@@ -5,10 +5,10 @@ In a large scale machine learning setup where the size of the training data is h
Polyak and Juditsky (1992) showed that the test performance of simple average of parameters obtained by Stochastic Gradient Descent (SGD) is as good as that of parameter values that are obtained by training the model over and over again, over the training dataset.
Hence, to accelerate the speed of Stochastic Gradient Descent, Averaged Stochastic Gradient Descent (ASGD) was proposed in Polyak and Juditsky (1992). For ASGD, the running average of parameters obtained by SGD, is used as the estimator for <imgsrc="./images/theta_star.gif"/><br/> . The averaging is done as follows:
Hence, to accelerate the speed of Stochastic Gradient Descent, Averaged Stochastic Gradient Descent (ASGD) was proposed in Polyak and Juditsky (1992). For ASGD, the running average of parameters obtained by SGD, is used as the estimator for <imgsrc="https://raw.githubusercontent.com/PaddlePaddle/Paddle/develop/doc/fluid/images/theta_star.gif"/><br/> . The averaging is done as follows:
@@ -40,11 +40,11 @@ computation is only specified in Python code which sits outside of PaddlePaddle,
Similar to how a compiler uses an intermediate representation (IR) so that the programmer does not need to manually optimize their code for most of the cases, we can have an intermediate representation in PaddlePaddle as well. The compiler optimizes the IR as follows:
PaddlePaddle can support model parallelism by converting the IR so that the user no longer needs to manually perform the computation and operations in the Python component:
The IR for PaddlePaddle after refactoring is called a `Block`, it specifies the computation dependency graph and the variables used in the computation.
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@@ -60,7 +60,7 @@ For a detailed explanation, refer to this document -
The revamped distributed training architecture can address the above discussed limitations. Below is the illustration of how it does so:
@@ -171,7 +171,7 @@ In the future, a more general placement algorithm should be implemented, which m
The local training architecture will be the same as the distributed training architecture, the difference is that everything runs locally, and there is just one PaddlePaddle runtime:
cudnn provides APIs to finish the whole series of computation, we can use them in our GPU kernel.
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@@ -124,7 +124,7 @@ for pass_id in range(PASS_NUM):
`is_infer` is an attribute. Once an operator is created, its attributes can not be changed. It suggests us that we shall maintain two `batch_norm_op` in the model, one's `is_infer` is `True`(we call it `infer_batch_norm_op`) and the other one's is `False`(we call it `train_batch_norm_op`). They share all parameters and variables, but be placed in two different branches. That is to say, if a network contains a `batch_norm_op`, it will fork into two branches, one go through `train_batch_norm_op` and the other one go through `infer_batch_norm_op`:
Just like what is shown in the above graph, the net forks before `batch_norm_op` and will never merge again. All the operators after `batch_norm_op` will duplicate.
@@ -6,17 +6,17 @@ A central problem in machine learning is how to design an algorithm that will pe
### Parameter Norm Penalties
Most common regularization approaches in deep learning are based on limiting the capacity of the models by adding a parameter norm penalty to the objective function `J`. This is given as follows:
The parameter `alpha` is a hyperparameter that weights the relative contribution of the norm penalty term, `omega`, relative to the standard objective function `J`.
The most commonly used norm penalties are the L2 norm penalty and the L1 norm penalty. These are given as follows:
@@ -7,14 +7,14 @@ It applies several important concepts in machine learning system design, includi
In our GAN design, we wrap it as a user-friendly easily customized python API to design different models. We take the conditional DC-GAN (Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks [https://arxiv.org/abs/1511.06434]) as an example due to its good performance on image generation.
Figure 1. The overall running logic of GAN. The black solid arrows indicate the forward pass; the green dashed arrows indicate the backward pass of generator training; the red dashed arrows indicate the backward pass of the discriminator training. The BP pass of the green (red) arrow should only update the parameters in the green (red) boxes. The diamonds indicate the data providers. d\_loss and g\_loss marked in red and green are the two targets we would like to run.
</p>
The operators, layers and functions required/optional to build a GAN demo is summarized in https://github.com/PaddlePaddle/Paddle/issues/4563.
