| R. J. Williams. Adaptive State Representation and Estimation Using Recurrent Connectionist Networks, chapter 4, pages 97--114. MIT Press, Cambridge, MA, 1990. |
.... the task requires the network to organize its internal state space such that it represents both continuous information (cart and pole velocities) and discrete information (mode of operation) Both this requirement and the requirement to remember information indefinitely have been described by Williams (1990) as examples that illustrate the promise of recurrent neural networks for control. It is hard to see how either a system based on traditional control theory (which is mainly concerned 14 with continuous systems, and which uses fixed size history windows) or a system based on traditional ....
Williams, R. J. (1990). Adaptive state representation and estimation using recurrent connectionist networks. In W. T. Miller, R. S. Sutton, & P. J. Werbos (Eds.), Neural networks for control. Cambridge, MA: MIT Press.
....for insects, with vast amounts of information coming in from their eyes, to use reactive strategies such as they are reputed to employ; but if one is trying to employ sparse data effectively to solve a simple task or rich data to solve a complex task then some kind of memory is called for. Williams 1990 suggests three classes of solution to this problem 2 . Two involve the use of tapped delay lines to make information about the past available to the model in the most direct way; but he comes down firmly on the side of the third, radical approach: the use of partially recurrent ....
....off from a wall and then immediately driving forwards into it again (cf. 4) If the model is to make helpful predictions in these cases, it needs some context information. History Models Perhaps the simplest form of context information is a history of what the robot has recently seen Williams 1990 s tapped delay line on the model s input. Here we consider only one step histories: in the notation of this paper, c t = v t 1 a t 1 ( means concatenation) The model 10 should now be able to make an appropriate warning prediction in situation (4) since it knows that the robot s ....
Williams 1990. Adaptive State Representation and Estimation Using Recurrent Connectionist Networks, in Miller, Sutton & Werbos 1990, p. 97.
....of the algorithm on problems from language induction to search and collection. The various parameter values for the program are set as described above unless otherwise noted. 4. 1 Williams Trigger Problem As an initial test, GNARL induced a solution for the enable trigger task proposed in [39]. Consider the finite state generator shown in Figure 5. At each time step the system receives two input bits, a, b) representing enable and trigger signals, respectively. This system begins in state S 1 , and switches to state S 2 only when enabled by a=1. The system remains in S 2 until it ....
....= population generations population 50 of the population removed each generation, giving 50 118 50 0.5 = 3000 network evaluations for this trial. a=1 output 0 a=0 b=0 b=1 output 1 S 1 S 2 Start output 0 output 0 Figure 5. An FSA that defines the enable trigger task [39]. The system is given a data stream of bit pairs (a 1 , b 1 ) a 2 , b 2 ) and produces an output of 0 s and 1 s. To capture this system s input output behavior, a connectionist network must learn to store state indefinitely. The Ohio State University January 17, 1996 12 increases ....
R. J. Williams, Adaptive State Representation and Estimation Using Recurrent Connectionist Networks, chapter 4, pages 97--114. MIT Press, Cambridge, MA, 1990.
....their internal state representation is adaptive rather than fixed, they can form delay line structures when necessary while also being able to create flip flops or other memory structures capable of preserving state over potentially unbounded periods of time. This point has been emphasized in (Williams, 1990) and similar arguments have been made by Mozer (1989; chapter , this volume] There are a number of possible reasons to pursue the development of learning algorithms for recurrent networks, and these may involve a variety of possible constraints on the algorithms one might be willing to ....
....a single processor machine were also compared. It was found that BPTT(9) ran 28 times faster on this task than RTRL, while RTRL(4) ran 9.8 times faster than RTRL. 11 For these studies the variant in which past weight values are stored in the history buffer was used. In another set of studies (Williams Peng, 1990), BPTT(16;8) was found to succeed as often as BPTT(9) on this task, while running twice as fast. 12 Note that BPTT(16;8) is thus well over 50 times faster than RTRL on this task. Insert Table 1 about here. ....
Williams, R. J. (1990). Adaptive state representation and estimation using recurrent connectionist networks. In: W. T. Miller, R. S. Sutton, & P. J. Werbos (Eds.) Neural Networks for Control. Cambridge: MIT Press/Bradford Books.
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R. J. Williams. Adaptive State Representation and Estimation Using Recurrent Connectionist Networks, chapter 4, pages 97--114. MIT Press, Cambridge, MA, 1990.
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