Python tensorflow.keras.backend.expand_dims() Examples

def _build_tf_cosine_similarity(max_rank=0, offset=1, eps=1e-12):
    # We build the graph (See utils.generic_utils.tf_recall_at_k for original implementation):
    tf_db = K.placeholder(ndim=2, dtype=K.floatx())  # Where to find
    tf_labels = K.placeholder(ndim=1, dtype=K.floatx())  # and their labels

    tf_batch_query = K.placeholder(ndim=2, dtype=K.floatx())  # Used in case of memory issues
    batch_labels = K.placeholder(ndim=2, dtype=K.floatx())  # and their labels

    all_representations_T = K.expand_dims(tf_db, axis=0)  # 1 x D x N
    batch_representations = K.expand_dims(tf_batch_query, axis=0)  # 1 x n x D
    sim = K.batch_dot(batch_representations, all_representations_T)  # 1 x n x N
    sim = K.squeeze(sim, axis=0)  # n x N
    sim /= tf.linalg.norm(tf_batch_query, axis=1, keepdims=True) + eps
    sim /= tf.linalg.norm(tf_db, axis=0, keepdims=True) + eps

    if max_rank > 0:  # computing r@K or mAP@K
        index_ranking = tf.nn.top_k(sim, k=max_rank + offset).indices
    else:
        index_ranking = tf.contrib.framework.argsort(sim, axis=-1, direction='DESCENDING', stable=True)

    top_k = index_ranking[:, offset:]
    tf_ranking = tf.gather(tf_labels, top_k)

    return tf_db, tf_labels, tf_batch_query, batch_labels, tf_ranking 

def _find_maxima(x, coordinate_scale=1, confidence_scale=255.0):

    x = K.cast(x, K.floatx())

    col_max = K.max(x, axis=1)
    row_max = K.max(x, axis=2)

    maxima = K.max(col_max, 1)
    maxima = K.expand_dims(maxima, -2) / confidence_scale

    cols = K.cast(K.argmax(col_max, -2), K.floatx())
    rows = K.cast(K.argmax(row_max, -2), K.floatx())
    cols = K.expand_dims(cols, -2) * coordinate_scale
    rows = K.expand_dims(rows, -2) * coordinate_scale

    maxima = K.concatenate([cols, rows, maxima], -2)

    return maxima 

def call(self, x, **kwargs):
        assert isinstance(x, list)
        inp_a, inp_b = x
        last_state = K.expand_dims(inp_b[:, -1, :], 1)
        m = []
        for i in range(self.output_dim):
            outp_a = inp_a * self.W[i]
            outp_last = last_state * self.W[i]
            outp_a = K.l2_normalize(outp_a, -1)
            outp_last = K.l2_normalize(outp_last, -1)
            outp = K.batch_dot(outp_a, outp_last, axes=[2, 2])
            m.append(outp)
        if self.output_dim > 1:
            persp = K.concatenate(m, 2)
        else:
            persp = m[0]
        return [persp, persp] 

def _batch_mgrid(self, n_batch, *args, **kwargs):
        """
        create batch of orthogonal grids
        similar to np.mgrid
        Parameters
        ----------
        n_batch : int
            number of grids to create
        args : int
            number of points on each axis
        low : float
            minimum coordinate value
        high : float
            maximum coordinate value
        Returns
        -------
        grids : tf.Tensor [n_batch, len(args), args[0], ...]
            batch of orthogonal grids
        """
        grid = self._mgrid(*args, **kwargs)
        grid = tf.expand_dims(grid, 0)
        grids = tf.tile(grid, [n_batch] + [1 for _ in range(len(args) + 1)])

        return grids 

def _mask_rotation_matrix_zyz(self, params):
        phi = params[0] * 2 * np.pi - np.pi;       theta = params[1] * 2 * np.pi - np.pi;     psi_t = params[2] * 2 * np.pi - np.pi;
        
