Topology-Matching Normalizing Flows for Out-of-Distribution Detection in Robot Learning
Authors: Jianxiang Feng
Jongseok Lee
Simon Geisler
Stephan Günnemann
Rudolph Triebel
Venue: CoRL 2023 Poster (2023)
Keywords: Normalizing Flows
Out-of-Distribution Detection
Robotic Introspection

Abstract: To facilitate reliable deployments of autonomous robots in the real world, Out-of-Distribution (OOD) detection capabilities are often required. A powerful approach for OOD detection is based on density estimation with Normalizing Flows (NFs). However, we find that prior work with NFs attempts to match the complex target distribution topologically with naı̈ve base distributions leading to adverse implications. In this work, we circumvent this topological mismatch using an expressive class-conditional base distribution trained with an information-theoretic objective to match the required topology. The proposed method enjoys the merits of wide compatibility with existing learned models without any performance degradation and minimum computation overhead while enhancing OOD detection capabilities. We demonstrate superior results in density estimation and 2D object detection benchmarks in comparison with extensive baselines. Moreover, we showcase the applicability of the method with a real-robot deployment.

Topology-Matching Normalizing Flows for Out-of-Distribution Detection in Robot Learning
Jianxiang Feng 1 Jongseok Lee Simon Geisler', Stephan Günnemann's Rudolph Triebel
Department of Informaties, Technical University of Munich (TUM)
2 Institute of Robotics and Mechatronics, German Aerospace Center (DLR)
3 Department of Informatics, Karlsruhe Institute of Technology (KIT)
jianxiang.fers feng@tum. de, {jongseok. 1ee, rudolph. triebel @dlr.. de, {geisler, guennemann @in. tum. de Bina
Abstract: To facilitate reliable deployments of autonomous robots in the real world,
(OOD) detection capabilities are often required. powerful approach for OOD detection is based on density estimation with Normal- izing Flows (NFs). However, we find that prior work with NFs attempts to match the complex target distribution topologically with naive base distributions leading to adverse implications. In this work, circumvent this topological mismatch us- ing expressive class-conditional base distribution trained with an information- theoretic objective to match the required topology. The proposed method enjoys the merits of wide compatibility with existing learned models without any perfor- mance degradation and minimum computation overhead while enhancing OOD detection capabilities. We demonstrate superior results density estimation and 2D object detection benchmarks in comparison with extensive baselines. More- over, we showcase the applicability of the method with real-robot deployment.
Keywords: Normalizing Flows, Out-of-Distributionn Robotic Introspection
Introduction
The reliable identification of Out-of-Distribution (OOD) data, which not well represented in the training set, poses pressing challenge on the path towards trustworthy open-world robotic sys- tems such self-driving cars [1], delivery drones [2] or healthcare robots [3]. For example, with widespread adoption in the perception pipeline, existing object detectors have been reported to over- confidently misclassify an OOD object into a known class, which might obfuscate the decision- making module and eventually cause catastrophic consequences in safety-critical scenarios [1, 4, 5J.
Normalizing Flows (NFs) are a popular class of generative models [6. 7, 8, 9] that may be used for OOD detection. NFs represent complex probability distributions [10] with a learnable series of transformations from simple base distribution
complex target distribution. However, NFs' expressivity [1] 12, 13] and numerical stability [14, 15) is limited by fundamental constraint: the supports of the base and target distribution should preserve similar topological properties (Definition 3. in Runde [16]). The topological properties subsume different geometrical characteristics of the target distribution, including its continuity, the number of connected components, or the number of modes. Increasing the capacity of the transformation may mitigate this constraint. Yet, this raises computation and memory demands [11, 17, 12]. An alternative overcome the topological mismatch is to increase the flexibility of the base distribution, which is surprisingly under-explored in the OOD detection literature.
Therefore, we propose to equip NFs with efficient but flexible base distributions for OOD detection robot learning. Concretely, we replace the frequently used uni-modal Gaussian base distribution
": work done when working at DLR. code: https://gthub..co/Di. wttptuuu..oo/D...RRRR.... R-RM
7th Conference Robot Learning (CoRL. 2023), Atlanta, USA.

