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new 728b8db Revise Symbol tutorial (#15343)
728b8db is described below
commit 728b8db572e3652ea76e89a0d8f91be8dc895e41
Author: Sergey Sokolov <[email protected]>
AuthorDate: Fri Jul 5 03:44:30 2019 -0700
Revise Symbol tutorial (#15343)
* Revise Symbol tutorial
* Force flaky build
* Address code review comments
* Split tie weight example into blocks
* Force build
---
docs/tutorials/basic/symbol.md | 370 +++++++++++++++++++++--------------------
1 file changed, 192 insertions(+), 178 deletions(-)
diff --git a/docs/tutorials/basic/symbol.md b/docs/tutorials/basic/symbol.md
index cff12ac..57e014f 100644
--- a/docs/tutorials/basic/symbol.md
+++ b/docs/tutorials/basic/symbol.md
@@ -17,50 +17,21 @@
# Symbol - Neural network graphs
-In a [previous tutorial](http://mxnet.io/tutorials/basic/ndarray.html), we
introduced `NDArray`,
-the basic data structure for manipulating data in MXNet.
-And just using NDArray by itself, we can execute a wide range of mathematical
operations.
-In fact, we could define and update a full neural network just by using
`NDArray`.
-`NDArray` allows you to write programs for scientific computation
-in an imperative fashion, making full use of the native control of any
front-end language. Gluon uses this approach under the hood (before
hybridization) to allow for flexible and debugable networks.
-So you might wonder, why don't we just use `NDArray` for all computation?
-
-MXNet also provides the Symbol API, an interface for symbolic programming.
-With symbolic programming, rather than executing operations step by step,
-we first define a *computation graph*.
-This graph contains placeholders for inputs and designated outputs.
-We can then compile the graph, yielding a function
-that can be bound to `NDArray`s and run.
-MXNet's Symbol API is similar to the network configurations
-used by [Caffe](http://caffe.berkeleyvision.org/)
-and the symbolic programming in
[Theano](http://deeplearning.net/software/theano/). And Gluon takes advantage
of this approach under the hood after the network has been hybridized.
-
-Another advantage conferred by symbolic approach is that
-we can optimize our functions before using them.
-For example, when we execute mathematical computations in imperative fashion,
-we don't know at the time that we run each operation,
-which values will be needed later on.
-But with symbolic programming, we declare the required outputs in advance.
-This means that we can recycle memory allocated in intermediate steps,
-as by performing operations in place. Symbolic API also uses less memory for
the
-same network. Refer to [How To](http://mxnet.io/faq/index.html) and
-[Architecture](http://mxnet.io/architecture/index.html) section to know more.
-
-In our design notes, we present [a more thorough discussion on the comparative
strengths
-of imperative and symbolic
programing](http://mxnet.io/architecture/program_model.html).
-But in this document, we'll focus on teaching you how to use MXNet's Symbol
API.
-In MXNet, we can compose Symbols from other Symbols, using operators,
-such as simple matrix operations (e.g. "+"),
-or whole neural network layers (e.g. convolution layer).
-Operator can take multiple input variables,
-can produce multiple output symbols
-and can maintain internal state symbols.
-
-For a visual explanation of these concepts, see
-[Symbolic Configuration and Execution in
Pictures](http://mxnet.io/api/python/symbol_in_pictures/symbol_in_pictures.html).
-
-To make things concrete, let's take a hands-on look at the Symbol API.
-There are a few different ways to compose a `Symbol`.
+In the [previous tutorial](http://mxnet.io/tutorials/basic/ndarray.html), we
introduced
[`NDArray`](https://mxnet.incubator.apache.org/api/python/ndarray/ndarray.html),
the basic data structure for manipulating data in MXNet.
+Just using `NDArray` by itself, we can execute a wide range of mathematical
operations. In fact, we could define and update a full neural network just by
using `NDArray`.
+
+`NDArray` allows you to write programs for scientific computation in an
imperative fashion, making full use of the native control of any front-end
language. Gluon API uses this approach under the hood (before hybridization) to
allow for flexible and debugable networks. So you might wonder, why don't we
just use `NDArray` for all computation?
+
+MXNet also provides the `Symbol API`, an interface for symbolic programming.
With symbolic programming, rather than executing operations step by step, we
first define a [computation
graph](https://mxnet.incubator.apache.org/versions/master/faq/visualize_graph.html).