        loc_r = params[3:6] * 0    # magnitude of Fourier transformation is translation-invariant 
        
        
        a1 = self._rotation_matrix_axis(2, psi_t)
        a2 = self._rotation_matrix_axis(1, theta)
        a3 = self._rotation_matrix_axis(2, phi)     
        rm = K.dot(K.dot(a3,a2),a1)
        
        rm = tf.transpose(rm)
        
        c = K.dot(-rm, K.expand_dims(loc_r))
        
        rm = K.flatten(rm)
        
        theta = K.concatenate([rm[:3], c[0], rm[3:6], c[1], rm[6:9], c[2]])

        return theta 

def _rotation_matrix_zyz(self, params):
        phi = params[0] * 2 * np.pi - np.pi;       theta = params[1] * 2 * np.pi - np.pi;     psi_t = params[2] * 2 * np.pi - np.pi;
        
        loc_r = params[3:6] * 2 - 1
        
        
        a1 = self._rotation_matrix_axis(2, psi_t)       # first rotate about z axis for angle psi_t
        a2 = self._rotation_matrix_axis(1, theta)
        a3 = self._rotation_matrix_axis(2, phi)     
        rm = K.dot(K.dot(a3,a2),a1)
        
        rm = tf.transpose(rm)
        
        c = K.dot(-rm, K.expand_dims(loc_r))
        
        rm = K.flatten(rm)
        
        theta = K.concatenate([rm[:3], c[0], rm[3:6], c[1], rm[6:9], c[2]])

        return theta 

def sequence_masking(x, mask, mode=0, axis=None):
    """为序列条件mask的函数
    mask: 形如(batch_size, seq_len)的0-1矩阵；
    mode: 如果是0，则直接乘以mask；
          如果是1，则在padding部分减去一个大正数。
    axis: 序列所在轴，默认为1；
    """
    if mask is None or mode not in [0, 1]:
        return x
    else:
        if axis is None:
            axis = 1
        if axis == -1:
            axis = K.ndim(x) - 1
        assert axis > 0, 'axis muse be greater than 0'
        for _ in range(axis - 1):
            mask = K.expand_dims(mask, 1)
        for _ in range(K.ndim(x) - K.ndim(mask) - axis + 1):
            mask = K.expand_dims(mask, K.ndim(mask))
        if mode == 0:
            return x * mask
        else:
            return x - (1 - mask) * 1e12 

def pool1d(
    x,
    pool_size,
    strides=1,
    padding='valid',
    data_format=None,
    pool_mode='max'
):
    """向量序列的pool函数
    """
    x = K.expand_dims(x, 1)
    x = K.pool2d(
        x,
        pool_size=(1, pool_size),
        strides=(1, strides),
        padding=padding,
        data_format=data_format,
        pool_mode=pool_mode
    )
    return x[:, 0] 

def call(self, inputs, **kwargs):
        sent1 = inputs[0]
        sent2 = inputs[1]

        v1 = K.expand_dims(sent1, -2) * self.kernel
        v2 = K.expand_dims(sent2, -2) * self.kernel
        v1 = K.l2_normalize(v1, axis=-1)
        v2 = K.l2_normalize(v2, axis=-1)
        matching = K.sum(v1 * v2, axis=-1)
        return matching 

def relative_logits_1d(self, q, rel_k, H, W, transpose_mask):
        rel_logits = tf.einsum('bhxyd,md->bhxym', q, rel_k)
        rel_logits = K.reshape(rel_logits, [-1, self.num_heads * H, W, 2 * W - 1])
        rel_logits = self.rel_to_abs(rel_logits)
        rel_logits = K.reshape(rel_logits, [-1, self.num_heads, H, W, W])
        rel_logits = K.expand_dims(rel_logits, axis=3)
        rel_logits = K.tile(rel_logits, [1, 1, 1, H, 1, 1])
        rel_logits = K.permute_dimensions(rel_logits, transpose_mask)
        rel_logits = K.reshape(rel_logits, [-1, self.num_heads, H * W, H * W])
        return rel_logits 