---

Input Images
Object Detector Backbone
Prediction Heads
Outputs
Valve
Regression
Unknown Valve
Out-uF Distribution Valve
Clossification
"Valve": *Valvee:
Base Distribution
Logity Latent Space
Bijection
Σn
To
pe (z)
T
(oly "Vlve") via cRSB
Po.
Topology Normalizing Flows
LoggLiielihoodd (LL)
Figure 1: The proposed architecture. We overcome the topological mismatch problem in NFs to accurately model In- Distribution (ID) density. That is, the Conditional Resampled Base Distribu- tions (cRSB) base distribution trained with Information Bottleneck (IB) pa: (z) y) can, e.g., adapt the numbers of modes match target distribution with complex topology. Then objects by low predicted log-lik ligeliiss more reliably (best viewed color).
identify OOD
with the cRSB, a class-conditional version of a learnable base distribution for mitigating the topo- logical problem in NFs Resampled Base Distributions (RSB) [13]. cRSB can learn the required topological properties, like adapting the number of modes, to match the unknown topological struc- ture of the latent class- specific target distribution (Figure 1). Moreover, we adapt our cRSB with an adapted IB objective [18] balance fusing class-conditional information with the marginalized cnormatiin-thhoreetee objective incorporate
density estimation capabilities in NFs. IB [19] is task-specific details e.g. class conditions, which are commonly ignored in pure generative model- ing. This delivers topology in the base distribution that is more accurately aligned to the one in the target distribution (see Figure 3).
Our OOD detection approach using topology-matching NFs is powerful and yet resource-efffiient for open-set object detection. It is applicable to diverse object detectors (e.g.. Paster-RCNN [20] and Yolov7 [21] used in this work) with minor changes and no loss of prediction performance. Moreover, our approach is sampling-free i.e., only single forward pass is required for efficient test-time inference while keeping the space memory tractable. As a result, our method is suitable for robotic applications that require a fast and robust perception module. We empirically show the state-of- the-art performance of the proposed idea using synthetic density estimation and 2D object detection tasks against extensive baselines. To further validate the applicability in robotics, we examine an object detector equipped with the proposed method an exemplary inspection and maintenance acrial robot, showing the practical benefits of negligible memory and run-time overhead.
Contributions. Our main contribution is a NFs-based OOD detection method that overcomes the topological constraints while taking class- class-conditie conditional information into account. We show that train- ing with IB yields effective representation with superior OOD detection capabilities. We conduct a comprehensive empirical evaluation using both synthetic density estimation and public object de- tection datasets followed by real-world robot deployment, which overall shows the effectiveness of the proposed approach.

---

2 Methodology
Problem Formulation Given an image X E A' and a trained object detector Fe that localizes set objects with corresponding bounding box coordinates b, E R$ as well as class label ye E y = {1, 2, ...,, C), : the task to distinguish if (x, V:) ID, i.e., drawn from Pid. or OOD, i.e., belongs the unknown distribution Pood. For conciseness, from now on we omit the suffix and denote the class label without further notice. As discussed, powerful OOD detection can be obtained via density estimation using NFs. This density estimator identifies OOD objects with low likelihoods after being trained only on data drawn from Pia. Following relevant prior [22, 23], we use the semantically rich logit space (pre-softmax layer) for density estimation. To note that, our method can be readily applied to other (iigh--imessiona) latent feature spaces.
NFs are known to be universal distribu- tion approximators [10]. That is, they model complex target distribution p(u) on space Rd by defining u as trans- formation Ta : Rd + Rd from a well- defined base distribution (z) where & and vi are model parameters, respectively: (z) where ~~ po (z( (z)
(a) p(uly = 0) (b) Pa.e (uly=0) (c) pa (zly = 0)
(I)
Figure 2: Filament connect modes in the modeled class-conditional distribution (b) if using (trainable) uni-modal base (c) for the multi-modal target (a).
where E Rd and Pv is commonly chosen as uni-modal Gaussian. By designing To to be diffeomorphism, that is, a bijection where both Ta and Tz² are differentiable, We can com- pute the likelihood of the input u exactly based on the ch formula [24]:
Polv (u) (T= (u)) det (et( (u))l,
where (u- E Rdxd is the Jacobian of the inverse TØ1 with respect to u. When the target
distribution is unknown but samples thereof are available, we can estimate the parameter (6, v)) by minimizing the forward Kullaback-Leible Divergence (KLD), which is equivalent to maximizing the expected Lik-Liieldhood (LL).
Topological Mismatch However, since the base distribution Po (z) is usually uni-modal Gaus- sian (e.g. Figure 2c) and T is diffeomorphism, problems arise for modeling data distribution with different topological properties. These include well-separated multi-modal distributions or distribu- tions with disconnected components (e.g., Figure 2a). For example, one can see that this leads to density filaments between the modes in Figure 2b. Cornish et al. [11] have shown that flows require a bijection with infinite bi-lipshitz constant when modeling target distribution with disconnected support using a unimodal base distribution. Besides the diminishing modeling performance, this ren- ders the bijection to be numerically "non-invertible", thus, causing optimization instability during training and unreliability of likelihood calculation [14].
2.1 Conditional Resampled Base Distributions
One possible partial mitigation is by enriching the expressiveness of the flows. For example, by (a) increasing the number of layers or parameters, (b) using more complex base distributions, or (c) employing multiple NFs, e.g., mixtures of NFs. It is important to note that especially (a) and (c) may escalate the computational cost and memory burden. Moreover, scaling the normalizing flow's expressivity, (a) or (c), often does not increase the stability of the optimization [15] or the likelihood calculation. For these reasons, we pursue (b) and attempt to compensate for the complexity of the transformation with the elasticity of the base distribution. In other words, we use a more flexible but efficient base distribution to trade off a costly but sufficiently expressive bijection of the normalizing flow. This way we aim to capture desirable topological properties of the target distribution [17]. Following the prior work [25], model the fidelitous distribution of data with task-specific condi- cass-conniiional base distribution. This way get similar benefits
tions, e.g. class labels, like combining multiple conditional flows (c). however, without having to burden the computational

