Calibrating the Rigged Lottery: Making All Tickets Reliable

Although sparse training has been successfully used in various resource-limited deep learning tasks to save memory, accelerate training, and reduce inference time, the reliability of the produced sparse models remains unexplored. Previous research has shown that deep neural networks tend to be over-confident, and we find that sparse training exacerbates this problem. Therefore, calibrating the sparse models is crucial for reliable prediction and decision-making. In this paper, we propose a new sparse training method to produce sparse models with improved confidence calibration. In contrast to previous research that uses only one mask to control the sparse topology, our method utilizes two masks, including a deterministic mask and a random mask. The former efficiently searches and activates important weights by exploiting the magnitude of weights and gradients. While the latter brings better exploration and finds more appropriate weight values by random updates. Theoretically, we prove our method can be viewed as a hierarchical variational approximation of a probabilistic deep Gaussian process. Extensive experiments on multiple datasets, model architectures, and sparsities show that our method reduces ECE values by up to 47.8% and simultaneously maintains or even improves accuracy with only a slight increase in computation and storage burden. Sparse training is gaining increasing attention and has been used in various deep neural network (DNN) learning tasks (Evci et al., 2020; Dietrich et al., 2021; Bibikar et al., 2022). In sparse training, a certain percentage of connections are maintained being removed to save memory, accelerate training, and reduce inference time, enabling DNNs for resource-constrained situations. The sparse topology is usually controlled by a mask, and various sparse training methods have been proposed to find a suitable mask to achieve comparable or even higher accuracy compared to dense training (Evci et al., 2020; Liu et al., 2021; Schwarz et al., 2021). However, in order to deploy the sparse models in real-world applications, a key question remains to be answered: how reliable are these models? There has been a line of work on studying the reliability of dense DNNs, which means that DNNs should know what it does not know (Guo et al., 2017; Nixon et al., 2019; Wang et al., 2021).