# Copyright 2018 DeepMind Technologies Limited
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ============================================================================
"""Code defining LEO inner loop.
See "Meta-Learning with Latent Embedding Optimization" by Rusu et al.
(https://arxiv.org/pdf/1807.05960.pdf).
"""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
from six.moves import range
from six.moves import zip
import sonnet as snt
import tensorflow as tf
import tensorflow_probability as tfp
import data as data_module
def get_orthogonality_regularizer(orthogonality_penalty_weight):
"""Returns the orthogonality regularizer."""
def orthogonality(weight):
"""Calculates the layer-wise penalty encouraging orthogonality."""
with tf.name_scope(None, "orthogonality", [weight]) as name:
w2 = tf.matmul(weight, weight, transpose_b=True)
wn = tf.norm(weight, ord=2, axis=1, keepdims=True) + 1e-32
correlation_matrix = w2 / tf.matmul(wn, wn, transpose_b=True)
matrix_size = correlation_matrix.get_shape().as_list()[0]
base_dtype = weight.dtype.base_dtype
identity = tf.eye(matrix_size, dtype=base_dtype)
weight_corr = tf.reduce_mean(
tf.squared_difference(correlation_matrix, identity))
return tf.multiply(
tf.cast(orthogonality_penalty_weight, base_dtype),
weight_corr,
name=name)
return orthogonality
class LEO(snt.AbstractModule):
"""Sonnet module implementing the inner loop of LEO."""
def __init__(self, config=None, use_64bits_dtype=True, name="leo"):
super(LEO, self).__init__(name=name)
self._float_dtype = tf.float64 if use_64bits_dtype else tf.float32
self._int_dtype = tf.int64 if use_64bits_dtype else tf.int32
self._inner_unroll_length = config["inner_unroll_length"]
self._finetuning_unroll_length = config["finetuning_unroll_length"]
self._inner_lr_init = config["inner_lr_init"]
self._finetuning_lr_init = config["finetuning_lr_init"]
self._num_latents = config["num_latents"]
self._dropout_rate = config["dropout_rate"]
self._kl_weight = config["kl_weight"] # beta
self._encoder_penalty_weight = config["encoder_penalty_weight"] # gamma
self._l2_penalty_weight = config["l2_penalty_weight"] # lambda_1
# lambda_2
self._orthogonality_penalty_weight = config["orthogonality_penalty_weight"]
assert self._inner_unroll_length > 0, ("Positive unroll length is necessary"
" to create the graph")
def _build(self, data, is_meta_training=True):
"""Connects the LEO module to the graph, creating the variables.
Args:
data: A data_module.ProblemInstance constaining Tensors with the
following shapes:
- tr_input: (N, K, dim)
- tr_output: (N, K, 1)
- tr_info: (N, K)
- val_input: (N, K_valid, dim)
- val_output: (N, K_valid, 1)
- val_info: (N, K_valid)
where N is the number of classes (as in N-way) and K and the and
K_valid are numbers of training and validation examples within a
problem instance correspondingly (as in K-shot), and dim is the
dimensionality of the embedding.
is_meta_training: A boolean describing whether we run in the training
mode.
Returns:
Tensor with the inner validation loss of LEO (include both adaptation in
the latent space and finetuning).
"""
if isinstance(data, list):
data = data_module.ProblemInstance(*data)
self.is_meta_training = is_meta_training
self.save_problem_instance_stats(data.tr_input)
latents, kl = self.forward_encoder(data)
tr_loss, adapted_classifier_weights, encoder_penalty = self.leo_inner_loop(
data, latents)
val_loss, val_accuracy = self.finetuning_inner_loop(
data, tr_loss, adapted_classifier_weights)
