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We investigate the QCD phase transition and its phase structure within Einstein-Maxwell-Dilaton-scalar system and compare the results with those obtained from the Einstein-Maxwell-Dilaton system. It is shown that both models reproduce behavior consistent with lattice QCD. In particular, the Einstein-Maxwell-Dilaton-scalar system exhibits a first-order phase transition in the pure gauge sector, aligning with predictions from Yang-Mills theory. Based on these models, we construct a holographic model for neutron stars, incorporating leptons to satisfy electric charge neutrality, and examine the cold equation of state, the mass-radius relation, and tidal deformability of neutron stars. It is demonstrated that the Einstein-Maxwell-Dilaton-scalar system enables us to describe neutron star properties that meet current astrophysical constraints., Comment: 24 pages, 10 figures, 1 table

The emergence of vision-language foundation models, such as CLIP, has revolutionized image-text representation, enabling a broad range of applications via prompt learning. Despite its promise, real-world datasets often contain noisy labels that can degrade prompt learning performance. In this paper, we demonstrate that using mean absolute error (MAE) loss in prompt learning, named PromptMAE, significantly enhances robustness against noisy labels while maintaining high accuracy. Though MAE is straightforward and recognized for its robustness, it is rarely used in noisy-label learning due to its slow convergence and poor performance outside prompt learning scenarios. To elucidate the robustness of PromptMAE, we leverage feature learning theory to show that MAE can suppress the influence of noisy samples, thereby improving the signal-to-noise ratio and enhancing overall robustness. Additionally, we introduce PromptOT, a prompt-based optimal transport data purification method to enhance the robustness further. PromptOT employs text encoder representations in vision-language models as prototypes to construct an optimal transportation matrix. This matrix effectively partitions datasets into clean and noisy subsets, allowing for the application of cross-entropy loss to the clean subset and MAE loss to the noisy subset. Our Noise-Label Prompt Learning method, named NLPrompt, offers a simple and efficient approach that leverages the expressive representation and precise alignment capabilities of vision-language models for robust prompt learning. We validate NLPrompt through extensive experiments across various noise settings, demonstrating significant performance improvements.

Recent advancements in text-to-video (T2V) generation using diffusion models have garnered significant attention. However, existing T2V models primarily focus on simple scenes featuring a single object performing a single motion. Challenges arise in scenarios involving multiple objects with distinct motions, often leading to incorrect video-text alignment between subjects and their corresponding motions. To address this challenge, we propose \textbf{S$^2$AG-Vid}, a training-free inference-stage optimization method that improves the alignment of multiple objects with their corresponding motions in T2V models. S$^2$AG-Vid initially applies a spatial position-based, cross-attention (CA) constraint in the early stages of the denoising process, facilitating multiple nouns distinctly attending to the correct subject regions. To enhance the motion-subject binding, we implement a syntax-guided contrastive constraint in the subsequent denoising phase, aimed at improving the correlations between the CA maps of verbs and their corresponding nouns.Both qualitative and quantitative evaluations demonstrate that the proposed framework significantly outperforms baseline approaches, producing higher-quality videos with improved subject-motion consistency.

Uncertain changes in data streams present challenges for machine learning models to dynamically adapt and uphold performance in real-time. Particularly, classification boundary change, also known as real concept drift, is the major cause of classification performance deterioration. However, accurately detecting real concept drift remains challenging because the theoretical foundations of existing drift detection methods - two-sample distribution tests and monitoring classification error rate, both suffer from inherent limitations such as the inability to distinguish virtual drift (changes not affecting the classification boundary, will introduce unnecessary model maintenance), limited statistical power, or high computational cost. Furthermore, no existing detection method can provide information on the trend of the drift, which could be invaluable for model maintenance. This work presents a novel real concept drift detection method based on Neighbor-Searching Discrepancy, a new statistic that measures the classification boundary difference between two samples. The proposed method is able to detect real concept drift with high accuracy while ignoring virtual drift. It can also indicate the direction of the classification boundary change by identifying the invasion or retreat of a certain class, which is also an indicator of separability change between classes. A comprehensive evaluation of 11 experiments is conducted, including empirical verification of the proposed theory using artificial datasets, and experimental comparisons with commonly used drift handling methods on real-world datasets. The results show that the proposed theory is robust against a range of distributions and dimensions, and the drift detection method outperforms state-of-the-art alternative methods.

