Differentiable Genetic Programming for High-dimensional Symbolic Regression

Symbolic regression (SR) is the process of discovering hidden relationships from data with mathematical expressions, which is considered an effective way to reach interpretable machine learning (ML). Genetic programming (GP) has been the dominator in solving SR problems. However, as the scale of SR problems increases, GP often poorly demonstrates and cannot effectively address the real-world high-dimensional problems. This limitation is mainly caused by the stochastic evolutionary nature of traditional GP in constructing the trees. In this paper, we propose a differentiable approach named DGP to construct GP trees towards high-dimensional SR for the first time. Specifically, a new data structure called differentiable symbolic tree is proposed to relax the discrete structure to be continuous, thus a gradient-based optimizer can be presented for the efficient optimization. In addition, a sampling method is proposed to eliminate the discrepancy caused by the above relaxation for valid symbolic expressions. Furthermore, a diversification mechanism is introduced to promote the optimizer escaping from local optima for globally better solutions. With these designs, the proposed DGP method can efficiently search for the GP trees with higher performance, thus being capable of dealing with high-dimensional SR. To demonstrate the effectiveness of DGP, we conducted various experiments against the state of the arts based on both GP and deep neural networks. The experiment results reveal that DGP can outperform these chosen peer competitors on high-dimensional regression benchmarks with dimensions varying from tens to thousands. In addition, on the synthetic SR problems, the proposed DGP method can also achieve the best recovery rate even with different noisy levels. It is believed this work can facilitate SR being a powerful alternative to interpretable ML for a broader range of real-world problems.

Efficient Evaluation Methods for Neural Architecture Search: A Survey

Neural Architecture Search (NAS) has received increasing attention because of its exceptional merits in automating the design of Deep Neural Network (DNN) architectures. However, the performance evaluation process, as a key part of NAS, often requires training a large number of DNNs. This inevitably causes NAS computationally expensive. In past years, many Efficient Evaluation Methods (EEMs) have been proposed to address this critical issue. In this paper, we comprehensively survey these EEMs published up to date, and provide a detailed analysis to motivate the further development of this research direction. Specifically, we divide the existing EEMs into four categories based on the number of DNNs trained for constructing these EEMs. The categorization can reflect the degree of efficiency in principle, which can in turn help quickly grasp the methodological features. In surveying each category, we further discuss the design principles and analyze the strength and weaknesses to clarify the landscape of existing EEMs, thus making easily understanding the research trends of EEMs. Furthermore, we also discuss the current challenges and issues to identify future research directions in this emerging topic. To the best of our knowledge, this is the first work that extensively and systematically surveys the EEMs of NAS.