Differentiable architecture search is prevalent in the field of NAS because of its simplicity and efficiency, where two paradigms, multi-path algorithms and single-path methods, are dominated. Multi-path framework (e.g. DARTS) is intuitive but suffers from memory usage and training collapse. Single-path methods (e.g. GDAS and Proxyless-NAS) mitigate the memory issue and shrink the gap between searching and evaluation but sacrifice the performance. In this paper, we propose a conceptually simple yet efficient method to bridge these two paradigms, referred as Mutually-aware Sub-Graphs Differentiable Architecture Search (MSG-DAS). The core of our framework is a differentiable Gumbel-TopK sampler that produces multiple mutually exclusive single-path sub-graphs. To alleviate the severer skip-connect issue brought by multiple sub-graphs setting, we propose a Dropblock-Identity module to stabilize the optimization. To make best use of the available models (super-net and sub-graphs), we introduce a memoryefficient super-net guidance distillation to improve training. The proposed framework strikes a balance between flexible memory usage and searching quality. We demonstrate the effectiveness of our methods on ImageNet and CIFAR10, where the searched models show a comparable performance as the most recent approaches.
Sparse inverse covariance selection is a fundamental problem for analyzing dependencies in high dimensional data. However, such a problem is difficult to solve since it is NP-hard. Existing solutions are primarily based on convex approximation and iterative hard thresholding, which only lead to sub-optimal solutions. In this work, we propose a coordinate-wise optimization algorithm to solve this problem which is guaranteed to converge to a coordinate-wise minimum point. The algorithm iteratively and greedily selects one variable or swaps two variables to identify the support set, and then solves a reduced convex optimization problem over the support set to achieve the greatest descent. As a side contribution of this paper, we propose a Newton-like algorithm to solve the reduced convex sub-problem, which is proven to always converge to the optimal solution with global linear convergence rate and local quadratic convergence rate. Finally, we demonstrate the efficacy of our method on synthetic data and real-world data sets. As a result, the proposed method consistently outperforms existing solutions in terms of accuracy.
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