nips nips2013 nips2013-339 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Pierre Baldi, Peter J. Sadowski
Abstract: Dropout is a relatively new algorithm for training neural networks which relies on stochastically “dropping out” neurons during training in order to avoid the co-adaptation of feature detectors. We introduce a general formalism for studying dropout on either units or connections, with arbitrary probability values, and use it to analyze the averaging and regularizing properties of dropout in both linear and non-linear networks. For deep neural networks, the averaging properties of dropout are characterized by three recursive equations, including the approximation of expectations by normalized weighted geometric means. We provide estimates and bounds for these approximations and corroborate the results with simulations. Among other results, we also show how dropout performs stochastic gradient descent on a regularized error function. 1
Reference: text
sentIndex sentText sentNum sentScore
1 edu Abstract Dropout is a relatively new algorithm for training neural networks which relies on stochastically “dropping out” neurons during training in order to avoid the co-adaptation of feature detectors. [sent-4, score-0.296]
2 We introduce a general formalism for studying dropout on either units or connections, with arbitrary probability values, and use it to analyze the averaging and regularizing properties of dropout in both linear and non-linear networks. [sent-5, score-1.529]
3 For deep neural networks, the averaging properties of dropout are characterized by three recursive equations, including the approximation of expectations by normalized weighted geometric means. [sent-6, score-0.983]
4 We provide estimates and bounds for these approximations and corroborate the results with simulations. [sent-7, score-0.045]
5 Among other results, we also show how dropout performs stochastic gradient descent on a regularized error function. [sent-8, score-0.661]
6 1 Introduction Dropout is an algorithm for training neural networks that was described at NIPS 2012 [7]. [sent-9, score-0.188]
7 In its most simple form, during training, at each example presentation, feature detectors are deleted with probability q = 1 − p = 0. [sent-10, score-0.107]
8 The main motivation behind the algorithm is to prevent the co-adaptation of feature detectors, or overfitting, by forcing neurons to be robust and rely on population behavior, rather than on the activity of other specific units. [sent-14, score-0.113]
9 In [7], dropout is reported to achieve state-of-the-art performance on several benchmark datasets. [sent-15, score-0.661]
10 In spite of the impressive results that have been reported, little is known about dropout from a theoretical standpoint, in particular about its averaging, regularization, and convergence properties. [sent-17, score-0.729]
11 5, whether different values of q can be used including different values for different layers or different units, and whether dropout can be applied to the connections rather than the units. [sent-19, score-0.696]
12 2 Dropout in Linear Networks It is instructive to first look at some of the properties of dropout in linear networks, since these can be studied exactly in the most general setting of a multilayer feedforward network described by an underlying acyclic graph. [sent-21, score-0.85]
13 The activity in unit i of layer h can be expressed as: h Si (I) = hl l wij Sj l 0 (4) j 0 with E(Sj ) = Ij in the input layer. [sent-22, score-0.402]
14 In short, the ensemble average can easily be computed by hl hl feedforward propagation in the original network, simply replacing the weights wij by wij pl . [sent-23, score-0.788]
15 1 Dropout in Neural Networks Dropout in Shallow Neural Networks n Consider first a single logistic unit with n inputs O = σ(S) = 1/(1 + ce−λS ) and S = 1 wj Ij . [sent-25, score-0.172]
16 To achieve the greatest level of generality, we assume that the unit produces different outputs O1 , . [sent-26, score-0.11]
17 In the most relevant case, these outputs and these sums are associated with the m = 2n possible subnetworks of the unit. [sent-36, score-0.162]
18 , Pm could be generated, for instance, by using Bernoulli gating variables, although this is not necessary for this derivation. [sent-40, score-0.098]
19 It is useful to define the following four quantities: the mean E = Pi Oi ; the mean of the complements P E = Pi (1 − Oi ) = 1 − E; the weighted geometric mean (W GM ) G = i Oi i ; and the weighted geometric mean of the complements G = i (1 − Oi )Pi . [sent-41, score-0.382]
20 We also define the normalized weighted geometric mean N W GM = G/(G + G ). [sent-42, score-0.153]
21 We can now prove the key averaging theorem for logistic functions: N W GM (O1 , . [sent-43, score-0.159]
22 A similar result is true also for normalized exponential transfer functions. [sent-50, score-0.034]
23 Finally, one can also show that the only class of functions f that satisfy N W GM (f ) = f (E) are the constant functions and the logistic functions [1]. [sent-51, score-0.078]
24 Figure 2 Figure 3: In every hidden layer of a dropout trained network, the distribution of neuron activations O∗ is sparse and not symmetric. [sent-57, score-0.751]
25 Improving neural networks by preventing co-adaptation of feature detectors. [sent-109, score-0.18]
26 On the Ky Fan inequality and related inequalities i. [sent-116, score-0.065]
27 On the Ky Fan inequality and related inequalities ii. [sent-121, score-0.065]
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