This graph contains placeholders for inputs and designated outputs. We can
then compile the graph, yielding a function that can be bound to `NDArray`s and
run. MXNet's `Symbol API` is similar to the network configurations use [...]
+
+Another advantage conferred by symbolic approach is that we can optimize our
functions before using them. For example, when we execute mathematical
computations in imperative fashion, we don't know at the time that we run each
operation, which values will be needed later on. But with symbolic programming,
we declare the required outputs in advance. This means that we can recycle
memory allocated in intermediate steps, as by performing operations in place.
Symbolic API also uses less memo [...]
+same network. Refer to [How To](http://mxnet.io/faq/index.html) and
[Architecture](http://mxnet.io/architecture/index.html) section to know more.
+
+In our design notes, we present [a more thorough discussion on the comparative
strengths of imperative and symbolic
programing](http://mxnet.io/architecture/program_model.html). In this document,
however, we'll focus on explaining how to use MXNet's `Symbol API`.
+
+In MXNet, we can compose Symbols from other Symbols, using operators, such as
simple matrix operations (e.g. `+`), or whole neural network layers (e.g.
convolution layer). Operator can take multiple input variables, can produce
multiple output symbols and can maintain internal state symbols. For a visual
explanation of these concepts, see [Symbolic Configuration and Execution in
Pictures](http://mxnet.io/api/python/symbol_in_pictures/symbol_in_pictures.html).
+
+To make things concrete, let's take a hands-on look at the `Symbol API`. There
are a few different ways to compose a
[`Symbol`](http://mxnet.incubator.apache.org/api/python/symbol/symbol.html).
## Prerequisites
@@ -71,20 +42,14 @@ To complete this tutorial, we need:
```
pip install jupyter
```
-- GPUs - A section of this tutorial uses GPUs. If you don't have GPUs on your
machine, simply
-set the variable gpu_device to mx.cpu().
+- GPUs (optional). A section of this tutorial uses GPUs, if one is available.
If not, the code will automatically switch to CPU.
## Basic Symbol Composition
### Basic Operators
-The following example builds a simple expression: `a + b`.
-First, we create two placeholders with `mx.sym.Variable`,
-giving them the names `a` and `b`.
-We then construct the desired symbol by using the operator `+`.
-We don't need to name our variables while creating them,
-MXNet will automatically generate a unique name for each.
-In the example below, `c` is assigned a unique name automatically.
+The following example builds a simple expression: `a + b`. First, we create
two placeholders with `mx.sym.Variable`,
+giving them the names `a` and `b`. We then construct the desired symbol by
using the operator `+`. We don't need to name our variables while creating
them, MXNet will automatically generate a unique name for each. In the example
below, `c` is assigned a unique name automatically.
```python
import mxnet as mx
@@ -97,7 +62,7 @@ c = a + b
Most operators supported by `NDArray` are also supported by `Symbol`, for
example:
```python
-# elemental wise multiplication
+# element-wise multiplication
d = a * b
# matrix multiplication
e = mx.sym.dot(a, b)
@@ -106,12 +71,11 @@ f = mx.sym.reshape(d+e, shape=(1,4))
# broadcast
g = mx.sym.broadcast_to(f, shape=(2,4))
# plot
-mx.viz.plot_network(symbol=g, node_attrs={"shape":"oval","fixedsize":"false"})
+mx.viz.plot_network(symbol=g,
+ node_attrs={"shape": "oval", "fixedsize": "false"})
```
-The computations declared in the above examples can be bound to the input data
-for evaluation by using `bind` method. We discuss this further in the
-[Symbol Manipulation](#symbol-manipulation) section.
+The computations declared in the above examples can be bound to the input data
for evaluation by using `bind` method. We discuss this further in the [Symbol
Manipulation](#symbol-manipulation) section.
### Basic Neural Networks
@@ -125,23 +89,20 @@ net = mx.sym.FullyConnected(data=net, name='fc1',
num_hidden=128)
net = mx.sym.Activation(data=net, name='relu1', act_type="relu")
net = mx.sym.FullyConnected(data=net, name='fc2', num_hidden=10)
net = mx.sym.SoftmaxOutput(data=net, name='out')
-mx.viz.plot_network(net, shape={'data':(100,200)},
node_attrs={"shape":"oval","fixedsize":"false"})
+mx.viz.plot_network(net,
+ shape={'data':(100, 200)},
+ node_attrs={"shape": "oval", "fixedsize": "false"})
```
-Each symbol takes a (unique) string name. NDArray and Symbol both represent
-a single tensor. *Operators* represent the computation between tensors.
