516 lines
21 KiB
Python
516 lines
21 KiB
Python
# Copyright 2020 The TensorFlow Authors. All Rights Reserved.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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# ==============================================================================
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"""Adam optimizer implementation."""
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import tensorflow.compat.v2 as tf
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from keras import backend_config
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from keras.optimizers.legacy import optimizer_v2
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# isort: off
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from tensorflow.python.util.tf_export import keras_export
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@keras_export(
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"keras.optimizers.legacy.Adam",
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v1=["keras.optimizers.Adam", "keras.optimizers.legacy.Adam"],
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)
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class Adam(optimizer_v2.OptimizerV2):
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r"""Optimizer that implements the Adam algorithm.
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Adam optimization is a stochastic gradient descent method that is based on
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adaptive estimation of first-order and second-order moments.
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According to
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[Kingma et al., 2014](http://arxiv.org/abs/1412.6980),
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the method is "*computationally
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efficient, has little memory requirement, invariant to diagonal rescaling of
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gradients, and is well suited for problems that are large in terms of
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data/parameters*".
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Args:
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learning_rate: A `Tensor`, floating point value, or a schedule that is a
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`tf.keras.optimizers.schedules.LearningRateSchedule`, or a callable
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that takes no arguments and returns the actual value to use, The
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learning rate. Defaults to 0.001.
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beta_1: A float value or a constant float tensor, or a callable
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that takes no arguments and returns the actual value to use. The
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exponential decay rate for the 1st moment estimates. Defaults to 0.9.
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beta_2: A float value or a constant float tensor, or a callable
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that takes no arguments and returns the actual value to use, The
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exponential decay rate for the 2nd moment estimates. Defaults to 0.999.
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epsilon: A small constant for numerical stability. This epsilon is
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"epsilon hat" in the Kingma and Ba paper (in the formula just before
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Section 2.1), not the epsilon in Algorithm 1 of the paper. Defaults to
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1e-7.
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amsgrad: Boolean. Whether to apply AMSGrad variant of this algorithm from
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the paper "On the Convergence of Adam and beyond". Defaults to `False`.
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name: Optional name for the operations created when applying gradients.
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Defaults to `"Adam"`.
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**kwargs: keyword arguments. Allowed arguments are `clipvalue`,
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`clipnorm`, `global_clipnorm`.
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If `clipvalue` (float) is set, the gradient of each weight
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is clipped to be no higher than this value.
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If `clipnorm` (float) is set, the gradient of each weight
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is individually clipped so that its norm is no higher than this value.
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If `global_clipnorm` (float) is set the gradient of all weights is
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clipped so that their global norm is no higher than this value.
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Usage:
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>>> opt = tf.keras.optimizers.legacy.Adam(learning_rate=0.1)
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>>> var1 = tf.Variable(10.0)
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>>> loss = lambda: (var1 ** 2)/2.0 # d(loss)/d(var1) == var1
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>>> step_count = opt.minimize(loss, [var1]).numpy()
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>>> # The first step is `-learning_rate*sign(grad)`
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>>> var1.numpy()
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9.9
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Reference:
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- [Kingma et al., 2014](http://arxiv.org/abs/1412.6980)
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- [Reddi et al., 2018](
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https://openreview.net/pdf?id=ryQu7f-RZ) for `amsgrad`.
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Notes:
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The default value of 1e-7 for epsilon might not be a good default in
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general. For example, when training an Inception network on ImageNet a
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current good choice is 1.0 or 0.1. Note that since Adam uses the
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formulation just before Section 2.1 of the Kingma and Ba paper rather than
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the formulation in Algorithm 1, the "epsilon" referred to here is "epsilon
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hat" in the paper.
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The sparse implementation of this algorithm (used when the gradient is an
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IndexedSlices object, typically because of `tf.gather` or an embedding
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lookup in the forward pass) does apply momentum to variable slices even if
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they were not used in the forward pass (meaning they have a gradient equal
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to zero). Momentum decay (beta1) is also applied to the entire momentum
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accumulator. This means that the sparse behavior is equivalent to the dense
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behavior (in contrast to some momentum implementations which ignore momentum
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unless a variable slice was actually used).
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"""
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_HAS_AGGREGATE_GRAD = True
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def __init__(
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self,
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learning_rate=0.001,
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beta_1=0.9,
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beta_2=0.999,
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epsilon=1e-7,
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amsgrad=False,
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name="Adam",
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**kwargs
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):
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super().__init__(name, **kwargs)
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self._set_hyper("learning_rate", kwargs.get("lr", learning_rate))
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self._set_hyper("decay", self._initial_decay)
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self._set_hyper("beta_1", beta_1)
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self._set_hyper("beta_2", beta_2)
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self.epsilon = epsilon or backend_config.epsilon()
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self.amsgrad = amsgrad
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def _create_slots(self, var_list):
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# Create slots for the first and second moments.
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# Separate for-loops to respect the ordering of slot variables from v1.
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for var in var_list:
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self.add_slot(var, "m")
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for var in var_list:
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self.add_slot(var, "v")
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if self.amsgrad:
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for var in var_list:
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self.add_slot(var, "vhat")
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def _prepare_local(self, var_device, var_dtype, apply_state):
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super()._prepare_local(var_device, var_dtype, apply_state)
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local_step = tf.cast(self.iterations + 1, var_dtype)
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beta_1_t = tf.identity(self._get_hyper("beta_1", var_dtype))
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beta_2_t = tf.identity(self._get_hyper("beta_2", var_dtype))
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beta_1_power = tf.pow(beta_1_t, local_step)
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beta_2_power = tf.pow(beta_2_t, local_step)
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lr = apply_state[(var_device, var_dtype)]["lr_t"] * (
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tf.sqrt(1 - beta_2_power) / (1 - beta_1_power)
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)
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apply_state[(var_device, var_dtype)].update(
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dict(
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lr=lr,
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epsilon=tf.convert_to_tensor(self.epsilon, var_dtype),
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beta_1_t=beta_1_t,
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beta_1_power=beta_1_power,
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one_minus_beta_1_t=1 - beta_1_t,
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beta_2_t=beta_2_t,
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beta_2_power=beta_2_power,
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one_minus_beta_2_t=1 - beta_2_t,
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)
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)
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def set_weights(self, weights):
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params = self.weights
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# If the weights are generated by Keras V1 optimizer, it includes vhats
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# even without amsgrad, i.e, V1 optimizer has 3x + 1 variables, while V2
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# optimizer has 2x + 1 variables. Filter vhats out for compatibility.
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num_vars = int((len(params) - 1) / 2)
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if len(weights) == 3 * num_vars + 1:
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weights = weights[: len(params)]
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super().set_weights(weights)
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def _resource_apply_dense(self, grad, var, apply_state=None):
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var_device, var_dtype = var.device, var.dtype.base_dtype
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coefficients = (apply_state or {}).get(
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(var_device, var_dtype)
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) or self._fallback_apply_state(var_device, var_dtype)
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m = self.get_slot(var, "m")
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v = self.get_slot(var, "v")
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if not self.amsgrad:
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return tf.raw_ops.ResourceApplyAdam(
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var=var.handle,
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m=m.handle,
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v=v.handle,
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beta1_power=coefficients["beta_1_power"],
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beta2_power=coefficients["beta_2_power"],
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lr=coefficients["lr_t"],
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beta1=coefficients["beta_1_t"],
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beta2=coefficients["beta_2_t"],
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epsilon=coefficients["epsilon"],
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grad=grad,
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use_locking=self._use_locking,
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)
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else:
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vhat = self.get_slot(var, "vhat")
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return tf.raw_ops.ResourceApplyAdamWithAmsgrad(
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var=var.handle,
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m=m.handle,
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v=v.handle,
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vhat=vhat.handle,
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beta1_power=coefficients["beta_1_power"],
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beta2_power=coefficients["beta_2_power"],
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lr=coefficients["lr_t"],
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beta1=coefficients["beta_1_t"],
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beta2=coefficients["beta_2_t"],
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epsilon=coefficients["epsilon"],
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grad=grad,
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use_locking=self._use_locking,
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)
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def _resource_apply_sparse(self, grad, var, indices, apply_state=None):
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var_device, var_dtype = var.device, var.dtype.base_dtype
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coefficients = (apply_state or {}).get(
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(var_device, var_dtype)
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) or self._fallback_apply_state(var_device, var_dtype)
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# m_t = beta1 * m + (1 - beta1) * g_t
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m = self.get_slot(var, "m")
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m_scaled_g_values = grad * coefficients["one_minus_beta_1_t"]
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m_t = tf.compat.v1.assign(
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m, m * coefficients["beta_1_t"], use_locking=self._use_locking
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)
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with tf.control_dependencies([m_t]):
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m_t = self._resource_scatter_add(m, indices, m_scaled_g_values)
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# v_t = beta2 * v + (1 - beta2) * (g_t * g_t)
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v = self.get_slot(var, "v")
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v_scaled_g_values = (grad * grad) * coefficients["one_minus_beta_2_t"]
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v_t = tf.compat.v1.assign(
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v, v * coefficients["beta_2_t"], use_locking=self._use_locking
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)
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with tf.control_dependencies([v_t]):
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v_t = self._resource_scatter_add(v, indices, v_scaled_g_values)
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if not self.amsgrad:
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v_sqrt = tf.sqrt(v_t)
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var_update = tf.compat.v1.assign_sub(
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var,
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coefficients["lr"] * m_t / (v_sqrt + coefficients["epsilon"]),
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use_locking=self._use_locking,
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)
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return tf.group(*[var_update, m_t, v_t])
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else:
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v_hat = self.get_slot(var, "vhat")
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v_hat_t = tf.maximum(v_hat, v_t)
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with tf.control_dependencies([v_hat_t]):
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v_hat_t = tf.compat.v1.assign(
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v_hat, v_hat_t, use_locking=self._use_locking
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)
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v_hat_sqrt = tf.sqrt(v_hat_t)
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var_update = tf.compat.v1.assign_sub(
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var,
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coefficients["lr"]
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* m_t
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/ (v_hat_sqrt + coefficients["epsilon"]),
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use_locking=self._use_locking,
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)
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return tf.group(*[var_update, m_t, v_t, v_hat_t])
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def get_config(self):
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config = super().get_config()
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config.update(
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{
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"learning_rate": self._serialize_hyperparameter(
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"learning_rate"
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),
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"decay": self._initial_decay,
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"beta_1": self._serialize_hyperparameter("beta_1"),
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"beta_2": self._serialize_hyperparameter("beta_2"),
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"epsilon": self.epsilon,
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"amsgrad": self.amsgrad,
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}
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)
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return config
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class NonFusedAdam(optimizer_v2.OptimizerV2):
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r"""Optimizer that implements the Adam algorithm without fused kernels.
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Adam optimization is a stochastic gradient descent method that is based on
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adaptive estimation of first-order and second-order moments.
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According to the paper
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[Adam: A Method for Stochastic Optimization. Kingma et al.,
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2014](http://arxiv.org/abs/1412.6980), the method is "*computationally
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efficient, has little memory requirement, invariant to diagonal rescaling of
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gradients, and is well suited for problems that are large in terms of
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data/parameters*".
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For AMSGrad see [On The Convergence Of Adam And Beyond.
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Reddi et al., 5-8](https://openreview.net/pdf?id=ryQu7f-RZ).
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**If amsgrad = False**:
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initialize $m_0$ as 1st moment vector
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initialize $v_0$ as 2nd moment vector
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The update rule for $\theta$ with gradient $g$ uses an optimization
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described at the end of section 2 of the paper:
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$$lr_t = \mathrm{learning\_rate} *
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\sqrt{1 - \beta_2^t} / (1 - \beta_1^t)$$
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$$m_t = \beta_1 * m_{t-1} + (1 - \beta_1) * g$$
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$$v_t = \beta_2 * v_{t-1} + (1 - \beta_2) * g^2$$
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$$\theta_t = \theta_{t-1} - lr_t * m_t / (\sqrt{v_t} + \epsilon)$$
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**If amsgrad = True**:
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initialize $m_0$ as 1st moment vector
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initialize $v_0$ as 2nd moment vector
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initialize $\hat{v}_0$ as 2nd moment vector
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The update rule for $\theta$ with gradient $g$ uses an optimization
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described at the end of section 2 of the paper:
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$$lr_t = \mathrm{learning\_rate} *
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\sqrt{1 - \beta_2^t} / (1 - \beta_1^t)$$
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$$m_t = \beta_1 * m_{t-1} + (1 - \beta_1) * g$$
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$$v_t = \beta_2 * v_{t-1} + (1 - \beta_2) * g^2$$
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$$\hat{v}_t = \max(\hat{v}_{t-1}, v_t)$$
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$$\theta_t = \theta_{t-1} - lr_t * m_t / (\sqrt{\hat{v}_t} + \epsilon)$$
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The default value of 1e-7 for epsilon might not be a good default in
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general. For example, when training an Inception network on ImageNet a
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current good choice is 1.0 or 0.1. Note that since Adam uses the
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formulation just before Section 2.1 of the Kingma and Ba paper rather than
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the formulation in Algorithm 1, the "epsilon" referred to here is "epsilon
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hat" in the paper.
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The sparse implementation of this algorithm (used when the gradient is an
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IndexedSlices object, typically because of `tf.gather` or an embedding
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lookup in the forward pass) does apply momentum to variable slices even if
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they were not used in the forward pass (meaning they have a gradient equal
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to zero). Momentum decay (beta1) is also applied to the entire momentum
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accumulator. This means that the sparse behavior is equivalent to the dense
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behavior (in contrast to some momentum implementations which ignore momentum
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unless a variable slice was actually used).
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Usage:
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>>> opt = tf.keras.optimizers.legacy.Adam(learning_rate=0.1)
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>>> var1 = tf.Variable(10.0)
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>>> loss = lambda: (var1 ** 2)/2.0 # d(loss)/d(var1) == var1
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>>> step_count = opt.minimize(loss, [var1]).numpy()
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>>> # The first step is `-learning_rate*sign(grad)`
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>>> var1.numpy()
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9.9
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"""
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_HAS_AGGREGATE_GRAD = True
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def __init__(
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self,
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learning_rate=0.001,
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beta_1=0.9,
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beta_2=0.999,
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epsilon=1e-7,
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amsgrad=False,
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name="Adam",
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**kwargs
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):
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"""Construct a new Adam optimizer.
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Args:
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learning_rate: A `Tensor`, floating point value, or a schedule that is
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a `tf.keras.optimizers.schedules.LearningRateSchedule`, or a
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callable that takes no arguments and returns the actual value to
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use, The learning rate. Defaults to 0.001.
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beta_1: A float value or a constant float tensor, or a callable that
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takes no arguments and returns the actual value to use. The
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exponential decay rate for the 1st moment estimates. Defaults to
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0.9.
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beta_2: A float value or a constant float tensor, or a callable that
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takes no arguments and returns the actual value to use, The
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exponential decay rate for the 2nd moment estimates. Defaults to
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0.999.
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epsilon: A small constant for numerical stability. This epsilon is
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"epsilon hat" in the Kingma and Ba paper (in the formula just before
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Section 2.1), not the epsilon in Algorithm 1 of the paper. Defaults
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to 1e-7.
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amsgrad: Boolean. Whether to apply AMSGrad variant of this algorithm
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from the paper "On the Convergence of Adam and beyond". Defaults to
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`False`.
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name: Optional name for the operations created when applying
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gradients. Defaults to "Adam".
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**kwargs: keyword arguments. Allowed to be {`clipnorm`, `clipvalue`,
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`lr`, `decay`}. `clipnorm` is clip gradients by norm; `clipvalue` is
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clip gradients by value, `decay` is included for backward
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compatibility to allow time inverse decay of learning rate. `lr` is
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included for backward compatibility, recommended to use
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`learning_rate` instead.
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"""
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super().__init__(name, **kwargs)
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self._set_hyper("learning_rate", kwargs.get("lr", learning_rate))
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self._set_hyper("decay", self._initial_decay)
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self._set_hyper("beta_1", beta_1)
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self._set_hyper("beta_2", beta_2)
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self.epsilon = epsilon or backend_config.epsilon()
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self.amsgrad = amsgrad
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def _create_slots(self, var_list):
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# Create slots for the first and second moments.
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# Separate for-loops to respect the ordering of slot variables from v1.
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for var in var_list:
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self.add_slot(var, "m")
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for var in var_list:
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self.add_slot(var, "v")
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if self.amsgrad:
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for var in var_list:
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self.add_slot(var, "vhat")
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def _prepare_local(self, var_device, var_dtype, apply_state):
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super()._prepare_local(var_device, var_dtype, apply_state)
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local_step = tf.cast(self.iterations + 1, var_dtype)
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beta_1_t = tf.identity(self._get_hyper("beta_1", var_dtype))
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beta_2_t = tf.identity(self._get_hyper("beta_2", var_dtype))
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beta_1_power = tf.pow(beta_1_t, local_step)
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beta_2_power = tf.pow(beta_2_t, local_step)
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lr = apply_state[(var_device, var_dtype)]["lr_t"] * (
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tf.sqrt(1 - beta_2_power) / (1 - beta_1_power)
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)
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apply_state[(var_device, var_dtype)].update(
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dict(
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lr=lr,
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epsilon=tf.convert_to_tensor(self.epsilon, var_dtype),
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beta_1_t=beta_1_t,
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beta_1_power=beta_1_power,
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one_minus_beta_1_t=1 - beta_1_t,
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beta_2_t=beta_2_t,
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beta_2_power=beta_2_power,
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one_minus_beta_2_t=1 - beta_2_t,
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)
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)
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def set_weights(self, weights):
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params = self.weights
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# If the weights are generated by Keras V1 optimizer, it includes vhats
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# even without amsgrad, i.e, V1 optimizer has 3x + 1 variables, while V2
