Portland State University PDXScholar Student Research Symposium Student Research Symposium 2013 May 8th, 11:00 AM Training an Asymmetric Signal Perceptron in an Artificial Chemistry Peter Banda Portland State University Follow this and additional works at: https://pdxscholar.library.pdx.edu/studentsymposium Part of the Chemistry Commons Let us know how access to this document benefits you Banda, Peter, "Training an Asymmetric Signal Perceptron in an Artificial Chemistry" (2013) Student Research Symposium https://pdxscholar.library.pdx.edu/studentsymposium/2013/Poster/8 This Poster is brought to you for free and open access It has been accepted for inclusion in Student Research Symposium by an authorized administrator of PDXScholar Please contact us if we can make this document more accessible: pdxscholar@pdx.edu Training an Asymmetric Signal Perceptron in an Artificial Chemistry Peter Banda teuscher.:Lab | Department of Computer Science www.teuscher-lab.com | banda@pdx.edu | Portland State University Abstract Results Autonomous learning implemented purely by means of a synthetic chemical system has not been previously realized Learning promotes reusability, and minimizes the system design to simple input-output specification ASP is simpler since it requires just 12 species and 16 reactions as opposed to 14 species and 30 reactions required by WRP ASP employs the Runge-Kutta numerical integration of the rate differential equations, which produces a higher-precision concentration series In this poster, I present a simulated chemical system, the first full-featured implementation of a perceptron in an artificial (simulated) chemistry, which can successfully learn all 14 linearly separable logic functions A perceptron is the simplest system capable of learning inspired by the functioning of a biological neuron My newest model called the asymmetric signal perceptron (ASP) is, as opposed to its predecessors such as the weight-race perceptron (WRP), substantially simpler by exploiting asymmetric chemical arithmetics and is fully described by mass-action kinetics I suggest that DNA strand displacement could, in principle, provide an implementation substrate for my model, allowing the chemical perceptron to perform reusable, programmable and adaptable wet biochemical computing ASP learns by a more biologically plausible reinforcement method (penalty signal) ASP determines the output value by thresholding as opposed to the comparison of positive and negative output species concentrations ASP is transformable to the DNA-strand displacement primitives by Soloveichik’s method giving our symbolic species DNA-strand counterparts Problem and Approach Issues of biochemical computing: time-consuming and costly design, no reset, no reusability (hard-wired purpose), lacks programming paradigms ● I address these issues by introducing an artificial chemical machine capable of learning = chemical perceptron A perceptron inspired by the functioning of a biological neuron (Figure 1) ● Figure 2: Qualitative diagram WRP’s (left) and ASP's (right) reactions required for linear integration of inputs and weights Each node represents species, solid lines are reactions, and dashed green lines are catalyses Serves as a general template that can be trained to act as desired binary function Strict online (autonomous) learning; no external help needed ● Desired Output CONST0 NAND Figure 4: Mean and standard deviation of the 14 correct learning rate averages Each average corresponds to one linearly separable binary function, for which 104 runs were performed Desired Output Conclusion [Hebb, 1949] The first full-featured implementation of online learning in (simulated) chemistry called the chemical perceptron Inputs Weights Linear Integration Weights Output Inputs Learning as well as linear integration of weights are handled internally A chemical perceptron Outputs Figure 1: Model of a perceptron An activation function f processes the dot product of weights and inputs w · xT, producing output y During the learning process, the actual output y and the desired output d is compared, the error is fed back to the perceptron and triggers an adaptation of the participating weights • • NAND • Model • Two-input binary perceptron implemented in an unstructured artificial chemistry driven by mass-action or Michaelis-Menten kinetics ● Penalty Signal CONST0 Two models: ● • • Weight-race perceptron (WRP) – symmetric design, uses two species to represent and 1, learned by desired output (Figure (left)) Optimal rate constants found by genetic algorithms ● Operate in two modes: • ● Asymmetric Signal Perceptron (ASP) – asymmetric design, uses a single species with 0.5 threshold to represent and 1, learned by reinforcements (Figure (right)) ● • • Binary function mode – output molecules produced as a product of weightspecies driven catalysis; input molecules injected Learning mode (weight adaptation) – the concentration of weight species change as a result of discrepancy between actual and desired output; input and desired-output (or penalty signal) molecules injected (Figure 3) is reusable, since it recovers its internal ready state after each processing; both WRP and ASP versions learn successfully all 14 linearly-separable logic functions with correct rate of 100%; is robust to perturbations of rate constants that alleviates reaction-timing restrictions for real chemical implementation (using DNA-strand displacement technique); is implemented in artificial chemistry, but real chemistry extension possible (DNA strand displacement) → applications: chemical hardware abstraction (prog interface), ALIFE, spiders; and can serve as basis of programmable and adaptable wet chemical computing Next steps: random DNA circuits with complex dynamics, and Reservoir Computing Weights References Input Output Figure 3: Left: Qualitative diagram WRP’s (top) and ASP’s (top) reactions employed in the learning mode Each node represents a species, solid lines are reactions, and dashed lines are catalyses Right: Training of WRP (top) and ASP (bottom) to perform NAND function starting from the CONST0 setting Random inputs with desired output (or penalty signal) are repeatedly provided to circuits, and so the concentration of weight species are adapted towards required function Constant 0s gradually change to the NAND function outputs 1, 1, 1, [1] Banda, P., Teuscher, C., Lakin, M R.: Online learning in a chemical perceptron Artificial life 19(2) (2013) [2] Dittrich, P., Ziegler, J., Banzhaf, W.: Artificial chemistries - a review Artificial Life 7(3) (2001) 225– 275 [3] Hebb, D O.: The organization of behavior John Wiley & Sons, New York (1949) [4] Kim, J., Hopfield, J J., Winfree, E.: Neural network computation by in vitro transcriptional circuits In Advances in Neural Information Processing Systems Volume 17., MIT Press (2004) 681–688 [5] Soloveichik, D., Seelig, G., Winfree, E.: DNA as a universal substrate for chemical kinetics Proceedings of the National Academy of Sciences of the United States of America 107(12) (March 2010) 5393–5398 .. .Training an Asymmetric Signal Perceptron in an Artificial Chemistry Peter Banda teuscher.:Lab | Department of Computer Science www.teuscher-lab.com | banda@pdx.edu | Portland State... online learning in (simulated) chemistry called the chemical perceptron Inputs Weights Linear Integration Weights Output Inputs Learning as well as linear integration of weights are handled... species, solid lines are reactions, and dashed lines are catalyses Right: Training of WRP (top) and ASP (bottom) to perform NAND function starting from the CONST0 setting Random inputs with desired