def call(self, inputs, mask=None):
        """
        convert to query, key, value vectors, shaped [batch_size*num_head, time_step, embed_dim]
        """
        multihead_query = K.concatenate(tf.split(K.dot(inputs, self.w_q),
                                                 self.num_heads, axis=2), axis=0)
        multihead_key = K.concatenate(tf.split(K.dot(inputs, self.w_k),
                                               self.num_heads, axis=2), axis=0)
        multihead_value = K.concatenate(tf.split(K.dot(inputs, self.w_v),
                                                 self.num_heads, axis=2), axis=0)

        """scaled dot product"""
        scaled = K.int_shape(inputs)[-1] ** -0.5
        attend = K.batch_dot(multihead_query, multihead_key, axes=2) * scaled
        # apply mask before normalization (softmax)
        if mask is not None:
            multihead_mask = K.tile(mask, [self.num_heads, 1])
            attend *= K.expand_dims(K.cast(multihead_mask, K.floatx()), 2)
            attend *= K.expand_dims(K.cast(multihead_mask, K.floatx()), 1)
        # normalization
        attend = attend / K.cast(K.sum(attend, axis=-1, keepdims=True) + K.epsilon(), K.floatx())
        # apply attention
        attend = K.batch_dot(attend, multihead_value, axes=(2, 1))
        attend = tf.concat(tf.split(attend, self.num_heads, axis=0), axis=2)
        attend = K.dot(attend, self.w_final)

        if self.residual:
            attend = attend + inputs
        if self.normalize:
            mean = K.mean(attend, axis=-1, keepdims=True)
            std = K.mean(attend, axis=-1, keepdims=True)
            attend = self.gamma * (attend - mean) / (std + K.epsilon()) + self.beta

        return attend 

def _build_tf_l2_similarity(max_rank=0, offset=1):
    # We build the graph (See utils.generic_utils.tf_recall_at_k for original implementation):
    tf_db = K.placeholder(ndim=2, dtype=K.floatx())  # Where to find
    tf_labels = K.placeholder(ndim=1, dtype=K.floatx())  # and their labels

    tf_batch_query = K.placeholder(ndim=2, dtype=K.floatx())  # Used in case of memory issues
    batch_labels = K.placeholder(ndim=2, dtype=K.floatx())  # and their labels

    all_representations_T = K.expand_dims(tf_db, axis=0)  # 1 x D x N
    batch_representations = K.expand_dims(tf_batch_query, axis=0)  # 1 x n x D
    dist = -2. * K.batch_dot(batch_representations, all_representations_T)  # 1 x n x N
    dist = K.squeeze(dist, axis=0)  # n x N
    dist += K.sum(tf_batch_query * tf_batch_query, axis=1, keepdims=True)
    dist += K.sum(tf_db * tf_db, axis=0, keepdims=True)

    if max_rank > 0:  # computing r@K or mAP@K
        # top_k finds the k greatest entries and we want the lowest. Note that distance with itself will be last ranked
        dist = -dist
        index_ranking = tf.nn.top_k(dist, k=max_rank + offset).indices
    else:
        index_ranking = tf.contrib.framework.argsort(dist, axis=-1, direction='ASCENDING', stable=True)

    index_ranking = index_ranking[:, offset:]

    tf_ranking = tf.gather(tf_labels, index_ranking)

