# -*- coding: UTF-8 -*- # !/usr/bin/python # @time :2019/5/10 10:49 # @author :Mo # @function : 1. create model of keras-bert for get [-2] layers # 2. create model of AttentionWeightedAverage for get avg attention pooling # 3. create layer of # code class NonMaskingLayer from https://github.com/jacoxu # code class AttentionWeightedAverage from https://github.com/BrikerMan/Kashgari # code class CRF most from https://github.com/keras-team/keras-contrib, a little of 'theano' from https://github.com/BrikerMan/Kashgari from __future__ import absolute_import from __future__ import division from keras.engine import InputSpec import keras.backend as k_keras from keras.engine import Layer from keras import initializers from keras import backend as K from keras import regularizers from keras import activations from keras import constraints import warnings import os # crf_loss from keras.losses import sparse_categorical_crossentropy from keras.losses import categorical_crossentropy class NonMaskingLayer(Layer): """ fix convolutional 1D can't receive masked input, detail: https://github.com/keras-team/keras/issues/4978 thanks for https://github.com/jacoxu """ def __init__(self, **kwargs): self.supports_masking = True super(NonMaskingLayer, self).__init__(**kwargs) def build(self, input_shape): pass def compute_mask(self, input, input_mask=None): # do not pass the mask to the next layers return None def call(self, x, mask=None): return x def compute_output_shape(self, input_shape): return input_shape class AttentionWeightedAverage(Layer): ''' codes from: https://github.com/BrikerMan/Kashgari detail: https://github.com/BrikerMan/Kashgari/blob/master/kashgari/tasks/classification/models.py Computes a weighted average of the different channels across timesteps. Uses 1 parameter pr. channel to compute the attention value for a single timestep. ''' def __init__(self, return_attention=False, **kwargs): self.init = initializers.get('uniform') self.supports_masking = True self.return_attention = return_attention super(AttentionWeightedAverage, self).__init__(**kwargs) def build(self, input_shape): self.input_spec = [InputSpec(ndim=3)] assert len(input_shape) == 3 self.W = self.add_weight(shape=(input_shape[2], 1), name='{}_w'.format(self.name), initializer=self.init) self.trainable_weights = [self.W] super(AttentionWeightedAverage, self).build(input_shape) def call(self, x, mask=None): # computes a probability distribution over the timesteps # uses 'max trick' for numerical stability # reshape is done to avoid issue with Tensorflow # and 1-dimensional weights logits = k_keras.dot(x, self.W) x_shape = k_keras.shape(x) logits = k_keras.reshape(logits, (x_shape[0], x_shape[1])) ai = k_keras.exp(logits - k_keras.max(logits, axis=-1, keepdims=True)) # masked timesteps have zero weight if mask is not None: mask = k_keras.cast(mask, k_keras.floatx()) ai = ai * mask att_weights = ai / (k_keras.sum(ai, axis=1, keepdims=True) + k_keras.epsilon()) weighted_input = x * k_keras.expand_dims(att_weights) result = k_keras.sum(weighted_input, axis=1) if self.return_attention: return [result, att_weights] return result def get_output_shape_for(self, input_shape): return self.compute_output_shape(input_shape) def compute_output_shape(self, input_shape): output_len = input_shape[2] if self.return_attention: return [(input_shape[0], output_len), (input_shape[0], input_shape[1])] return (input_shape[0], output_len) def compute_mask(self, input, input_mask=None): if isinstance(input_mask, list): return [None] * len(input_mask) else: return None # crf_loss def crf_nll(y_true, y_pred): """The negative log-likelihood for linear chain Conditional Random Field (CRF). This loss function is only used when the `layers.CRF` layer is trained in the "join" mode. # Arguments y_true: tensor with true targets. y_pred: tensor with predicted targets. # Returns A scalar representing corresponding to the negative log-likelihood. # Raises TypeError: If CRF is not the last layer. # About GitHub If you open an issue