[Dl輪読会]bayesian dark knowledge
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August 19, 16
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2016/8/19
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http://deeplearning.jp/seminar-2/
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Bayesian Dark Knowledge August 18, 2016
Bayesian Dark Knowledge Contents 1 Introduction 2 Background Knowledge 3 Bayesian Dark Knowledge 4 How to improve the original Bayeisan Dark Knowledge
Bayesian Dark Knowledge Introduction Introduction ”Bayesian Dark Knowledge” is a method unifying SGLD with distillation. SGLD is a method for learning large-scale Bayesian models like Bayeisn Networks. SGLD makes it possible to avoid overfitting. Distillatoin is a method for training student networks using soft labels created by teacher networks.
Bayesian Dark Knowledge Background Knowledge SGLD MLA(Metropolis Adjusted Langevin Dynamics) The objetive: sample from p(θ), which is often p(θ|Data). The method is based on a Langevin diffusion, with stationary distribution p(θ) defined by 1 dθ(t) = ∇θ L(θ(t))dt + N(0, Idt). 2 But, isotropic diffusion is inefficient. So, pre-conditioning matrix M is introduced. M is usually set to the inverse of the Fisher information matrix. 1 dθ(t) = M∇θ L(θ(t))dt + N(0, Mdt). 2
Bayesian Dark Knowledge Background Knowledge SGLD SGLD SGLD is a method combining with SGD and MLA. The formula is as follows: ∆θt = ϵt N∑ (∇ log p(θt )+ ∇ log p(xti |θt ))+ηt , ηt ∼ N(0, ϵt ). 2 n Note that in the SGD, the noise term is removed. Rejection rates go to zero asympotically. In the initial phase, SGD like update. In the latter phase, MLA like update.
Bayesian Dark Knowledge Background Knowledge Distillation By learning the ensembles networks or the large networks, we can get the good accuracy. The above networks are called teacher networks. However, the model size is large. After learning the teacher networks, we want to transfter the knowledge in a function into a single smaller model. When trasnfering the knowledge, it is better to use soft targets, which are created by teacher networks, instead of the original labels, i.e., hard targets.
Bayesian Dark Knowledge Bayesian Dark Knowledge Overview Overview Bayesian Dark knowledge is a method of combining SGLD with the concept of distillation. SGLD is a useful method for learning Bayeisan Deep Networks. The problem is that SGLD needs to archive many copies of parameters. The motivation is replacing a set of neural networks with a single deep network.
Bayesian Dark Knowledge Bayesian Dark Knowledge Methods
Bayesian Dark Knowledge Bayesian Dark Knowledge Algorithm Algorithm
Bayesian Dark Knowledge Bayesian Dark Knowledge Points The method does not require to archive the weights. In the distillation phase, θ is updated online. The variance of the prior of teacher networks is smaller than the variance of the prior of student networks.
Bayesian Dark Knowledge Bayesian Dark Knowledge Results
Bayesian Dark Knowledge How to improve the original Bayeisan Dark Knowledge How to improve? SGLD phase Slow mixing rate. The above method does not consider the local geometric structure. Distillation phase We do not have the knoweledge about p(x). We sample from the actual data only.
Bayesian Dark Knowledge How to improve the original Bayeisan Dark Knowledge Preconditioned SGLD p-SGLD That combines RMSprop with Riemannian SGLD. RMSprop is an method of adaptive learning rate considering the curvature.
Bayesian Dark Knowledge How to improve the original Bayeisan Dark Knowledge References A. Korattikara et.al ”Baysian Dark Knowledge” G. Hinton ”Distilling the Knowledge in a Neural Network” C. Li et.al ”Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks”