def sgd_momentum(w, dw, config=None):
'''
Performs stochastic gradient descent with momentum.
config format:
- learning_rate: Scalar learning rate.
- momentum: Scalar between 0 and 1 giving the momentum value.
Setting momentum = 0 reduces to sgd.
- velocity: A numpy array of the same shape as w and dw used to store a moving
average of the gradients.
'''
if config is None:
config = {}
config.setdefault('learning_rate', 1e-2)
config.setdefault('momentum', 0.9)
v = config.get('velocity', np.zeros_like(w))
next_w = None
v = config['momentum'] * v + config['learning_rate'] * dw
next_w = w - v
config['velocity'] = v
return next_w, config
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