|
| 1 | +import numpy as np |
| 2 | +import torch |
| 3 | + |
| 4 | + |
| 5 | +class _NumpyTransducer(torch.autograd.Function): |
| 6 | + @staticmethod |
| 7 | + def forward( |
| 8 | + ctx, |
| 9 | + log_probs, |
| 10 | + logit_lengths, |
| 11 | + target_lengths, |
| 12 | + targets, |
| 13 | + blank=-1, |
| 14 | + ): |
| 15 | + device = log_probs.device |
| 16 | + log_probs = log_probs.cpu().data.numpy() |
| 17 | + logit_lengths = logit_lengths.cpu().data.numpy() |
| 18 | + target_lengths = target_lengths.cpu().data.numpy() |
| 19 | + targets = targets.cpu().data.numpy() |
| 20 | + |
| 21 | + gradients, costs, _, _ = __class__.compute( |
| 22 | + log_probs=log_probs, |
| 23 | + logit_lengths=logit_lengths, |
| 24 | + target_lengths=target_lengths, |
| 25 | + targets=targets, |
| 26 | + blank=blank, |
| 27 | + ) |
| 28 | + |
| 29 | + costs = torch.FloatTensor(costs).to(device=device) |
| 30 | + gradients = torch.FloatTensor(gradients).to(device=device) |
| 31 | + ctx.grads = torch.autograd.Variable(gradients) |
| 32 | + |
| 33 | + return costs |
| 34 | + |
| 35 | + @staticmethod |
| 36 | + def backward(ctx, output_gradients): |
| 37 | + return ctx.grads, None, None, None, None, None, None, None, None |
| 38 | + |
| 39 | + @staticmethod |
| 40 | + def compute_alpha_one_sequence(log_probs, targets, blank=-1): |
| 41 | + max_T, max_U, D = log_probs.shape |
| 42 | + alpha = np.zeros((max_T, max_U), dtype=np.float32) |
| 43 | + for t in range(1, max_T): |
| 44 | + alpha[t, 0] = alpha[t - 1, 0] + log_probs[t - 1, 0, blank] |
| 45 | + |
| 46 | + for u in range(1, max_U): |
| 47 | + alpha[0, u] = alpha[0, u - 1] + log_probs[0, u - 1, targets[u - 1]] |
| 48 | + |
| 49 | + for t in range(1, max_T): |
| 50 | + for u in range(1, max_U): |
| 51 | + skip = alpha[t - 1, u] + log_probs[t - 1, u, blank] |
| 52 | + emit = alpha[t, u - 1] + log_probs[t, u - 1, targets[u - 1]] |
| 53 | + alpha[t, u] = np.logaddexp(skip, emit) |
| 54 | + |
| 55 | + cost = -(alpha[-1, -1] + log_probs[-1, -1, blank]) |
| 56 | + return alpha, cost |
| 57 | + |
| 58 | + @staticmethod |
| 59 | + def compute_beta_one_sequence(log_probs, targets, blank=-1): |
| 60 | + max_T, max_U, D = log_probs.shape |
| 61 | + beta = np.zeros((max_T, max_U), dtype=np.float32) |
| 62 | + beta[-1, -1] = log_probs[-1, -1, blank] |
| 63 | + |
| 64 | + for t in reversed(range(max_T - 1)): |
| 65 | + beta[t, -1] = beta[t + 1, -1] + log_probs[t, -1, blank] |
| 66 | + |
| 67 | + for u in reversed(range(max_U - 1)): |
| 68 | + beta[-1, u] = beta[-1, u + 1] + log_probs[-1, u, targets[u]] |
| 69 | + |
| 70 | + for t in reversed(range(max_T - 1)): |
| 71 | + for u in reversed(range(max_U - 1)): |
| 72 | + skip = beta[t + 1, u] + log_probs[t, u, blank] |
| 73 | + emit = beta[t, u + 1] + log_probs[t, u, targets[u]] |
| 74 | + beta[t, u] = np.logaddexp(skip, emit) |
| 75 | + |
| 76 | + cost = -beta[0, 0] |
| 77 | + return beta, cost |
| 78 | + |
| 79 | + @staticmethod |
| 80 | + def compute_gradients_one_sequence( |
