Loss disentanglement

Overview

A network that regresses several quantities at once, such as depth, size and angle, often sums their errors into one loss. The quantities have different units and meanings, so their errors can pull against each other 1905.12365 §1. Loss disentanglement is one fix for this. It splits the loss into one term per parameter group. In each term, only that group comes from the prediction and every other group is set to the ground truth, so each term is still the same kind of box loss 1905.12365 §5.1.

This is not the same as disentangled representation, which concerns latent codes. Here the split is over the terms of a loss.

The method needs two properties. The box loss must be zero when the prediction equals the target, and the map from network output to box must be one-to-one 1905.12365 §5.1.

Variants

Only one paper with a card covers this technique, so there is one variant.

Per-group box loss (MonoDIS)

For 2D boxes, the loss has two groups, size and centre, and uses the signed IoU loss 1905.12365 §5.1 1905.12365 eq. 1. For 3D boxes, it has four groups, depth, projected centre, rotation and dimensions, and uses the Huber loss over the eight box corners 1905.12365 §5.1 1905.12365 eq. 2. The paper applies the split to both losses in its main experiments 1905.12365 §5.1. Card: Disentangling Monocular 3D Object Detection.

Reported effect

All numbers are author-reported on the KITTI validation split, car class, 3D AP40, Easy / Moderate / Hard 1905.12365 tab. 3.

The gain from the split by itself is small in these rows. The larger gains in the same table come from the other changes the paper makes, which the rows do not separate 1905.12365 tab. 3. The AP11 rows on the same split show the same small gain 1905.12365 tab. 5. The paper calls the training more stable and faster, but this comparison is not shown in a table 1905.12365 §5.2 1905.12365 fig. 7.

When to use which

Open points that the paper does not settle:

• Whether the sum over groups is normalised, and whether the Huber terms are summed or averaged before the 1/8 factor 1905.12365 §4.3 1905.12365 §5.1.
• The units of the Huber threshold δ = 3.0 1905.12365 §7.2.
• How the 3D head's training boxes are matched to ground truth 1905.12365 §4.3.

Implementation sketch

Language-agnostic pseudocode of the generic split. The paper's concrete groups are in the card's Method section 1905.12365 §5.1.

# Disentangled loss over k parameter groups  [arxiv:1905.12365 §5.1]
# Input:  prediction theta, ground-truth box y_hat, groups G_1..G_k
# Output: scalar loss

def disentangled_loss(theta, y_hat, groups, psi, psi_inv, box_loss):
    # 1. Ground-truth parametrisation  [arxiv:1905.12365 §5.1]
    theta_hat = psi_inv(y_hat)
    total = 0
    for group in groups:
        # 2. Keep group j from the prediction, the rest from ground truth
        mixed = theta_hat.copy()
        mixed[group] = theta[group]
        # 3. Map back to a box and apply the ordinary box loss  [§5.1]
        total += box_loss(psi(mixed), y_hat)
    # 4. Whether this sum is normalised is not stated  [§5.1]
    return total

Contradictions

None known. Only one card cites this technique, so there is no cross-paper comparison.

Papers

• Disentangling Monocular 3D Object Detection: splits the 2D and 3D box losses into per-group terms for monocular 3D car detection.