Deep Learning is attracting much attention in object recognition and speech processing. A benefit of using the deep learning is that it provides automatic pre-training. Several proposed methods that include auto-encoder are being successfully used in various applications. Moreover, deep learning uses a multilayer network that consists of many layers, a huge number of units, and huge amount of data. Thus, executing deep learning requires heavy computation, so deep learning is usually utilized with parallel computation with many cores or many machines. Deep learning employs the gradient algorithm, however this traps the learning into the saddle point or local minima. To avoid this difficulty, a rectified linear unit (ReLU)is proposed to speed up the learning convergence. However, the reasons the convergence is speeded up are not well understood.In this paper, we analyze the ReLU by a using simpler network called the soft-committee machine and clarify the reason for the speedup. We also train the network in an on-line manner. The soft-committee machine provides a good test bed to analyze deep learning. The results provide some reasons for the speedup of the convergence of the deep learning.
Deep learning is the state-of-the-art in fields such as visual object recognition and speech recognition. This learning uses a large number of layers and a huge number of units and connections. Therefore, overfitting is a serious problem with it, and the dropout which is a kind of regularization tool is used. However, in online learning, the effect of dropout is not well known. This paper presents our investigation on the effect of dropout in online learning. We analyzed the effect of dropout on convergence speed near the singular point. Our results indicated that dropout is effective in online learning. Dropout tends to avoid the singular point for convergence speed near that point. B B B NM B N1 J J J J N1 NK
This paper describes a novel method, which we call correlated topographic analysis (CTA), to estimate non-Gaussian components and their ordering (topography). The method is inspired by a central motivation of recent variants of independent component analysis (ICA), namely, to make use of the residual statistical dependency which ICA cannot remove. We assume that components nearby on the topographic arrangement have both linear and energy correlations, while faraway components are statistically independent. We use these dependencies to fix the ordering of the components. We start by proposing the generative model for the components. Then, we derive an approximation of the likelihood based on the model. Furthermore, since gradient methods tend to get stuck in local optima, we propose a three-step optimization method which dramatically improves topographic estimation. Using simulated data, we show that CTA estimates an ordering of the components and generalizes a previous method in terms of topography estimation. Finally, to demonstrate that CTA is widely applicable, we learn topographic representations for three kinds of real data: natural images, outputs of simulated complex cells and text data.
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