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The deployment of Deep Neural Networks (DNNs) on edge devices is hindered by the substantial gap between performance requirements and available computational power. While recent research has made significant strides in developing pruning methods to build a sparse network for reducing the computing overhead of DNNs, there remains considerable accuracy loss, especially at high pruning ratios. We find that the architectures designed for dense networks by differentiable architecture search methods are ineffective when pruning mechanisms are applied to them. The main reason is that the current methods do not support sparse architectures in their search space and use a search objective that is made for dense networks and does not focus on sparsity.This paper proposes a new method to search for sparsity-friendly neural architectures. It is done by adding two new sparse operations to the search space and modifying the search objective. We propose two novel parametric SparseConv and SparseLinear operations in order to expand the search space to include sparse operations. In particular, these operations make a flexible search space due to using sparse parametric versions of linear and convolution operations. The proposed search objective lets us train the architecture based on the sparsity of the search space operations. Quantitative analyses demonstrate that architectures found through DASS outperform those used in the state-of-the-art sparse networks on the CIFAR-10 and ImageNet datasets. In terms of performance and hardware effectiveness, DASS increases the accuracy of the sparse version of MobileNet-v2 from 73.44% to 81.35% (+7.91% improvement) with a 3.87× faster inference time.