    return tf_db, tf_labels, tf_batch_query, batch_labels, tf_ranking 

def create_model(self) -> Model:
        input = []
        if self.use_matrix:
            for i in range(self.num_context_turns + 1):
                input.append(Input(shape=(self.max_sequence_length,)))
            context = input[:self.num_context_turns]
            response = input[-1]
            emb_layer = self.embedding_layer()
            emb_c = [emb_layer(el) for el in context]
            emb_r = emb_layer(response)
        else:
            for i in range(self.num_context_turns + 1):
                input.append(Input(shape=(self.max_sequence_length, self.embedding_dim,)))
            context = input[:self.num_context_turns]
            response = input[-1]
            emb_c = context
            emb_r = response
        lstm_layer = self.lstm_layer()
        lstm_c = [lstm_layer(el) for el in emb_c]
        lstm_r = lstm_layer(emb_r)
        pooling_layer = GlobalMaxPooling1D(name="pooling")
        lstm_c = [pooling_layer(el) for el in lstm_c]
        lstm_r = pooling_layer(lstm_r)
        lstm_c = [Lambda(lambda x: K.expand_dims(x, 1))(el) for el in lstm_c]
        lstm_c = Lambda(lambda x: K.concatenate(x, 1))(lstm_c)
        gru_layer = GRU(2 * self.hidden_dim, name="gru")
        gru_c = gru_layer(lstm_c)

        if self.triplet_mode:
            dist = Lambda(self._pairwise_distances)([gru_c, lstm_r])
        else:
            dist = Lambda(self._diff_mult_dist)([gru_c, lstm_r])
            dist = Dense(1, activation='sigmoid', name="score_model")(dist)
        model = Model(context + [response], dist)
        return model 

def _batch_all_triplet_loss(self, y_true: Tensor, pairwise_dist: Tensor) -> Tensor:
        anchor_positive_dist = K.expand_dims(pairwise_dist, 2)
        anchor_negative_dist = K.expand_dims(pairwise_dist, 1)
        triplet_loss = anchor_positive_dist - anchor_negative_dist + self.margin
        mask = self._get_triplet_mask(y_true, pairwise_dist)
        triplet_loss = mask * triplet_loss
        triplet_loss = K.clip(triplet_loss, 0.0, None)
        valid_triplets = K.cast(K.greater(triplet_loss, 1e-16), K.dtype(triplet_loss))
        num_positive_triplets = K.sum(valid_triplets)
        triplet_loss = K.sum(triplet_loss) / (num_positive_triplets + 1e-16)
        return triplet_loss 

def _get_triplet_mask(self, y_true: Tensor, pairwise_dist: Tensor) -> Tensor:
        # mask label(a) != label(p)
        mask1 = K.expand_dims(K.equal(K.expand_dims(y_true, 0), K.expand_dims(y_true, 1)), 2)
        mask1 = K.cast(mask1, K.dtype(pairwise_dist))
        # mask a == p
        mask2 = K.expand_dims(K.not_equal(pairwise_dist, 0.0), 2)
        mask2 = K.cast(mask2, K.dtype(pairwise_dist))
        # mask label(n) == label(a)
        mask3 = K.expand_dims(K.not_equal(K.expand_dims(y_true, 0), K.expand_dims(y_true, 1)), 1)
        mask3 = K.cast(mask3, K.dtype(pairwise_dist))
        return mask1 * mask2 * mask3 

def _get_anchor_positive_triplet_mask(self, y_true: Tensor, pairwise_dist: Tensor) -> Tensor:
        # mask label(a) != label(p)
        mask1 = K.equal(K.expand_dims(y_true, 0), K.expand_dims(y_true, 1))
        mask1 = K.cast(mask1, K.dtype(pairwise_dist))
        # mask a == p
        mask2 = K.not_equal(pairwise_dist, 0.0)
        mask2 = K.cast(mask2, K.dtype(pairwise_dist))
        return mask1 * mask2 

def _get_anchor_negative_triplet_mask(self, y_true: Tensor, pairwise_dist: Tensor) -> Tensor:
        # mask label(n) == label(a)
        mask = K.not_equal(K.expand_dims(y_true, 0), K.expand_dims(y_true, 1))
        mask = K.cast(mask, K.dtype(pairwise_dist))
        return mask 