-Operators take symbol (or NDArray) as inputs and might also additionally accept
-other hyperparameters such as the number of hidden neurons (*num_hidden*) or
the
-activation type (*act_type*) and produce the output.
+Each `Symbol` takes a unique string name. `NDArray` and `Symbol` both
represent a single tensor. *Operators* represent the computation between
tensors. Operators take `Symbol` or `NDArray` as inputs and might also
additionally accept other hyperparameters such as the number of hidden neurons
(`num_hidden`) or the activation type (`act_type`) and produce the output.
-We can view a symbol simply as a function taking several arguments.
-And we can retrieve those arguments with the following method call:
+We can view a `Symbol` simply as a function taking several arguments. And we
can retrieve those arguments with the following method call:
```python
net.list_arguments()
```
-These arguments are the parameters and inputs needed by each symbol:
+These arguments are the parameters and inputs needed by each `Symbol`:
- *data*: Input data needed by the variable *data*.
- *fc1_weight* and *fc1_bias*: The weight and bias for the first fully
connected layer *fc1*.
@@ -157,16 +118,12 @@ net = mx.symbol.FullyConnected(data=net, weight=w,
name='fc1', num_hidden=128)
net.list_arguments()
```
-In the above example, `FullyConnected` layer has 3 inputs: data, weight, bias.
-When any input is not specified, a variable will be automatically generated
for it.
+In the above example, `FullyConnected` layer has 3 inputs: data, weight, bias.
When any input is not specified, a variable will be automatically generated for
it.
## More Complicated Composition
-MXNet provides well-optimized symbols for layers commonly used in deep learning
-(see [src/operator](https://github.com/dmlc/mxnet/tree/master/src/operator)).
-We can also define new operators in Python. The following example first
-performs an element-wise add between two symbols, then feeds them to the fully
-connected operator:
+MXNet provides well-optimized Symbols for layers commonly used in deep
learning (see
[src/operator](https://github.com/dmlc/mxnet/tree/master/src/operator)). We can
also define new operators in Python. The following example first
+performs an element-wise add between two Symbols, then feeds them to the fully
connected operator:
```python
lhs = mx.symbol.Variable('data1')
@@ -175,8 +132,7 @@ net = mx.symbol.FullyConnected(data=lhs + rhs, name='fc1',
num_hidden=128)
net.list_arguments()
```
-We can also construct a symbol in a more flexible way than the single forward
-composition depicted in the preceding example:
+We can also construct a `Symbol` in a more flexible way than the single
forward composition depicted in the preceding example:
```python
data = mx.symbol.Variable('data')
@@ -188,14 +144,9 @@ composed = net2(data2=net1, name='composed')
composed.list_arguments()
```
-In this example, *net2* is used as a function to apply to an existing symbol
*net1*,
-and the resulting *composed* symbol will have all the attributes of *net1* and
*net2*.
+In this example, `net2` is used as a function to apply to an existing `Symbol`
`net1`, and the resulting *composed* `Symbol` will have all the attributes of
`net1` and `net2`.
-Once you start building some bigger networks, you might want to name some
-symbols with a common prefix to outline the structure of your network.
-You can use the
-[Prefix](https://github.com/dmlc/mxnet/blob/master/python/mxnet/name.py)
-NameManager as follows:
+Once you start building some bigger networks, you might want to name some
symbols with a common prefix to outline the structure of your network. You can
use the [Prefix
class](https://github.com/apache/incubator-mxnet/blob/master/python/mxnet/name.py#L93)
as follows:
```python
data = mx.sym.Variable("data")
@@ -209,63 +160,76 @@ net.list_arguments()
### Modularized Construction for Deep Networks
-Constructing a *deep* network layer by layer, (like the Google Inception
network),
-can be tedious owing to the large number of layers.
-So, for such networks, we often modularize the construction.
+Constructing a *deep* network layer by layer, (like the Google Inception
network), can be tedious owing to the large number of layers. So, for such
networks, we often modularize the construction.
-For example, in Google Inception network,
-we can first define a factory function which chains the convolution,
-batch normalization and rectified linear unit (ReLU) activation layers
together.