Supervised learning aims to train a classifier under the assumption that training and test data are from the same distribution. To ease the above assumption, researchers have studied a more realistic setting: out-of-distribution (OOD) detection, where test data may come from classes that are unknown during training (i.e., OOD data). Due to the unavailability and diversity of OOD data, good generalization ability is crucial for effective OOD detection algorithms, and corresponding learning theory is still an open problem. To study the generalization of OOD detection, this paper investigates the probably approximately correct (PAC) learning theory of OOD detection that fits the commonly used evaluation metrics in the literature. First, we find a necessary condition for the learnability of OOD detection. Then, using this condition, we prove several impossibility theorems for the learnability of OOD detection under some scenarios. Although the impossibility theorems are frustrating, we find that some conditions of these impossibility theorems may not hold in some practical scenarios. Based on this observation, we next give several necessary and sufficient conditions to characterize the learnability of OOD detection in some practical scenarios. Lastly, we offer theoretical support for representative OOD detection works based on our OOD theory., Comment: Accepted by JMLR in 7th of April, 2024. This is a journal extension of the previous NeurIPS 2022 Outstanding Paper "Is Out-of-distribution Detection Learnable?" [arXiv:2210.14707]

Out-of-distribution (OOD) detection aims at identifying samples from unknown classes, playing a crucial role in trustworthy models against errors on unexpected inputs. Extensive research has been dedicated to exploring OOD detection in the vision modality. Vision-language models (VLMs) can leverage both textual and visual information for various multi-modal applications, whereas few OOD detection methods take into account information from the text modality. In this paper, we propose a novel post hoc OOD detection method, called NegLabel, which takes a vast number of negative labels from extensive corpus databases. We design a novel scheme for the OOD score collaborated with negative labels. Theoretical analysis helps to understand the mechanism of negative labels. Extensive experiments demonstrate that our method NegLabel achieves state-of-the-art performance on various OOD detection benchmarks and generalizes well on multiple VLM architectures. Furthermore, our method NegLabel exhibits remarkable robustness against diverse domain shifts. The codes are available at https://github.com/tmlr-group/NegLabel., Comment: ICLR 2024 Spotlight

Image interpolation based on diffusion models is promising in creating fresh and interesting images. Advanced interpolation methods mainly focus on spherical linear interpolation, where images are encoded into the noise space and then interpolated for denoising to images. However, existing methods face challenges in effectively interpolating natural images (not generated by diffusion models), thereby restricting their practical applicability. Our experimental investigations reveal that these challenges stem from the invalidity of the encoding noise, which may no longer obey the expected noise distribution, e.g., a normal distribution. To address these challenges, we propose a novel approach to correct noise for image interpolation, NoiseDiffusion. Specifically, NoiseDiffusion approaches the invalid noise to the expected distribution by introducing subtle Gaussian noise and introduces a constraint to suppress noise with extreme values. In this context, promoting noise validity contributes to mitigating image artifacts, but the constraint and introduced exogenous noise typically lead to a reduction in signal-to-noise ratio, i.e., loss of original image information. Hence, NoiseDiffusion performs interpolation within the noisy image space and injects raw images into these noisy counterparts to address the challenge of information loss. Consequently, NoiseDiffusion enables us to interpolate natural images without causing artifacts or information loss, thus achieving the best interpolation results., Comment: ICLR 2024

Post-hoc out-of-distribution (OOD) detection has garnered intensive attention in reliable machine learning. Many efforts have been dedicated to deriving score functions based on logits, distances, or rigorous data distribution assumptions to identify low-scoring OOD samples. Nevertheless, these estimate scores may fail to accurately reflect the true data density or impose impractical constraints. To provide a unified perspective on density-based score design, we propose a novel theoretical framework grounded in Bregman divergence, which extends distribution considerations to encompass an exponential family of distributions. Leveraging the conjugation constraint revealed in our theorem, we introduce a \textsc{ConjNorm} method, reframing density function design as a search for the optimal norm coefficient $p$ against the given dataset. In light of the computational challenges of normalization, we devise an unbiased and analytically tractable estimator of the partition function using the Monte Carlo-based importance sampling technique. Extensive experiments across OOD detection benchmarks empirically demonstrate that our proposed \textsc{ConjNorm} has established a new state-of-the-art in a variety of OOD detection setups, outperforming the current best method by up to 13.25$\%$ and 28.19$\%$ (FPR95) on CIFAR-100 and ImageNet-1K, respectively., Comment: ICLR24 poster