def _find_subpixel_maxima(
    x, kernel_size, sigma, upsample_factor, coordinate_scale=1.0, confidence_scale=1.0
):

    kernel = gaussian_kernel_2d(kernel_size, sigma)
    kernel = tf.expand_dims(kernel, 0)

    x_shape = tf.shape(x)
    rows = x_shape[1]
    cols = x_shape[2]

    max_vals = tf.reduce_max(tf.reshape(x, [-1, rows * cols]), axis=1)
    max_vals = tf.reshape(max_vals, [-1, 1]) / confidence_scale

    row_pad = rows // 2 - kernel_size // 2
    col_pad = cols // 2 - kernel_size // 2
    padding = [[0, 0], [row_pad, row_pad - 1], [col_pad, col_pad - 1]]
    kernel = tf.pad(kernel, padding)

    row_center = row_pad + (kernel_size // 2)
    col_center = col_pad + (kernel_size // 2)
    center = tf.stack([row_center, col_center])
    center = tf.expand_dims(center, 0)
    center = tf.cast(center, dtype=tf.float32)

    shifts = _upsampled_registration(x, kernel, upsample_factor)
    shifts = center - shifts
    shifts *= coordinate_scale
    maxima = tf.concat([shifts[:, ::-1], max_vals], -1)

    return maxima 

def box_iou(b1, b2):
    """
    Return iou tensor

    Parameters
    ----------
    b1: tensor, shape=(i1,...,iN, 4), xywh
    b2: tensor, shape=(j, 4), xywh

    Returns
    -------
    iou: tensor, shape=(i1,...,iN, j)
    """
    # Expand dim to apply broadcasting.
    b1 = K.expand_dims(b1, -2)
    b1_xy = b1[..., :2]
    b1_wh = b1[..., 2:4]
    b1_wh_half = b1_wh/2.
    b1_mins = b1_xy - b1_wh_half
    b1_maxes = b1_xy + b1_wh_half

    # Expand dim to apply broadcasting.
    b2 = K.expand_dims(b2, 0)
    b2_xy = b2[..., :2]
    b2_wh = b2[..., 2:4]
    b2_wh_half = b2_wh/2.
    b2_mins = b2_xy - b2_wh_half
    b2_maxes = b2_xy + b2_wh_half

    intersect_mins = K.maximum(b1_mins, b2_mins)
    intersect_maxes = K.minimum(b1_maxes, b2_maxes)
    intersect_wh = K.maximum(intersect_maxes - intersect_mins, 0.)
    intersect_area = intersect_wh[..., 0] * intersect_wh[..., 1]
    b1_area = b1_wh[..., 0] * b1_wh[..., 1]
    b2_area = b2_wh[..., 0] * b2_wh[..., 1]
    iou = intersect_area / (b1_area + b2_area - intersect_area)

    return iou 

def box_iou(b1, b2):
    """
    Return iou tensor

    Parameters
    ----------
    b1: tensor, shape=(i1,...,iN, 4), xywh
    b2: tensor, shape=(j, 4), xywh

    Returns
    -------
    iou: tensor, shape=(i1,...,iN, j)
    """
    # Expand dim to apply broadcasting.
    #b1 = K.expand_dims(b1, -2)
    b1_xy = b1[..., :2]
    b1_wh = b1[..., 2:4]
    b1_wh_half = b1_wh/2.
    b1_mins = b1_xy - b1_wh_half
    b1_maxes = b1_xy + b1_wh_half