or a pull request about CRF, please add `cc @lzfelix` to notify Luiz Felix. """ crf, idx = y_pred._keras_history[:2] if crf._outbound_nodes: raise TypeError('When learn_model="join", CRF must be the last layer.') if crf.sparse_target: y_true = K.one_hot(K.cast(y_true[:, :, 0], 'int32'), crf.units) X = crf._inbound_nodes[idx].input_tensors[0] mask = crf._inbound_nodes[idx].input_masks[0] nloglik = crf.get_negative_log_likelihood(y_true, X, mask) # 新加的 # nloglik = k_keras.abs(nloglik) return nloglik def crf_loss(y_true, y_pred): """General CRF loss function depending on the learning mode. # Arguments y_true: tensor with true targets. y_pred: tensor with predicted targets. # Returns If the CRF layer is being trained in the join mode, returns the negative log-likelihood. Otherwise returns the categorical crossentropy implemented by the underlying Keras backend. # About GitHub If you open an issue or a pull request about CRF, please add `cc @lzfelix` to notify Luiz Felix. """ crf, idx = y_pred._keras_history[:2] if crf.learn_mode == 'join': return crf_nll(y_true, y_pred) else: if crf.sparse_target: return sparse_categorical_crossentropy(y_true, y_pred) else: return categorical_crossentropy(y_true, y_pred) # crf_marginal_accuracy, crf_viterbi_accuracy def _get_accuracy(y_true, y_pred, mask, sparse_target=False): """ :param y_true: :param y_pred: :param mask: :param sparse_target: :return: """ y_pred = K.argmax(y_pred, -1) if sparse_target: y_true = K.cast(y_true[:, :, 0], K.dtype(y_pred)) else: y_true = K.argmax(y_true, -1) judge = K.cast(K.equal(y_pred, y_true), K.floatx()) if mask is None: return K.mean(judge) else: mask = K.cast(mask, K.floatx()) return K.sum(judge * mask) / K.sum(mask) def crf_viterbi_accuracy(y_true, y_pred): '''Use Viterbi algorithm to get best path, and compute its accuracy. `y_pred` must be an output from CRF.''' crf, idx = y_pred._keras_history[:2] X = crf._inbound_nodes[idx].input_tensors[0] mask = crf._inbound_nodes[idx].input_masks[0] y_pred = crf.viterbi_decoding(X, mask) return _get_accuracy(y_true, y_pred, mask, crf.sparse_target) def crf_marginal_accuracy(y_true, y_pred): '''Use time-wise marginal argmax as prediction. `y_pred` must be an output from CRF with `learn_mode="marginal"`.''' crf, idx = y_pred._keras_history[:2] X = crf._inbound_nodes[idx].input_tensors[0] mask = crf._inbound_nodes[idx].input_masks[0] y_pred = crf.get_marginal_prob(X, mask) return _get_accuracy(y_true, y_pred, mask, crf.sparse_target) def crf_accuracy(y_true, y_pred): '''Ge default accuracy based on CRF `test_mode`.''' crf, idx = y_pred._keras_history[:2] if crf.test_mode == 'viterbi': return crf_viterbi_accuracy(y_true, y_pred) else: return crf_marginal_accuracy(y_true, y_pred) def to_tuple(shape): """This functions is here to fix an inconsistency between keras and tf.keras. In tf.keras, the input_shape argument is an tuple with `Dimensions` objects. In keras, the input_shape is a simple tuple of ints or `None`. We'll work with tuples of ints or `None` to be consistent with keras-team/keras. So we must apply this function to all input_shapes of the build methods in custom layers. """ if os.environ.get("TF_KERAS")==1: import tensorflow as tf return tuple(tf.TensorShape(shape).as_list()) else: return shape class CRF(Layer): """ codes from: https://github.com/keras-team/keras-contrib detail: https://github.com/keras-team/keras-contrib/blob/fff264273d5347613574ff533c598f55f15d4763/keras_contrib/layers/crf.py An implementation of linear chain conditional random field (CRF). An linear chain CRF is defined to maximize the following likelihood function: $$ L(W, U, b; y_1, ..., y_n) := \frac{1}{Z} \sum_{y_1, ..., y_n} \exp(-a_1' y_1 - a_n' y_n - \sum_{k=1^n}((f(x_k' W + b) y_k) + y_1' U y_2)), $$ where: $Z$: normalization constant $x_k, y_k$: inputs and outputs This implementation has two modes for optimization: 1. (`join mode`) optimized by maximizing join likelihood, which is optimal in theory of statistics. Note that in this case, CRF must be the output/last layer. 