Python keras.backend.exp() Examples

def call(self, x, mask=None):
        # size of x :[batch_size, sel_len, attention_dim]
        # size of u :[batch_size, attention_dim]
        # uit = tanh(xW+b)
        uit = K.tanh(K.bias_add(K.dot(x, self.W), self.b))
        ait = K.dot(uit, self.u)
        ait = K.squeeze(ait, -1)

        ait = K.exp(ait)

        if mask is not None:
            # Cast the mask to floatX to avoid float64 upcasting in theano
            ait *= K.cast(mask, K.floatx())
        ait /= K.cast(K.sum(ait, axis=1, keepdims=True) + K.epsilon(), K.floatx())
        ait = K.expand_dims(ait)
        weighted_input = x * ait
        output = K.sum(weighted_input, axis=1)

        return output 

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.dot(x, self.W)
        x_shape = K.shape(x)
        logits = K.reshape(logits, (x_shape[0], x_shape[1]))
        ai = K.exp(logits - K.max(logits, axis=-1, keepdims=True))

        # masked timesteps have zero weight
        if mask is not None:
            mask = K.cast(mask, K.floatx())
            ai = ai * mask
        att_weights = ai / (K.sum(ai, axis=1, keepdims=True) + K.epsilon())
        weighted_input = x * K.expand_dims(att_weights)
        result = K.sum(weighted_input, axis=1)
        if self.return_attention:
            return [result, att_weights]
        return result 

def gen_cosine_amp(amp=100, period=1000, x0=0, xn=50000, step=1, k=0.0001):
	"""Generates an absolute cosine time series with the amplitude
	exponentially decreasing

	Arguments:
	    amp: amplitude of the cosine function
	    period: period of the cosine function
	    x0: initial x of the time series
	    xn: final x of the time series
	    step: step of the time series discretization
	    k: exponential rate
	"""
	cos = np.zeros(((xn - x0) * step, 1, 1))
	for i in range(len(cos)):
		idx = x0 + i * step
		cos[i, 0, 0] = amp * np.cos(2 * np.pi * idx / period)
		cos[i, 0, 0] = cos[i, 0, 0] * np.exp(-k * idx)
	return cos 

def sampling(self, args):
        """Reparametrisation by sampling from Gaussian, N(0,I)
        To sample from epsilon = Norm(0,I) instead of from likelihood Q(z|X)
        with latent variables z: z = z_mean + sqrt(var) * epsilon

        Parameters
        ----------
        args : tensor
            Mean and log of variance of Q(z|X).
    
        Returns
        -------
        z : tensor
            Sampled latent variable.
        """

        z_mean, z_log = args
        batch = K.shape(z_mean)[0]  # batch size
        dim = K.int_shape(z_mean)[1]  # latent dimension
        epsilon = K.random_normal(shape=(batch, dim))  # mean=0, std=1.0

        return z_mean + K.exp(0.5 * z_log) * epsilon 

def build_encoder(self):
        # Encoder

        img = Input(shape=self.img_shape)

        h = Flatten()(img)
        h = Dense(512)(h)
        h = LeakyReLU(alpha=0.2)(h)
        h = Dense(512)(h)
        h = LeakyReLU(alpha=0.2)(h)
        mu = Dense(self.latent_dim)(h)
        log_var = Dense(self.latent_dim)(h)
        latent_repr = merge([mu, log_var],
                mode=lambda p: p[0] + K.random_normal(K.shape(p[0])) * K.exp(p[1] / 2),
                output_shape=lambda p: p[0])

        return Model(img, latent_repr) 

def call(self, x, mask=None):
        uit = dot_product(x, self.W)

        if self.bias:
            uit += self.b

        uit = K.tanh(uit)
        ait = dot_product(uit, self.u)

        a = K.exp(ait)

        # apply mask after the exp. will be re-normalized next
        if mask is not None:
            # Cast the mask to floatX to avoid float64 upcasting in theano
            a *= K.cast(mask, K.floatx())

        # in some cases especially in the early stages of training the sum may be almost zero
        # and this results in NaN's. A workaround is to add a very small positive number ε to the sum.
        # a /= K.cast(K.sum(a, axis=1, keepdims=True), K.floatx())
        a /= K.cast(K.sum(a, axis=1, keepdims=True) + K.epsilon(), K.floatx())

        a = K.expand_dims(a)
        weighted_input = x * a
        return K.sum(weighted_input, axis=1) 

def sampling(args: tuple):
    """
    Reparameterization trick by sampling z from unit Gaussian
    :param args: (tensor, tensor) mean and log of variance of q(z|x)
    :returns tensor: sampled latent vector z
    """

