code: def adadelta(
      loss_or_grads, params, learning_rate=1.0, rho=0.95, epsilon=1e-6
  ):
      """ Adadelta updates
  
      Scale learning rates by the ratio of accumulated gradients to accumulated
      updates, see [1]_ and notes for further description.
  
      Parameters
      ----------
      loss_or_grads : symbolic expression or list of expressions
          A scalar loss expression, or a list of gradient expressions
      params : list of shared variables
          The variables to generate update expressions for
      learning_rate : float or symbolic scalar
          The learning rate controlling the size of update steps
      rho : float or symbolic scalar
          Squared gradient moving average decay factor
      epsilon : float or symbolic scalar
          Small value added for numerical stability
  
      Returns
      -------
      OrderedDict
          A dictionary mapping each parameter to its update expression
  
      Notes
      -----
      rho should be between 0 and 1. A value of rho close to 1 will decay the
      moving average slowly and a value close to 0 will decay the moving average
      fast.
  
      rho = 0.95 and epsilon=1e-6 are suggested in the paper and reported to
      work for multiple datasets (MNIST, speech).
  
      In the paper, no learning rate is considered (so learning_rate=1.0).
      Probably best to keep it at this value.
      epsilon is important for the very first update (so the numerator does
      not become 0).
  
      Using the step size eta and a decay factor rho the learning rate is
      calculated as:
  
      .. math::
         r_t &= \\rho r_{t-1} + (1-\\rho)*g^2\\\\
         \\eta_t &= \\eta \\frac{\\sqrt{s_{t-1} + \\epsilon}}
                               {\sqrt{r_t + \epsilon}}\\\\
         s_t &= \\rho s_{t-1} + (1-\\rho)*(\\eta_t*g)^2
  
      References
      ----------
      .. [1] Zeiler, M. D. (2012):
             ADADELTA: An Adaptive Learning Rate Method.
             arXiv Preprint arXiv:1212.5701.
      """
      grads = get_or_compute_grads(loss_or_grads, params)
      updates = OrderedDict()
  
      # Using theano constant to prevent upcasting of float32
      one = T.constant(1)
  
      for param, grad in zip(params, grads):
          value = param.get_value(borrow=True)
          # accu: accumulate gradient magnitudes
          accu = theano.shared(
              np.zeros(value.shape, dtype=value.dtype),
              broadcastable=param.broadcastable,
          )
          # delta_accu: accumulate update magnitudes (recursively!)
          delta_accu = theano.shared(
              np.zeros(value.shape, dtype=value.dtype),
              broadcastable=param.broadcastable,
          )
  
          # update accu (as in rmsprop)
          accu_new = rho * accu + (one - rho) * grad**2
          updates[accu] = accu_new
  
          # compute parameter update, using the 'old' delta_accu
          update = (
              grad
              * T.sqrt(delta_accu + epsilon)
              / T.sqrt(accu_new + epsilon)
          )
          updates[param] = param - learning_rate * update
  
          # update delta_accu (as accu, but accumulating updates)
          delta_accu_new = rho * delta_accu + (one - rho) * update**2
          updates[delta_accu] = delta_accu_new
  
      return updates
  
file_path: Lasagne/lasagne/updates.py
imports: from collections import OrderedDict
  import numpy
  import theano
  import theano.tensor
  from .None import utils
label_desc: Use image node_id 9 for calling a global function with example usage: adadelta(loss_or_grads, params, learning_rate, rho, epsilon) and returns: updates