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In this work, we study robust deep learning against abnormal training datafrom the perspective of example weighting built in empirical loss functions,i.e., gradient magnitude with respect to logits, an angle that is notthoroughly studied so far. Consequently, we have two key findings: (1) MeanAbsolute Error (MAE) Does Not Treat Examples Equally. We present newobservations and insightful analysis about MAE, which is theoretically provedto be noise-robust. First, we reveal its underfitting problem in practice.Second, we analyse that MAE's noise-robustness is from emphasising on uncertainexamples instead of treating training samples equally, as claimed in priorwork. (2) The Variance of Gradient Magnitude Matters. We propose an effectiveand simple solution to enhance MAE's fitting ability while preserving itsnoise-robustness. Without changing MAE's overall weighting scheme, i.e., whatexamples get higher weights, we simply change its weighting variancenon-linearly so that the impact ratio between two examples are adjusted. Oursolution is termed Improved MAE (IMAE). We prove IMAE's effectiveness usingextensive experiments: image classification under clean labels, synthetic labelnoise, and real-world unknown noise.

IMAE for Noise-Robust Learning: Mean Absolute Error Does Not Treat Examples Equally and Gradient Magnitude's Variance Matters