|
|
# optimizer has 2x + 1 variables. Filter vhats out for compatibility.
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|
num_vars = int((len(params) - 1) / 2)
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|
if len(weights) == 3 * num_vars + 1:
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|
weights = weights[: len(params)]
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|
super().set_weights(weights)
|
|
|
|
@tf.function(jit_compile=True)
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|
def _resource_apply_dense(self, grad, var, apply_state=None):
|
|
var_device, var_dtype = var.device, var.dtype.base_dtype
|
|
coefficients = (apply_state or {}).get(
|
|
(var_device, var_dtype)
|
|
) or self._fallback_apply_state(var_device, var_dtype)
|
|
|
|
m = self.get_slot(var, "m")
|
|
v = self.get_slot(var, "v")
|
|
|
|
alpha = (
|
|
coefficients["lr_t"]
|
|
* tf.sqrt(1 - coefficients["beta_2_power"])
|
|
/ (1 - coefficients["beta_1_power"])
|
|
)
|
|
m.assign_add((grad - m) * (1 - coefficients["beta_1_t"]))
|
|
v.assign_add((tf.square(grad) - v) * (1 - coefficients["beta_2_t"]))
|
|
if self.amsgrad:
|
|
vhat = self.get_slot(var, "vhat")
|
|
vhat.assign(tf.maximum(vhat, v))
|
|
v = vhat
|
|
var.assign_sub((m * alpha) / (tf.sqrt(v) - coefficients["epsilon"]))
|
|
|
|
@tf.function(jit_compile=True)
|
|
def _resource_apply_sparse(self, grad, var, indices, apply_state=None):
|
|
var_device, var_dtype = var.device, var.dtype.base_dtype
|
|
coefficients = (apply_state or {}).get(
|
|
(var_device, var_dtype)
|
|
) or self._fallback_apply_state(var_device, var_dtype)
|
|
|
|
# m_t = beta1 * m + (1 - beta1) * g_t
|
|
m = self.get_slot(var, "m")
|
|
m_scaled_g_values = grad * coefficients["one_minus_beta_1_t"]
|
|
m.assign(m * coefficients["beta_1_t"])
|
|
m.scatter_add(tf.IndexedSlices(m_scaled_g_values, indices))
|
|
|
|
# v_t = beta2 * v + (1 - beta2) * (g_t * g_t)
|
|
v = self.get_slot(var, "v")
|
|
v_scaled_g_values = (grad * grad) * coefficients["one_minus_beta_2_t"]
|
|
v.assign(v * coefficients["beta_2_t"])
|
|
v.scatter_add(tf.IndexedSlices(v_scaled_g_values, indices))
|
|
|
|
if not self.amsgrad:
|
|
var.assign_sub(
|
|
coefficients["lr"] * m / (tf.sqrt(v) + coefficients["epsilon"])
|
|
)
|
|
else:
|
|
v_hat = self.get_slot(var, "vhat")
|
|
v_hat.assign(tf.maximum(v_hat, v))
|
|
var.assign_sub(
|
|
coefficients["lr"]
|
|
* m
|
|
/ (tf.sqrt(v_hat) + coefficients["epsilon"])
|
|
)
|
|
|
|
def get_config(self):
|
|
config = super().get_config()
|
|
config.update(
|
|
{
|
|
"learning_rate": self._serialize_hyperparameter(
|
|
"learning_rate"
|
|
),
|
|
"decay": self._initial_decay,
|
|
"beta_1": self._serialize_hyperparameter("beta_1"),
|
|
"beta_2": self._serialize_hyperparameter("beta_2"),
|
|
"epsilon": self.epsilon,
|
|
"amsgrad": self.amsgrad,
|
|
}
|
|
)
|
|
return config
|