2. (`marginal mode`) return marginal probabilities on each time step and optimized via composition likelihood (product of marginal likelihood), i.e., using `categorical_crossentropy` loss. Note that in this case, CRF can be either the last layer or an intermediate layer (though not explored). For prediction (test phrase), one can choose either Viterbi best path (class indices) or marginal probabilities if probabilities are needed. However, if one chooses *join mode* for training, Viterbi output is typically better than marginal output, but the marginal output will still perform reasonably close, while if *marginal mode* is used for training, marginal output usually performs much better. The default behavior and `metrics.crf_accuracy` is set according to this observation. In addition, this implementation supports masking and accepts either onehot or sparse target. If you open a issue or a pull request about CRF, please add 'cc @lzfelix' to notify Luiz Felix. # Examples ```python from keras_contrib.layers import CRF from keras_contrib.losses import crf_loss from keras_contrib.metrics import crf_viterbi_accuracy model = Sequential() model.add(Embedding(3001, 300, mask_zero=True)(X) # use learn_mode = 'join', test_mode = 'viterbi', # sparse_target = True (label indice output) crf = CRF(10, sparse_target=True) model.add(crf) # crf_accuracy is default to Viterbi acc if using join-mode (default). # One can add crf.marginal_acc if interested, but may slow down learning model.compile('adam', loss=crf_loss, metrics=[crf_viterbi_accuracy]) # y must be label indices (with shape 1 at dim 3) here, # since `sparse_target=True` model.fit(x, y) # prediction give onehot representation of Viterbi best path y_hat = model.predict(x_test) ``` The following snippet shows how to load a persisted model that uses the CRF layer: ```python from keras.models import load_model from keras_contrib.losses import import crf_loss from keras_contrib.metrics import crf_viterbi_accuracy custom_objects={'CRF': CRF, 'crf_loss': crf_loss, 'crf_viterbi_accuracy': crf_viterbi_accuracy} loaded_model = load_model('', custom_objects=custom_objects) ``` # Arguments units: Positive integer, dimensionality of the output space. learn_mode: Either 'join' or 'marginal'. The former train the model by maximizing join likelihood while the latter maximize the product of marginal likelihood over all time steps. One should use `losses.crf_nll` for 'join' mode and `losses.categorical_crossentropy` or `losses.sparse_categorical_crossentropy` for `marginal` mode. For convenience, simply use `losses.crf_loss`, which will decide the proper loss as described. test_mode: Either 'viterbi' or 'marginal'. The former is recommended and as default when `learn_mode = 'join'` and gives one-hot representation of the best path at test (prediction) time, while the latter is recommended and chosen as default when `learn_mode = 'marginal'`, which produces marginal probabilities for each time step. For evaluating metrics, one should use `metrics.crf_viterbi_accuracy` for 'viterbi' mode and 'metrics.crf_marginal_accuracy' for 'marginal' mode, or simply use `metrics.crf_accuracy` for both which automatically decides it as described. One can also use both for evaluation at training. sparse_target: Boolean (default False) indicating if provided labels are one-hot or indices (with shape 1 at dim 3). use_boundary: Boolean (default True) indicating if trainable start-end chain energies should be added to model. use_bias: Boolean, whether the layer uses a bias vector. kernel_initializer: Initializer for the `kernel` weights matrix, used for the linear transformation of the inputs. (see [initializers](../initializers.md)). chain_initializer: Initializer for the `chain_kernel` weights matrix, used for the CRF chain energy. (see [initializers](../initializers.md)). boundary_initializer: Initializer for the `left_boundary`, 'right_boundary' weights vectors, used for the start/left and end/right boundary energy. (see [initializers](../initializers.md)). bias_initializer: Initializer for the bias vector (see [initializers](../initializers.md)). activation: Activation function to use (see [activations](../activations.md)). If you pass None, no activation is applied (ie. "linear" activation: `a(x) = x`). kernel_regularizer: Regularizer function applied to the `kernel` weights matrix (see [regularizer](../regularizers.md)). chain_regularizer: Regularizer function applied to the `chain_kernel` weights matrix (see [regularizer](../regularizers.md)). boundary_regularizer: Regularizer function applied to the 'left_boundary', 'right_boundary' weight vectors (see [regularizer](../regularizers.md)). bias_regularizer: Regularizer function applied to the bias vector (see [regularizer](../regularizers.md)). kernel_constraint: Constraint function applied to the `kernel` weights matrix (see [constraints](../constraints.md)). chain_constraint: Constraint function applied to the `chain_kernel` weights matrix (see [constraints](../constraints.md)). boundary_constraint: Constraint function applied to the `left_boundary`, `right_boundary` weights vectors (see [constraints](../constraints.md)). bias_constraint: Constraint function applied to the bias vector (see [constraints](../constraints.md)). input_dim: dimensionality of the input (integer). This argument (or alternatively, the keyword argument `input_shape`) is required when using this layer as the first layer in a model. unroll: Boolean (default False). If True, the network will be unrolled, else a symbolic loop will be used. Unrolling can speed-up a RNN, although it tends to be more memory-intensive. Unrolling is only suitable for short sequences. # Input shape 3D tensor with shape `(nb_samples, timesteps, input_dim)`. # Output shape 3D tensor with shape `(nb_samples, timesteps, units)`. # Masking This layer supports masking for input data with a variable number of timesteps. To introduce masks to your data, use an [Embedding](embeddings.md) layer with the `mask_zero` parameter set to `True`. """ def __init__(self, units, learn_mode='join', test_mode=None, sparse_target=False, use_boundary=True, use_bias=True, activation='linear', kernel_initializer='glorot_uniform', chain_initializer='orthogonal', bias_initializer='zeros', boundary_initializer='zeros', kernel_regularizer=None, chain_regularizer=None, boundary_regularizer=None, bias_regularizer=None, kernel_constraint=None, chain_constraint=None, boundary_constraint=None, bias_constraint=None, input_dim=None, unroll=False, **kwargs): super(CRF, self).__init__(**kwargs) self.supports_masking = True self.units = units self.learn_mode = learn_mode assert self.learn_mode in ['join', 'marginal'] self.test_mode = test_mode if self.test_mode is None: self.test_mode = 'viterbi' if self.learn_mode == 'join' else 'marginal' else: assert self.test_mode in ['viterbi', 'marginal'] self.sparse_target = sparse_target self.use_boundary = use_boundary self.use_bias = use_bias self.activation = activations.get(activation) self.kernel_initializer = initializers.get(kernel_initializer) self.chain_initializer = initializers.get(chain_initializer) self.boundary_initializer = initializers.get(boundary_initializer) self.bias_initializer = initializers.get(bias_initializer) self.kernel_regularizer = regularizers.get(kernel_regularizer) self.chain_regularizer = regularizers.get(chain_regularizer) self.boundary_regularizer = regularizers.get(boundary_regularizer) self.bias_regularizer = regularizers.get(bias_regularizer) self.kernel_constraint = constraints.get(kernel_constraint) self.chain_constraint = constraints.get(chain_constraint) self.boundary_constraint = constraints.get(boundary_constraint) self.bias_constraint = constraints.get(bias_constraint) self.unroll = unroll def build(self, input_shape): # input_shape = to_tuple(input_shape) self.input_spec = [InputSpec(shape=input_shape)] self.input_dim = input_shape[-1] self.kernel = self.add_weight(shape=(self.input_dim, self.units), name='kernel', initializer=self.kernel_initializer, regularizer=self.kernel_regularizer, constraint=self.kernel_constraint) self.chain_kernel = self.add_weight(shape=(self.units, self.units), name='chain_kernel', initializer=self.chain_initializer, regularizer=self.chain_regularizer, constraint=self.chain_constraint) if self.use_bias: self.bias = self.add_weight(shape=(self.units,), name='bias', initializer=self.bias_initializer, regularizer=self.bias_regularizer, constraint=self.bias_constraint) else: self.bias = 0 if self.use_boundary: self.left_boundary = self.add_weight(shape=(self.units,), name='left_boundary', initializer=self.boundary_initializer, regularizer=self.boundary_regularizer, constraint=self.boundary_constraint) self.right_boundary = self.add_weight(shape=(self.units,), name='right_boundary', initializer=self.boundary_initializer, regularizer=self.boundary_regularizer, constraint=self.boundary_constraint) self.built = True def call(self, X, mask=None): if mask is not None: assert K.ndim(mask) == 2, 'Input mask to CRF must have dim 2 if not None' if self.test_mode == 'viterbi': test_output = self.viterbi_decoding(X, mask) else: test_output = self.get_marginal_prob(X, mask) self.uses_learning_phase = True if self.learn_mode == 'join': train_output = K.zeros_like(K.dot(X, self.kernel)) out = K.in_train_phase(train_output, test_output) else: if self.test_mode == 'viterbi': train_output = self.get_marginal_prob(X, mask) out = K.in_train_phase(train_output, test_output) else: out = test_output return out def compute_output_shape(self, input_shape): return input_shape[:2] + (self.units,) def compute_mask(self, input, mask=None): if mask is not None and self.learn_mode == 'join': return K.any(mask, axis=1) return mask def get_config(self): config = { 'units': self.units, 'learn_mode': self.learn_mode, 'test_mode': self.test_mode, 'use_boundary': self.use_boundary, 'use_bias': self.use_bias, 'sparse_target': self.sparse_target, 'kernel_initializer': initializers.serialize(self.kernel_initializer), 'chain_initializer': initializers.serialize(self.chain_initializer), 'boundary_initializer': initializers.serialize( self.boundary_initializer), 'bias_initializer': initializers.serialize(self.bias_initializer), 'activation': activations.serialize(self.activation), 'kernel_regularizer': regularizers.serialize(self.kernel_regularizer), 'chain_regularizer': regularizers.serialize(self.chain_regularizer), 'boundary_regularizer': regularizers.serialize( self.boundary_regularizer), 'bias_regularizer': regularizers.serialize(self.bias_regularizer), 'kernel_constraint': constraints.serialize(self.kernel_constraint), 'chain_constraint': constraints.serialize(self.chain_constraint), 'boundary_constraint': constraints.serialize(self.boundary_constraint), 'bias_constraint': constraints.serialize(self.bias_constraint), 'input_dim': self.input_dim, 'unroll': self.unroll} base_config = super(CRF, self).get_config() return dict(list(base_config.items()) + list(config.items())) @property def loss_function(self): warnings.warn('CRF.loss_function is deprecated ' 'and it might be removed in the future. Please ' 'use losses.crf_loss instead.') return crf_loss @property def accuracy(self): warnings.warn('CRF.accuracy is deprecated and it ' 'might be removed in the future. Please ' 'use metrics.crf_accuracy') if self.test_mode == 'viterbi': return crf_viterbi_accuracy else: return crf_marginal_accuracy @property def viterbi_acc(self): warnings.warn('CRF.viterbi_acc is deprecated and it might ' 'be removed in the future. Please ' 'use metrics.viterbi_acc instead.') return crf_viterbi_accuracy @property def marginal_acc(self): warnings.warn('CRF.moarginal_acc is deprecated and it ' 'might be removed in the future. Please ' 'use metrics.marginal_acc instead.') return crf_marginal_accuracy @staticmethod def softmaxNd(x, axis=-1): m = K.max(x, axis=axis, keepdims=True) exp_x = K.exp(x - m) prob_x = exp_x / K.sum(exp_x, axis=axis, keepdims=True) return prob_x @staticmethod def shift_left(x, offset=1): assert offset > 