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5.2. Parameter Management¶
Once we have chosen an architecture and set our hyperparameters, we proceed to the training loop, where our goal is to find parameter values that minimize our objective function. After training, we will need these parameters in order to make future predictions. Additionally, we will sometimes wish to extract the parameters either to reuse them in some other context, to save our model to disk so that it may be exectuted in other software, or for examination in the hopes of gaining scientific understanding.
Most of the time, we will be able to ignore the nitty-gritty details of how parameters are declared and manipulated, relying on DJL to do the heavy lifting. However, when we move away from stacked architectures with standard layers, we will sometimes need to get into the weeds of declaring and manipulating parameters. In this section, we cover the following:
Accessing parameters for debugging, diagnostics, and visualiziations.
Parameter initialization.
Sharing parameters across different model components.
We start by focusing on an MLP with one hidden layer.
%load ../utils/djl-imports
NDManager manager = NDManager.newBaseManager();
NDArray x = manager.randomUniform(0, 1, new Shape(2, 4));
SequentialBlock net = new SequentialBlock();
net.add(Linear.builder().setUnits(8).build());
net.add(Activation.reluBlock());
net.add(Linear.builder().setUnits(1).build());
net.setInitializer(new NormalInitializer(), Parameter.Type.WEIGHT);
net.initialize(manager, DataType.FLOAT32, x.getShape());
ParameterStore ps = new ParameterStore(manager, false);
net.forward(ps, new NDList(x), false).head(); // forward computation
ND: (2, 1) gpu(0) float32
[[-2.03669551e-05],
[-1.32092864e-05],
]
5.2.1. Parameter Access¶
Let us start with how to access parameters from the models that you
already know. Each layer’s parameters are conveniently stored in a
Pair<String, Parameter> consisting of a unique String that
serves as a key for the layer and the Parameter itself. The
ParameterList is an extension of PairList and is returned with a
call to the getParameters() method on a Block. We can inspect
the parameters of the net defined above. When a model is defined via
the SequentialBlock class, we can access any layer’s
Pair<String, Parameter> by calling get() on the
ParameterList and passing in the index of the parameter we want.
Calling getKey() and getValue() on a Pair<String, Parameter>
will get the parameter’s name and Parameter respectively. We can
also directly get the Parameter we want from the ParameterList
by calling get() and passing in its unique key(the String
portion of the Pair<String, Parameter>. If we call valueAt() and
pass in the index, we will get the Parameter directly as well.
ParameterList params = net.getParameters();
// Print out all the keys (unique!)
for (var pair : params) {
System.out.println(pair.getKey());
}
// Use the unique key to access the Parameter
NDArray dense0Weight = params.get("01Linear_weight").getArray();
NDArray dense0Bias = params.get("01Linear_bias").getArray();
// Use indexing to access the Parameter
NDArray dense1Weight = params.valueAt(2).getArray();
NDArray dense1Bias = params.valueAt(3).getArray();
System.out.println(dense0Weight);
System.out.println(dense0Bias);
System.out.println(dense1Weight);
System.out.println(dense1Bias);
01Linear_weight
01Linear_bias
03Linear_weight
03Linear_bias
weight: (8, 4) gpu(0) float32 hasGradient
[[ 0.0014, -0.0122, 0.0031, 0.0111],
[-0.0004, -0.0071, -0.0129, -0.0088],
[-0.0006, -0.0082, 0.0143, -0.0013],
[ 0.0028, 0.0083, -0.0075, -0.0138],
[ 0.01 , -0.0114, -0.0035, 0.0054],
[-0.015 , -0.0122, 0.0124, -0.0027],
[-0.0147, -0.0099, 0.0028, 0.0095],
[ 0.0079, -0.0132, 0.0047, 0.0124],
]
bias: (8) gpu(0) float32 hasGradient
[0., 0., 0., 0., 0., 0., 0., 0.]
weight: (1, 8) gpu(0) float32 hasGradient
[[ 0.0084, 0.0148, 0.0031, 0.004 , -0.0089, 0.0029, -0.0037, -0.0014],
]
bias: (1) gpu(0) float32 hasGradient
[0.]
The output tells us a few important things. First, each fully-connected
layer has two parameters, e.g., dense0Weight and dense0Bias,
corresponding to that layer’s weights and biases, respectively. The
params variable is a ParameterList which contain the key-value
pairs of the layer name and a parameter of the Parameter class. With
a Parameter, we can get the underlying numerical values as
NDArrays by calling getArray() on them! Both the weights and
biases are stored as single precision floats(FLOAT32).
