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Sparse neural networks are effective approaches to reduce the resource requirements for the deployment of deep neural networks. Recently, the concept of adaptive sparse connectivity, has emerged to allow training sparse neural networks from scratch by optimizing the sparse structure during training. However, comparing different sparse topologies and determining how sparse topologies evolve during training, especially for the situation in which the sparse structure optimization is involved, remain as challenging open questions. This comparison becomes increasingly complex as the number of possible topological comparisons increases exponentially with the size of networks. In this work, we introduce an approach to understand and compare sparse neural network topologies from the perspective of graph theory. We first propose Neural Network Sparse Topology Distance (NNSTD) to measure the distance between different sparse neural networks. Further, we demonstrate that sparse neural networks can outperform over-parameterized models in terms of performance, even without any further structure optimization. To the end, we also show that adaptive sparse connectivity can always unveil a plenitude of sparse sub-networks with very different topologies which outperform the dense model, by quantifying and comparing their topological evolutionary processes. The latter findings complement the Lottery Ticket Hypothesis by showing that there is a much more efficient and robust way to find "winning tickets". Altogether, our results start enabling a better theoretical understanding of sparse neural networks, and demonstrate the utility of using graph theory to analyze them.

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Deep reinforcement learning has achieved significant success in many decisionmaking tasks in various fields. However, it requires a large training time of dense neural networks to obtain a good performance. This hinders its applicability on lowresource devices where memory and computation are strictly constrained. In a step towards enabling deep reinforcement learning agents to be applied to low-resource devices, in this work, we propose for the first time to dynamically train deep reinforcement learning agents with sparse neural networks from scratch. We adopt the evolution principles of dynamic sparse training in the reinforcement learning paradigm and introduce a training algorithm that optimizes the sparse topology and the weight values jointly to dynamically fit the incoming data. Our approach is easy to be integrated into existing deep reinforcement learning algorithms and has many favorable advantages. First, it allows for significant compression of the network size which reduces the memory and computation costs substantially. This would accelerate not only the agent inference but also its training process. Second, it speeds up the agent learning process and allows for reducing the number of required training steps. Third, it can achieve higher performance than training the dense counterpart network. We evaluate our approach on OpenAI gym continuous control tasks 1 . The experimental results show the effectiveness of our approach in achieving higher performance than one of the state-of-art baselines with a 50% reduction in the network size and floating-point operations (FLOPs). Moreover, our proposed approach can reach the same performance achieved by the dense network with a 40-50% reduction in the number of training steps.