Using unlabeled data to regularize the machine learning models has demonstrated promise for improving safety and reliability in detecting out-of-distribution (OOD) data. Harnessing the power of unlabeled in-the-wild data is non-trivial due to the heterogeneity of both in-distribution (ID) and OOD data. This lack of a clean set of OOD samples poses significant challenges in learning an optimal OOD classifier. Currently, there is a lack of research on formally understanding how unlabeled data helps OOD detection. This paper bridges the gap by introducing a new learning framework SAL (Separate And Learn) that offers both strong theoretical guarantees and empirical effectiveness. The framework separates candidate outliers from the unlabeled data and then trains an OOD classifier using the candidate outliers and the labeled ID data. Theoretically, we provide rigorous error bounds from the lens of separability and learnability, formally justifying the two components in our algorithm. Our theory shows that SAL can separate the candidate outliers with small error rates, which leads to a generalization guarantee for the learned OOD classifier. Empirically, SAL achieves state-of-the-art performance on common benchmarks, reinforcing our theoretical insights. Code is publicly available at https://github.com/deeplearning-wisc/sal., Comment: ICLR 2024

Recent diffusion-based image editing approaches have exhibited impressive editing capabilities in images with simple compositions. However, localized editing in complex scenarios has not been well-studied in the literature, despite its growing real-world demands. Existing mask-based inpainting methods fall short of retaining the underlying structure within the edit region. Meanwhile, mask-free attention-based methods often exhibit editing leakage and misalignment in more complex compositions. In this work, we develop MAG-Edit, a training-free, inference-stage optimization method, which enables localized image editing in complex scenarios. In particular, MAG-Edit optimizes the noise latent feature in diffusion models by maximizing two mask-based cross-attention constraints of the edit token, which in turn gradually enhances the local alignment with the desired prompt. Extensive quantitative and qualitative experiments demonstrate the effectiveness of our method in achieving both text alignment and structure preservation for localized editing within complex scenarios., Comment: for project page, see https://mag-edit.github.io/

We investigate the chemical potential effects of the equation of state and the chiral transition in an Einstein-Maxwell-dilaton-scalar system, which is obtained from an improved soft-wall AdS/QCD model coupled with an Einstein-Maxwell-dilaton system. The equations of state obtained from the model are in quantitative agreement with the lattice results at both zero and nonzero chemical potentials. The sensible chiral transition behaviors can be realized in the model. The QCD phase diagram with a CEP has also been obtained from the model.

Out-of-distribution (OOD) detection discerns OOD data where the predictor cannot make valid predictions as in-distribution (ID) data, thereby increasing the reliability of open-world classification. However, it is typically hard to collect real out-of-distribution (OOD) data for training a predictor capable of discerning ID and OOD patterns. This obstacle gives rise to data generation-based learning methods, synthesizing OOD data via data generators for predictor training without requiring any real OOD data. Related methods typically pre-train a generator on ID data and adopt various selection procedures to find those data likely to be the OOD cases. However, generated data may still coincide with ID semantics, i.e., mistaken OOD generation remains, confusing the predictor between ID and OOD data. To this end, we suggest that generated data (with mistaken OOD generation) can be used to devise an auxiliary OOD detection task to facilitate real OOD detection. Specifically, we can ensure that learning from such an auxiliary task is beneficial if the ID and the OOD parts have disjoint supports, with the help of a well-designed training procedure for the predictor. Accordingly, we propose a powerful data generation-based learning method named Auxiliary Task-based OOD Learning (ATOL) that can relieve the mistaken OOD generation. We conduct extensive experiments under various OOD detection setups, demonstrating the effectiveness of our method against its advanced counterparts., Comment: Accepted by NeurIPS 2023

Open-world classification systems should discern out-of-distribution (OOD) data whose labels deviate from those of in-distribution (ID) cases, motivating recent studies in OOD detection. Advanced works, despite their promising progress, may still fail in the open world, owing to the lack of knowledge about unseen OOD data in advance. Although one can access auxiliary OOD data (distinct from unseen ones) for model training, it remains to analyze how such auxiliary data will work in the open world. To this end, we delve into such a problem from a learning theory perspective, finding that the distribution discrepancy between the auxiliary and the unseen real OOD data is the key to affecting the open-world detection performance. Accordingly, we propose Distributional-Augmented OOD Learning (DAL), alleviating the OOD distribution discrepancy by crafting an OOD distribution set that contains all distributions in a Wasserstein ball centered on the auxiliary OOD distribution. We justify that the predictor trained over the worst OOD data in the ball can shrink the OOD distribution discrepancy, thus improving the open-world detection performance given only the auxiliary OOD data. We conduct extensive evaluations across representative OOD detection setups, demonstrating the superiority of our DAL over its advanced counterparts.

