Towards Unknown-aware Learning with Virtual Outlier Synthesis

1 INTRODUCTION . Modern deep neural networks have achieved unprecedented success in known contexts for which they are trained , yet they often struggle to handle the unknowns . In particular , neural networks have been shown to produce high posterior probability for out-of-distribution ( OOD ) test inputs ( Nguyen et al. , 2015 ) , which arise from unknown categories and should not be predicted by the model . Taking self-driving car as an example , an object detection model trained to recognize in-distribution objects ( e.g. , cars , stop signs ) can produce a high-confidence prediction for an unseen object of a moose ; see Figure 1 ( a ) . Such a failure case raises concerns in model reliability , and worse , may lead to catastrophe when deployed in safety-critical applications . The vulnerability to OOD inputs arises due to the lack explicit knowledge of unknowns during training time . In particular , neural networks are typically optimized only on the in-distribution ( ID ) data . The resulting decision boundary , despite being useful on ID tasks such as classification , can be ill-fated for OOD detection . We illustrate this in Figure 1 . The ID data ( gray ) consists of three classconditional Gaussians , on which a three-way softmax classifier is trained . The resulting classifier is overconfident for regions far away from the ID data ( see the red shade in Figure 1 ( b ) ) , causing trouble for OOD detection . Ideally , a model should learn a more compact decision boundary that produces low uncertainty for the ID data , with high OOD uncertainty elsewhere ( e.g. , Figure 1 ( c ) ) . However , achieving this goal is non-trivial due to the lack of supervision signal of unknowns . This motivates the question : Can we synthesize virtual outliers for effective model regularization ? In this paper , we propose a novel unknown-aware learning framework dubbed VOS ( Virtual Outlier Synthesis ) , which optimizes the dual objectives of both ID task and OOD detection performance . In a nutshell , VOS consists of three components tackling challenges of outlier synthesis and effective model regularization with synthesized outliers . To synthesize the outliers , we estimate the class-conditional distribution in the feature space , and sample outliers from the low-likelihood region of ID classes ( Section 3.1 ) . Key to our method , we show that sampling in the feature space is more tractable than synthesizing images in the high-dimensional pixel space ( Lee et al. , 2018a ) . Alongside , we propose a novel unknown-aware training objective , which contrastively shapes the uncertainty surface between the ID data and synthesized outliers ( Section 3.2 ) . During training , VOS simultaneously performs the ID task ( e.g. , classification or object detection ) as well as the OOD uncertainty regularization . During inference time , the uncertainty estimation branch produces a larger probabilistic score for ID data and vice versa , which enables effective OOD detection ( Section 3.3 ) . VOS offers several compelling advantages compared to existing solutions . ( 1 ) VOS is a general learning framework that is effective for both object detection and image classification tasks , whereas previous methods were primarily driven by image classification . Image-level detection can be limiting as an image could be OOD in certain regions while being in-distribution elsewhere . Our work bridges a critical research gap since OOD detection for object detection is timely yet underexplored in literature . ( 2 ) VOS enables adaptive outlier synthesis , which can be flexibly and conveniently used for any ID data without manual data collection or cleaning . In contrast , previous methods using outlier exposure ( Hendrycks et al. , 2019 ) require an auxiliary image dataset that is sufficiently diverse , which can be arguably prohibitive to obtain . Moreover , one needs to perform careful data cleaning to ensure the auxiliary outlier dataset does not overlap with ID data . ( 3 ) VOS synthesizes outliers that can estimate a compact decision boundary between ID and OOD data . In contrast , existing solutions use outliers that are either too trivial to regularize the OOD estimator , or too hard to be separated from ID data , resulting in sub-optimal performance . Our key contributions and results are summarized as follows : • We propose a new framework VOS addressing a pressing issue—unknown-aware deep learning that optimizes for both ID and OOD performance . VOS establishes state-of-the-art results on a challenging object detection task . Compared to the best method , VOS reduces the FPR95 by up to 7.87 % while preserving the accuracy on the ID task . • We conduct extensive ablations and reveal important insights by contrasting different outlier synthesis approaches . We show that VOS is more advantageous than generating outliers directly in the high-dimensional pixel space ( e.g. , using GAN ( Lee et al. , 2018a ) ) or using noise as outliers . • We comprehensively evaluate our method on common OOD detection benchmarks , along with a more challenging yet underexplored task in the context of object detection . Our effort facilitates future research to evaluate OOD detection in a real-world setting . 