| 81 | + log_probs, alpha, beta, targets, blank=-1 |
| 82 | + ): |
| 83 | + max_T, max_U, D = log_probs.shape |
| 84 | + gradients = np.full(log_probs.shape, float("-inf")) |
| 85 | + cost = -beta[0, 0] |
| 86 | + |
| 87 | + gradients[-1, -1, blank] = alpha[-1, -1] |
| 88 | + |
| 89 | + gradients[:-1, :, blank] = alpha[:-1, :] + beta[1:, :] |
| 90 | + |
| 91 | + for u, l in enumerate(targets): |
| 92 | + gradients[:, u, l] = alpha[:, u] + beta[:, u + 1] |
| 93 | + |
| 94 | + gradients = -(np.exp(gradients + log_probs + cost)) |
| 95 | + return gradients |
| 96 | + |
| 97 | + @staticmethod |
| 98 | + def compute( |
| 99 | + log_probs, |
| 100 | + logit_lengths, |
| 101 | + target_lengths, |
| 102 | + targets, |
| 103 | + blank=-1, |
| 104 | + ): |
| 105 | + gradients = np.zeros_like(log_probs) |
| 106 | + B_tgt, max_T, max_U, D = log_probs.shape |
| 107 | + B_src = logit_lengths.shape[0] |
| 108 | + |
| 109 | + H = int(B_tgt / B_src) |
| 110 | + |
| 111 | + alphas = np.zeros((B_tgt, max_T, max_U)) |
| 112 | + betas = np.zeros((B_tgt, max_T, max_U)) |
| 113 | + betas.fill(float("-inf")) |
| 114 | + alphas.fill(float("-inf")) |
| 115 | + costs = np.zeros(B_tgt) |
| 116 | + for b_tgt in range(B_tgt): |
| 117 | + b_src = int(b_tgt / H) |
| 118 | + T = int(logit_lengths[b_src]) |
| 119 | + # NOTE: see https://arxiv.org/pdf/1211.3711.pdf Section 2.1 |
| 120 | + U = int(target_lengths[b_tgt]) + 1 |
| 121 | + |
| 122 | + seq_log_probs = log_probs[b_tgt, :T, :U, :] |
| 123 | + seq_targets = targets[b_tgt, : int(target_lengths[b_tgt])] |
| 124 | + alpha, alpha_cost = __class__.compute_alpha_one_sequence( |
| 125 | + log_probs=seq_log_probs, targets=seq_targets, blank=blank |
| 126 | + ) |
| 127 | + |
| 128 | + beta, beta_cost = __class__.compute_beta_one_sequence( |
| 129 | + log_probs=seq_log_probs, targets=seq_targets, blank=blank |
| 130 | + ) |
| 131 | + |
| 132 | + seq_gradients = __class__.compute_gradients_one_sequence( |
| 133 | + log_probs=seq_log_probs, |
| 134 | + alpha=alpha, |
| 135 | + beta=beta, |
| 136 | + targets=seq_targets, |
| 137 | + blank=blank, |
| 138 | + ) |
| 139 | + np.testing.assert_almost_equal(alpha_cost, beta_cost, decimal=2) |
| 140 | + gradients[b_tgt, :T, :U, :] = seq_gradients |
| 141 | + costs[b_tgt] = beta_cost |
| 142 | + alphas[b_tgt, :T, :U] = alpha |
| 143 | + betas[b_tgt, :T, :U] = beta |
| 144 | + |
| 145 | + return gradients, costs, alphas, betas |
| 146 | + |
| 147 | + |
| 148 | +class NumpyTransducerLoss(torch.nn.Module): |
| 149 | + def __init__(self, blank=-1): |
| 150 | + super().__init__() |
| 151 | + self.blank = blank |
| 152 | + |
| 153 | + def forward( |
| 154 | + self, |
| 155 | + logits, |
| 156 | + logit_lengths, |
| 157 | + target_lengths, |
| 158 | + targets, |
| 159 | + ): |
| 160 | + log_probs = torch.nn.functional.log_softmax(logits, dim=-1) |
| 161 | + return _NumpyTransducer.apply( |
| 162 | + log_probs, |
| 163 | + logit_lengths, |
| 164 | + target_lengths, |
| 165 | + targets, |
| 166 | + self.blank, |
| 167 | + ) |
0 commit comments