val_loss += self._kl_weight * kl
val_loss += self._encoder_penalty_weight * encoder_penalty
# The l2 regularization is is already added to the graph when constructing
# the snt.Linear modules. We pass the orthogonality regularizer separately,
# because it is not used in self.grads_and_vars.
regularization_penalty = (
self._l2_regularization + self._decoder_orthogonality_reg)
batch_val_loss = tf.reduce_mean(val_loss)
batch_val_accuracy = tf.reduce_mean(val_accuracy)
return batch_val_loss + regularization_penalty, batch_val_accuracy
@snt.reuse_variables
def leo_inner_loop(self, data, latents):
with tf.variable_scope("leo_inner"):
inner_lr = tf.get_variable(
"lr", [1, 1, self._num_latents],
dtype=self._float_dtype,
initializer=tf.constant_initializer(self._inner_lr_init))
starting_latents = latents
loss, _ = self.forward_decoder(data, latents)
for _ in range(self._inner_unroll_length):
loss_grad = tf.gradients(loss, latents) # dLtrain/dz
latents -= inner_lr * loss_grad[0]
loss, classifier_weights = self.forward_decoder(data, latents)
if self.is_meta_training:
encoder_penalty = tf.losses.mean_squared_error(
labels=tf.stop_gradient(latents), predictions=starting_latents)
encoder_penalty = tf.cast(encoder_penalty, self._float_dtype)
else:
encoder_penalty = tf.constant(0., self._float_dtype)
return loss, classifier_weights, encoder_penalty
@snt.reuse_variables
def finetuning_inner_loop(self, data, leo_loss, classifier_weights):
tr_loss = leo_loss
with tf.variable_scope("finetuning"):
finetuning_lr = tf.get_variable(
"lr", [1, 1, self.embedding_dim],
dtype=self._float_dtype,
initializer=tf.constant_initializer(self._finetuning_lr_init))
for _ in range(self._finetuning_unroll_length):
loss_grad = tf.gradients(tr_loss, classifier_weights)
classifier_weights -= finetuning_lr * loss_grad[0]
tr_loss, _ = self.calculate_inner_loss(data.tr_input, data.tr_output,
classifier_weights)
val_loss, val_accuracy = self.calculate_inner_loss(
data.val_input, data.val_output, classifier_weights)
return val_loss, val_accuracy
@snt.reuse_variables
def forward_encoder(self, data):
encoder_outputs = self.encoder(data.tr_input)
relation_network_outputs = self.relation_network(encoder_outputs)
latent_dist_params = self.average_codes_per_class(relation_network_outputs)
latents, kl = self.possibly_sample(latent_dist_params)
return latents, kl
@snt.reuse_variables
def forward_decoder(self, data, latents):
weights_dist_params = self.decoder(latents)
# Default to glorot_initialization and not stddev=1.
fan_in = self.embedding_dim.value
fan_out = self.num_classes.value
stddev_offset = np.sqrt(2. / (fan_out + fan_in))
classifier_weights, _ = self.possibly_sample(weights_dist_params,
stddev_offset=stddev_offset)
tr_loss, _ = self.calculate_inner_loss(data.tr_input, data.tr_output,
classifier_weights)
return tr_loss, classifier_weights
@snt.reuse_variables
def encoder(self, inputs):
with tf.variable_scope("encoder"):
after_dropout = tf.nn.dropout(inputs, rate=self.dropout_rate)
regularizer = tf.contrib.layers.l2_regularizer(self._l2_penalty_weight)
initializer = tf.initializers.glorot_uniform(dtype=self._float_dtype)
encoder_module = snt.Linear(
self._num_latents,
use_bias=False,
regularizers={"w": regularizer},
initializers={"w": initializer},
)
outputs = snt.BatchApply(encoder_module)(after_dropout)
return outputs
@snt.reuse_variables
def relation_network(self, inputs):
with tf.variable_scope("relation_network"):
regularizer = tf.contrib.layers.l2_regularizer(self._l2_penalty_weight)
initializer = tf.initializers.glorot_uniform(dtype=self._float_dtype)
relation_network_module = snt.nets.MLP(
[2 * self._num_latents] * 3,
use_bias=False,
regularizers={"w": regularizer},
initializers={"w": initializer},
)
total_num_examples = self.num_examples_per_class*self.num_classes
inputs = tf.reshape(inputs, [total_num_examples, self._num_latents])
left = tf.tile(tf.expand_dims(inputs, 1), [1, total_num_examples, 1])
right = tf.tile(tf.expand_dims(inputs, 0), [total_num_examples, 1, 1])
concat_codes = tf.concat([left, right], axis=-1)
outputs = snt.BatchApply(relation_network_module)(concat_codes)
outputs = tf.reduce_mean(outputs, axis=1)
# 2 * latents, because we are returning means and variances of a Gaussian
outputs = tf.reshape(outputs, [self.num_classes,
self.num_examples_per_class,
2 * self._num_latents])
return outputs
@snt.reuse_variables
def decoder(self, inputs):
with tf.variable_scope("decoder"):
l2_regularizer = tf.contrib.layers.l2_regularizer(self._l2_penalty_weight)
orthogonality_reg = get_orthogonality_regularizer(
self._orthogonality_penalty_weight)
initializer = tf.initializers.glorot_uniform(dtype=self._float_dtype)
# 2 * embedding_dim, because we are returning means and variances
decoder_module = snt.Linear(
2 * self.embedding_dim,
use_bias=False,
regularizers={"w": l2_regularizer},
initializers={"w": initializer},
)
outputs = snt.BatchApply(decoder_module)(inputs)
self._orthogonality_reg = orthogonality_reg(decoder_module.w)
return outputs
def average_codes_per_class(self, codes):
codes = tf.reduce_mean(codes, axis=1, keep_dims=True) # K dimension
# Keep the shape (N, K, *)
codes = tf.tile(codes, [1, self.num_examples_per_class, 1])
return codes
def possibly_sample(self, distribution_params, stddev_offset=0.):
means, unnormalized_stddev = tf.split(distribution_params, 2, axis=-1)
stddev = tf.exp(unnormalized_stddev)
stddev -= (1. - stddev_offset)
stddev = tf.maximum(stddev, 1e-10)
distribution = tfp.distributions.Normal(loc=means, scale=stddev)
if not self.is_meta_training:
return means, tf.constant(0., dtype=self._float_dtype)
samples = distribution.sample()
kl_divergence = self.kl_divergence(samples, distribution)
return samples, kl_divergence
def kl_divergence(self, samples, normal_distribution):
random_prior = tfp.distributions.Normal(
loc=tf.zeros_like(samples), scale=tf.ones_like(samples))
kl = tf.reduce_mean(
normal_distribution.log_prob(samples) - random_prior.log_prob(samples))
return kl
def predict(self, inputs, weights):
after_dropout = tf.nn.dropout(inputs, rate=self.dropout_rate)
