Chris Yeung created SINGA-505:
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             Summary: Buffer Operators / Change the Autograd operators to be 
bufferable
                 Key: SINGA-505
                 URL: https://issues.apache.org/jira/browse/SINGA-505
             Project: Singa
          Issue Type: Improvement
          Components: Core
            Reporter: Chris Yeung


We can buffer the operators, so that we can extract all the operators in 
autograd to build a graph after schedule, where the simplest scheduling can use 
the FIFO principle from the buffered operators. A more complex scheduleing 
algorithm could be implemented which consider the dependency of operators that 
could make it parallel. One more clear advantage is that when we run the graph 
we only need to run the buffered operators called by the autograd function, 
then there will be no need to run the autograd python code again throughout the 
training process.

So this ticket uses for two purpose:

1. Change the core components (e.g. tensor,device) to support buffering.

2. Change all the autograd operator to be bufferable, i.e. the input and output 
should be inside the block. For example, the SoftMax backward cannot be 
buffered because it is not doing the operating through the block, and it was 
using numpy:
    def backward(self, dy):
        # calculations are made on numpy array
        if self.axis == 1:
            dy = singa.DefaultTranspose(dy)
        grad = ctensor2numpy(dy)
        output = ctensor2numpy(self.output)
        out_1 = np.einsum("ki,ki->ki", grad, output)
        medium_out = np.einsum("ki,kj->kij", output, output)
        out_2 = np.einsum("kij,kj->ki", medium_out, grad)
        out = out_1 - out_2
        dx = CTensor(out_1.shape)
        dx.CopyFloatDataFromHostPtr(out.flatten())
        if self.axis == 0:
            return dx
        elif self.axis == 1:
            return singa.DefaultTranspose(dx)



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