Event Abstract Back to Event An agent-based neural computational model with learning Hideaki Suzuki1*, Hiroyuki Ohsaki2 and Hidefumi Sawai1 1 National Institute of Information and Communications Technology, Japan 2 Osaka University, Graduate School of Information Science and Technology, Japan As is well-known, a natural neuron is made up of a huge number of biomolecules from a nanoscopic point of view. A conventional `artificial neural network' (ANN) consists of nodes with static functions, but a more realistic model for the brain could be implemented with functional molecular agents which move around the neural network and cause a change in the neural functionality. One such network-based computational model with movable agents is `program-flow computing' [Suzuki 2008], in which programs (agents) move from node to node and bring different functions to CPUs (nodes). This model is also closely related to `active network' [TennenhouseWetherall 1996] which enables a router (node) to have various functions by delivering packets (agents) with encapsulated programs. Based upon these previous studies, recently, a novel network-based computational model named "Algorithmically Transitive Network (ATN)" was proposed by the authors [Suzuki et al. 2010]. The distinctive features of the ATN are: (1) [Calculation] A program is represented by a `data-flow network' like the `data-flow computer' [Sharp 1992]. (2) [Supervised Learning] After the calculation, triggered from the teaching signals, the network propagates differential coefficients of the energy function backward and adjusts node parameters. (3) [Topological Reformation] The network topology (algorithm) can be modified or improved during execution through conducting programs of movable agents. As in the data-flow computer, the ATN's calculation is propelled by the nodes reading the input `tokens' on their incoming edges, firing, and creating the output tokens on their outgoing edges. Table 1 lists up arithmetic/logic functions a node operation can have. The firing produces not only the arithmetic value X but also the logic (regulating) value R which represent the probability of the token itself existing in the network. Note that for the backward propagation, all the X and R's functions have differentiable formulas: sig(z)=1/(1+exp(-z)) and delta(z)=4sig(z)sig(-z). v in node 'c', s in node 'C', and b in judging nodes are node parameters adjusted by the learning. The learning begins with the evaluation of an energy function at the answer nodes. This causes backward propagation of differential coefficients of the energy function with respect to token variables or node parameters. After the differential coefficients are obtained for all the constant and judging nodes, we revise the node parameters using the steepest descent method. To ensure the convergence of this learning, we also formulate a formula for the learning coefficient (eta). After this, the topological reformation takes place. We prepare six different agents that simplify or complexify the network. The operations create/delete nodes and edges, and renovate the network's algorithm based on the information accumulated during the learning. To demonstrate the learning capability, the ATN is applied to some symbolic regression problems. Figure 1 shows a representative result for a one-variable quadratic function. In this experiment, we have 6 nodes and 12 agents at first (Fig. 1(a)), but after 80,000 time steps (about 800 forward- and backward propagation), we finally have a 39-node 158-agent network (Fig. 1(b)). Figure 1(c) shows the change of the sensor-answer (input-output) plot during this run. We can see from this figure that the final function of the ATN perfectly agrees with the target function. Using the same parameter setting, we also conducted ten different runs, out of which nine runs succeeded in finding desirable functions. Now we are refining and generalizing the model by incorporating such various program elements as conditional branch, loop, and so on.