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Abstract Information processing under conditions of uncertainty requires the involvement of cognitive control. Despite behavioral evidence of the supramodal function (i.e., independent of sensory modality) of cognitive control, the underlying neural mechanism needs to be directly tested. This study used functional magnetic imaging together with visual and auditory perceptual decision-making tasks to examine brain activation as a function of uncertainty in the two stimulus modalities. The results revealed a monotonic increase in activation in the cortical regions of the cognitive control network (CCN) as a function of uncertainty in the visual and auditory modalities. The intrinsic connectivity between the CCN and sensory regions was similar for the visual and auditory modalities. Furthermore, multivariate patterns of activation in the CCN predicted the level of uncertainty within and across stimulus modalities. These findings suggest that the CCN implements cognitive control by processing uncertainty as abstract information independent of stimulus modality. 

Deep learning architectures are usually proposed with millions of parameters, resulting in a memory issue when training deep neural networks with stochastic gradient descent type methods using large batch sizes. However, training with small batch sizes tends to produce low quality solution due to the large variance of stochastic gradients. In this paper, we tackle this problem by proposing a new framework for training deep neural network with small batches/noisy gradient. During optimization, our method iteratively applies a proximal type regularizer to make loss function strongly convex. Such regularizer stablizes the gradient, leading to better training performance. We prove that our algorithm achieves comparable convergence rate as vanilla SGD even with small batch size. Our framework is simple to implement and can be potentially combined with many existing optimization algorithms. Empirical results show that our method outperforms SGD and Adam when batch size is small. Our implementation is available at https://github.com/huiqu18/TRAlgorithm.