    # unpack the input tuple
    z_mean, z_log_var = args

    # mini-batch size
    mb_size = K.shape(z_mean)[0]

    # latent space size
    dim = K.int_shape(z_mean)[1]

    # random normal vector with mean=0 and std=1.0
    epsilon = K.random_normal(shape=(mb_size, dim))

    return z_mean + K.exp(0.5 * z_log_var) * epsilon 

def call(self, x, mask=None):
        eij = dot_product(x, self.W)

        if self.bias:
            eij += self.b

        eij = K.tanh(eij)

        a = K.exp(eij)

        if mask is not None:
            a *= K.cast(mask, K.floatx())

        a /= K.cast(K.sum(a, axis=1, keepdims=True) + K.epsilon(), K.floatx())

        weighted_input = x * K.expand_dims(a)

        result = K.sum(weighted_input, axis=1)

        if self.return_attention:
            return [result, a]
        return result 

def yolo_head(feats, anchors, num_classes, input_shape, calc_loss=False):
    num_anchors = len(anchors)
    # [1, 1, 1, num_anchors, 2]
    anchors_tensor = K.reshape(K.constant(anchors), [1, 1, 1, num_anchors, 2])

    # 获得x，y的网格
    # (13, 13, 1, 2)
    grid_shape = K.shape(feats)[1:3] # height, width
    grid_y = K.tile(K.reshape(K.arange(0, stop=grid_shape[0]), [-1, 1, 1, 1]),
        [1, grid_shape[1], 1, 1])
    grid_x = K.tile(K.reshape(K.arange(0, stop=grid_shape[1]), [1, -1, 1, 1]),
        [grid_shape[0], 1, 1, 1])
    grid = K.concatenate([grid_x, grid_y])
    grid = K.cast(grid, K.dtype(feats))

    # (batch_size,13,13,3,85)
    feats = K.reshape(feats, [-1, grid_shape[0], grid_shape[1], num_anchors, num_classes + 5])

    # 将预测值调成真实值
    # box_xy对应框的中心点
    # box_wh对应框的宽和高
    box_xy = (K.sigmoid(feats[..., :2]) + grid) / K.cast(grid_shape[::-1], K.dtype(feats))
    box_wh = K.exp(feats[..., 2:4]) * anchors_tensor / K.cast(input_shape[::-1], K.dtype(feats))
    box_confidence = K.sigmoid(feats[..., 4:5])
    box_class_probs = K.sigmoid(feats[..., 5:])

    # 在计算loss的时候返回如下参数
    if calc_loss == True:
        return grid, feats, box_xy, box_wh
    return box_xy, box_wh, box_confidence, box_class_probs

#---------------------------------------------------#
#   用于计算每个预测框与真实框的iou
#---------------------------------------------------# 

def vae_loss(self, x, x_decoded_mean_squash):
        x = K.flatten(x)
        x_decoded_mean_squash = K.flatten(x_decoded_mean_squash)
        xent_loss = img_rows * img_cols * metrics.binary_crossentropy(x, x_decoded_mean_squash)
        kl_loss = - 0.5 * K.mean(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)
        return K.mean(xent_loss + kl_loss) 

def vae_loss(self, inputs, outputs, z_mean, z_log):
        """ Loss = Recreation loss + Kullback-Leibler loss
        for probability function divergence (ELBO).
        gamma > 1 and capacity != 0 for beta-VAE
        """

        reconstruction_loss = self.loss(inputs, outputs)
        reconstruction_loss *= self.n_features_
        kl_loss = 1 + z_log - K.square(z_mean) - K.exp(z_log)
        kl_loss = -0.5 * K.sum(kl_loss, axis=-1)
        kl_loss = self.gamma * K.abs(kl_loss - self.capacity)

        return K.mean(reconstruction_loss + kl_loss) 

def _negative_log_likelihood(E, risk):  
    hazard_ratio = K.exp(risk)
    log_risk = K.log(K.cumsum(hazard_ratio))
    uncensored_likelihood = risk - log_risk
    censored_likelihood = uncensored_likelihood * E
    neg_likelihood = -K.sum(censored_likelihood)
    return neg_likelihood 

def vae_loss(self, x, x_decoded_mean):
        xent_loss = original_dim * metrics.binary_crossentropy(x, x_decoded_mean)
        kl_loss = - 0.5 * K.sum(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)
        return K.mean(xent_loss + kl_loss) 

def sampling(args):
    z_mean, z_std = args
    epsilon_std = 1.0
    epsilon = KBack.random_normal(shape=(z_mean._keras_shape[1],),
                                  mean=0.,
                                  stddev=epsilon_std)
    return z_mean + z_std * epsilon
    # return z_mean + KBack.exp(z_std / 2) * epsilon 

def yolo_head(feats, anchors, num_classes, input_shape, calc_loss=False):