0 return K.concatenate([x[:, offset:], K.zeros_like(x[:, :offset])], axis=1) @staticmethod def shift_right(x, offset=1): assert offset > 0 return K.concatenate([K.zeros_like(x[:, :offset]), x[:, :-offset]], axis=1) def add_boundary_energy(self, energy, mask, start, end): start = K.expand_dims(K.expand_dims(start, 0), 0) end = K.expand_dims(K.expand_dims(end, 0), 0) if mask is None: energy = K.concatenate([energy[:, :1, :] + start, energy[:, 1:, :]], axis=1) energy = K.concatenate([energy[:, :-1, :], energy[:, -1:, :] + end], axis=1) else: mask = K.expand_dims(K.cast(mask, K.floatx())) start_mask = K.cast(K.greater(mask, self.shift_right(mask)), K.floatx()) end_mask = K.cast(K.greater(self.shift_left(mask), mask), K.floatx()) energy = energy + start_mask * start energy = energy + end_mask * end return energy def get_log_normalization_constant(self, input_energy, mask, **kwargs): """Compute logarithm of the normalization constant Z, where Z = sum exp(-E) -> logZ = log sum exp(-E) =: -nlogZ """ # should have logZ[:, i] == logZ[:, j] for any i, j logZ = self.recursion(input_energy, mask, return_sequences=False, **kwargs) return logZ[:, 0] def get_energy(self, y_true, input_energy, mask): """Energy = a1' y1 + u1' y1 + y1' U y2 + u2' y2 + y2' U y3 + u3' y3 + an' y3 """ input_energy = K.sum(input_energy * y_true, 2) # (B, T) # (B, T-1) chain_energy = K.sum(K.dot(y_true[:, :-1, :], self.chain_kernel) * y_true[:, 1:, :], 2) if mask is not None: mask = K.cast(mask, K.floatx()) # (B, T-1), mask[:,:-1]*mask[:,1:] makes it work with any padding chain_mask = mask[:, :-1] * mask[:, 1:] input_energy = input_energy * mask chain_energy = chain_energy * chain_mask total_energy = K.sum(input_energy, -1) + K.sum(chain_energy, -1) # (B, ) return total_energy def get_negative_log_likelihood(self, y_true, X, mask): """Compute the loss, i.e., negative log likelihood (normalize by number of time steps) likelihood = 1/Z * exp(-E) -> neg_log_like = - log(1/Z * exp(-E)) = logZ + E """ input_energy = self.activation(K.dot(X, self.kernel) + self.bias) if self.use_boundary: input_energy = self.add_boundary_energy(input_energy, mask, self.left_boundary, self.right_boundary) energy = self.get_energy(y_true, input_energy, mask) logZ = self.get_log_normalization_constant(input_energy, mask, input_length=K.int_shape(X)[1]) nloglik = logZ + energy if mask is not None: nloglik = nloglik / K.sum(K.cast(mask, K.floatx()), 1) else: nloglik = nloglik / K.cast(K.shape(X)[1], K.floatx()) return nloglik def step(self, input_energy_t, states, return_logZ=True): # not in the following `prev_target_val` has shape = (B, F) # where B = batch_size, F = output feature dim # Note: `i` is of float32, due to the behavior of `K.rnn` prev_target_val, i, chain_energy = states[:3] t = K.cast(i[0, 0], dtype='int32') if len(states) > 3: if K.backend() == 'theano': m = states[3][:, t:(t + 2)] else: m = K.tf.slice(states[3], [0, t], [-1, 2]) input_energy_t = input_energy_t * K.expand_dims(m[:, 0]) # (1, F, F)*(B, 1, 1) -> (B, F, F) chain_energy = chain_energy * K.expand_dims( K.expand_dims(m[:, 0] * m[:, 1])) if return_logZ: # # shapes: (1, B, F) + (B, F, 1) -> (B, F, F) # energy = chain_energy + K.expand_dims(input_energy_t - prev_target_val, 2) # new_target_val = K.logsumexp(-energy, 1) # shapes: (B, F) # return new_target_val, [new_target_val, i + 1] energy = chain_energy + K.expand_dims(input_energy_t - prev_target_val, 2) new_target_val = K.logsumexp(-energy, 1) # added from here if len(states) > 3: if K.backend() == 'theano': m = states[3][:, t:(t + 2)] else: m = K.slice(states[3], [0, t], [-1, 2]) is_valid = K.expand_dims(m[:, 0]) new_target_val = is_valid * new_target_val + (1 - is_valid) * prev_target_val # added until here return new_target_val, [new_target_val, i + 1] else: energy = chain_energy + K.expand_dims(input_energy_t + prev_target_val, 2) min_energy = K.min(energy, 1) # cast for tf-version `K.rnn argmin_table = K.cast(K.argmin(energy, 1), K.floatx()) return argmin_table, [min_energy, i + 1] def