5.2.1.1. Targeted Parameters¶
Parameters are complex objects, containing data, gradients, and additional information. That’s why we need to request the data explicitly. Note that the bias vector consists of zeroes because we have not updated the network since it was initialized.
Note that unlike the biases, the weights are nonzero. This is because
unlike biases, weights are initialized randomly. In addition to
getArray(), each Parameter also provides a requireGradient()
method which returns whether the parameter needs gradients to be
computed (which we set on the NDArray with attachGradient()).
The gradient has the same shape as the weight. To actually access the
gradient, we simply call getGradient() on the NDArray. Because
we have not invoked backpropagation for this network yet, its values are
all 0. We would invoke it by creating a GradientCollector instance
and run our calculations inside it.
dense0Weight.getGradient();
ND: (8, 4) gpu(0) float32
[[0., 0., 0., 0.],
[0., 0., 0., 0.],
[0., 0., 0., 0.],
[0., 0., 0., 0.],
[0., 0., 0., 0.],
[0., 0., 0., 0.],
[0., 0., 0., 0.],
[0., 0., 0., 0.],
]
5.2.1.2. Collecting Parameters from Nested Blocks¶
Let us see how the parameter naming conventions work if we nest multiple blocks inside each other. For that we first define a function that produces Blocks (a Block factory, so to speak) and then combine these inside yet larger Blocks.
public SequentialBlock block1() {
SequentialBlock net = new SequentialBlock();
net.add(Linear.builder().setUnits(32).build());
net.add(Activation.reluBlock());
net.add(Linear.builder().setUnits(16).build());
net.add(Activation.reluBlock());
return net;
}
public SequentialBlock block2() {
SequentialBlock net = new SequentialBlock();
for (int i = 0; i < 4; i++) {
net.add(block1());
}
return net;
}
SequentialBlock rgnet = new SequentialBlock();
rgnet.add(block2());
rgnet.add(Linear.builder().setUnits(10).build());
rgnet.setInitializer(new NormalInitializer(), Parameter.Type.WEIGHT);
rgnet.initialize(manager, DataType.FLOAT32, x.getShape());
rgnet.forward(ps, new NDList(x), false).singletonOrThrow();
ND: (2, 10) gpu(0) float32
[[-9.05861164e-15, -1.80095078e-14, -2.33998527e-14, -1.86868902e-14, 7.10750259e-15, 5.75573922e-15, 9.72335378e-16, 1.06593548e-14, 9.80970201e-15, -8.17016641e-15],
[-4.27109291e-15, -7.85593921e-15, -9.57490109e-15, -7.16382689e-15, 2.99069440e-15, 2.62443375e-15, 6.40666075e-16, 4.29879427e-15, 4.13538595e-15, -3.19015266e-15],
]
Now that we have designed the network, let us see how it is organized.
We can get the list of named parameters by calling getParameters().
However, we not only want to see the parameters, but also how our
network is structured. To see our network architecture, we can simply
print out the block whose architecture we want to see.
