Improving a Network Generalization Ability by Selecting Examples

Kinzel, Wolfgang; Ruján, P.

doi:10.1209/0295-5075/13/5/016

Cited by 107 publications

(58 citation statements)

References 6 publications

(3 reference statements)

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“…At fixed B, the relevant quantities which describe the progress of learning for a perceptron are the normalized scalar products (Vallet 1989;Kinzel and Rujan 1990;Opper et al 1990;Biehl and Riegler 1994) …”

Section: Discussionmentioning

confidence: 99%

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Learning with incomplete information and the mathematical structure behind it

Kühn

Stamatescu

2007

Biol Cybern

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We investigate the problem of learning with incomplete information as exemplified by learning with delayed reinforcement. We study a two phase learning scenario in which a phase of Hebbian associative learning based on momentary internal representations is supplemented by an 'unlearning' phase depending on a graded reinforcement signal. The reinforcement signal quantifies the success-rate globally for a number of learning steps in phase one, and 'unlearning' is indiscriminate with respect to associations learnt in that phase. Learning according to this model is studied via simulations and analytically within a student-teacher scenario for both single layer networks and, for a committee machine. Success and speed of learning depend on the ratio lambda of the learning rates used for the associative Hebbian learning phase and for the unlearning-correction in response to the reinforcement signal, respectively. Asymptotically perfect generalization is possible only, if this ratio exceeds a critical value lambda( c ), in which case the generalization error exhibits a power law decay with the number of examples seen by the student, with an exponent that depends in a non-universal manner on the parameter lambda. We find these features to be robust against a wide spectrum of modifications of microscopic modelling details. Two illustrative applications-one of a robot learning to navigate a field containing obstacles, and the problem of identifying a specific component in a collection of stimuli-are also provided.

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Section: Discussionmentioning

confidence: 99%

“…The remainder of the analysis follows standard online learning reasoning (Vallet 1989;Kinzel and Rujan 1990;Biehl and Riegler 1994); it consists (i) in noting that for all finite bag sizes L the single-bag increments of the order parameters in (13) and (14) are infinitesimal in the thermodynamic limit N → ∞,…”

Section: Discussionmentioning

confidence: 99%

Learning with incomplete information and the mathematical structure behind it

Kühn

Stamatescu

2007

Biol Cybern

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“…But the partners can influence the local field. Instead of using random inputs, they are able to select input vectors with a fixed |h k | (queries [12]) in their own hidden units. This essentially modifies the functional dependency between overlap ρ k and frequency of repulsive steps p r .…”

Section: Queriesmentioning

confidence: 99%

Neural cryptography with queries

2005

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Abstract. Neural cryptography is based on synchronization of tree parity machines by mutual learning. We extend previous key-exchange protocols by replacing random inputs with queries depending on the current state of the neural networks. The probability of a successful attack is calculated for different model parameters using numerical simulations. The results show that queries restore the security against cooperating attackers. The success probability can be reduced without increasing the average synchronization time.

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“…The usefulness of the TL lies in the possibility of transforming the stochastic difference equations into a closed set of deterministic differential equations (Kinzel & Ruján, 1990;Kinouchi & Caticha, 1992a). The idea is to choose a continuous time scale α such that for the TL regime p/N → α, where p is the number of examples already presented.…”

Section: Emergence Of the Macroscopic Dynamicsmentioning

confidence: 99%

Untitled

1998

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Abstract.We review the application of statistical mechanics methods to the study of online learning of a drifting concept in the limit of large systems. The model where a feed-forward network learns from examples generated by a time dependent teacher of the same architecture is analyzed. The best possible generalization ability is determined exactly, through the use of a variational method. The constructive variational method also suggests a learning algorithm. It depends, however, on some unavailable quantities, such as the present performance of the student. The construction of estimators for these quantities permits the implementation of a very effective, highly adaptive algorithm. Several other algorithms are also studied for comparison with the optimal bound and the adaptive algorithm, for different types of time evolution of the rule.

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Improving a Network Generalization Ability by Selecting Examples

Abstract: We show that the generalization ability of simple Perceptron-like devices is strongly enhanced by allowing the network itself to select the training examples. Analytic and numerical results are obtained for the Hebb and for the optimal Perceptron learning rule, respectively.

Cited by 107 publications

References 6 publications

Learning with incomplete information and the mathematical structure behind it

Learning with incomplete information and the mathematical structure behind it

Neural cryptography with queries

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