MSE

A purely point-wise loss (such as MSE) drives the model to output the conditional mean, producing a blurring effect that flattens heavy precipitation centers and smooths rainbands, thereby systematically underestimating extremes.

Many of the proposed new objective functions show either limited or unstable improvements compared to a well-tuned MSE baseline.

Quantile loss delivers consistent overall performance improvements over MSE across all tested backbone networks.

Quantile loss is more robust to outliers than MSE and can implicitly characterize the asymmetry of prediction errors.

MSE implicitly assumes homoscedasticity (equal error variance everywhere), which often does not hold in real-world tabular data.

The PSNR calculation formula is PSNR = 10 · log₁₀(MAX² / MSE), where MAX is typically 255 for 8-bit images.

Training the student model with pixel-level loss functions (L1+MSE) caused the output images to appear gray and flat, resembling an average of all possible results—a classic failure mode of regression-based losses on generative tasks.

The previously dominant view held that velocity fields trained with mean squared error (MSE) systematically underestimate velocity magnitudes, and that velocity scaling is a correction for this error.

The study points out that MSE training does not produce a velocity magnitude gap, and that the velocity magnitudes learned by the model are not systematically too small.

In traditional signal processing, denoising and decoding are often optimized in a decoupled manner, and MSE minimization tends to produce overly smoothed outputs that may erase subtle frequency features important for decoding.