Image-based Reinforcement Learning is a practical yet challenging task. A major hurdle lies in extracting control-centric representations while disregarding irrelevant information. While approaches that follow the bisimulation principle exhibit the potential in learning state representations to address this issue, they still grapple with the limited expressive capacity of latent dynamics and the inadaptability to sparse reward environments. To address these limitations, we introduce ReBis, which aims to capture control-centric information by integrating reward-free control information alongside reward-specific knowledge. ReBis utilizes a transformer architecture to implicitly model the dynamics and incorporates block-wise masking to eliminate spatiotemporal redundancy. Moreover, ReBis combines bisimulation-based loss with asymmetric reconstruction loss to prevent feature collapse in environments with sparse rewards. Empirical studies on two large benchmarks, including Atari games and DeepMind Control Suit, demonstrate that ReBis has superior performance compared to existing methods, proving its effectiveness.

Continual Named Entity Recognition (CNER) is a burgeoning area, which involves updating an existing model by incorporating new entity types sequentially. Nevertheless, continual learning approaches are often severely afflicted by catastrophic forgetting. This issue is intensified in CNER due to the consolidation of old entity types from previous steps into the non-entity type at each step, leading to what is known as the semantic shift problem of the non-entity type. In this paper, we introduce a pooled feature distillation loss that skillfully navigates the trade-off between retaining knowledge of old entity types and acquiring new ones, thereby more effectively mitigating the problem of catastrophic forgetting. Additionally, we develop a confidence-based pseudo-labeling for the non-entity type, \emph{i.e.,} predicting entity types using the old model to handle the semantic shift of the non-entity type. Following the pseudo-labeling process, we suggest an adaptive re-weighting type-balanced learning strategy to handle the issue of biased type distribution. We carried out comprehensive experiments on ten CNER settings using three different datasets. The results illustrate that our method significantly outperforms prior state-of-the-art approaches, registering an average improvement of $6.3$\% and $8.0$\% in Micro and Macro F1 scores, respectively., Comment: Accepted by EMNLP2023 main conference as a long paper

Adapting models deployed to test distributions can mitigate the performance degradation caused by distribution shifts. However, privacy concerns may render model parameters inaccessible. One promising approach involves utilizing zeroth-order optimization (ZOO) to train a data adaptor to adapt the test data to fit the deployed models. Nevertheless, the data adaptor trained with ZOO typically brings restricted improvements due to the potential corruption of data features caused by the data adaptor. To address this issue, we revisit ZOO in the context of test-time data adaptation. We find that the issue directly stems from the unreliable estimation of the gradients used to optimize the data adaptor, which is inherently due to the unreliable nature of the pseudo-labels assigned to the test data. Based on this observation, we propose pseudo-label-robust data adaptation (SODA) to improve the performance of data adaptation. Specifically, SODA leverages high-confidence predicted labels as reliable labels to optimize the data adaptor with ZOO for label prediction. For data with low-confidence predictions, SODA encourages the adaptor to preserve data information to mitigate data corruption. Empirical results indicate that SODA can significantly enhance the performance of deployed models in the presence of distribution shifts without requiring access to model parameters.

Out-of-distribution (OOD) generalization is indispensable for learning models in the wild, where testing distribution typically unknown and different from the training. Recent methods derived from causality have shown great potential in achieving OOD generalization. However, existing methods mainly focus on the invariance property of causes, while largely overlooking the property of \textit{sufficiency} and \textit{necessity} conditions. Namely, a necessary but insufficient cause (feature) is invariant to distribution shift, yet it may not have required accuracy. By contrast, a sufficient yet unnecessary cause (feature) tends to fit specific data well but may have a risk of adapting to a new domain. To capture the information of sufficient and necessary causes, we employ a classical concept, the probability of sufficiency and necessary causes (PNS), which indicates the probability of whether one is the necessary and sufficient cause. To associate PNS with OOD generalization, we propose PNS risk and formulate an algorithm to learn representation with a high PNS value. We theoretically analyze and prove the generalizability of the PNS risk. Experiments on both synthetic and real-world benchmarks demonstrate the effectiveness of the proposed method. The details of the implementation can be found at the GitHub repository: https://github.com/ymy4323460/CaSN.

