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Distributed representations accelerate evolution of adaptive behaviours.

Stone JV - PLoS Comput. Biol. (2007)

Bottom Line: Using linear neural network models, it is proved that if skills are stored as distributed representations, then within-lifetime learning of part of a skill can induce automatic learning of the remaining parts of that skill.More importantly, it is shown that this "free-lunch" learning (FLL) is responsible for accelerated evolution of skills, when compared with networks which either 1) cannot benefit from FLL or 2) cannot learn.Specifically, it is shown that FLL accelerates the appearance of adaptive behaviour, both in its innate form and as FLL-induced behaviour, and that FLL can accelerate the rate at which learned behaviours become innate.

View Article: PubMed Central - PubMed

Affiliation: Psychology Department, Sheffield University, Sheffield, United Kingdom. j.v.stone@shef.ac.uk

ABSTRACT
Animals with rudimentary innate abilities require substantial learning to transform those abilities into useful skills, where a skill can be considered as a set of sensory-motor associations. Using linear neural network models, it is proved that if skills are stored as distributed representations, then within-lifetime learning of part of a skill can induce automatic learning of the remaining parts of that skill. More importantly, it is shown that this "free-lunch" learning (FLL) is responsible for accelerated evolution of skills, when compared with networks which either 1) cannot benefit from FLL or 2) cannot learn. Specifically, it is shown that FLL accelerates the appearance of adaptive behaviour, both in its innate form and as FLL-induced behaviour, and that FLL can accelerate the rate at which learned behaviours become innate.

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Network Fitness Error FunctionThe response of the network to a given input vector x is y = w · x. Given a desired (target) output d, the solid curve shows how the fitness penalty D for an incorrect response increases sharply (to unity) if the magnitude of the difference e = y − d is greater than 0.1 (i.e., if e2 > 0.01). For comparison, the quadratic error function e2 = (y − d)2, which is minimised during learning, is shown as a dashed curve. The range of e-values shown are typical for the simulations reported here. See Methods section for details.
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pcbi-0030147-g003: Network Fitness Error FunctionThe response of the network to a given input vector x is y = w · x. Given a desired (target) output d, the solid curve shows how the fitness penalty D for an incorrect response increases sharply (to unity) if the magnitude of the difference e = y − d is greater than 0.1 (i.e., if e2 > 0.01). For comparison, the quadratic error function e2 = (y − d)2, which is minimised during learning, is shown as a dashed curve. The range of e-values shown are typical for the simulations reported here. See Methods section for details.

Mentions: Networks that exhibited high levels of FLL were preferentially selected for mating. Only associations A2 were learned, but the fitness of each network depended on its performance on both the learned associations A2 and on the unlearned associations A1. The fitness FFLL(K) of the Kth network is defined in terms of its innate performance error Epre on A = A1 ∪ A2, and on its performance error Epost on A after learning A2:where Epre and Epost are:where and are the network's output errors in response to the ith input vector before and after learning A2 (respectively). The parameter c = 0.05 defines the balance between performance error on innate versus post-learning (e.g., FLL-induced) behaviours, and is interpreted as a cost-of-learning parameter (see below). The network's fitness error Di is a function of the difference ei = yi − di between the network's response yi to the ith input vector and the desired output value di:This ensures that output errors above Dthresh have a disproportionately large and detrimental effect on fitness, as shown in Figure 3. This, in turn, ensures that only those networks with “good” performance are likely to be selected for reproduction. The value of Dthresh was set to 0.01.


Distributed representations accelerate evolution of adaptive behaviours.

Stone JV - PLoS Comput. Biol. (2007)

Network Fitness Error FunctionThe response of the network to a given input vector x is y = w · x. Given a desired (target) output d, the solid curve shows how the fitness penalty D for an incorrect response increases sharply (to unity) if the magnitude of the difference e = y − d is greater than 0.1 (i.e., if e2 > 0.01). For comparison, the quadratic error function e2 = (y − d)2, which is minimised during learning, is shown as a dashed curve. The range of e-values shown are typical for the simulations reported here. See Methods section for details.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC1937014&req=5

pcbi-0030147-g003: Network Fitness Error FunctionThe response of the network to a given input vector x is y = w · x. Given a desired (target) output d, the solid curve shows how the fitness penalty D for an incorrect response increases sharply (to unity) if the magnitude of the difference e = y − d is greater than 0.1 (i.e., if e2 > 0.01). For comparison, the quadratic error function e2 = (y − d)2, which is minimised during learning, is shown as a dashed curve. The range of e-values shown are typical for the simulations reported here. See Methods section for details.
Mentions: Networks that exhibited high levels of FLL were preferentially selected for mating. Only associations A2 were learned, but the fitness of each network depended on its performance on both the learned associations A2 and on the unlearned associations A1. The fitness FFLL(K) of the Kth network is defined in terms of its innate performance error Epre on A = A1 ∪ A2, and on its performance error Epost on A after learning A2:where Epre and Epost are:where and are the network's output errors in response to the ith input vector before and after learning A2 (respectively). The parameter c = 0.05 defines the balance between performance error on innate versus post-learning (e.g., FLL-induced) behaviours, and is interpreted as a cost-of-learning parameter (see below). The network's fitness error Di is a function of the difference ei = yi − di between the network's response yi to the ith input vector and the desired output value di:This ensures that output errors above Dthresh have a disproportionately large and detrimental effect on fitness, as shown in Figure 3. This, in turn, ensures that only those networks with “good” performance are likely to be selected for reproduction. The value of Dthresh was set to 0.01.

Bottom Line: Using linear neural network models, it is proved that if skills are stored as distributed representations, then within-lifetime learning of part of a skill can induce automatic learning of the remaining parts of that skill.More importantly, it is shown that this "free-lunch" learning (FLL) is responsible for accelerated evolution of skills, when compared with networks which either 1) cannot benefit from FLL or 2) cannot learn.Specifically, it is shown that FLL accelerates the appearance of adaptive behaviour, both in its innate form and as FLL-induced behaviour, and that FLL can accelerate the rate at which learned behaviours become innate.

View Article: PubMed Central - PubMed

Affiliation: Psychology Department, Sheffield University, Sheffield, United Kingdom. j.v.stone@shef.ac.uk

ABSTRACT
Animals with rudimentary innate abilities require substantial learning to transform those abilities into useful skills, where a skill can be considered as a set of sensory-motor associations. Using linear neural network models, it is proved that if skills are stored as distributed representations, then within-lifetime learning of part of a skill can induce automatic learning of the remaining parts of that skill. More importantly, it is shown that this "free-lunch" learning (FLL) is responsible for accelerated evolution of skills, when compared with networks which either 1) cannot benefit from FLL or 2) cannot learn. Specifically, it is shown that FLL accelerates the appearance of adaptive behaviour, both in its innate form and as FLL-induced behaviour, and that FLL can accelerate the rate at which learned behaviours become innate.

Show MeSH