From bb0a11cd14902971902987e2ed6f7107ae758bef Mon Sep 17 00:00:00 2001 From: Yi Wang Date: Mon, 4 Sep 2017 13:01:18 -0700 Subject: [PATCH] Add a graph building example --- doc/design/graph.md | 51 ++++++++++++++ .../images/graph_construction_example.bash | 11 +++ .../images/graph_construction_example.dot | 63 ++++++++++++++++++ .../images/graph_construction_example_all.png | Bin 0 -> 60087 bytes ..._construction_example_forward_backward.png | Bin 0 -> 55715 bytes ...raph_construction_example_forward_only.png | Bin 0 -> 32082 bytes 6 files changed, 125 insertions(+) create mode 100644 doc/design/graph.md create mode 100755 doc/design/images/graph_construction_example.bash create mode 100644 doc/design/images/graph_construction_example.dot create mode 100644 doc/design/images/graph_construction_example_all.png create mode 100644 doc/design/images/graph_construction_example_forward_backward.png create mode 100644 doc/design/images/graph_construction_example_forward_only.png diff --git a/doc/design/graph.md b/doc/design/graph.md new file mode 100644 index 0000000000..87f696f90f --- /dev/null +++ b/doc/design/graph.md @@ -0,0 +1,51 @@ +# Design Doc: Computations as Graphs + +A primary goal of the refactorization of PaddlePaddle is a more flexible representation of deep learning computation, in particular, a graph of operators and variables, instead of sequences of layers as before. + +This document explains that the construction of a graph as three steps: + +- construct the forward part +- construct the backward part +- construct the optimization part + +Let us take the problem of image classification as a simple example. The application program that trains the model looks like: + +```python +x = layer.data("images") +l = layer.data("label") +y = layer.fc(x) +cost = layer.mse(y, l) +optimize(cost) +train(cost, reader=mnist.train()) +``` + +### Forward Part + +The first four lines of above program build the forward part of the graph. + +![](images/graph_construction_example_forward_only.png) + +In particular, the first line `x = layer.data("images")` creates variable x and a Feed operator that copies a column from the minibatch to x. `y = layer.fc(x)` creates not only the FC operator and output variable y, but also two parameters, W and b. + +In this example, all operators are created as `OpDesc` protobuf messages, and all variables are `VarDesc`. These protobuf messages are saved in a `BlockDesc` protobuf message. + +### Backward Part + +The fifth line `optimize(cost)` calls two functions, `ConstructBackwardGraph` and `ConstructOptimizationGraph`. + +`ConstructBackwardGraph` traverses the forward graph in the `BlockDesc` protobuf message and builds the backward part. + +![](images/graph_construction_example_forward_backward.png) + +According to the chain rule of gradient computation, `ConstructBackwardGraph` would + +1. create a gradient operator G for each operator F, +1. make all inputs, outputs, and outputs' gradient of F as inputs of G, +1. create gradients for all inputs of F, except for those who don't have gradients, like x and l, and +1. make all these gradients as outputs of G. + +### Optimization Part + +For each parameter, like W and b created by `layer.fc`, marked as double circles in above graphs, `ConstructOptimizationGraph` creates an optimization operator to apply its gradient. Here results in the complete graph: + +![](images/graph_construction_example_all.png) diff --git a/doc/design/images/graph_construction_example.bash