Out-of-distribution (OOD) detection is crucial to modern deep learning applications by identifying and alerting about the OOD samples that should not be tested or used for making predictions. Current OOD detection methods have made significant progress when in-distribution (ID) and OOD samples are drawn from static distributions. However, this can be unrealistic when applied to real-world systems which often undergo continuous variations and shifts in ID and OOD distributions over time. Therefore, for an effective application in real-world systems, the development of OOD detection methods that can adapt to these dynamic and evolving distributions is essential. In this paper, we propose a novel and more realistic setting called continuously adaptive out-of-distribution (CAOOD) detection which targets on developing an OOD detection model that enables dynamic and quick adaptation to a new arriving distribution, with insufficient ID samples during deployment time. To address CAOOD, we develop meta OOD learning (MOL) by designing a learning-to-adapt diagram such that a good initialized OOD detection model is learned during the training process. In the testing process, MOL ensures OOD detection performance over shifting distributions by quickly adapting to new distributions with a few adaptations. Extensive experiments on several OOD benchmarks endorse the effectiveness of our method in preserving both ID classification accuracy and OOD detection performance on continuously shifting distributions., Comment: Accepted by ICCV 2023

Multi-tenancy in public clouds may lead to co-location interference on shared resources, which possibly results in performance degradation of cloud applications. Cloud providers want to know when such events happen and how serious the degradation is, to perform interference-aware migrations and alleviate the problem. However, virtual machines (VM) in Infrastructure-as-a-Service public clouds are black-boxes to providers, where application-level performance information cannot be acquired. This makes performance monitoring intensely challenging as cloud providers can only rely on low-level metrics such as CPU usage and hardware counters. We propose a novel machine learning framework, Alioth, to monitor the performance degradation of cloud applications. To feed the data-hungry models, we first elaborate interference generators and conduct comprehensive co-location experiments on a testbed to build Alioth-dataset which reflects the complexity and dynamicity in real-world scenarios. Then we construct Alioth by (1) augmenting features via recovering low-level metrics under no interference using denoising auto-encoders, (2) devising a transfer learning model based on domain adaptation neural network to make models generalize on test cases unseen in offline training, and (3) developing a SHAP explainer to automate feature selection and enhance model interpretability. Experiments show that Alioth achieves an average mean absolute error of 5.29% offline and 10.8% when testing on applications unseen in the training stage, outperforming the baseline methods. Alioth is also robust in signaling quality-of-service violation under dynamicity. Finally, we demonstrate a possible application of Alioth's interpretability, providing insights to benefit the decision-making of cloud operators. The dataset and code of Alioth have been released on GitHub., Comment: Accepted by 2023 IEEE International Parallel & Distributed Processing Symposium (IPDPS)

Achieving a reliable LiDAR-based object detector in autonomous driving is paramount, but its success hinges on obtaining large amounts of precise 3D annotations. Active learning (AL) seeks to mitigate the annotation burden through algorithms that use fewer labels and can attain performance comparable to fully supervised learning. Although AL has shown promise, current approaches prioritize the selection of unlabeled point clouds with high uncertainty and/or diversity, leading to the selection of more instances for labeling and reduced computational efficiency. In this paper, we resort to a novel kernel coding rate maximization (KECOR) strategy which aims to identify the most informative point clouds to acquire labels through the lens of information theory. Greedy search is applied to seek desired point clouds that can maximize the minimal number of bits required to encode the latent features. To determine the uniqueness and informativeness of the selected samples from the model perspective, we construct a proxy network of the 3D detector head and compute the outer product of Jacobians from all proxy layers to form the empirical neural tangent kernel (NTK) matrix. To accommodate both one-stage (i.e., SECOND) and two-stage detectors (i.e., PVRCNN), we further incorporate the classification entropy maximization and well trade-off between detection performance and the total number of bounding boxes selected for annotation. Extensive experiments conducted on two 3D benchmarks and a 2D detection dataset evidence the superiority and versatility of the proposed approach. Our results show that approximately 44% box-level annotation costs and 26% computational time are reduced compared to the state-of-the-art AL method, without compromising detection performance., Comment: To appear in ICCV 2023

