Implementing custom loss function in keras with different sizes for y_true and y_pred

Question

I am new to Keras. I need some help in writing a custom loss function in keras with TensorFlow backend for the following loss equation.

The parameters passed to the loss function are :

1. y_true would be of shape (batch_size, N, 2). Here, we are passing N (x, y) coordinates in each sample in the batch.
2. y_pred would be of shape (batch_size, 256, 256, N). Here, we are passing N predicted heatmaps of 256 x 256 pixels in each sample in the batch.

i ∈ [0, 255]

j ∈ [0, 255]

Mn(i, j) represents value at pixel location (i, j) for the n^th predicted heatmap.

Mn∼(i, j) = Guassian2D((i, j), y_truen, std) where

std = standard deviation, same standard deviation for both the dimensions (5 px).

y_true_n is the n^th (x, y) coordinate. This is the mean.

For details of this, please check the l₂ loss described in this paper Human Pose Estimation.

Note : I mentioned batch_size in shape of y_true and y_pred. I assumed that Keras calls loss function on the entire batch and not on individual samples in the batch. Correct me if I am wrong.

def l2_loss(y_true, y_pred):
     loss = 0
     n = y_true.shape[0]
     for j in range(n):
        for i in range(num_joints):
            yv, xv = tf.meshgrid(tf.arange(0, im_height), tf.arange(0, im_width))
            z = np.array([xv, yv]).transpose(1, 2, 0)
            ground = np.exp(-0.5*(((z - y_true[j, i, :])**2).sum(axis=2))/(sigma**2))
            loss = loss + np.sum((ground - y_pred[j,:, :, i])**2)
     return loss/num_joints

This is the code I have writen so far. I know that this won't run as we can't use direct numpy ndarrays inside a keras loss function. Also, I need to eliminate loops!

Answer 1

You can pretty much just translate the numpy functions into Keras backend functions. The only thing to notice is to set up the right broadcast shape.

def l2_loss_keras(y_true, y_pred):
    # set up meshgrid: (height, width, 2)
    meshgrid = K.tf.meshgrid(K.arange(im_height), K.arange(im_width))
    meshgrid = K.cast(K.transpose(K.stack(meshgrid)), K.floatx())

    # set up broadcast shape: (batch_size, height, width, num_joints, 2)
    meshgrid_broadcast = K.expand_dims(K.expand_dims(meshgrid, 0), -2)
    y_true_broadcast = K.expand_dims(K.expand_dims(y_true, 1), 2)
    diff = meshgrid_broadcast - y_true_broadcast

    # compute loss: first sum over (height, width), then take average over num_joints
    ground = K.exp(-0.5 * K.sum(K.square(diff), axis=-1) / sigma ** 2)
    loss = K.sum(K.square(ground - y_pred), axis=[1, 2])
    return K.mean(loss, axis=-1)

To verify it:

def l2_loss_numpy(y_true, y_pred):
     loss = 0
     n = y_true.shape[0]
     for j in range(n):
        for i in range(num_joints):
            yv, xv = np.meshgrid(np.arange(0, im_height), np.arange(0, im_width))
            z = np.stack([xv, yv]).transpose(1, 2, 0)
            ground = np.exp(-0.5*(((z - y_true[j, i, :])**2).sum(axis=2))/(sigma**2))
            loss = loss + np.sum((ground - y_pred[j,:, :, i])**2)
     return loss/num_joints

batch_size = 32
num_joints = 10
sigma = 5
im_width = 256
im_height = 256

y_true = 255 * np.random.rand(batch_size, num_joints, 2)
y_pred = 255 * np.random.rand(batch_size, im_height, im_width, num_joints)

print(l2_loss_numpy(y_true, y_pred))
45448272129.0

print(K.eval(l2_loss_keras(K.variable(y_true), K.variable(y_pred))).sum())
4.5448e+10

The number is truncated under the default dtype float32. If you run it with dtype set to float64:

y_true = 255 * np.random.rand(batch_size, num_joints, 2)
y_pred = 255 * np.random.rand(batch_size, im_height, im_width, num_joints)

print(l2_loss_numpy(y_true, y_pred))
45460126940.6

print(K.eval(l2_loss_keras(K.variable(y_true), K.variable(y_pred))).sum())
45460126940.6

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EDIT:

It seems that Keras requires y_true and y_pred to have the same number of dimensions. For example, on the following testing model:

X = np.random.rand(batch_size, 256, 256, 3)
model = Sequential([Dense(10, input_shape=(256, 256, 3))])
model.compile(loss=l2_loss_keras, optimizer='adam')
model.fit(X, y_true, batch_size=8)

ValueError: Cannot feed value of shape (8, 10, 2) for Tensor 'dense_2_target:0', which has shape '(?, ?, ?, ?)'

To deal with this problem, you can add a dummy dimension with expand_dims before feeding y_true into the model:

def l2_loss_keras(y_true, y_pred):
    ...

    y_true_broadcast = K.expand_dims(y_true, 1)  # change this line

    ...

model.fit(X, np.expand_dims(y_true, axis=1), batch_size=8)