recursion(self, input_energy, mask=None, go_backwards=False, return_sequences=True, return_logZ=True, input_length=None): """Forward (alpha) or backward (beta) recursion If `return_logZ = True`, compute the logZ, the normalization constant: \[ Z = \sum_{y1, y2, y3} exp(-E) # energy = \sum_{y1, y2, y3} exp(-(u1' y1 + y1' W y2 + u2' y2 + y2' W y3 + u3' y3)) = sum_{y2, y3} (exp(-(u2' y2 + y2' W y3 + u3' y3)) sum_{y1} exp(-(u1' y1' + y1' W y2))) \] Denote: \[ S(y2) := sum_{y1} exp(-(u1' y1 + y1' W y2)), \] \[ Z = sum_{y2, y3} exp(log S(y2) - (u2' y2 + y2' W y3 + u3' y3)) \] \[ logS(y2) = log S(y2) = log_sum_exp(-(u1' y1' + y1' W y2)) \] Note that: yi's are one-hot vectors u1, u3: boundary energies have been merged If `return_logZ = False`, compute the Viterbi's best path lookup table. """ chain_energy = self.chain_kernel # shape=(1, F, F): F=num of output features. 1st F is for t-1, 2nd F for t chain_energy = K.expand_dims(chain_energy, 0) # shape=(B, F), dtype=float32 prev_target_val = K.zeros_like(input_energy[:, 0, :]) if go_backwards: input_energy = K.reverse(input_energy, 1) if mask is not None: mask = K.reverse(mask, 1) initial_states = [prev_target_val, K.zeros_like(prev_target_val[:, :1])] constants = [chain_energy] if mask is not None: mask2 = K.cast(K.concatenate([mask, K.zeros_like(mask[:, :1])], axis=1), K.floatx()) constants.append(mask2) def _step(input_energy_i, states): return self.step(input_energy_i, states, return_logZ) target_val_last, target_val_seq, _ = K.rnn(_step, input_energy, initial_states, constants=constants, input_length=input_length, unroll=self.unroll) if return_sequences: if go_backwards: target_val_seq = K.reverse(target_val_seq, 1) return target_val_seq else: return target_val_last def forward_recursion(self, input_energy, **kwargs): return self.recursion(input_energy, **kwargs) def backward_recursion(self, input_energy, **kwargs): return self.recursion(input_energy, go_backwards=True, **kwargs) def get_marginal_prob(self, X, mask=None): input_energy = self.activation(K.dot(X, self.kernel) + self.bias) if self.use_boundary: input_energy = self.add_boundary_energy(input_energy, mask, self.left_boundary, self.right_boundary) input_length = K.int_shape(X)[1] alpha = self.forward_recursion(input_energy, mask=mask, input_length=input_length) beta = self.backward_recursion(input_energy, mask=mask, input_length=input_length) if mask is not None: input_energy = input_energy * K.expand_dims(K.cast(mask, K.floatx())) margin = -(self.shift_right(alpha) + input_energy + self.shift_left(beta)) return self.softmaxNd(margin) def viterbi_decoding(self, X, mask=None): input_energy = self.activation(K.dot(X, self.kernel) + self.bias) if self.use_boundary: input_energy = self.add_boundary_energy( input_energy, mask, self.left_boundary, self.right_boundary) argmin_tables = self.recursion(input_energy, mask, return_logZ=False) argmin_tables = K.cast(argmin_tables, 'int32') # backward to find best path, `initial_best_idx` can be any, # as all elements in the last argmin_table are the same argmin_tables = K.reverse(argmin_tables, 1) # matrix instead of vector is required by tf `K.rnn` initial_best_idx = [K.expand_dims(argmin_tables[:, 0, 0])] if K.backend() == 'theano': initial_best_idx = [K.T.unbroadcast(initial_best_idx[0], 1)] def gather_each_row(params, indices): n = K.shape(indices)[0] if K.backend() == 'theano': return params[K.T.arange(n), indices] else: indices = K.transpose(K.stack([K.tf.range(n), indices])) return K.tf.gather_nd(params, indices) def find_path(argmin_table, best_idx): next_best_idx = gather_each_row(argmin_table, best_idx[0][:, 0]) next_best_idx = K.expand_dims(next_best_idx) if K.backend() == 'theano': next_best_idx = K.T.unbroadcast(next_best_idx, 1) return next_best_idx, [next_best_idx] _, best_paths, _ = K.rnn(find_path, argmin_tables, initial_best_idx, input_length=K.int_shape(X)[1], unroll=self.unroll) best_paths = K.reverse(best_paths, 1) best_paths = K.squeeze(best_paths, 2) return K.one_hot(best_paths, self.units)