2 PROBLEM SETUP . We start by formulating the problem of OOD detection in the setting of object detection . Our framework can be easily generalized to image classification when the bounding box is the entire image ( see Section 4.2 ) . Most previous formulations of OOD detection treat entire images as anomalies , which can lead to ambiguity shown in Figure 1 . In particular , natural images are composed of numerous objects and components . Knowing which regions of an image are anomalous could allow for safer handling of unfamiliar objects . This setting is more realistic in practice , yet also more challenging as it requires reasoning OOD uncertainty at the fine-grained object level . Specifically , we denote the input and label space by X = Rd and Y = { 1 , 2 , ... , K } , respectively . Let x ∈ X be the input image , b ∈ R4 be the bounding box coordinates associated with object instances in the image , and y ∈ Y be the semantic label for K-way classification . An object detection model is trained on in-distribution data D = { ( xi , bi , yi ) } Ni=1 drawn from an unknown joint distribution P . We use neural networks with parameters θ to model the bounding box regression pθ ( b|x ) and the classification pθ ( y|x , b ) . The OOD detection can be formulated as a binary classification problem , which distinguishes between the in- vs. out-of-distribution objects . Let PX denote the marginal probability distribution on X . Given a test input x∗ ∼ PX , as well as an object instance b∗ predicted by the object detector , the goal is to predict pθ ( g|x∗ , b∗ ) . We use g = 1 to indicate a detected object being in-distribution , and g = 0 being out-of-distribution , with semantics outside the support of Y . 3 METHOD . Our novel unknown-aware learning framework is illustrated in Figure 2 . Our framework encompasses three novel components and addresses the following questions : ( 1 ) how to synthesize the virtual outliers ( Section 3.1 ) , ( 2 ) how to leverage the synthesized outliers for effective model regularization ( Section 3.2 ) , and ( 3 ) how to perform OOD detection during inference time ( Section 3.3 ) ? 3.1 VOS : VIRTUAL OUTLIER SYNTHESIS . Our framework VOS generates virtual outliers for model regularization , without relying on external data . While a straightforward idea is to train generative models such as GANs ( Goodfellow et al. , 2014 ; Lee et al. , 2018a ) , synthesizing images in the high-dimensional pixel space can be difficult to optimize . Instead , our key idea is to synthesize virtual outliers in the feature space , which is more tractable given lower dimensionality . Moreover , our method is based on a discriminatively trained classifier in the object detector , which circumvents the difficult optimization process in training generative models . Specifically , we assume the feature representation of object instances forms a class-conditional multivariate Gaussian distribution ( see Figure 3 ) : pθ ( h ( x , b ) |y = k ) = N ( µk , Σ ) , where µk is the Gaussian mean of class k ∈ { 1 , 2 , .. , K } , Σ is the tied covariance matrix , and h ( x , b ) ∈ Rm is the latent representation of an object instance ( x , b ) . To extract the latent representation , we use the penultimate layer of the neural network . The dimensionality m is significantly smaller than the input dimension d. To estimate the parameters of the class-conditional Gaussian , we compute empirical class mean µ̂k and covariance Σ̂ of training samples { ( xi , bi , yi ) } Ni=1 : µ̂k = 1 Nk ∑ i : yi=k h ( xi , bi ) ( 1 ) Σ̂ = 1 N ∑ k ∑ i : yi=k ( h ( xi , bi ) − µ̂k ) ( h ( xi , bi ) − µ̂k ) > , ( 2 ) where Nk is the number of objects in class k , and N is the total number of objects . We use online estimation for efficient training , where we maintain a class-conditional queue with |Qk| object instances from each class . In each iteration , we enqueue the embeddings of objects to their corresponding class-conditional queues , and dequeue the same number of object embeddings . Sampling from the feature representation space . We propose sampling the virtual outliers from the feature representation space , using the multivariate distributions estimated above . Ideally , these virtual outliers should help estimate a more compact decision boundary between ID and OOD data . To achieve this , we propose sampling the virtual outliers Vk from the -likelihood region of the estimated class-conditional distribution : Vk = { vk| 1 ( 2π ) m/2|Σ̂|1/2 exp ( −1 2 ( vk − µ̂k ) > Σ̂−1 ( vk − µ̂k ) ) < } , ( 3 ) where vk ∼ N ( µ̂k , Σ̂ ) denotes the sampled virtual outliers for class k , which are in the sublevel set based on the likelihood . is sufficiently small so that the sampled outliers are near class boundary . Classification outputs for virtual outliers . For a given sampled virtual outlier v ∈ Rm , the output of the classification branch can be derived through a linear transformation : f ( v ; θ ) =W > clsv , ( 4 ) where Wcls ∈ Rm×K is the weight of the last fully connected layer . We proceed with describing how to regularize the output of virtual outliers for improved OOD detection . 