/* Network Architecture for RgNet */
rgnet
SequentialBlock(2, 4) {
SequentialBlock(2, 4) {
SequentialBlock(2, 4) {
Linear(2, 4) -> (2, 32)
ReLU(2, 32) -> (2, 32)
Linear(2, 32) -> (2, 16)
ReLU(2, 16) -> (2, 16)
} -> (2, 16)
SequentialBlock(2, 16) {
Linear(2, 16) -> (2, 32)
ReLU(2, 32) -> (2, 32)
Linear(2, 32) -> (2, 16)
ReLU(2, 16) -> (2, 16)
} -> (2, 16)
SequentialBlock(2, 16) {
Linear(2, 16) -> (2, 32)
ReLU(2, 32) -> (2, 32)
Linear(2, 32) -> (2, 16)
ReLU(2, 16) -> (2, 16)
} -> (2, 16)
SequentialBlock(2, 16) {
Linear(2, 16) -> (2, 32)
ReLU(2, 32) -> (2, 32)
Linear(2, 32) -> (2, 16)
ReLU(2, 16) -> (2, 16)
} -> (2, 16)
} -> (2, 16)
Linear(2, 16) -> (2, 10)
} -> (2, 10)
/* Parameters for RgNet */
for (var param : rgnet.getParameters()) {
System.out.println(param.getValue().getArray());
}
weight: (32, 4) gpu(0) float32 hasGradient
[ Exceed max print size ]
bias: (32) gpu(0) float32 hasGradient
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., ... 12 more]
weight: (16, 32) gpu(0) float32 hasGradient
[ Exceed max print size ]
bias: (16) gpu(0) float32 hasGradient
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]
weight: (32, 16) gpu(0) float32 hasGradient
[ Exceed max print size ]
bias: (32) gpu(0) float32 hasGradient
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., ... 12 more]
weight: (16, 32) gpu(0) float32 hasGradient
[ Exceed max print size ]
bias: (16) gpu(0) float32 hasGradient
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]
weight: (32, 16) gpu(0) float32 hasGradient
[ Exceed max print size ]
bias: (32) gpu(0) float32 hasGradient
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., ... 12 more]
weight: (16, 32) gpu(0) float32 hasGradient
[ Exceed max print size ]
bias: (16) gpu(0) float32 hasGradient
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]
weight: (32, 16) gpu(0) float32 hasGradient
[ Exceed max print size ]
bias: (32) gpu(0) float32 hasGradient
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., ... 12 more]
weight: (16, 32) gpu(0) float32 hasGradient
[ Exceed max print size ]
bias: (16) gpu(0) float32 hasGradient
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]
weight: (10, 16) gpu(0) float32 hasGradient
[ Exceed max print size ]
bias: (10) gpu(0) float32 hasGradient
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]
Since the layers are hierarchically nested, we can also access them by
calling their getChildren() method to get a BlockList(also an
extension of PairList) of their inner blocks. It shares methods with
ParameterList and as such we can use their familiar structure to
access the blocks. We can call get(i) to get the
Pair<String, Block> at the index i we want, and then finally
getValue() to get the actual block. We can do this in one step as
shown above with valueAt(i). Then we have to repeat that to get that
blocks child and so on.
Here, we access the first major block, within it the second subblock, and within that the bias of the first layer, with as follows:
Block majorBlock1 = rgnet.getChildren().get(0).getValue();
Block subBlock2 = majorBlock1.getChildren().valueAt(1);
Block linearLayer1 = subBlock2.getChildren().valueAt(0);
NDArray bias = linearLayer1.getParameters().valueAt(1).getArray();
bias
bias: (32) gpu(0) float32 hasGradient
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., ... 12 more]
5.2.2. Parameter Initialization¶
Now that we know how to access the parameters, let us look at how to
initialize them properly. We discussed the need for initialization in
Section 4.8. By default, DJL initializes weight
matrices based on your set initializer and the bias parameters are all
set to \(0\). However, we will often want to initialize our weights
according to various other protocols. DJL’s
ai.djl.training.initializer package provides a variety of preset
initialization methods. If we want to create a custom initializer, we
need to do some extra work.
5.2.2.1. Built-in Initialization¶
In DJL, when setting the initializer for blocks, the default
setInitializer() function does not overwrite any previous set
initializers. So if you set an initializer earlier, but decide you want
to change your initializer and call setInitializer() again, the
second setInitializer() will NOT overwrite your first one.
Additionally, when you call setInitializer() on a block, all
internal blocks will also call setInitializer() with the same given
initializer.
This means that we can call setInitializer() on the highest level of
a block and know that all internal blocks that do not have an
initializer already set will be set to that given initializer.
This setup has the advantage that we don’t have to worry about our
setInitializer() overriding our previous initializers on
internal blocks!
If you want to however, you can explicitly set an initializer for a
Parameter by calling its setInitializer() function directly.
Let us begin by calling on built-in initializers. The code below
initializes all parameters to a given constant value 1, by using the
ConstantInitializer() initializer.
