6.4. Lazy Initialization¶ Open the notebook in SageMaker Studio Lab
So far, it might seem that we got away with being sloppy in setting up our networks. Specifically, we did the following unintuitive things, which might not seem like they should work:
We defined the network architectures without specifying the input dimensionality.
We added layers without specifying the output dimension of the previous layer.
We even “initialized” these parameters before providing enough information to determine how many parameters our models should contain.
You might be surprised that our code runs at all. After all, there is no way the deep learning framework could tell what the input dimensionality of a network would be. The trick here is that the framework defers initialization, waiting until the first time we pass data through the model, to infer the sizes of each layer on the fly.
Later on, when working with convolutional neural networks, this technique will become even more convenient since the input dimensionality (e.g., the resolution of an image) will affect the dimensionality of each subsequent layer. Hence the ability to set parameters without the need to know, at the time of writing the code, the value of the dimension can greatly simplify the task of specifying and subsequently modifying our models. Next, we go deeper into the mechanics of initialization.
import torch
from torch import nn
from d2l import torch as d2l
from mxnet import np, npx
from mxnet.gluon import nn
npx.set_np()
import jax
from flax import linen as nn
from jax import numpy as jnp
from d2l import jax as d2l
No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)
import tensorflow as tf
To begin, let’s instantiate an MLP.
net = nn.Sequential(nn.LazyLinear(256), nn.ReLU(), nn.LazyLinear(10))
net = nn.Sequential()
net.add(nn.Dense(256, activation='relu'))
net.add(nn.Dense(10))
net = nn.Sequential([nn.Dense(256), nn.relu, nn.Dense(10)])
net = tf.keras.models.Sequential([
tf.keras.layers.Dense(256, activation=tf.nn.relu),
tf.keras.layers.Dense(10),
])
At this point, the network cannot possibly know the dimensions of the input layer’s weights because the input dimension remains unknown.
Consequently the framework has not yet initialized any parameters. We confirm by attempting to access the parameters below.
net[0].weight
<UninitializedParameter>
Consequently the framework has not yet initialized any parameters. We confirm by attempting to access the parameters below.
print(net.collect_params)
print(net.collect_params())
<bound method Block.collect_params of Sequential(
(0): Dense(-1 -> 256, Activation(relu))
(1): Dense(-1 -> 10, linear)
)>
sequential0_ (
Parameter dense0_weight (shape=(256, -1), dtype=float32)
Parameter dense0_bias (shape=(256,), dtype=float32)
Parameter dense1_weight (shape=(10, -1), dtype=float32)
Parameter dense1_bias (shape=(10,), dtype=float32)
)
Note that while the parameter objects exist, the input dimension to each
layer is listed as -1. MXNet uses the special value -1 to indicate that
the parameter dimension remains unknown. At this point, attempts to
access net[0].weight.data() would trigger a runtime error stating
that the network must be initialized before the parameters can be
accessed. Now let’s see what happens when we attempt to initialize
parameters via the initialize method.
net.initialize()
net.collect_params()
[22:11:11] ../src/storage/storage.cc:196: Using Pooled (Naive) StorageManager for CPU
sequential0_ (
Parameter dense0_weight (shape=(256, -1), dtype=float32)
Parameter dense0_bias (shape=(256,), dtype=float32)
Parameter dense1_weight (shape=(10, -1), dtype=float32)
Parameter dense1_bias (shape=(10,), dtype=float32)
)
As we can see, nothing has changed. When input dimensions are unknown, calls to initialize do not truly initialize the parameters. Instead, this call registers to MXNet that we wish (and optionally, according to which distribution) to initialize the parameters.
As mentioned in Section 6.2.1, parameters and the
network definition are decoupled in Jax and Flax, and the user handles
both manually. Flax models are stateless hence there is no
parameters attribute.
Consequently the framework has not yet initialized any parameters. We confirm by attempting to access the parameters below.
[net.layers[i].get_weights() for i in range(len(net.layers))]
[[], []]
Note that each layer objects exist but the weights are empty. Using
net.get_weights() would throw an error since the weights have not
been initialized yet.
Next let’s pass data through the network to make the framework finally initialize parameters.
X = torch.rand(2, 20)
net(X)
net[0].weight.shape
torch.Size([256, 20])
X = np.random.uniform(size=(2, 20))
net(X)
net.collect_params()
sequential0_ (
Parameter dense0_weight (shape=(256, 20), dtype=float32)
Parameter dense0_bias (shape=(256,), dtype=float32)
Parameter dense1_weight (shape=(10, 256), dtype=float32)
Parameter dense1_bias (shape=(10,), dtype=float32)
)
params = net.init(d2l.get_key(), jnp.zeros((2, 20)))
jax.tree_util.tree_map(lambda x: x.shape, params).tree_flatten_with_keys()
(((DictKey(key='params'),
{'layers_0': {'bias': (256,), 'kernel': (20, 256)},
'layers_2': {'bias': (10,), 'kernel': (256, 10)}}),),
('params',))
X = tf.random.uniform((2, 20))
net(X)
[w.shape for w in net.get_weights()]
[(20, 256), (256,), (256, 10), (10,)]
As soon as we know the input dimensionality, 20, the framework can identify the shape of the first layer’s weight matrix by plugging in the value of 20. Having recognized the first layer’s shape, the framework proceeds to the second layer, and so on through the computational graph until all shapes are known. Note that in this case, only the first layer requires lazy initialization, but the framework initializes sequentially. Once all parameter shapes are known, the framework can finally initialize the parameters.
The following method passes in dummy inputs through the network for a dry run to infer all parameter shapes and subsequently initializes the parameters. It will be used later when default random initializations are not desired.
@d2l.add_to_class(d2l.Module) #@save
def apply_init(self, inputs, init=None):
self.forward(*inputs)
if init is not None:
self.net.apply(init)
Parameter initialization in Flax is always done manually and handled by the user. The following method takes a dummy input and a key dictionary as argument. This key dictionary has the rngs for initializing the model parameters and dropout rng for generating the dropout mask for the models with dropout layers. More about dropout will be covered later in Section 5.6. Ultimately the method initializes the model returning the parameters. We have been using it under the hood in the previous sections as well.
@d2l.add_to_class(d2l.Module) #@save
def apply_init(self, dummy_input, key):
params = self.init(key, *dummy_input) # dummy_input tuple unpacked
return params
6.4.1. Summary¶
Lazy initialization can be convenient, allowing the framework to infer parameter shapes automatically, making it easy to modify architectures and eliminating one common source of errors. We can pass data through the model to make the framework finally initialize parameters.
6.4.2. Exercises¶
What happens if you specify the input dimensions to the first layer but not to subsequent layers? Do you get immediate initialization?
What happens if you specify mismatching dimensions?
What would you need to do if you have input of varying dimensionality? Hint: look at the parameter tying.