Qingyu Song

Qingyu Song, Wei Lin, Juncheng Wang et al.

Learning to optimize (L2O) is an emerging technique to solve mathematical optimization problems with learning-based methods. Although with great success in many real-world scenarios such as wireless communications, computer networks, and electronic design, existing L2O works lack theoretical demonstration of their performance and robustness in out-of-distribution (OOD) scenarios. We address this gap by providing comprehensive proofs. First, we prove a sufficient condition for a robust L2O model with homogeneous convergence rates over all In-Distribution (InD) instances. We assume an L2O model achieves robustness for an InD scenario. Based on our proposed methodology of aligning OOD problems to InD problems, we also demonstrate that the L2O model's convergence rate in OOD scenarios will deteriorate by an equation of the L2O model's input features. Moreover, we propose an L2O model with a concise gradient-only feature construction and a novel gradient-based history modeling method. Numerical simulation demonstrates that our proposed model outperforms the state-of-the-art baseline in both InD and OOD scenarios and achieves up to 10 $\times$ convergence speedup. The code of our method can be found from https://github.com/NetX-lab/GoMathL2O-Official.

Qingyu Song, Changan Wang, Zhengkai Jiang et al.

Localizing individuals in crowds is more in accordance with the practical demands of subsequent high-level crowd analysis tasks than simply counting. However, existing localization based methods relying on intermediate representations (\textit{i.e.}, density maps or pseudo boxes) serving as learning targets are counter-intuitive and error-prone. In this paper, we propose a purely point-based framework for joint crowd counting and individual localization. For this framework, instead of merely reporting the absolute counting error at image level, we propose a new metric, called density Normalized Average Precision (nAP), to provide more comprehensive and more precise performance evaluation. Moreover, we design an intuitive solution under this framework, which is called Point to Point Network (P2PNet). P2PNet discards superfluous steps and directly predicts a set of point proposals to represent heads in an image, being consistent with the human annotation results. By thorough analysis, we reveal the key step towards implementing such a novel idea is to assign optimal learning targets for these proposals. Therefore, we propose to conduct this crucial association in an one-to-one matching manner using the Hungarian algorithm. The P2PNet not only significantly surpasses state-of-the-art methods on popular counting benchmarks, but also achieves promising localization accuracy. The codes will be available at: https://github.com/TencentYoutuResearch/CrowdCounting-P2PNet.

Changan Wang, Qingyu Song, Boshen Zhang et al.

Recently, the problem of inaccurate learning targets in crowd counting draws increasing attention. Inspired by a few pioneering work, we solve this problem by trying to predict the indices of pre-defined interval bins of counts instead of the count values themselves. However, an inappropriate interval setting might make the count error contributions from different intervals extremely imbalanced, leading to inferior counting performance. Therefore, we propose a novel count interval partition criterion called Uniform Error Partition (UEP), which always keeps the expected counting error contributions equal for all intervals to minimize the prediction risk. Then to mitigate the inevitably introduced discretization errors in the count quantization process, we propose another criterion called Mean Count Proxies (MCP). The MCP criterion selects the best count proxy for each interval to represent its count value during inference, making the overall expected discretization error of an image nearly negligible. As far as we are aware, this work is the first to delve into such a classification task and ends up with a promising solution for count interval partition. Following the above two theoretically demonstrated criterions, we propose a simple yet effective model termed Uniform Error Partition Network (UEPNet), which achieves state-of-the-art performance on several challenging datasets. The codes will be available at: https://github.com/TencentYoutuResearch/CrowdCounting-UEPNet.