+For example, in Google Inception network, we can first define a factory
function which chains the convolution, batch normalization and rectified linear
unit (ReLU) activation layers together.
```python
-def ConvFactory(data, num_filter, kernel, stride=(1,1), pad=(0, 0),name=None,
suffix=''):
- conv = mx.sym.Convolution(data=data, num_filter=num_filter, kernel=kernel,
- stride=stride, pad=pad, name='conv_%s%s' %(name, suffix))
- bn = mx.sym.BatchNorm(data=conv, name='bn_%s%s' %(name, suffix))
- act = mx.sym.Activation(data=bn, act_type='relu', name='relu_%s%s'
- %(name, suffix))
+def ConvFactory(data, num_filter, kernel,
+ stride=(1, 1), pad=(0, 0), name=None, suffix=''):
+ conv = mx.sym.Convolution(data=data, num_filter=num_filter,
+ kernel=kernel, stride=stride, pad=pad,
+ name='conv_%s%s' % (name, suffix))
+
+ bn = mx.sym.BatchNorm(data=conv, name='bn_%s%s' % (name, suffix))
+
+ act = mx.sym.Activation(data=bn, act_type='relu',
+ name='relu_%s%s' % (name, suffix))
return act
+
prev = mx.sym.Variable(name="Previous Output")
-conv_comp = ConvFactory(data=prev, num_filter=64, kernel=(7,7), stride=(2, 2))
+conv_comp = ConvFactory(data=prev, num_filter=64, kernel=(7, 7), stride=(2, 2))
shape = {"Previous Output" : (128, 3, 28, 28)}
-mx.viz.plot_network(symbol=conv_comp, shape=shape,
node_attrs={"shape":"oval","fixedsize":"false"})
+mx.viz.plot_network(symbol=conv_comp, shape=shape,
+ node_attrs={"shape": "oval", "fixedsize": "false"})
```
-Then we can define a function that constructs an inception module based on
-factory function `ConvFactory`.
+Then we can define a function that constructs an inception module based on
factory function `ConvFactory`.
```python
-def InceptionFactoryA(data, num_1x1, num_3x3red, num_3x3, num_d3x3red,
num_d3x3,
- pool, proj, name):
+def InceptionFactoryA(data, num_1x1, num_3x3red, num_3x3, num_d3x3red,
+ num_d3x3, pool, proj, name):
# 1x1
- c1x1 = ConvFactory(data=data, num_filter=num_1x1, kernel=(1, 1),
name=('%s_1x1' % name))
+ c1x1 = ConvFactory(data=data, num_filter=num_1x1, kernel=(1, 1),
+ name=('%s_1x1' % name))
+
# 3x3 reduce + 3x3
- c3x3r = ConvFactory(data=data, num_filter=num_3x3red, kernel=(1, 1),
name=('%s_3x3' % name), suffix='_reduce')
- c3x3 = ConvFactory(data=c3x3r, num_filter=num_3x3, kernel=(3, 3), pad=(1,
1), name=('%s_3x3' % name))
+ c3x3r = ConvFactory(data=data, num_filter=num_3x3red, kernel=(1, 1),
+ name=('%s_3x3' % name), suffix='_reduce')
+ c3x3 = ConvFactory(data=c3x3r, num_filter=num_3x3, kernel=(3, 3),
+ pad=(1, 1), name=('%s_3x3' % name))
+
# double 3x3 reduce + double 3x3
- cd3x3r = ConvFactory(data=data, num_filter=num_d3x3red, kernel=(1, 1),
name=('%s_double_3x3' % name), suffix='_reduce')
- cd3x3 = ConvFactory(data=cd3x3r, num_filter=num_d3x3, kernel=(3, 3),
pad=(1, 1), name=('%s_double_3x3_0' % name))
- cd3x3 = ConvFactory(data=cd3x3, num_filter=num_d3x3, kernel=(3, 3),
pad=(1, 1), name=('%s_double_3x3_1' % name))
+ cd3x3r = ConvFactory(data=data, num_filter=num_d3x3red, kernel=(1, 1),
+ name=('%s_double_3x3' % name), suffix='_reduce')
+ cd3x3 = ConvFactory(data=cd3x3r, num_filter=num_d3x3, kernel=(3, 3),
+ pad=(1, 1), name=('%s_double_3x3_0' % name))
+ cd3x3 = ConvFactory(data=cd3x3, num_filter=num_d3x3, kernel=(3, 3),
+ pad=(1, 1), name=('%s_double_3x3_1' % name))
+
# pool + proj
- pooling = mx.sym.Pooling(data=data, kernel=(3, 3), stride=(1, 1), pad=(1,
1), pool_type=pool, name=('%s_pool_%s_pool' % (pool, name)))
- cproj = ConvFactory(data=pooling, num_filter=proj, kernel=(1, 1),
name=('%s_proj' % name))