b/doc/design/images/graph_construction_example.bash new file mode 100755 index 0000000000..35e6997abd --- /dev/null +++ b/doc/design/images/graph_construction_example.bash @@ -0,0 +1,11 @@ +cat ./graph_construction_example.dot | \ + sed 's/color=red/color=red, style=invis/g' | \ + sed 's/color=green/color=green, style=invis/g' | \ + dot -Tpng > graph_construction_example_forward_only.png + +cat ./graph_construction_example.dot | \ + sed 's/color=green/color=green, style=invis/g' | \ + dot -Tpng > graph_construction_example_forward_backward.png + +cat ./graph_construction_example.dot | \ + dot -Tpng > graph_construction_example_all.png diff --git a/doc/design/images/graph_construction_example.dot b/doc/design/images/graph_construction_example.dot new file mode 100644 index 0000000000..b77ddd448e --- /dev/null +++ b/doc/design/images/graph_construction_example.dot @@ -0,0 +1,63 @@ +digraph ImageClassificationGraph { + ///////// The forward part ///////// + FeedX [label="Feed", color=blue, shape=box]; + FeedY [label="Feed", color=blue, shape=box]; + FC [label="FC", color=blue, shape=box]; + MSE [label="MSE", color=blue, shape=box]; + + x [label="x", color=blue, shape=oval]; + l [label="l", color=blue, shape=oval]; + y [label="y", color=blue, shape=oval]; + W [label="W", color=blue, shape=doublecircle]; + b [label="b", color=blue, shape=doublecircle]; + cost [label="cost", color=blue, shape=oval]; + + FeedX -> x -> FC -> y -> MSE -> cost [color=blue]; + FeedY -> l -> FC [color=blue]; + W -> FC [color=blue]; + b -> FC [color=blue]; + l -> MSE [color=blue]; + + ////////// The backward part ///////// + MSE_Grad [label="MSE_grad", color=red, shape=box]; + FC_Grad [label="FC_grad", color=red, shape=box]; + + d_cost [label="d cost", color=red, shape=oval]; + d_y [label="d y", color=red, shape=oval]; + d_b [label="d b", color=red, shape=oval]; + d_W [label="d W", color=red, shape=oval]; + + cost -> MSE_Grad [color=red]; + d_cost -> MSE_Grad [color=red]; + x -> MSE_Grad [color=red]; + l -> MSE_Grad [color=red]; + y -> MSE_Grad -> d_y [color=red]; + + x -> FC_Grad [color=red]; + y -> FC_Grad [color=red]; + d_y -> FC_Grad [color=red]; + W -> FC_Grad -> d_W [color=red]; + b -> FC_Grad -> d_b [color=red]; + + ////////// The optimizaiton part ////////// + + OPT_W [label="SGD", color=green, shape=box]; + OPT_b [label="SGD", color=green, shape=box]; + + d_W -> OPT_W -> W [color=green]; + d_b -> OPT_b -> b [color=green]; + + ////////// Groupings ////////// + + subgraph clusterMSE { + style=invis; + MSE; + MSE_Grad; + } + + subgraph clusterFC { + style=invis; + FC; + FC_Grad; + } +} diff --git a/doc/design/images/graph_construction_example_all.png b/doc/design/images/graph_construction_example_all.png new file mode 100644 index 0000000000000000000000000000000000000000..3ee61f9ef4544da786480f188403742d48a1d9e3 GIT binary patch literal 60087 zcmZ_01yog0*Def)PNhLXkgkIWNS7#i=#cJ~Mj9!REfPe%>KtSw7M+N>< zq4>2I_=EUPSyBw4WPp4N0YMZ&`t?gyH^iM3v}D5eiS`F%uThj}F;G=i*=aKK3?!Z# zAiVotG#Ku^zTd}(mWn72M-Mgnj$jl?Wk5`bN2K)dp?G?;XZ_~<^mM{J#yr7b@#3#O zr@Z~W)YN*lvxS0H_l1*B!M^DK^%M2O&oh<@Q%`qRseUbr{9iu==l1{gA5mn?1m9Sw zSQCFi(tnTRYo_J&;J-%pMJMF;yA0438khfPSSox_^Bt~iD)##W6n10O{ZWNqb_3)F z%VK9|gCe3{+icvHE4PW+pZeH#wxeBh6 z@sl1CMLkx1R&p36&-JxykY}pjP1bsOroS^c_;%te5iwWpe*R4IT2NFynwkpqKfg~Z zpfD07N+0ZSitStBi|@_`nju8$MLX%rWR}CN&IXTpP|wfyn&FE+4f4Ml-Qj%+ahL;x zA`ND&&4OjifpG3w1R>A*Nwa>(nb$;S$W2$cq&x$y0+0CB$+3$CJom?ep%%Bxiks+lL=T$u0wWRIMZGA+9{C^FA@n=Oq%^wi}`uB<~P zn~(>>)vxVaey6S~

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