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  1. We studied a local normalization paradigm, namely weighted normalization, that better reflects the current understanding of the brain. Specifically, the normalization weight is trainable, and has a more realistic surround pool selection. Weighted normalization outperformed other normalizations in image classification tasks on Cifar10, Imagenet and a customized textured MNIST dataset. The superior performance is more prominent when the CNN is shallow. The good performance of weighted normalization may be related to its statistical effect of gaussianizing the responses. 
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  2. Deep convolutional neural networks (CNNs) are becoming increasingly popular models to predict neural responses in visual cortex. However, contextual effects, which are prevalent in neural processing and in perception, are not explicitly handled by current CNNs, including those used for neural prediction. In primary visual cortex, neural responses are modulated by stimuli spatially surrounding the classical receptive field in rich ways. These effects have been modeled with divisive normalization approaches, including flexible models, where spatial normalization is recruited only to the degree that responses from center and surround locations are deemed statistically dependent. We propose a flexible normalization model applied to midlevel representations of deep CNNs as a tractable way to study contextual normalization mechanisms in midlevel cortical areas. This approach captures nontrivial spatial dependencies among midlevel features in CNNs, such as those present in textures and other visual stimuli, that arise from tiling high-order features geometrically. We expect that the proposed approach can make predictions about when spatial normalization might be recruited in midlevel cortical areas. We also expect this approach to be useful as part of the CNN tool kit, therefore going beyond more restrictive fixed forms of normalization. 
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