Note that this will not do anything currently since we have already set our initializer in the previous code block. We can verify this by checking the weight of a parameter.
net.setInitializer(new ConstantInitializer(1), Parameter.Type.WEIGHT);
net.initialize(manager, DataType.FLOAT32, x.getShape());
Block linearLayer = net.getChildren().get(0).getValue();
NDArray weight = linearLayer.getParameters().get(0).getValue().getArray();
weight
weight: (8, 4) gpu(0) float32 hasGradient
[[ 0.0014, -0.0122, 0.0031, 0.0111],
[-0.0004, -0.0071, -0.0129, -0.0088],
[-0.0006, -0.0082, 0.0143, -0.0013],
[ 0.0028, 0.0083, -0.0075, -0.0138],
[ 0.01 , -0.0114, -0.0035, 0.0054],
[-0.015 , -0.0122, 0.0124, -0.0027],
[-0.0147, -0.0099, 0.0028, 0.0095],
[ 0.0079, -0.0132, 0.0047, 0.0124],
]
We can see these initializations however if we create a new network. Let us write a function to create these network architectures for us conveniently.
public SequentialBlock getNet() {
SequentialBlock net = new SequentialBlock();
net.add(Linear.builder().setUnits(8).build());
net.add(Activation.reluBlock());
net.add(Linear.builder().setUnits(1).build());
return net;
}
If we run our previous initializer on this new net and check a parameter, we’ll see that everything is initialized properly! (to 7777!)
SequentialBlock net = getNet();
net.setInitializer(new ConstantInitializer(7777), Parameter.Type.WEIGHT);
net.initialize(manager, DataType.FLOAT32, x.getShape());
Block linearLayer = net.getChildren().valueAt(0);
NDArray weight = linearLayer.getParameters().valueAt(0).getArray();
weight
weight: (8, 4) gpu(0) float32 hasGradient
[[7777., 7777., 7777., 7777.],
[7777., 7777., 7777., 7777.],
[7777., 7777., 7777., 7777.],
[7777., 7777., 7777., 7777.],
[7777., 7777., 7777., 7777.],
[7777., 7777., 7777., 7777.],
[7777., 7777., 7777., 7777.],
[7777., 7777., 7777., 7777.],
]
We can also initialize all parameters as Gaussian random variables with standard deviation \(.01\).
net = getNet();
net.setInitializer(new NormalInitializer(), Parameter.Type.WEIGHT);
net.initialize(manager, DataType.FLOAT32, x.getShape());
Block linearLayer = net.getChildren().valueAt(0);
NDArray weight = linearLayer.getParameters().valueAt(0).getArray();
weight
weight: (8, 4) gpu(0) float32 hasGradient
[[-0.0177, 0.0105, 0.0094, 0.0044],
[-0.0022, -0.0001, 0.0036, -0.004 ],
[-0.0125, -0.0027, 0.0097, 0.0101],
[ 0.0065, -0.002 , 0.0073, -0.0172],
[ 0.0097, 0.0089, -0.0052, -0.0107],
[-0.0029, 0.0028, -0.0105, -0.0018],
[ 0.0054, 0.003 , 0.002 , 0.0024],
[ 0.015 , 0.0065, 0.0025, 0.0031],
]
We can also apply different initializers for certain Blocks. For
example, below we initialize the first layer with the
XavierInitializer initializer and initialize the second layer to a
constant value of 0.
We will do this without the getNet() function as it will be easier
to have the reference to each block we want to set.
net = new SequentialBlock();
Linear linear1 = Linear.builder().setUnits(8).build();
net.add(linear1);
net.add(Activation.reluBlock());
Linear linear2 = Linear.builder().setUnits(1).build();
net.add(linear2);
linear1.setInitializer(new XavierInitializer(), Parameter.Type.WEIGHT);
linear1.initialize(manager, DataType.FLOAT32, x.getShape());
linear2.setInitializer(Initializer.ZEROS, Parameter.Type.WEIGHT);
linear2.initialize(manager, DataType.FLOAT32, x.getShape());
System.out.println(linear1.getParameters().valueAt(0).getArray());
System.out.println(linear2.getParameters().valueAt(0).getArray());
weight: (8, 4) gpu(0) float32 hasGradient
[[ 0.0278, -0.6041, 0.4178, 0.353 ],
[-0.3376, -0.6848, 0.9613, 0.4915],
[ 0.0134, 0.7977, -0.7357, 0.3095],
[-0.2741, 0.9281, -0.7897, 0.6313],
[ 0.6626, -0.855 , 0.8329, -0.8253],
[-0.0768, -0.2861, -0.5441, -0.3841],
[ 0.7445, -0.1896, 0.9236, -0.9658],
[-0.8702, -0.7979, -0.647 , 0.4605],
]
weight: (1, 4) gpu(0) float32 hasGradient
[[0., 0., 0., 0.],
]
Finally, we can directly access the Parameter.setInitializer() and
set their initializers individually.