3.2 UNKNOWN-AWARE TRAINING OBJECTIVE . We now introduce a new training objective for unknown-aware learning , leveraging the virtual outliers in Section 3.1 . The key idea is to perform visual recognition task while regularizing the model to produce a low OOD score for ID data , and a high OOD score for the synthesized outlier . Uncertainty regularization for classification . For simplicity , we first describe the regularization in the multi-class classification setting . The regularization loss should ideally optimize for the separability between the ID vs. OOD data under some function that captures the data density . However , directly estimating log p ( x ) can be computationally intractable as it requires sampling from the entire space X . We note that the log partition function E ( x ; θ ) : = − log ∑K k=1 e fk ( x ; θ ) is proportional to log p ( x ) with some unknown factor , which can be seen from the following : p ( y|x ) = p ( x , y ) p ( x ) = efy ( x ; θ ) ∑K k=1 e fk ( x ; θ ) , where fy ( x ; θ ) denotes the y-th element of logit output corresponding to the label y . The negative log partition function is also known as the free energy , which was shown to be an effective uncertainty measurement for OOD detection ( Liu et al. , 2020a ) . Our idea is to explicitly perform a level-set estimation based on the energy function ( threshold at 0 ) , where the ID data has negative energy values and the synthesized outlier has positive energy : Luncertainty = Ev∼V 1 { E ( v ; θ ) > 0 } + Ex∼D 1 { E ( x ; θ ) ≤ 0 } This is a simpler objective than estimating density . Since the 0/1 loss is intractable , we replace it with the binary sigmoid loss , a smooth approximation of the 0/1 loss , yielding the following : Luncertainty = Ev∼V [ − log 1 1 + exp−θu·E ( v ; θ ) ] + Ex∼D [ − log exp −θu·E ( x ; θ ) 1 + exp−θu·E ( x ; θ ) ] . ( 5 ) Here θu is a learnable parameter modulating the slope of the sigmoid function . The learning process shapes the uncertainty surface , which predicts high probability for ID data and low probability for virtual outliers v. Liu et al . ( 2020a ) employed energy for model uncertainty regularization , however , the loss function is based on the squared hinge loss and requires tuning two margin hyperparameters . In contrast , our uncertainty regularization loss is completely hyperparameter-free and is much easier to use in practice . Moreover , VOS produces probabilistic score for OOD detection , whereas Liu et al . ( 2020a ) relies on non-probabilistic energy score . Object-level energy score . In case of object detection , we can replace the image-level energy with object-level energy score . For ID object ( x , b ) , the energy is defined as : E ( x , b ; θ ) = − log K∑ k=1 wk · expfk ( ( x , b ) ; θ ) , ( 6 ) where fk ( ( x , b ) ; θ ) = W > clsh ( x , b ) is the logit output for class k in the classification branch . The energy score for the virtual outlier can be defined in a similar way as above . In particular , we will show in Section 4 that a learnable w is more flexible than a constant w , given the inherent class imbalance in object detection datasets . Additional analysis on wk is in Appendix H. Overall training objective . In the case of object detection , the overall training objective combines the standard object detection loss , along with a regularization loss in terms of uncertainty : min θ E ( x , b , y ) ∼D [ Lcls + Lloc ] + β · Luncertainty , ( 7 ) where β is the weight of the uncertainty regularization . Lcls and Lloc are losses for classification and bounding box regression , respectively . This can be simplified to classification task without Lloc . We provide ablation studies in Section 4.1 demonstrating the superiority of our loss function .

Summary: This paper presents an approach for detecting out of distribution (OOD) samples by synthesizing outlier samples and considering an unknown-aware learning mechanism. The synthetic outlier samples are used to learn a tighter class boundary for in-distribution samples. The model is trained with an uncertainty-aware loss function that encourages a high probability score in distribution samples and a low probability score for OOD samples.