text: # Copyright 2021 The Flax Authors.
  #
  # 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
  #
  #     http://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.
  
  from .. import struct
  
  from jax import lax
  import jax.numpy as jnp
  
  import numpy as np
  
  from .base import OptimizerDef
  
  @struct.dataclass
  class _LAMBHyperParams:
    learning_rate: np.ndarray
    beta1: np.ndarray
    beta2: np.ndarray
    weight_decay: np.ndarray
    eps: np.ndarray
  
  
  @struct.dataclass
  class _LAMBParamState:
    grad_ema: np.ndarray
    grad_sq_ema: np.ndarray
  
  
  class LAMB(OptimizerDef):
    """Layerwise adaptive moments for batch (LAMB) optimizer.
  
    See https://arxiv.org/abs/1904.00962
    """
  
    def __init__(self, learning_rate=None, beta1=0.9, beta2=0.999, weight_decay=0,
                 eps=1e-6):
      """Constructor for the LAMB optimizer.
  
      Args:
        learning_rate: the step size used to update the parameters.
        beta1: the coefficient used for the moving average of the gradient
          (default: 0.9).
        beta2: the coefficient used for the moving average of the squared gradient
          (default: 0.999).
        weight_decay: weight decay coefficient to apply
        eps: epsilon used for Adam update computation (default: 1e-6).
      """
  
      hyper_params = _LAMBHyperParams(
          learning_rate, beta1, beta2, weight_decay, eps)
      super().__init__(hyper_params)
  
    def init_param_state(self, param):
      return _LAMBParamState(jnp.zeros_like(param), jnp.zeros_like(param))
  
    def apply_param_gradient(self, step, hyper_params, param, state, grad):
      assert hyper_params.learning_rate is not None, 'no learning rate provided.'
      beta1 = hyper_params.beta1
      beta2 = hyper_params.beta2
      weight_decay = hyper_params.weight_decay
      learning_rate = hyper_params.learning_rate
  
      grad_sq = lax.square(grad)
      grad_ema = beta1 * state.grad_ema + (1. - beta1) * grad
      grad_sq_ema = beta2 * state.grad_sq_ema + (1. - beta2) * grad_sq
  
      t = jnp.array(step + 1, lax.dtype(param.dtype))
      grad_ema_corr = grad_ema / (1. - beta1 ** t)
      grad_sq_ema_corr = grad_sq_ema / (1. - beta2 ** t)
  
      update = grad_ema_corr / (jnp.sqrt(grad_sq_ema_corr) + hyper_params.eps)
  
      if weight_decay != 0.0:
        update += weight_decay * param
  
      param_norm = jnp.linalg.norm(param)
      update_norm = jnp.linalg.norm(update)
      trust_ratio = jnp.where(
          param_norm + update_norm > 0., param_norm / update_norm, 1.)
  
      new_param = param - trust_ratio * learning_rate * update
      new_state = _LAMBParamState(grad_ema, grad_sq_ema)
      return new_param, new_state
  