net = getNet();
ParameterList params = net.getParameters();
params.get("01Linear_weight").setInitializer(new NormalInitializer());
params.get("03Linear_weight").setInitializer(Initializer.ONES);
net.initialize(manager, DataType.FLOAT32, new Shape(2, 4));
System.out.println(params.valueAt(0).getArray());
System.out.println(params.valueAt(2).getArray());
weight: (8, 4) gpu(0) float32 hasGradient
[[-1.15521299e-03, 7.32516497e-03, 6.36620028e-03, -1.50065892e-03],
[ 2.41896766e-03, 1.46766659e-02, -5.15699200e-03, -9.57099814e-03],
[-1.89914349e-02, 9.95623507e-03, -1.23957479e-02, -1.58190250e-03],
[ 1.43888686e-02, 1.27938064e-03, -4.72124293e-03, -1.26627041e-02],
[ 7.73682771e-03, -1.27218431e-02, 2.34187441e-03, -2.64764996e-03],
[-1.18591927e-03, -7.90396240e-03, -1.40495235e-02, -9.98240503e-05],
[-2.49697431e-03, 1.20517462e-02, 4.49518068e-03, -1.74778444e-03],
[ 3.18636792e-03, 8.12058279e-04, 2.10815314e-02, 2.31559388e-04],
]
weight: (1, 8) gpu(0) float32 hasGradient
[[1., 1., 1., 1., 1., 1., 1., 1.],
]
5.2.2.2. Custom Initialization¶
Sometimes, the initialization methods we need are not standard in DJL.
In these cases, we can define a class to implement the Initializer
interface. We only have to implement the initialize() function,
which takes an NDManager, a Shape, and the DataType. We then
create the NDArray with the aforementioned Shape and
DataType and initialize it to what we want! You can also design your
initializer to take in some parameters. Simply declare them as fields in
the class and pass them in as inputs to the constructor! In the example
below, we define an initializer for the following strange distribution:
static class MyInit implements Initializer {
public MyInit() {}
@Override
public NDArray initialize(NDManager manager, Shape shape, DataType dataType) {
System.out.printf("Init %s\n", shape.toString());
// Here we generate data points
// from a uniform distribution [-10, 10]
NDArray data = manager.randomUniform(-10, 10, shape, dataType);
// We keep the data points whose absolute value is >= 5
// and set the others to 0.
// This generates the distribution `w` shown above.
NDArray absGte5 = data.abs().gte(5); // returns boolean NDArray where
// true indicates abs >= 5 and
// false otherwise
return data.mul(absGte5); // keeps true indices and sets false indices to 0.
// special operation when multiplying a numerical
// NDArray with a boolean NDArray
}
}
net = getNet();
net.setInitializer(new MyInit(), Parameter.Type.WEIGHT);
net.initialize(manager, DataType.FLOAT32, x.getShape());
Block linearLayer = net.getChildren().valueAt(0);
NDArray weight = linearLayer.getParameters().valueAt(0).getArray();
weight
Init (8, 4)
Init (1, 8)
weight: (8, 4) gpu(0) float32 hasGradient
[[-9.1163, -6.9159, 0. , -8.4723],
[ 0. , 0. , -0. , 0. ],
[-0. , -8.671 , -0. , -5.3997],
[ 8.7472, 0. , -8.2616, 9.9264],
[-6.2768, 0. , 0. , 8.6895],
[-5.7016, -0. , 0. , -6.9426],
[-7.707 , -5.926 , -7.6513, -5.6711],
[ 0. , -8.0809, 6.4497, 0. ],
]
Note that we always have the option of setting parameters directly by
calling getValue().getArray() to access the underlying NDArray.
A note for advanced users: you cannot directly modify parameters within
a GarbageCollector scope. You must modify them outside the
GarbageCollector scope to avoid confusing the automatic
differentiation mechanics.