+ pooling = mx.sym.Pooling(data=data, kernel=(3, 3), stride=(1, 1),
+ pad=(1, 1), pool_type=pool,
+ name=('%s_pool_%s_pool' % (pool, name)))
+ cproj = ConvFactory(data=pooling, num_filter=proj, kernel=(1, 1),
+ name=('%s_proj' % name))
+
# concat
- concat = mx.sym.Concat(*[c1x1, c3x3, cd3x3, cproj],
name='ch_concat_%s_chconcat' % name)
+ concat = mx.sym.Concat(*[c1x1, c3x3, cd3x3, cproj],
+ name='ch_concat_%s_chconcat' % name)
return concat
+
prev = mx.sym.Variable(name="Previous Output")
in3a = InceptionFactoryA(prev, 64, 64, 64, 64, 96, "avg", 32, name="in3a")
-mx.viz.plot_network(symbol=in3a, shape=shape,
node_attrs={"shape":"oval","fixedsize":"false"})
+mx.viz.plot_network(symbol=in3a, shape=shape,
+ node_attrs={"shape": "oval", "fixedsize": "false"})
```
-Finally, we can obtain the whole network by chaining multiple inception
-modules. See a complete example
-[here](https://github.com/dmlc/mxnet/blob/master/example/image-classification/symbols/inception-bn.py).
+Finally, we can obtain the whole network by chaining multiple inception
modules. See a complete example
[here](https://github.com/dmlc/mxnet/blob/master/example/image-classification/symbols/inception-bn.py).
### Group Multiple Symbols
-To construct neural networks with multiple loss layers, we can use
-`mxnet.sym.Group` to group multiple symbols together. The following example
-groups two outputs:
+To construct neural networks with multiple loss layers, we can use
`mxnet.sym.Group` to group multiple Symbols together. The following example
groups two outputs:
```python
net = mx.sym.Variable('data')
@@ -279,48 +243,35 @@ group.list_outputs()
## Relations to NDArray
-As you can see now, both `Symbol` and `NDArray` provide multi-dimensional array
-operations, such as `c = a + b` in MXNet. We briefly clarify the differences
here.
+As you can see now, both `Symbol` and `NDArray` provide multi-dimensional
array operations, such as `c = a + b` in MXNet. We briefly clarify the
differences here.
-The `NDArray` provides an imperative programming alike interface, in which the
-computations are evaluated sentence by sentence. While `Symbol` is closer to
-declarative programming, in which we first declare the computation and then
-evaluate with data. Examples in this category include regular expressions and
-SQL.
+The `NDArray` provides an imperative programming alike interface, in which the
computations are evaluated sentence by sentence. While `Symbol` is closer to
declarative programming, in which we first declare the computation and then
evaluate with data. Examples in this category include regular expressions and
SQL.
The pros for `NDArray`:
- Straightforward.
-- Easy to work with native language features (for loop, if-else condition, ..)
- and libraries (numpy, ..).
+- Easy to work with native language features (for loop, if-else condition, ..)
and libraries (numpy, ..).
- Easy step-by-step code debugging.
The pros for `Symbol`:
-- Provides almost all functionalities of NDArray, such as `+`, `*`, `sin`,
- `reshape` etc.
+- Provides almost all functionalities of NDArray, such as `+`, `*`, `sin`,
`reshape` etc.
- Easy to save, load and visualize.
- Easy for the backend to optimize the computation and memory usage.
## Symbol Manipulation
-One important difference of `Symbol` compared to `NDArray` is that we first
-declare the computation and then bind the computation with data to run.
-
-In this section, we introduce the functions to manipulate a symbol directly.
But
-note that, most of them are wrapped by the high-level packages: `Module` and
`Gluon`.
