The paper addresses the challenge of out-of-distribution (OOD) detection, where machine learning models need to identify inputs that do not belong to the training distribution. The authors propose a new learning framework called SAL (Separate And Learn), which leverages unlabeled wild data to improve the model's ability to detect OOD samples. The framework consists of two main components: filtering and classification. 1. **Filtering**: SAL uses singular value decomposition on the gradients of a classifier trained on labeled in-distribution (ID) data to identify candidate outliers from the unlabeled wild data. The filtering score is based on the projection of gradients onto the top singular vector, which is theoretically justified to separate OOD data from ID data. 2. **Classification**: After filtering, SAL trains an OOD classifier using the filtered outliers and labeled ID data. The theoretical analysis provides error bounds for both the filtering and classification steps, ensuring that the overall OOD classifier performs well. Empirical results on various benchmarks show that SAL outperforms state-of-the-art methods, achieving superior false positive rates and maintaining high accuracy on ID samples. The paper also discusses the impact of different parameters and compares SAL with other filtering scores, further validating its effectiveness. Overall, SAL offers both theoretical guarantees and practical benefits for OOD detection.The paper addresses the challenge of out-of-distribution (OOD) detection, where machine learning models need to identify inputs that do not belong to the training distribution. The authors propose a new learning framework called SAL (Separate And Learn), which leverages unlabeled wild data to improve the model's ability to detect OOD samples. The framework consists of two main components: filtering and classification. 1. **Filtering**: SAL uses singular value decomposition on the gradients of a classifier trained on labeled in-distribution (ID) data to identify candidate outliers from the unlabeled wild data. The filtering score is based on the projection of gradients onto the top singular vector, which is theoretically justified to separate OOD data from ID data. 2. **Classification**: After filtering, SAL trains an OOD classifier using the filtered outliers and labeled ID data. The theoretical analysis provides error bounds for both the filtering and classification steps, ensuring that the overall OOD classifier performs well. Empirical results on various benchmarks show that SAL outperforms state-of-the-art methods, achieving superior false positive rates and maintaining high accuracy on ID samples. The paper also discusses the impact of different parameters and compares SAL with other filtering scores, further validating its effectiveness. Overall, SAL offers both theoretical guarantees and practical benefits for OOD detection.