Recently, there has been a growing interest in automating the process of neural architecture design, and the Differentiable Architecture Search (DARTS) method makes the process available within a few GPU days. In particular, a hypernetwork called one-shot model is introduced, over which the architecture can be searched continuously with gradient descent. However, the performance of DARTS is often observed to collapse when the number of search epochs becomes large. Meanwhile, lots of "skip-connects" are found in the selected architectures. In this paper, we claim that the cause of the collapse is that there exist cooperation and competition in the bi-level optimization in DARTS, where the architecture parameters and model weights are updated alternatively. Therefore, we propose a simple and effective algorithm, named "DARTS+", to avoid the collapse and improve the original DARTS, by "early stopping" the search procedure when meeting a certain criterion. We demonstrate that the proposed early stopping criterion is effective in avoiding the collapse issue. We also conduct experiments on benchmark datasets and show the effectiveness of our DARTS+ algorithm, where DARTS+ achieves 2.32% test error on CIFAR10, 14.87% on CIFAR100, and 23.7% on ImageNet. We further remark that the idea of "early stopping" is implicitly included in some existing DARTS variants by manually setting a small number of search epochs, while we give an explicit criterion for "early stopping".
In this paper, we study the Multi-Round Influence Maximization (MRIM) problem, where influence propagates in multiple rounds independently from possibly different seed sets, and the goal is to select seeds for each round to maximize the expected number of nodes that are activated in at least one round. MRIM problem models the viral marketing scenarios in which advertisers conduct multiple rounds of viral marketing to promote one product. We consider two different settings: 1) the non-adaptive MRIM, where the advertiser needs to determine the seed sets for all rounds at the very beginning, and 2) the adaptive MRIM, where the advertiser can select seed sets adaptively based on the propagation results in the previous rounds. For the non-adaptive setting, we design two algorithms that exhibit an interesting tradeoff between efficiency and effectiveness: a cross-round greedy algorithm that selects seeds at a global level and achieves 1/2−ε approximation ratio, and a within-round greedy algorithm that selects seeds round by round and achieves 1 −e −(1−1/e ) − ε ≈ 0.46 − ε approximation ratio but saves running time by a factor related to the number of rounds. For the adaptive setting, we design an adaptive algorithm that guarantees 1 − e −(1−1/e ) − ε approximation to the adaptive optimal solution. In all cases, we further design scalable algorithms based on the reverse influence sampling approach and achieve near-linear running time. We conduct experiments on several real-world networks and demonstrate that our algorithms are effective for the MRIM task.
Recently, self-supervised learning has attracted great attention since it only requires unlabeled data for training. Contrastive learning is a popular approach for self-supervised learning and empirically performs well in practice. However, the theoretical understanding of its generalization ability on downstream tasks is not well studied. To this end, we present a theoretical explanation of how contrastive self-supervised pre-trained models generalize to downstream tasks. Concretely, we quantitatively show that the selfsupervised model has generalization ability on downstream classification tasks if it embeds input data into a feature space with distinguishing centers of classes and closely clustered intra-class samples. With the above conclusion, we further explore SimCLR and Barlow Twins, which are two canonical contrastive self-supervised methods. We prove that the aforementioned feature space can be obtained via any of the methods, and thus explain their success on the generalization on downstream classification tasks. Finally, various experiments are also conducted to verify our theoretical findings.
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