Deriving reliable region-word alignment from image-text pairs is critical to learnobject-level vision-language representations for open-vocabulary object detection.Existing methods typically rely on pre-trained or self-trained vision-languagemodels for alignment, which are prone to limitations in localization accuracy orgeneralization capabilities. In this paper, we propose CoDet, a novel approachthat overcomes the reliance on pre-aligned vision-language space by reformulatingregion-word alignment as a co-occurring object discovery problem. Intuitively, bygrouping images that mention a shared concept in their captions, objects corresponding to the shared concept shall exhibit high co-occurrence among the group.CoDet then leverages visual similarities to discover the co-occurring objects andalign them with the shared concept. Extensive experiments demonstrate that CoDethas superior performances and compelling scalability in open-vocabulary detection,e.g., by scaling up the visual backbone, CoDet achieves 37.0 $AP^m_{novel}$ and 44.7 $AP^m_{all}$ on OV-LVIS, surpassing the previous SoTA by 4.2 $AP^m_{novel}$ and 9.8 $AP^m_{all}$. Code is available at https://github.com/CVMI-Lab/CoDet.

Deriving reliable region-word alignment from image-text pairs is critical to learnobject-level vision-language representations for open-vocabulary object detection.Existing methods typically rely on pre-trained or self-trained vision-languagemodels for alignment, which are prone to limitations in localization accuracy orgeneralization capabilities. In this paper, we propose CoDet, a novel approachthat overcomes the reliance on pre-aligned vision-language space by reformulatingregion-word alignment as a co-occurring object discovery problem. Intuitively, bygrouping images that mention a shared concept in their captions, objects corresponding to the shared concept shall exhibit high co-occurrence among the group.CoDet then leverages visual similarities to discover the co-occurring objects andalign them with the shared concept. Code is available at https://github.com/CVMI-Lab/CoDet.

Selecting the best code solution from multiple generated ones is an essential task in code generation, which can be achieved by using some reliable validators (e.g., developer-written test cases) for assistance. Since reliable test cases are not always available and can be expensive to build in practice, researchers propose to automatically generate test cases to assess code solutions. However, when both code solutions and test cases are plausible and not reliable, selecting the best solution becomes challenging. Although some heuristic strategies have been proposed to tackle this problem, they lack a strong theoretical guarantee and it is still an open question whether an optimal selection strategy exists. Our work contributes in two ways. First, we show that within a Bayesian framework, the optimal selection strategy can be defined based on the posterior probability of the observed passing states between solutions and tests. The problem of identifying the best solution is then framed as an integer programming problem. Second, we propose an efficient approach for approximating this optimal (yet uncomputable) strategy, where the approximation error is bounded by the correctness of prior knowledge. We then incorporate effective prior knowledge to tailor code generation tasks. Both theoretical and empirical studies confirm that existing heuristics are limited in selecting the best solutions with plausible test cases. Our proposed approximated optimal strategy B4 significantly surpasses existing heuristics in selecting code solutions generated by large language models (LLMs) with LLM-generated tests, achieving a relative performance improvement by up to 50% over the strongest heuristic and 246% over the random selection in the most challenging scenarios. Our code is publicly available at https://github.com/ZJU-CTAG/B4.