One of the key steps in Neural Architecture Search (NAS) is to estimate the performance of candidate architectures. Existing methods either directly use the validation performance or learn a predictor to estimate the performance. However, these methods can be either computationally expensive or very inaccurate, which may severely affect the search efficiency and performance. Moreover, as it is very difficult to annotate architectures with accurate performance on specific tasks, learning a promising performance predictor is often non-trivial due to the lack of labeled data. In this paper, we argue that it may not be necessary to estimate the absolute performance for NAS. On the contrary, we may need only to understand whether an architecture is better than a baseline one. However, how to exploit this comparison information as the reward and how to well use the limited labeled data remains two great challenges. In this paper, we propose a novel Contrastive Neural Architecture Search (CTNAS) method which performs architecture search by taking the comparison results between architectures as the reward. Specifically, we design and learn a Neural Architecture Comparator (NAC) to compute the probability of candidate architectures being better than a baseline one. Moreover, we present a baseline updating scheme to improve the baseline iteratively in a curriculum learning manner. More critically, we theoretically show that learning NAC is equivalent to optimizing the ranking over architectures. Extensive experiments in three search spaces demonstrate the superiority of our CTNAS over existing methods.

Mathematical expression recognition (MER) aims to convert an image of mathematical expressions into a Latex sequence. In practice, the task of MER is challenging, since 1) the images of mathematical expressions often contain complex structure relationships, e.g., fractions, matrixes, and subscripts; 2) the generated Latex sequences can be very complex and they have to satisfy strict syntax rules. Existing methods, however, often ignore the complex dependence among image regions, resulting in poor feature representation. In addition, they may fail to capture the rigorous relations among different formula symbols as they consider MER as a common language generation task. To address these issues, we propose a Structure-Aware Sequence-Level (SASL) model for MER. First, to better represent and recognize the visual content of formula images, we propose a structure-aware module to capture the relationship among different symbols. Meanwhile, the sequence-level modeling helps the model to concentrate on the generation of entire sequences. To make the problem feasible, we cast the generation problem into a Markov decision process (MDP) and seek to learn a Latex sequence generating policy. Based on MDP, we learn SASL by maximizing the matching score of each image-sequence pair to obtain the generation policy. Extensive experiments on the IM2LATEX-100K dataset verify the effectiveness and superiority of the proposed method.