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| #------------------------------------------------------------- |
| |
| /* |
| * LSTM layer. |
| */ |
| source("nn/layers/sigmoid.dml") as sigmoid |
| source("nn/layers/tanh.dml") as tanh |
| |
| forward = function(matrix[double] X, matrix[double] W, matrix[double] b, |
| boolean return_sequences, matrix[double] out0, matrix[double] c0) |
| return (matrix[double] out, matrix[double] c) { |
| /* |
| * Computes the forward pass for an LSTM layer with M neurons. |
| * The input data has N sequences of T examples, each with D features. |
| * |
| * In an LSTM, an internal cell state is maintained, additive |
| * interactions operate over the cell state at each timestep, and |
| * some amount of this cell state is exposed as output at each |
| * timestep. Additionally, the output of the previous timestep is fed |
| * back in as an additional input at the current timestep. |
| * |
| * Reference: |
| * - Long Short-Term Memory, Hochreiter, 1997 |
| * - http://deeplearning.cs.cmu.edu/pdfs/Hochreiter97_lstm.pdf |
| * |
| * Inputs: |
| * - X: Inputs, of shape (N, T*D). |
| * - W: Weights, of shape (D+M, 4M). |
| * - b: Biases, of shape (1, 4M). |
| * - return_sequences: Whether to return `out` at all timesteps, |
| * or just for the final timestep. |
| * - out0: Outputs from previous timestep, of shape (N, M). |
| * Note: This is *optional* and could just be an empty matrix. |
| * - c0: Initial cell state, of shape (N, M). |
| * Note: This is *optional* and could just be an empty matrix. |
| * |
| * Outputs: |
| * - out: If `return_sequences` is True, outputs for all timesteps, |
| * of shape (N, T*M). Else, outputs for the final timestep, of |
| * shape (N, M). |
| * - c: Cell state for final timestep, of shape (N, M). |
| */ |
| out = 0; c = c0; |
| [out, c] = lstm(X, W, b, out0, c0, return_sequences) |
| } |
| |
| backward = function(matrix[double] dout, matrix[double] dc, |
| matrix[double] X, matrix[double] W, matrix[double] b, |
| boolean given_sequences, matrix[double] out0, matrix[double] c0) |
| return (matrix[double] dX, matrix[double] dW, matrix[double] db, |
| matrix[double] dout0, matrix[double] dc0) { |
| /* |
| * Computes the backward pass for an LSTM layer with M neurons. |
| * |
| * Inputs: |
| * - dout: Gradient wrt `out`. If `given_sequences` is `True`, |
| * contains gradients on outputs for all timesteps, of |
| * shape (N, T*M). Else, contains the gradient on the output |
| * for the final timestep, of shape (N, M). |
| * - dc: Gradient wrt `c` (from later in time), of shape (N, M). |
| * This would come from later in time if the cell state was used |
| * downstream as the initial cell state for another LSTM layer. |
| * Typically, this would be used when a sequence was cut at |
| * timestep `T` and then continued in the next batch. If `c` |
| * was not used downstream, then `dc` would be an empty matrix. |
| * - X: Inputs, of shape (N, T*D). |
| * - W: Weights, of shape (D+M, 4M). |
| * - b: Biases, of shape (1, 4M). |
| * - given_sequences: Whether `dout` is for all timesteps, |
| * or just for the final timestep. This is based on whether |
| * `return_sequences` was true in the forward pass. |
| * - out0: Outputs from previous timestep, of shape (N, M). |
| * Note: This is *optional* and could just be an empty matrix. |
| * - c0: Initial cell state, of shape (N, M). |
| * Note: This is *optional* and could just be an empty matrix. |
| * - cache_out: Cache of outputs, of shape (T, N*M). |
| * Note: This is used for performance during training. |
| * - cache_c: Cache of cell state, of shape (T, N*M). |
| * Note: This is used for performance during training. |
| * - cache_ifog: Cache of intermediate values, of shape (T, N*4*M). |
| * Note: This is used for performance during training. |
| * |
| * Outputs: |
| * - dX: Gradient wrt `X`, of shape (N, T*D). |
| * - dW: Gradient wrt `W`, of shape (D+M, 4M). |
| * - db: Gradient wrt `b`, of shape (1, 4M). |
| * - dout0: Gradient wrt `out0`, of shape (N, M). |
| * - dc0: Gradient wrt `c0`, of shape (N, M). |
| */ |
| dX = X; dW = W; db = b; dout0 = out0; dc0 = c0 |
| [dX, dW, db, dout0, dc0] = lstm_backward(X, W, b, out0, c0, given_sequences, dout, dc) |
| } |
| |
| init = function(int N, int D, int M) |
| return (matrix[double] W, matrix[double] b, matrix[double] out0, matrix[double] c0) { |
| /* |
| * Initialize the parameters of this layer. |
| * |
| * Note: This is just a convenience function, and parameters |
| * may be initialized manually if needed. |
| * |
| * We use the Glorot uniform heuristic which limits the magnification |
| * of inputs/gradients during forward/backward passes by scaling |
| * uniform weights by a factor of sqrt(6/(fan_in + fan_out)). |
| * - http://jmlr.org/proceedings/papers/v9/glorot10a/glorot10a.pdf |
| * |
| * Inputs: |
| * - N: Number of examples in batch. |
| * - D: Dimensionality of the input features (number of features). |
| * - M: Number of neurons in this layer. |
| * |
| * Outputs: |
| * - W: Weights, of shape (D+M, 4M). |
| * - b: Biases, of shape (1, 4M). |
| * - out0: Empty previous timestep output matrix, of shape (N, M). |
| * - c0: Empty initial cell state matrix, of shape (N, M). |
| */ |
| fan_in = D+M |
| fan_out = 4*M |
| scale = sqrt(6/(fan_in+fan_out)) |
| W = rand(rows=D+M, cols=4*M, min=-scale, max=scale, pdf="uniform") |
| b = matrix(0, rows=1, cols=4*M) |
| out0 = matrix(0, rows=N, cols=M) |
| c0 = matrix(0, rows=N, cols=M) |
| } |
| |