    num_anchors = len(anchors)

    anchors_tensor = K.reshape(K.constant(anchors), [1, 1, 1, num_anchors, 2])

    grid_shape = K.shape(feats)[1:3]
    grid_y = K.tile(K.reshape(K.arange(0, stop=grid_shape[0]), [-1, 1, 1, 1]),
        [1, grid_shape[1], 1, 1])
    grid_x = K.tile(K.reshape(K.arange(0, stop=grid_shape[1]), [1, -1, 1, 1]),
        [grid_shape[0], 1, 1, 1])
    grid = K.concatenate([grid_x, grid_y])
    grid = K.cast(grid, K.dtype(feats))

    feats = K.reshape(
        feats, [-1, grid_shape[0], grid_shape[1], num_anchors, num_classes + 5])


    box_xy = (K.sigmoid(feats[..., :2]) + grid) / K.cast(grid_shape[::-1], K.dtype(feats))
    box_wh = K.exp(feats[..., 2:4]) * anchors_tensor / K.cast(input_shape[::-1], K.dtype(feats))
    box_confidence = K.sigmoid(feats[..., 4:5])
    box_class_probs = K.sigmoid(feats[..., 5:])

    if calc_loss == True:
        return grid, feats, box_xy, box_wh
    return box_xy, box_wh, box_confidence, box_class_probs 

def _to_normal2d(output_batch) -> ds.MultivariateNormalTriL:
    """
    :param output_batch: (n_samples, 5)
    :return
    """

    # mean of x and y
    x_mean = Lambda(lambda o: o[:, 0])(output_batch)
    y_mean = Lambda(lambda o: o[:, 1])(output_batch)

    # std of x and y
    # std is must be 0 or positive
    x_std = Lambda(lambda o: K.exp(o[:, 2]))(output_batch)
    y_std = Lambda(lambda o: K.exp(o[:, 3]))(output_batch)

    # correlation coefficient
    # correlation coefficient range is [-1, 1]
    cor = Lambda(lambda o: K.tanh(o[:, 4]))(output_batch)

    loc = Concatenate()([
        Lambda(lambda x_mean: K.expand_dims(x_mean, 1))(x_mean),
        Lambda(lambda y_mean: K.expand_dims(y_mean, 1))(y_mean)
    ])

    x_var = Lambda(lambda x_std: K.square(x_std))(x_std)
    y_var = Lambda(lambda y_std: K.square(y_std))(y_std)
    xy_cor = Multiply()([x_std, y_std, cor])

    cov = Lambda(lambda inputs: K.stack(inputs, axis=0))(
        [x_var, xy_cor, xy_cor, y_var])
    cov = Lambda(lambda cov: K.permute_dimensions(cov, (1, 0)))(cov)
    cov = Reshape((2, 2))(cov)

    scale_tril = Lambda(lambda cov: tf.cholesky(cov))(cov)
    mvn = ds.MultivariateNormalTriL(loc, scale_tril)

    return mvn 

def yolo_head(feats, anchors, num_classes, input_shape, calc_loss=False):
    '''Convert final layer features to bounding box parameters'''

    num_anchors = len(anchors)

    # Reshape to batch, height, width, num_anchors, box_params.
    anchors_tensor = K.reshape(K.constant(anchors), [1, 1, 1, num_anchors, 2])

    # height, width
    grid_shape = K.shape(feats)[1:3]
    grid_y = K.tile(K.reshape(K.arange(0, stop=grid_shape[0]), [-1, 1, 1, 1]),
                    [1, grid_shape[1], 1, 1])
    grid_x = K.tile(K.reshape(K.arange(0, stop=grid_shape[1]), [1, -1, 1, 1]),
                    [grid_shape[0], 1, 1, 1])
    grid = K.concatenate([grid_x, grid_y])
    grid = K.cast(grid, K.dtype(feats))

    feats = K.reshape(
        feats, [-1, grid_shape[0], grid_shape[1], num_anchors, num_classes + 5])

    # Adjust preditions to each spatial grid point and anchor size.
    box_xy = (K.sigmoid(feats[..., :2]) + grid) / K.cast(grid_shape[::-1],
                                                         K.dtype(feats))
    box_wh = K.exp(feats[..., 2:4]) * anchors_tensor / K.cast(input_shape[::-1],
                                                              K.dtype(feats))
    box_confidence = K.sigmoid(feats[..., 4:5])
    box_class_probs = K.sigmoid(feats[..., 5:])

    if calc_loss == True:
        return grid, feats, box_xy, box_wh
    return box_xy, box_wh, box_confidence, box_class_probs 

def call(self, x, mask=None):
        eij = dot_product(x, self.W)

        if self.bias:
            eij += self.b

        eij = K.tanh(eij)

        a = K.exp(eij)

