Localization with Sampling-Argmax

Soft-argmax operation is commonly adopted in detection-based methods to localize the target position in a differentiable manner. However, training the neural network with soft-argmax makes the shape of the probability map unconstrained. Consequently, the model lacks pixel-wise supervision through the map during training, leading to performance degradation. In this work, we propose sampling-argmax, a differentiable training method that imposes implicit constraints to the shape of the probability map by minimizing the expectation of the localization error. To approximate the expectation, we introduce a continuous formulation of the output distribution and develop a differentiable sampling process.