J. Judd. Learning in neural networks. In M. Kaufmann, editor, 1st Annual Workshop on Computational Learning Theory, pages 2--8, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....propositional formulas [31] 6. The intersection of k halfspaces, for constant k 2, and dually, the union of k halfspaces (simple generalization of [14] 7. Various restricted architectures for feed forward neural networks, including the following: a) Depth two, fan in 3 nets, among others [40]. b) Three unit nets with a single hidden unit, with each unit computing a linear threshold [14] c) Three unit nets with a single hidden unit, with each unit computing a nonbinary (piecewise linear) sigmoidal activation function [25] d) For constant k 2, k cascade threshold nets [45] 5. ....

S. Judd, Learning in neural networks. In Proc. 1st Annu. Workshop on Comput. Learning Theory, pages 2--8, Morgan Kaufmann, San Mateo, CA, 1988.

.... 1= Formally, we say that a learning algorithm L is ecient with respect to accuracy , example size n and sample length m if its running time is polynomial in the length m of the training sample and if there is a value of m L ( sucient for pac learning that is polynomial in n and 1= Judd [15] was the rst to show that learning in neural networks can be hard, in the formal complexity theoretic sense. We now describe a simple hardness result from [3,4] along the lines of one due to Blum and Rivest [7] Before doing so, we recall that, in complexity theory, two important classes of ....

S. Judd, Learning in neural networks, in Proc. 1st Annual Workshop on Computational Learning Theory, Morgan Kaufmann, San Mateo, CA, 1988, pp. 2-8.

....H = S H n and the H CONSISTENCY problem is NPhard. Then, unless RP equals NP, there is no PAC learning algorithm for H which runs in time polynomial in ffl Gamma1 and n. ut The fact that computational complexity theoretic hardness results hold for neural networks was first shown by Judd [61]. In this section we shall prove a simple hardness result from [9, 10] along the lines of one due to Blum and Rivest [34] The network has n inputs and k 1 computation units (k 1) The first k computation units are in parallel and each of them is connected to all the inputs. The last ....

S. Judd. Learning in neural networks. In Proc. 1st Annu. Workshop on Comput. Learning Theory, pages 2--8. Morgan Kaufmann, San Mateo, CA, 1988.

....m and its sample complexity m 0 (n; 1=2; 1=m ) is polynomial in n and m = 1= the running time of L is polynomial in n and m . ut 7. HARDNESS RESULTS FOR NEURAL NETWORKS The fact that computational complexity theoretic hardness results hold for neural networks was rst shown by Judd (1988). In this section we shall prove a simple hardness result along the lines of one due to Blum and Rivest (1988) The machine has n input nodes and k 1 computation nodes (k 1) The rst k computation nodes are in parallel and each of them is connected to all the input nodes. The last ....

Judd (1988): J.S. Judd, Learning in neural networks. In Proceedings of the 1988 Workshop on Computational Learning Theory. Morgan Kaufmann, San Mateo, CA.

....Learning algorithms, Regularization, Polynomial complexity. 1 Introduction Neural network learning has been proved intractable, under some assumptions. The loading problem, defined by Judd as can a machine with a specific architecture learn a given task has been proved to be NP complete [16, 17]. For poorly constrained architectures, such as threshold units, Judd shows that deciding if a given task is learnable by a given network architecture can take exponential time. The case of multilayer perceptrons, with threshold units, has been addressed by Blum and Rivest also. In [4] they prove ....

J. Judd. Learning in neural networks. In M. Kaufmann, editor, 1st Annual Workshop on Computational Learning Theory, pages 2--8, 1988.

....exist a set of edge weigh ts so that the network produces the correct output for all the train ing examples Judd s problem is analogous to a rule strength syn thesis problem . The model used in h is work clarifies th is relationship. Figure 13 is an example of feed forward net presen ted by Judd [26]. The learning problem is to find functions for a, b, and c, such that the output ( f) of the H istorical note: the resu lt that RS is NP Complete dates to January 1985. The au thor did not know of Judd s 27 result un til October 1987. Select other window ....

....f) of the H istorical note: the resu lt that RS is NP Complete dates to January 1985. The au thor did not know of Judd s 27 result un til October 1987. Select other window and hit enter to continue. ## ## 25 Figure 13 A neural network ( adapted from Judd [26]) net handles given cases. Judd calls the cases data. Th is is a more general setting than the one used elsewhere in rule strength synthesis and refinement, since the functions for a, b, and c are not fixed a priori, while we fix integrators and combinators. However, Judd s NPcompleteness ....

Judd, S. "Learn ing in Neu ral Networks." Proceedings of the 1988 W orkshop on Computational Learning Theory (COLT-88) , 2-8.

....may need to be done, even small improvements in learning speed can multiply to produce a large improvement. For example, a neural network for protein structure determination (cf. Qian and Sejnowski, 1988 ] might require days to train without transfer, and only hours with transfer. Furthermore, Judd [ 1988 ] has shown that neural network learning is NP complete, 14 and so may take a long time in the worst case for large problems. It is therefore essential to develop heuristic methods to limit search. Learning speed is also widely acknowledged to be a central problem in neural network training. As ....

Stephen Judd. Learning in neural networks. In Proceedings of the 1988 Workshop on Computational Learning Theory, pages 2--8. Morgan Kaufmann, 1988.

....results in of this paper. Hancock [23] has shown that learning decision trees of size n by decision trees of size n cannot be done in polynomial time unless RP = NP . Representation based hardness results for learning various classes of neural networks can also be derived from the results of Judd [25] and Blum and Rivest [12] The first representation independent hardness results for the distribution free model follow from the work of Goldreich, Goldwasser and Micali [22] whose true motivation was to find easy tocompute functions whose output on random inputs appears random to all ....

....behavior, sometimes referred to as the loading problem. Theorem 11 states that even if we allow a much larger net than is actually required, finding these weights is computationally intractable, even for only a constant number of hidden layers . This result should be contrasted with those of Judd [25] and Blum and Rivest [12] which rely on the weaker assumption P 6= NP but do not prove hardness for relaxed consistency and do not allow the hypothesis network to be substantially larger than the smallest consistent network. We also make no assumptions on the topology of the output circuit. ....

S. Judd. Learning in neural networks. Proceedings of the 1988 Workshop on Computational Learning Theory, Morgan Kaufmann Publishers, 1988, pp. 2-8.

....Suppose H = S Hn and the H CONSISTENCY problem is NP hard. Then, unless RP equals NP, there is no PAC learning algorithm for H which runs in time polynomial in ffl Gamma1 and n. The fact that computational complexity theoretic hardness results hold for neural networks was first shown by Judd [66]. In this section we shall prove a simple hardness result from [10, 11] along the lines of one due to Blum and Rivest [36] Neural Computing Surveys 1, 1 47, 1997, http: www.icsi.berkeley.edu jagota NCS 23 The network has n inputs and k 1 computation units (k 1) The first k computation ....

S. Judd. Learning in neural networks. In Proc. 1st Annu. Workshop on Comput. Learning Theory, pages 2--8. Morgan Kaufmann, San Mateo, CA, 1988.

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J. Judd. Learning in neural networks. In M. Kaufmann, editor, 1st Annual Workshop on Computational Learning Theory, pages 2--8, 1988.

No context found.

Judd, S. "Learning in Neural Networks." Proceedings of the 1988 Workshop on Computational Learning Theory (COLT-88), 2-8.

No context found.

Judd, S. "Learn ing in Neu ral Networks." Proceedings of the 1988 W orkshop on Computational Learning Theory (COLT-88) , 2-8.

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