    # Expand dim to apply broadcasting.
    b2 = K.expand_dims(b2, 0)
    b2_xy = b2[..., :2]
    b2_wh = b2[..., 2:4]
    b2_wh_half = b2_wh/2.
    b2_mins = b2_xy - b2_wh_half
    b2_maxes = b2_xy + b2_wh_half

    intersect_mins = K.maximum(b1_mins, b2_mins)
    intersect_maxes = K.minimum(b1_maxes, b2_maxes)
    intersect_wh = K.maximum(intersect_maxes - intersect_mins, 0.)
    intersect_area = intersect_wh[..., 0] * intersect_wh[..., 1]
    b1_area = b1_wh[..., 0] * b1_wh[..., 1]
    b2_area = b2_wh[..., 0] * b2_wh[..., 1]
    iou = intersect_area / (b1_area + b2_area - intersect_area)

    return iou 

def call(self, inputs, **kwargs):
        sent1 = inputs[0]
        sent2 = inputs[1]

        v1 = K.expand_dims(sent1, -2) * self.kernel
        v2 = K.expand_dims(sent2, -2) * self.kernel
        v1 = K.l2_normalize(v1, axis=-1)
        v2 = K.l2_normalize(v2, axis=-1)
        matching = K.max(K.sum(K.expand_dims(v1, 2) * K.expand_dims(v2, 1), axis=-1), axis=-2)
        return matching 

def call(self, inputs, **kwargs):
        sent1 = inputs[0]
        sent2 = inputs[1]

        v1 = K.expand_dims(sent1, -2) * self.kernel
        v2 = self.kernel * K.expand_dims(sent2, 1)
        v2 = K.expand_dims(v2, 1)
        v1 = K.l2_normalize(v1, axis=-1)
        v2 = K.l2_normalize(v2, axis=-1)
        matching = K.sum(v1 * v2, axis=-1)
        return matching 

def call(self, x, **kwargs):
        # (x - y)^2 = x^2 + y^2 - 2 * x * y
        x_sq = K.expand_dims(K.sum(x ** 2, axis=2), axis=-1)
        y_sq = K.reshape(K.sum(self.kernel ** 2, axis=1),
                         (1, 1, self.n_shapelets))
        xy = K.dot(x, K.transpose(self.kernel))
        return (x_sq + y_sq - 2 * xy) / K.int_shape(self.kernel)[1] 

def mi_loss(self, y_true, y_pred):
        """Mutual information loss computed from the joint
           distribution matrix and the marginals

        Arguments:
            y_true (tensor): Not used since this is
                unsupervised learning
            y_pred (tensor): stack of softmax predictions for
                the Siamese latent vectors (Z and Zbar)
        """
        size = self.args.batch_size
        n_labels = y_pred.shape[-1]
        # lower half is Z
        Z = y_pred[0: size, :]
        Z = K.expand_dims(Z, axis=2)
        # upper half is Zbar
        Zbar = y_pred[size: y_pred.shape[0], :]
        Zbar = K.expand_dims(Zbar, axis=1)
        # compute joint distribution (Eq 10.3.2 & .3)
        P = K.batch_dot(Z, Zbar)
        P = K.sum(P, axis=0)
        # enforce symmetric joint distribution (Eq 10.3.4)
        P = (P + K.transpose(P)) / 2.0
        # normalization of total probability to 1.0
        P = P / K.sum(P)
        # marginal distributions (Eq 10.3.5 & .6)
        Pi = K.expand_dims(K.sum(P, axis=1), axis=1)
        Pj = K.expand_dims(K.sum(P, axis=0), axis=0)
        Pi = K.repeat_elements(Pi, rep=n_labels, axis=1)
        Pj = K.repeat_elements(Pj, rep=n_labels, axis=0)
        P = K.clip(P, K.epsilon(), np.finfo(float).max)
        Pi = K.clip(Pi, K.epsilon(), np.finfo(float).max)
        Pj = K.clip(Pj, K.epsilon(), np.finfo(float).max)
        # negative MI loss (Eq 10.3.7)
        neg_mi = K.sum((P * (K.log(Pi) + K.log(Pj) - K.log(P))))
        # each head contribute 1/n_heads to the total loss
        return neg_mi/self.args.heads 