// '__'i() is an inplace operation to modify the original NDArray
NDArray weightLayer = net.getChildren().valueAt(0)
.getParameters().valueAt(0).getArray();
weightLayer.addi(7);
weightLayer.divi(9);
weightLayer.set(new NDIndex(0, 0), 2020); // set the (0, 0) index to 2020
weightLayer;
weight: (8, 4) gpu(0) float32 hasGradient
[[ 2.02000000e+03, 9.33975633e-03, 7.77777791e-01, -1.63584173e-01],
[ 7.77777791e-01, 7.77777791e-01, 7.77777791e-01, 7.77777791e-01],
[ 7.77777791e-01, -1.85668409e-01, 7.77777791e-01, 1.77807391e-01],
[ 1.74969053e+00, 7.77777791e-01, -1.40176028e-01, 1.88070786e+00],
[ 8.03590342e-02, 7.77777791e-01, 7.77777791e-01, 1.74327302e+00],
[ 1.44270793e-01, 7.77777791e-01, 7.77777791e-01, 6.38061110e-03],
[-7.85554796e-02, 1.19334698e-01, -7.23678768e-02, 1.47656441e-01],
[ 7.77777791e-01, -1.20095044e-01, 1.49441588e+00, 7.77777791e-01],
]
5.2.3. Tied Parameters¶
Often, we want to share parameters across multiple layers. Later we will see that when learning word embeddings, it might be sensible to use the same parameters both for encoding and decoding words. We discussed one such case when we introduced Section 5.1. Let us see how to do this a bit more elegantly. In the following we allocate a dense layer and then use its parameters specifically to set those of another layer.
SequentialBlock net = new SequentialBlock();
// We need to give the shared layer a name
// such that we can reference its parameters
Block shared = Linear.builder().setUnits(8).build();
SequentialBlock sharedRelu = new SequentialBlock();
sharedRelu.add(shared);
sharedRelu.add(Activation.reluBlock());
net.add(Linear.builder().setUnits(8).build());
net.add(Activation.reluBlock());
net.add(sharedRelu);
net.add(sharedRelu);
net.add(Linear.builder().setUnits(10).build());
NDArray x = manager.randomUniform(-10f, 10f, new Shape(2, 20), DataType.FLOAT32);
net.setInitializer(new NormalInitializer(), Parameter.Type.WEIGHT);
net.initialize(manager, DataType.FLOAT32, x.getShape());
net.forward(ps, new NDList(x), false).singletonOrThrow();
ND: (2, 10) gpu(0) float32
[[ 9.12869041e-07, -5.45645150e-07, -7.63911885e-08, -1.30723640e-06, 5.81459858e-09, 3.53183111e-07, -1.83811517e-06, 6.10700113e-08, -1.29771331e-06, -4.32388333e-07],
[ 2.56628596e-07, -8.86486617e-08, -3.76434087e-07, -6.47941434e-08, -1.70266688e-07, -7.75124704e-07, -5.09972665e-07, -2.44016348e-07, 8.00716009e-07, -2.85646138e-08],
]
// Check that the parameters are the same
NDArray shared1 = net.getChildren().valueAt(2)
.getParameters().valueAt(0).getArray();
NDArray shared2 = net.getChildren().valueAt(3)
.getParameters().valueAt(0).getArray();
shared1.eq(shared2);
ND: (8, 8) gpu(0) boolean
[[ true, true, true, true, true, true, true, true],
[ true, true, true, true, true, true, true, true],
[ true, true, true, true, true, true, true, true],
[ true, true, true, true, true, true, true, true],
[ true, true, true, true, true, true, true, true],
[ true, true, true, true, true, true, true, true],
[ true, true, true, true, true, true, true, true],
[ true, true, true, true, true, true, true, true],
]
This example shows that the parameters of the second and third layer are
tied. They are not just equal, they are represented by the same exact
NDArray. Thus, if we change one of the parameters, the other one
changes, too. You might wonder, when parameters are tied what happens
to the gradients? Since the model parameters contain gradients, the
gradients of the second hidden layer and the third hidden layer are
added together in shared.getGradient() during backpropagation.
5.2.4. Summary¶
We have several ways to access, initialize, and tie model parameters.
We can use custom initialization.
DJL has a sophisticated mechanism for accessing parameters in a unique and hierarchical manner.
5.2.5. Exercises¶
Use the FancyMLP defined in Section 5.1 and access the parameters of the various layers.
Look at the DJL documentation and explore different initializers.
Try accessing the model parameters after
net.initialize()and beforepredictor.predict(x)to observe the shape of the model parameters. What changes? Why?Construct a multilayer perceptron containing a shared parameter layer and train it. During the training process, observe the model parameters and gradients of each layer.
Why is sharing parameters a good idea?