        # apply mask after the exp. will be re-normalized next
        if mask is not None:
            # Cast the mask to floatX to avoid float64 upcasting in theano
            a *= K.cast(mask, K.floatx())

        # in some cases especially in the early stages of training the sum may be almost zero
        # and this results in NaN's. A workaround is to add a very small positive number ε to the sum.
        # a /= K.cast(K.sum(a, axis=1, keepdims=True), K.floatx())
        a /= K.cast(K.sum(a, axis=1, keepdims=True) + K.epsilon(), K.floatx())

        weighted_input = x * K.expand_dims(a)

        result = K.sum(weighted_input, axis=1)

        if self.return_attention:
            return [result, a]
        return result 

def sampling(args):
    z_mean, z_log_var = args
    epsilon = K.random_normal(shape=(K.shape(z_mean)[0], latent_dim),
                              mean=0., stddev=epsilon_std)
    return z_mean + K.exp(z_log_var) * epsilon 

def vae_loss(self, x, x_decoded_mean_squash):
        x = K.flatten(x)
        x_decoded_mean_squash = K.flatten(x_decoded_mean_squash)
        xent_loss = img_rows * img_cols * metrics.binary_crossentropy(x, x_decoded_mean_squash)
        kl_loss = - 0.5 * K.mean(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)
        return K.mean(xent_loss + kl_loss) 

def safe_exp_np(w, thresh):
  """Safe exponential function for numpy tensors."""

  slope = np.exp(thresh)
  lin_bool = w > thresh

  lin_region = lin_bool.astype(float)

  lin_out = slope*(w - thresh + 1.)

  exp_out = np.exp(np.where(lin_bool, np.zeros_like(w), w))

  out = lin_region*lin_out + (1.-lin_region)*exp_out

  return out 

def sampling(args):
    z_mean, z_log_var = args
    epsilon = K.random_normal(shape=(K.shape(z_mean)[0], latent_dim),
                              mean=0., stddev=epsilon_std)
    return z_mean + K.exp(z_log_var) * epsilon 

def vae_loss(self, x, x_decoded_mean_squash):
        x = K.flatten(x)
        x_decoded_mean_squash = K.flatten(x_decoded_mean_squash)
        xent_loss = img_rows * img_cols * metrics.binary_crossentropy(x, x_decoded_mean_squash)
        kl_loss = - 0.5 * K.mean(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)
        return K.mean(xent_loss + kl_loss) 

def vae_loss(self, x, x_decoded_mean_squash):
        x = K.flatten(x)
        x_decoded_mean_squash = K.flatten(x_decoded_mean_squash)
        xent_loss = img_rows * img_cols * metrics.binary_crossentropy(x, x_decoded_mean_squash)
        kl_loss = - 0.5 * K.mean(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)
        return K.mean(xent_loss + kl_loss) 

def sampling(args):
    z_mean, z_log_var = args
    epsilon = K.random_normal(shape=(K.shape(z_mean)[0], latent_dim),
                              mean=0., stddev=epsilon_std)
    return z_mean + K.exp(z_log_var) * epsilon

# note that "output_shape" isn't necessary with the TensorFlow backend
# so you could write `Lambda(sampling)([z_mean, z_log_var])` 

def vae_loss(self, x, x_decoded_mean):
        xent_loss = original_dim * metrics.binary_crossentropy(x, x_decoded_mean)
        kl_loss = - 0.5 * K.sum(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)
        return K.mean(xent_loss + kl_loss) 

def sampling(args):
    z_mean, z_log_var = args
    epsilon = K.random_normal(shape=(K.shape(z_mean)[0], latent_dim),
                              mean=0., stddev=epsilon_std)
    return z_mean + K.exp(z_log_var) * epsilon 

def vae_loss(self, x, x_decoded_mean):
        xent_loss = original_dim * metrics.binary_crossentropy(x, x_decoded_mean)
        kl_loss = - 0.5 * K.sum(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)
        return K.mean(xent_loss + kl_loss) 

def vae_loss(self, x, x_decoded_mean_squash):
        x = K.flatten(x)
        x_decoded_mean_squash = K.flatten(x_decoded_mean_squash)
        xent_loss = img_rows * img_cols * metrics.binary_crossentropy(x, x_decoded_mean_squash)
        kl_loss = - 0.5 * K.mean(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)
        return K.mean(xent_loss + kl_loss) 

def vae_loss(self, x, x_decoded_mean):
        xent_loss = original_dim * metrics.binary_crossentropy(x, x_decoded_mean)
        kl_loss = - 0.5 * K.sum(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)
        return K.mean(xent_loss + kl_loss)