+One important difference of `Symbol` compared to `NDArray` is that we first
declare the computation and then bind the computation with data to run. In this
section, we introduce the functions to manipulate a `Symbol` directly. But note
that, most of them are wrapped by the high-level packages:
[`Module`](https://mxnet.incubator.apache.org/api/python/module/module.html)
and [`Gluon`](https://mxnet.incubator.apache.org/api/python/gluon/gluon.html).
### Shape and Type Inference
-For each symbol, we can query its arguments, auxiliary states and outputs.
-We can also infer the output shape and type of the symbol given the known input
-shape or type of some arguments, which facilitates memory allocation.
+For each `Symbol`, we can query its arguments, auxiliary states and outputs.
We can also infer the output shape and type of the `Symbol` given the known
input shape or type of some arguments, which facilitates memory allocation.
```python
arg_name = c.list_arguments() # get the names of the inputs
out_name = c.list_outputs() # get the names of the outputs
# infers output shape given the shape of input arguments
-arg_shape, out_shape, _ = c.infer_shape(a=(2,3), b=(2,3))
+arg_shape, out_shape, _ = c.infer_shape(a=(2, 3), b=(2, 3))
# infers output type given the type of input arguments
arg_type, out_type, _ = c.infer_type(a='float32', b='float32')
{'input' : dict(zip(arg_name, arg_shape)),
@@ -331,13 +282,9 @@ arg_type, out_type, _ = c.infer_type(a='float32',
b='float32')
### Bind with Data and Evaluate
-The symbol `c` constructed above declares what computation should be run. To
-evaluate it, we first need to feed the arguments, namely free variables, with
data.
+The `Symbol` `c` constructed above declares what computation should be run. To
evaluate it, we first need to feed the arguments, namely free variables, with
data.
-We can do it by using the `bind` method, which accepts device context and
-a `dict` mapping free variable names to `NDArray`s as arguments and returns an
-executor. The executor provides `forward` method for evaluation and an
attribute
-`outputs` to get all the results.
+We can do it by using the
[`bind`](https://mxnet.incubator.apache.org/api/python/symbol/symbol.html#mxnet.symbol.Symbol.bind)
method, which accepts device context and a `dict` mapping free variable names
to `NDArray`s as arguments and returns an
[`Executor`](https://mxnet.incubator.apache.org/api/python/executor/executor.html#mxnet.executor.Executor).
The `Executor` provides
[`forward`](https://mxnet.incubator.apache.org/api/python/executor/executor.html#mxnet.executor.Executor.forward)
[...]
```python
ex = c.bind(ctx=mx.cpu(), args={'a' : mx.nd.ones([2,3]),
@@ -347,11 +294,10 @@ print('number of outputs = %d\nthe first output = \n%s' %
(
len(ex.outputs), ex.outputs[0].asnumpy()))
```
-We can evaluate the same symbol on GPU with different data.
+We can evaluate the same `Symbol` on GPU with different data.
-**Note** In order to execute the following section on a cpu set gpu_device to
mx.cpu().
```python
-gpu_device=mx.gpu() # Change this to mx.cpu() in absence of GPUs.
+gpu_device = mx.gpu() if mx.test_utils.list_gpus() else mx.cpu()
ex_gpu = c.bind(ctx=gpu_device, args={'a' : mx.nd.ones([3,4], gpu_device)*2,
'b' : mx.nd.ones([3,4], gpu_device)*3})
@@ -359,8 +305,7 @@ ex_gpu.forward()
ex_gpu.outputs[0].asnumpy()
```
-We can also use `eval` method to evaluate the symbol. It combines calls to
`bind`
-and `forward` methods.
+We can also use
[eval](https://mxnet.incubator.apache.org/api/python/symbol/symbol.html#mxnet.symbol.Symbol.eval)
method to evaluate the `Symbol`. It combines calls to `bind` and `forward`
methods.
```python
ex = c.eval(ctx = mx.cpu(), a = mx.nd.ones([2,3]), b = mx.nd.ones([2,3]))
@@ -368,24 +313,13 @@ print('number of outputs = %d\nthe first output = \n%s' %
(
len(ex), ex[0].asnumpy()))
```
-For neural nets, a more commonly used pattern is ```simple_bind```, which
-creates all of the argument arrays for you. Then you can call ```forward```,
-and ```backward``` (if the gradient is needed) to get the gradient.