The local beat-to-beat local pulse pressure (PP) and blood pressure waveform of arteries, especially central arteries, are important indicators of the course of cardiovascular diseases (CVDs). Nevertheless, noninvasive measurement of them remains a challenge in the clinic. This work presents a three-element image-free ultrasound system with a low-computational method for real-time measurement of local pulse wave velocity (PWV) and diameter waveforms, enabling real-time and noninvasive continuous PP and blood pressure waveforms measurement without calibration. The developed system has been well-validated in vitro and in vivo. In in vitro cardiovascular phantom experiments, the results demonstrated high accuracy in the measurement of PP (error < 3 mmHg) and blood pressure waveform (root-mean-square-errors (RMSE) < 2 mmHg, correlation coefficient (r) > textgreater 0.99). In subsequent human carotid experiments, the system was compared with an arterial tonometer, which showed excellent PP accuracy (mean absolute error (MAE) = 3.7 +- 3.4 mmHg) and pressure waveform similarity (RMSE = 3.7 +- 1.6 mmHg, r = 0.98 +- 0.01). Furthermore, comparative experiments with the volume clamp device demonstrated the system's ability to accurately trace blood pressure changes (induced by deep breathing) over a period of one minute, with the MAE of DBP, MAP, and SBP within 5 +- 8 mmHg. The present results demonstrate the accuracy and reliability of the developed system for continuous and noninvasive measurement of arterial PP and blood pressure waveform measurements, with potential applications in the diagnosis and prevention of CVDs., Comment: 13 pages, 12 figures

Domain generalization (DG) aims to tackle the distribution shift between training domains and unknown target domains. Generating new domains is one of the most effective approaches, yet its performance gain depends on the distribution discrepancy between the generated and target domains. Distributionally robust optimization is promising to tackle distribution discrepancy by exploring domains in an uncertainty set. However, the uncertainty set may be overwhelmingly large, leading to low-confidence prediction in DG. It is because a large uncertainty set could introduce domains containing semantically different factors from training domains. To address this issue, we propose to perform a $\textbf{mo}$derately $\textbf{d}$istributional $\textbf{e}$xploration (MODE) for domain generalization. Specifically, MODE performs distribution exploration in an uncertainty $\textit{subset}$ that shares the same semantic factors with the training domains. We show that MODE can endow models with provable generalization performance on unknown target domains. The experimental results show that MODE achieves competitive performance compared to state-of-the-art baselines., Comment: Accepted by ICML 2023

In this paper, we study the processes of $e^{+}e^{-}$ annihilation into two body final states, either two pseudoscalar mesons or one meson with a photon. The hadronic vacuum polarization form factors are calculated within the framework of resonance chiral theory in the energy region of $E \lesssim 2$ GeV, with final state interactions taken into account. A joint analysis on the processes of $e^{+}e^{-} \rightarrow \pi^{+}\pi^{-}$, $K^{+}K^{-}$, $K_{L}^{0}K_{S}^{0}$, $\pi^{0}\gamma$, and $\eta\gamma$ has been performed, and the latest experimental data are included. Based on the vacuum polarization form factors of these processes, we estimate their contributions to the lowest order of anomalous magnetic moment of the muon, $(g-2)_\mu$. Combined with other contributions from hadronic vacuum polarization and other interactions from the standard model, the discrepancy between theoretical prediction and experimental measurement is $\Delta a_{\mu}=(24.1\pm5.4)\times 10^{-10}$, i.e., 4.5$\sigma$., Comment: 45 pages, 6 figures, to be the same as the published version

Supervised learning aims to train a classifier under the assumption that training and test data are from the same distribution. To ease the above assumption, researchers have studied a more realistic setting: out-of-distribution (OOD) detection, where test data may come from classes that are unknown during training (i.e., OOD data). Due to the unavailability and diversity of OOD data, good generalization ability is crucial for effective OOD detection algorithms. To study the generalization of OOD detection, in this paper, we investigate the probably approximately correct (PAC) learning theory of OOD detection, which is proposed by researchers as an open problem. First, we find a necessary condition for the learnability of OOD detection. Then, using this condition, we prove several impossibility theorems for the learnability of OOD detection under some scenarios. Although the impossibility theorems are frustrating, we find that some conditions of these impossibility theorems may not hold in some practical scenarios. Based on this observation, we next give several necessary and sufficient conditions to characterize the learnability of OOD detection in some practical scenarios. Lastly, we also offer theoretical supports for several representative OOD detection works based on our OOD theory., Comment: NeurIPS 2022 Outstanding Paper