def call(self, inputs, **kwargs):
        """ student t-distribution, as same as used in t-SNE algorithm.
                 q_ij = 1/(1+dist(x_i, u_j)^2), then normalize it.
        Arguments:
            inputs: the variable containing data, shape=(n_samples, n_features)
        Return:
            q: student's t-distribution, or soft labels for each sample. shape=(n_samples, n_clusters)
        """
        q = 1.0 / (1.0 + (K.sum(K.square(K.expand_dims(inputs, axis=1) - self.clusters), axis=2) / self.alpha))
        q **= (self.alpha + 1.0) / 2.0
        q = K.transpose(K.transpose(q) / K.sum(q, axis=1))
        return q 

def call(self, x):
        x_orig = x

        # x reshape
        this_bs_int = K.shape(x)[0]
        this_bs = tf.cast(this_bs_int, 'float32')  # this batch size
        prev_count = self.count
        x = K.batch_flatten(x)  # B x N

        # update mean
        new_mean, new_count = _mean_update(self.mean, self.count, x, self.cap)        

        # new C update. Should be B x N x N
        x = K.expand_dims(x, -1)
        C_delta = K.batch_dot(x, K.permute_dimensions(x, [0, 2, 1]))

        # update cov
        prev_cap = K.minimum(prev_count, self.cap)
        C = self.cov * (prev_cap - 1) + K.sum(C_delta, 0)
        new_cov = C / (prev_cap + this_bs - 1)

        # updates
        updates = [(self.count, new_count), (self.mean, new_mean), (self.cov, new_cov)]
        self.add_update(updates, x_orig)

        # prep for broadcasting :(
        p = tf.concat((K.reshape(this_bs_int, (1,)), K.shape(self.cov)), 0)
        z = tf.ones(p)

        return K.minimum(1., new_count/self.cap) * (z * K.expand_dims(new_cov, 0)) 

def call(self, x):
        # get new mean and count
        this_bs_int = K.shape(x)[0]
        new_mean, new_count = _mean_update(self.mean, self.count, x, self.cap)
        
        # update op
        updates = [(self.count, new_count), (self.mean, new_mean)]
        self.add_update(updates, x)

        # prep for broadcasting :(
        p = tf.concat((K.reshape(this_bs_int, (1,)), K.shape(self.mean)), 0)
        z = tf.ones(p)
        
        # the first few 1000 should not matter that much towards this cost
        return K.minimum(1., new_count/self.cap) * (z * K.expand_dims(new_mean, 0)) 

def call(self, inputs, **kwargs):
        sent1 = inputs[0]
        sent2 = inputs[1]

        v1 = K.expand_dims(sent1, -2) * self.kernel
        v2 = K.expand_dims(sent2, -2) * self.kernel
        v1 = K.l2_normalize(v1, axis=-1)
        v2 = K.l2_normalize(v2, axis=-1)
        matching = K.sum(v1 * v2, axis=-1)
        return matching 

def _single_matmul(self, x, mult):
        x = K.expand_dims(x, -2)
        y = tf.matmul(x, mult)[...,0,:]
        return y 

def _spectrogram_mono(self, x):
        '''x.shape : (None, 1, len_src),
        returns 2D batch of a mono power-spectrogram'''
        x = K.permute_dimensions(x, [0, 2, 1])
        x = K.expand_dims(x, 3)  # add a dummy dimension (channel axis)
        subsample = (self.n_hop, 1)
        output_real = K.conv2d(
            x,
            self.dft_real_kernels,
            strides=subsample,
            padding=self.padding,
            data_format='channels_last',
        )
        output_imag = K.conv2d(
            x,
            self.dft_imag_kernels,
            strides=subsample,
            padding=self.padding,
            data_format='channels_last',
        )
        output = output_real ** 2 + output_imag ** 2
        # now shape is (batch_sample, n_frame, 1, freq)
        if self.image_data_format == 'channels_last':
            output = K.permute_dimensions(output, [0, 3, 1, 2])
        else:
            output = K.permute_dimensions(output, [0, 2, 3, 1])
        return output