# This is 3-dimensional equivalent of a matrix product, where we sum over
# the last (embedding_dim) dimension. We get [N, K, N, K] tensor as output.
per_image_predictions = tf.einsum("ijk,lmk->ijlm", after_dropout, weights)
# Predictions have shape [N, K, N]: for each image ([N, K] of them), what
# is the probability of a given class (N)?
predictions = tf.reduce_mean(per_image_predictions, axis=-1)
return predictions
def calculate_inner_loss(self, inputs, true_outputs, classifier_weights):
model_outputs = self.predict(inputs, classifier_weights)
model_predictions = tf.argmax(
model_outputs, -1, output_type=self._int_dtype)
accuracy = tf.contrib.metrics.accuracy(model_predictions,
tf.squeeze(true_outputs, axis=-1))
return self.loss_fn(model_outputs, true_outputs), accuracy
def save_problem_instance_stats(self, instance):
num_classes, num_examples_per_class, embedding_dim = instance.get_shape()
if hasattr(self, "num_classes"):
assert self.num_classes == num_classes, (
"Given different number of classes (N in N-way) in consecutive runs.")
if hasattr(self, "num_examples_per_class"):
assert self.num_examples_per_class == num_examples_per_class, (
"Given different number of examples (K in K-shot) in consecutive"
"runs.")
if hasattr(self, "embedding_dim"):
assert self.embedding_dim == embedding_dim, (
"Given different embedding dimension in consecutive runs.")
self.num_classes = num_classes
self.num_examples_per_class = num_examples_per_class
self.embedding_dim = embedding_dim
@property
def dropout_rate(self):
return self._dropout_rate if self.is_meta_training else 0.0
def loss_fn(self, model_outputs, original_classes):
original_classes = tf.squeeze(original_classes, axis=-1)
# Tensorflow doesn't handle second order gradients of a sparse_softmax yet.
one_hot_outputs = tf.one_hot(original_classes, depth=self.num_classes)
return tf.nn.softmax_cross_entropy_with_logits_v2(
labels=one_hot_outputs, logits=model_outputs)
def grads_and_vars(self, metatrain_loss):
"""Computes gradients of metatrain_loss, avoiding NaN.
Uses a fixed penalty of 1e-4 to enforce only the l2 regularization (and not
minimize the loss) when metatrain_loss or any of its gradients with respect
to trainable_vars are NaN. In practice, this approach pulls the variables
back into a feasible region of the space when the loss or its gradients are
not defined.
Args:
metatrain_loss: A tensor with the LEO meta-training loss.
Returns:
A tuple with:
metatrain_gradients: A list of gradient tensors.
metatrain_variables: A list of variables for this LEO model.
"""
metatrain_variables = self.trainable_variables
metatrain_gradients = tf.gradients(metatrain_loss, metatrain_variables)
nan_loss_or_grad = tf.logical_or(
tf.is_nan(metatrain_loss),
tf.reduce_any([tf.reduce_any(tf.is_nan(g))
for g in metatrain_gradients]))
regularization_penalty = (
1e-4 / self._l2_penalty_weight * self._l2_regularization)
zero_or_regularization_gradients = [
g if g is not None else tf.zeros_like(v)
for v, g in zip(tf.gradients(regularization_penalty,
metatrain_variables), metatrain_variables)]
metatrain_gradients = tf.cond(nan_loss_or_grad,
lambda: zero_or_regularization_gradients,
lambda: metatrain_gradients, strict=True)
return metatrain_gradients, metatrain_variables
@property
def _l2_regularization(self):
return tf.cast(
tf.reduce_sum(tf.get_collection(tf.GraphKeys.REGULARIZATION_LOSSES)),
dtype=self._float_dtype)
@property
def _decoder_orthogonality_reg(self):
return self._orthogonality_reg
中解码器将潜在代码映射为分类器参数，然后将分类器参数用于更新分类器，再通过更新后的分类器求损失，这些对应哪段代码？
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该博客介绍了自描述数字的概念，即每个位置上的数字等于该数字在数中出现的次数。提供了一个输入样例，解释了如何判断一个正整数是否为自描述数字，并给出了用Python解决该问题的方案。
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