+For neural nets, a more commonly used pattern is
[simple_bind](https://mxnet.incubator.apache.org/api/python/symbol/symbol.html#mxnet.symbol.Symbol.simple_bind),
which creates all of the argument arrays for you. Then you can call `forward`,
and
[`backward`](https://mxnet.incubator.apache.org/api/python/executor/executor.html#mxnet.executor.Executor.backward)
to get gradients if needed.
### Load and Save
-Logically symbols correspond to ndarrays. They both represent a tensor. They
both
-are inputs/outputs of operators. We can either serialize a `Symbol` object by
-using `pickle`, or by using `save` and `load` methods directly as we discussed
in
-[NDArray
tutorial](http://mxnet.io/tutorials/basic/ndarray.html#serialize-from-to-distributed-filesystems).
+Logically Symbols correspond to NDArrays. They both represent a tensor. They
both are inputs/outputs of operators. We can either serialize a `Symbol` object
by using `pickle`, or by using `save` and `load` methods directly as it is
explained in [this NDArray
tutorial](http://mxnet.io/tutorials/basic/ndarray.html#serialize-from-to-distributed-filesystems).
-When serializing `NDArray`, we serialize the tensor data in it and directly
dump to
-disk in binary format.
-But symbol uses a concept of graph. Graphs are composed by chaining operators.
They are
-implicitly represented by output symbols. So, when serializing a `Symbol`, we
-serialize the graph of which the symbol is an output. While serialization,
Symbol
-uses more readable `json` format for serialization. To convert symbol to `json`
-string, use `tojson` method.
+When serializing `NDArray`, we serialize the tensor data in it and directly
dump to disk in binary format. But `Symbol` uses a concept of graph. Graphs are
composed by chaining operators. They are implicitly represented by output
Symbols. So, when serializing a `Symbol`, we serialize the graph of which the
`Symbol` is an output. While serialization, `Symbol` uses more readable `json`
format for serialization. To convert `Symbol` to `json` string, use
[`tojson`](https://mxnet.incubator.ap [...]
```python
print(c.tojson())
@@ -396,25 +330,16 @@ c.tojson() == c2.tojson()
## Customized Symbol
-Most operators such as `mx.sym.Convolution` and `mx.sym.Reshape` are
implemented
-in C++ for better performance. MXNet also allows users to write new operators
-using any front-end language such as Python. It often makes the developing and
-debugging much easier. To implement an operator in Python, refer to
-[How to create new operators](http://mxnet.io/faq/new_op.html).
+Most operators such as
[`mx.sym.Convolution`](https://mxnet.incubator.apache.org/api/python/symbol/symbol.html#mxnet.symbol.Convolution)
and
[`mx.sym.Reshape`](https://mxnet.incubator.apache.org/api/python/symbol/symbol.html#mxnet.symbol.reshape)
are implemented in C++ for better performance. MXNet also allows users to
write new operators using any front-end language such as Python. It often makes
the developing and debugging much easier. To implement an operator in Python,
refer to [How [...]
## Advanced Usages
### Type Cast
-By default, MXNet uses 32-bit floats.
-But for better accuracy-performance,
-we can also use a lower precision data type.
-For example, The Nvidia Tesla Pascal GPUs
-(e.g. P100) have improved 16-bit float performance,
-while GTX Pascal GPUs (e.g. GTX 1080) are fast on 8-bit integers.
+By default, MXNet uses 32-bit floats. But for better accuracy-performance, we
can also use a lower precision data type.
+For example, The NVIDIA Tesla Pascal GPUs (e.g. P100) have improved 16-bit
float performance, while GTX Pascal GPUs (e.g. GTX 1080) are fast on 8-bit
integers.
-To convert the data type as per the requirements,
-we can use `mx.sym.cast` operator as follows:
+To convert the data type as per the requirements, we can use
[`mx.sym.cast`](https://mxnet.incubator.apache.org/api/python/symbol/symbol.html#mxnet.symbol.cast)
operator as follows:
```python
a = mx.sym.Variable('data')
@@ -429,18 +354,107 @@ print({'input':arg, 'output':out})
### Variable Sharing
-To share the contents between several symbols,
-we can bind these symbols with the same array as follows:
+To share the contents between several Symbols, we can bind these Symbols with
the same array as follows:
```python
a = mx.sym.Variable('a')
b = mx.sym.Variable('b')
b = a + a * a
-data = mx.nd.ones((2,3))*2
+data = mx.nd.ones((2,3)) * 2
ex = b.bind(ctx=mx.cpu(), args={'a':data, 'b':data})
ex.forward()
ex.outputs[0].asnumpy()
```
+### Weight tying
+
+You can use same principle to tie weights of different layers. In the example
below two `FullyConnected` layers share same weights and biases, but process
different data. Let's demonstrate how we can do it.
