We focus on two supervised visual reasoning tasks whose labels encode a semantic relational rule between two or more objects in an image: the MNIST Parity task and the colorized Pentomino task. The objects in the images undergo random translation, scaling, rotation and coloring transformations. Thus these tasks involve invariant relational reasoning. We report uneven performance of various deep CNN models on these two tasks. For the MNIST Parity task, we report that the VGG19 model soundly outperforms a family of ResNet models. Moreover, the family of ResNet models exhibits a general sensitivity to random initialization for the MNIST Parity task. For the colorized Pentomino task, now both the VGG19 and ResNet models exhibit sluggish optimization and very poor test generalization, hovering around 30 test error. The CNN we tested all learn hierarchies of fully distributed features and thus encode the distributed representation prior. We are motivated by a hypothesis from cognitive neuroscience which posits that the human visual cortex is modularized, and this allows the visual cortex to learn higher order invariances. To this end, we consider a modularized variant of the ResNet model, referred to as a Residual Mixture Network (ResMixNet) which employs a mixture-of-experts architecture to interleave distributed representations with more specialized, modular representations. We show that very shallow ResMixNets are capable of learning each of the two tasks well, attaining less than 2 and 1 test error on the MNIST Parity and the colorized Pentomino tasks respectively. Most importantly, the ResMixNet models are extremely parameter efficient: generalizing better than various non-modular CNNs that have over 10x the number of parameters. These experimental results support the hypothesis that modularity is a robust prior for learning invariant relational reasoning.
With respect to the ResMixNet architecture, it is clearly built on top of the well established mixture of experts architecture @cite_40 @cite_47 . The most relevant work is @cite_36 . One major difference with our work is that @cite_36 applied modular MLPs to a task like Jittered MNIST, which does not have as many invariances as the MNIST Parity and the colorized Pentomino task, nor does it involve any relational reasoning. To this end, we believe that the higher order invariance setting is where the modularity prior can result in a significant performance gain which we showed in Section 4.
@cite_36 @cite_40 @cite_47
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We present a variety of new architectural features and training procedures that we apply to the generative adversarial networks (GANs) framework. Using our new techniques, we achieve state-of-the-art results in semi-supervised classification on MNIST, CIFAR-10 and SVHN. The generated images are of high quality as confirmed by a visual Turing test: our model generates MNIST samples that humans cannot distinguish from real data, and CIFAR-10 samples that yield a human error rate of 21.3 . We also present ImageNet samples with unprecedented resolution and show that our methods enable the model to learn recognizable features of ImageNet classes. Recovering images from undersampled linear measurements typically leads to an ill-posed linear inverse problem, that asks for proper statistical priors. Building effective priors is however challenged by the low train and test overhead dictated by real-time tasks; and the need for retrieving visually "plausible" and physically "feasible" images with minimal hallucination. To cope with these challenges, we design a cascaded network architecture that unrolls the proximal gradient iterations by permeating benefits from generative residual networks (ResNet) to modeling the proximal operator. A mixture of pixel-wise and perceptual costs is then deployed to train proximals. The overall architecture resembles back-and-forth projection onto the intersection of feasible and plausible images. Extensive computational experiments are examined for a global task of reconstructing MR images of pediatric patients, and a more local task of superresolving CelebA faces, that are insightful to design efficient architectures. Our observations indicate that for MRI reconstruction, a recurrent ResNet with a single residual block effectively learns the proximal. This simple architecture appears to significantly outperform the alternative deep ResNet architecture by 2dB SNR, and the conventional compressed-sensing MRI by 4dB SNR with 100x faster inference. For image superresolution, our preliminary results indicate that modeling the denoising proximal demands deep ResNets. We present a simple, highly modularized network architecture for image classification. Our network is constructed by repeating a building block that aggregates a set of transformations with the same topology. Our simple design results in a homogeneous, multi-branch architecture that has only a few hyper-parameters to set. This strategy exposes a new dimension, which we call "cardinality" (the size of the set of transformations), as an essential factor in addition to the dimensions of depth and width. On the ImageNet-1K dataset, we empirically show that even under the restricted condition of maintaining complexity, increasing cardinality is able to improve classification accuracy. Moreover, increasing cardinality is more effective than going deeper or wider when we increase the capacity. Our models, named ResNeXt, are the foundations of our entry to the ILSVRC 2016 classification task in which we secured 2nd place. We further investigate ResNeXt on an ImageNet-5K set and the COCO detection set, also showing better results than its ResNet counterpart. The code and models are publicly available online. We present a simple, highly modularized network architecture for image classification. Our network is constructed by repeating a building block that aggregates a set of transformations with the same topology. Our simple design results in a homogeneous, multi-branch architecture that has only a few hyper-parameters to set. This strategy exposes a new dimension, which we call cardinality (the size of the set of transformations), as an essential factor in addition to the dimensions of depth and width. On the ImageNet-1K dataset, we empirically show that even under the restricted condition of maintaining complexity, increasing cardinality is able to improve classification accuracy. Moreover, increasing cardinality is more effective than going deeper or wider when we increase the capacity. Our models, named ResNeXt, are the foundations of our entry to the ILSVRC 2016 classification task in which we secured 2nd place. We further investigate ResNeXt on an ImageNet-5K set and the COCO detection set, also showing better results than its ResNet counterpart. The code and models are publicly available online.