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Merge pull request PaddlePaddle#13 from reyoung/final_fixes
Update Develop Branch And Fix All unit tests.
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## Auto Gradient Checker Design | ||
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## Backgraound: | ||
- Operator forward computing is easy to check if the result is right because it has a clear definition. **But** backpropagation is a notoriously difficult algorithm to debug and get right: | ||
- 1. you should get the right backpropagation formula according to the forward computation. | ||
- 2. you should implement it right in CPP. | ||
- 3. it's difficult to prepare test data. | ||
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- Auto gradient check gets a numeric gradient by forward Operator and use it as a reference of the backward Operator's result. It has several advantages: | ||
- 1. numeric gradient checker only need forward operator. | ||
- 2. user only need to prepare the input data for forward Operator. | ||
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## Mathematical Theory | ||
The following two document from stanford has a detailed explanation of how to get numeric gradient and why it's useful. | ||
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- [Gradient checking and advanced optimization(en)](http://deeplearning.stanford.edu/wiki/index.php/Gradient_checking_and_advanced_optimization) | ||
- [Gradient checking and advanced optimization(cn)](http://ufldl.stanford.edu/wiki/index.php/%E6%A2%AF%E5%BA%A6%E6%A3%80%E9%AA%8C%E4%B8%8E%E9%AB%98%E7%BA%A7%E4%BC%98%E5%8C%96) | ||
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## Numeric Gradient Implementation | ||
### Python Interface | ||
```python | ||
def get_numeric_gradient(op, | ||
input_values, | ||
output_name, | ||
input_to_check, | ||
delta=0.005, | ||
local_scope=None): | ||
""" | ||
Get Numeric Gradient for an operator's input. | ||
:param op: C++ operator instance, could be an network | ||
:param input_values: The input variables. Should be an dictionary, key is | ||
variable name. Value is numpy array. | ||
:param output_name: The final output variable name. | ||
:param input_to_check: The input variable need to get gradient. | ||
:param delta: The perturbation value for numeric gradient method. The | ||
smaller delta is, the more accurate result will get. But if that delta is | ||
too small, it could occur numerical stability problem. | ||
:param local_scope: The local scope used for get_numeric_gradient. | ||
:return: The gradient array in numpy format. | ||
""" | ||
``` | ||
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### Explaination: | ||
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- Why need `output_name` | ||
- One Operator may have multiple Output, you can get independent gradient from each Output. So user should set one output to calculate. | ||
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- Why need `input_to_check` | ||
- One operator may have multiple inputs. Gradient Op can calculate the gradient of these Inputs at the same time. But Numeric Gradient needs to calculate them one by one. So `get_numeric_gradient` is designed to calculate the gradient for one input. If you need to compute multiple inputs, you can call `get_numeric_gradient` multiple times. | ||
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### Core Algorithm Implementation | ||
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```python | ||
# we only compute gradient of one element each time. | ||
# we use a for loop to compute the gradient of every element. | ||
for i in xrange(tensor_size): | ||
# get one input element throw it's index i. | ||
origin = tensor_to_check.get_float_element(i) | ||
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# add delta to it, run op and then get the sum of the result tensor. | ||
x_pos = origin + delta | ||
tensor_to_check.set_float_element(i, x_pos) | ||
y_pos = get_output() | ||
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# plus delta to this element, run op and get the sum of the result tensor. | ||
x_neg = origin - delta | ||
tensor_to_check.set_float_element(i, x_neg) | ||
y_neg = get_output() | ||
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# restore old value | ||
tensor_to_check.set_float_element(i, origin) | ||
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# compute the gradient of this element and store it into a numpy array. | ||
gradient_flat[i] = (y_pos - y_neg) / delta / 2 | ||
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# reshape the gradient result to the shape of the source tensor. | ||
return gradient_flat.reshape(tensor_to_check.get_dims()) | ||
``` | ||
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## Auto Graident Checker Framework | ||
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Each Operator Kernel has three kinds of Gradient: | ||
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- 1. Numeric Gradient | ||
- 2. CPU Operator Gradient | ||
- 3. GPU Operator Gradient(if supported) | ||
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Numeric Gradient Only relies on forward Operator. So we use Numeric Gradient as the reference value. | ||
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- 1. calculate the numeric gradient. | ||
- 2. calculate CPU kernel Gradient with the backward Operator and compare it with the numeric gradient. | ||
- 3. calculate GPU kernel Gradient with the backward Operator and compare it with the numeric gradient.(if support GPU) | ||
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#### Python Interface | ||
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```python | ||
def check_grad(self, | ||
forward_op, | ||
input_vars, | ||
inputs_to_check, | ||
output_name, | ||
no_grad_set=None, | ||
only_cpu=False, | ||
max_relative_error=0.005): | ||
""" | ||
:param forward_op: used to create backward_op | ||
:param input_vars: numpy value of input variable. The following | ||
computation will use these variables. | ||
:param inputs_to_check: inputs var names that should check gradient. | ||
:param output_name: output name that used to | ||
:param max_relative_error: The relative tolerance parameter. | ||
:param no_grad_set: used when create backward ops | ||
:param only_cpu: only compute and check gradient on cpu kernel. | ||
:return: | ||
""" | ||
``` | ||
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### How to check if two numpy array is close enough? | ||
if `abs_numeric_grad` is nearly zero, then use abs error for numeric_grad, not relative | ||
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```python | ||
numeric_grad = ... | ||
operator_grad = numpy.array(scope.find_var(grad_var_name(name)).get_tensor()) | ||
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abs_numeric_grad = numpy.abs(numeric_grad) | ||
# if abs_numeric_grad is nearly zero, then use abs error for numeric_grad, not relative | ||
# error. | ||
abs_numeric_grad[abs_numeric_grad < 1e-3] = 1 | ||
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diff_mat = numpy.abs(abs_numeric_grad - operator_grad) / abs_numeric_grad | ||
max_diff = numpy.max(diff_mat) | ||
``` | ||
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#### Notes: | ||
1,The Input data for auto gradient checker should be reasonable to avoid numeric problem. | ||
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#### Refs: | ||
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- [Gradient checking and advanced optimization(en)](http://deeplearning.stanford.edu/wiki/index.php/Gradient_checking_and_advanced_optimization) | ||
- [Gradient checking and advanced optimization(cn)](http://ufldl.stanford.edu/wiki/index.php/%E6%A2%AF%E5%BA%A6%E6%A3%80%E9%AA%8C%E4%B8%8E%E9%AB%98%E7%BA%A7%E4%BC%98%E5%8C%96) |
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