+
+In this example we first create training and evaluation datasets. Both of them
consist of two individual `NDArray`s. We are using `NDArrayIter` to iterate
over all of them.
+
+```python
+import numpy as np
+import mxnet as mx
+
+# Training data
+train_data_size = 4
+train_data1 = mx.random.uniform(shape=(train_data_size, 2))
+train_data2 = mx.random.uniform(shape=(train_data_size, 2))
+train_label = mx.nd.array([i % 2 for i in range(train_data_size)])
+batch_size = 3
+
+# Evaluation Data
+eval_data_size = 3
+eval_data1 = mx.random.uniform(shape=(eval_data_size, 2))
+eval_data2 = mx.random.uniform(shape=(eval_data_size, 2))
+eval_label = np.array([i % 2 for i in range(eval_data_size)])
+
+train_iter = mx.io.NDArrayIter({'inputs_left': train_data1,
+ 'inputs_right': train_data2},
+ train_label, batch_size, shuffle=True,
+ label_name='labels', last_batch_handle='pad')
+
+eval_iter = mx.io.NDArrayIter({'inputs_left': eval_data1,
+ 'inputs_right': eval_data2},
+ eval_label, batch_size, shuffle=False,
+ label_name='labels',
+ last_batch_handle='pad')
+```
+
+We define a `Symbol` for both `inputs_left` and `inputs_right` variables, and
separate symbols for `shared_weight` and `shared_bias`. We use `shared_weight`
and `shared_bias` symbols in both `FullyConnected` layers, making sure that
they are using the same data underlying the symbols. This is where weight tying
is happening.
+
+```python
+num_hidden_nodes = 2
+
+# Assume the left and right inputs have the same shape as each other
+inputs_left = mx.sym.var('inputs_left')
+inputs_right = mx.sym.var('inputs_right')
+labels = mx.symbol.Variable('labels')
+
+shared_weight = mx.symbol.Variable('shared_weight')
+shared_bias = mx.symbol.Variable('shared_bias')
+
+fc_left_sym = mx.sym.FullyConnected(data=inputs_left, weight=shared_weight,
+ bias=shared_bias,
+ num_hidden=num_hidden_nodes,
name='fc_left')
+
+fc_right_sym = mx.sym.FullyConnected(data=inputs_right, weight=shared_weight,
+ bias=shared_bias,
+ num_hidden=num_hidden_nodes,
name='fc_right')
+
+combined = mx.sym.concat(fc_left_sym, fc_right_sym)
+output = mx.sym.SoftmaxOutput(data=combined, label=labels, name='softmax')
+```
+
+In the next lines of the code, we use `Module API` to start the training. We
first create a `Module` object and then call `fit` providing data iterators. To
use trained model for prediction, we use `predict` method, providing evaluation
data iterator.
+
+```python
+model = mx.mod.Module(
+ symbol=output,
+ data_names=['inputs_left', 'inputs_right'],
+ label_names=['labels']
+)
+
+model.fit(train_iter, eval_iter,
+ optimizer_params={'learning_rate': 0.01, 'momentum': 0.9},
+ num_epoch=1,
+ eval_metric='acc')
+
+result = model.predict(eval_iter).asnumpy()
+print(result)
+```
+
+## Recommended Next Steps
+
+- Learn how to [use Module API to train neural
network](https://mxnet.incubator.apache.org/versions/master/tutorials/basic/module.html).
+
+- Explore ways you can [load data using Data
Iterators](https://mxnet.incubator.apache.org/versions/master/tutorials/basic/data.html).
+
+- [Use pretrained
models](https://mxnet.incubator.apache.org/versions/master/tutorials/python/predict_image.html)
for image object detection.
+
+- [Hybridize your
models](https://mxnet.incubator.apache.org/versions/master/tutorials/gluon/hybrid.html)
to get the best from both `Gluon` and `Symbol API`.
+
+- Convert your existing `Module API` code to `Gluon` as it is explained
[here](https://mxnet.incubator.apache.org/versions/master/tutorials/python/module_to_gluon.html).
+
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