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| |
| /* |
| * Stochastic Gradient Descent with Nesterov momentum (SGD-Nesterov) optimizer. |
| */ |
| |
| update = function(matrix[double] X, matrix[double] dX, double lr, double mu, matrix[double] v) |
| return (matrix[double] X, matrix[double] v) { |
| /* |
| * Performs an SGD update with Nesterov momentum. |
| * |
| * As with regular SGD with momentum, in SGD with Nesterov momentum, |
| * we assume that the parameters have a velocity that continues |
| * with some momentum, and that is influenced by the gradient. |
| * In this view specifically, we perform the position update from the |
| * position that the momentum is about to carry the parameters to, |
| * rather than from the previous position. Additionally, we always |
| * store the parameters in their position after momentum. |
| * |
| * Reference: |
| * - Advances in optimizing Recurrent Networks, Bengio et al., |
| * section 3.5. |
| * - http://arxiv.org/abs/1212.0901 |
| * |
| * Inputs: |
| * - X: Parameters to update, of shape (any, any). |
| * - dX: Gradient wrt `X` of a loss function being optimized, of |
| * same shape as `X`. |
| * - lr: Learning rate. |
| * - mu: Momentum value. |
| * Typical values are in the range of [0.5, 0.99], usually |
| * started at the lower end and annealed towards the higher end. |
| * - v: State maintaining the velocity of the parameters `X`, of same |
| * shape as `X`. |
| * |
| * Outputs: |
| * - X: Updated parameters X, of same shape as input X. |
| * - v: Updated velocity of the parameters X, of same shape as |
| * input v. |
| */ |
| v_prev = v |
| v = mu*v - lr*dX # update velocity |
| X = X - mu*v_prev + (1+mu)*v # update position, including momentum |
| } |
| |
| init = function(matrix[double] X) |
| return (matrix[double] v) { |
| /* |
| * Initialize the state for this optimizer. |
| * |
| * Note: This is just a convenience function, and state |
| * may be initialized manually if needed. |
| * |
| * Inputs: |
| * - X: Parameters to update, of shape (any, any). |
| * |
| * Outputs: |
| * - v: Initial velocity of the parameters `X`. |
| */ |
| v = matrix(0, rows=nrow(X), cols=ncol(X)) |
| } |
| |