t be denoted x t, y t, and u t, respectively. In this gate, u t+3 always equals the Boolean product of x t and y t. H. Eeckhaut & J. Van Campemhout [2] showed that all sixteen Boolean functions of two variables, as well as a 2-to- multiplexer can be built as a planar all-d-cell neuromaze. 3 Brain-building blocks Let us consider an idea of a very large-scale neuromaze occupying a space of billions cells. Such structure has two important shortcomings. First, pulse propagation across the structure may take too t=7 Figure 4. The T-cell with a single positive weight serves as a frequency divider. Indeed, for every two incoming pulses it returns only one pulse. The number shows the counter s state. NeuroMaze TM 3. Pro (see Figure 8) is a dedicated software tool for rapid prototyping of large-scale pulsed neural networks. Modules can be handcrafted layer-by-layer, synthesized with standard neural structure library, or imported from existing files. To simplify and speed up the design procedure, it provides a heuristic function for automatic creation of axonic paths. Modules are interconnected by signal channels between input/output cells and can be distributed in hundreds of stations. A designer may observe the pulse propagation in 2-D or 3-D mode, and record the procedure for further investigation [5].

3 t= t= States of cells can also be probed by editing the watch list and the stimulus spiketrain list. The prototypes created under NeuroMaze TM 3. Pro can be run on a PC, as well as on several types of dedicated hardware developed at ATR International, Kyoto. Hardware such as ATR s CAM-Brain Machine (CBM) [4] has been designed to support up to 74,465,28 of these pulsed neurons. The space of cells appeared sufficient to host a number of useful neuromazes, as for example an Inverter (Figure 6a), Learning Switch (Figure 6b), or a paw-movement module for a animal-shape robot (Figure 7ab). t=2 a. t=3 2 b. t=4 t=5 t=6 Figure 5. Phase shifter Figure 6. Neuromaze modules. (a) 8-Clock-Spiketrain Inverter converts the spiketrain p p...p 7 into p 7 p 6...p (in the presented case into ). (b) Learning switch that establishes connections between each of its 8 inputes and one of its 6 outputs based on reward and punishment. In this 3-dimensional picture every single-door S-cell is shown as a short blue pipe that is highlighted when it returns a pulse.

4 a. Acknowledgements This research was conducted as a part of the Research on Human Communication supported by the Telecommunications Advancement Organization of Japan (TAO). A. Stefanski s work was made possible owing to the Co-op Japan Program. b. Figure 7. Animal-shape Robot using neuromaze for motor torque control. (a) RobokoNeko with a raised paw ready to hit a ball (b) Control module for the right paw torque to raise the paw (built under NeuroMaze TM 3. Pro) 4 Concluding remarks It has been shown that neuromazes, using D-cells and T-cells, can simulate any and all Boolean functions. Furthermore, the pulses from neuromazes can be used to simulate both linear and non-linear functions, such as the required motor torque control for a robot. Currently, research is being conducted in order to make neuromazes evolvable. With evolvability, neuromaze artificial brains will enable future generation robots to learn and develop emergent thought. Note: The student version of the NeuroMaze TM 3. Pro with a User s Guide can be downloaded from References [] Buller A. CAM-Brain Machines and Pulsed Para-Neural networks: Toward a hardware for future robotic on-board brains, Proceedings of the Eight International Symposium on Artificial Life and Robotics, Oita, Japan, pp , January 24-26, 23. [2] Eeckhaut H. and Van Campenhout J Handcrafting Pulsed Neural Networks for the CAM-Brain Machine, Proceedings of the Eight International Symposium on Artificial Life and Robotics, Oita, Japan, pp , January 24-26, 23. [3] Jelinski D. and Joachimczak M Heuristicbased Computer Aided Synthesis of spatial β- type Pulsed Para-Neural Networks (3Dβ PPNNs), Proceedings of the Eight International Symposium on Artificial Life and Robotics, Oita, Japan, pp , January 24-26, 23. [4] Korkin M., Fehr G. and Jeffrey G. Evolving hardware on a large scale, Proceedings, The Second NASA/DoD Workshop on Evolvable Hardware, Pasadena, IEEE Comput. Soc., pp. 73-8, July 2. [5] Liu J. NeuroMaze TM. User s Guide, Version 3.. ATR Human Information Science Labs., Kyoto, Japan, 22.

5 Figure 8. NeuroMaze TM 3. Pro a tool for computer aided design of modular neuromazes. A given module can be handcrafted layer-by-layer and its 3-D view and pulse propagation immediately observed in special windows. A designer can use a library of standard structures, as well as heuristics for creation of axonic paths. Millions of interconnected modules can be distributed in hundreds of stations.