Gradient clipping is a widely-used technique in the training of deep networks, and is generally motivated from an optimisation lens: informally, it controls the dynamics of iterates, thus enhancing the rate of convergence to a local minimum. This intuition has been made precise in a line of recent works, which show that suitable clipping  can yield significantly faster convergence than vanilla gradient descent. In this paper, we propose a new lens for studying gradient clipping, namely, robustness: informally, one expects clipping to provide robustness to noise, since one does not overly trust any single sample. Surprisingly, we prove that  for the common problem of label noise in classification, standard gradient clipping does not in general provide robustness. On the other hand, we show that  a simple variant of gradient clipping is provably robust, and corresponds to suitably modifying the underlying loss function. This yields a simple, noise-robust alternative to the standard cross-entropy loss which performs well empirically. We established that gradient clipping by itself does not suffice to endow even simple models with label noise robustness; however, a simple variant resolves this issue. Experiments confirm that our composite loss-based gradient clipping performs well on datasets corrupted with label noise. One interesting direction for future work is to analyse the behaviour of gradient-clipping inspired losses for the more general problem of distributionally robust learning (Shafieezadeh-Abadeh et al., 2015; Namkoong & Duchi, 2016; Sinha et al., 2018; Duchi & Namkoong, 2019) .
Gradient clipping doesn't endow robustness to label noise, but a simple loss-based variant does.
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