---

Marginalized Mixture of Gaussians (MoG); Pa.e (u)
Ground Truth:
Ground Truth:
Marginalized cRSB: pa.
Margin. cRSB Base: Pv
p(u 0)
p(uly
Two Moons
Two Rings
Circle of Gauss.
Figure 3: Visualization of density estimation using Real NVP with class conditional MoG, where each class is modeled by uni-modal Gaussian, and cRSB well as the class class- marginalized density for the base distribution of cRSB.
cost on marginalization over classes. This is because, with (c), this operation requires repeated eval- uation of the flows when each flow of the NFs mixture is class-conding flas-coonitional [26]. Even though class-conditional distribution can specialize on a smaller fraction of the dataset containing similar instances, will manifest a multi-modal distribution.
Therefore, propose capture the complex topological properties in the target distribution with more expressive base distribution instead of the uni-model Gaussian. To the end, introduce cRSB by extending powerful unconditional base distribution RSB [13] with plass-conditions modeling. RSB deforms uni-modal Gaussian in learnalle manner to obtain more complex distributions via Learned accept/reject sampling (LARS) [27]. LARS iteratively re-weighs samples drawn from proposal distribution (2), e.g. standard Gaussian, through a learned acceptance function ap Rd > [0, 1]. To reduce the computation cost in practice, this process truncated by accepting the 7-th samples if the previous T - samples get rejected. To take into account class-conditional information, we conditionalize the learnable acceptance function (zly). As result, we have the conditional base distribution:
P& (zly) = or) ag (z(y) + (CTTT()
(3)
Z,
where ag Rd [0, 1 and or (1 2,, where Z, R is the normalization factor for ap (Z))) This factor can be estimated via Monte Carlo Sampling.
In Figure 3, we contrast the density estimation capabilities NFs with the common MoG [8, 25] base distribution and our cRSB on three tasks with class-conditional structure using an appropriate learning objective (see next section). We find that our cRSB learns appropriate apploogy-macchinn base distributions (right outer column) and result, the respective NFs do not have adverse effects like filaments between the modes.
2.2 Training with Information Bottleneck
Unfortunately. directly training NFs with conditional base distribution lead to underperfor- mance observed in experiments (see Table 2 and appendix) and reported by Fetaya et al. [25].

---

We attribute this to the lack of explicit control for the balance between generative and discrimi- native modeling in the likelihood-based training objective of NFs. To alleviate this, we train the normalizing flow with a class-conditional base distribution using the IB objective [19]. To abuse notations, we denote random variables by capital letters such as U, Z. Y, and their realizations by lowercase letters such as u, z. y. The IB minimizes the Mutual Information (MI) [UU Z) be- tween U and Z, while simultaneously maximizing the MI T(Z, Y) between Z and Y. Intuitively, the IB trades off between the objectives of modeling the class conditional information p(uly) with the marginalized density p(u), thus allowing to leverage the class-conditional structure to facilitate more effective density estimation for data characterized with semantic classes.
However, the IB is not directly applicable to latent class- consiioondiiinaal distributions in NFs since the bijection Te is lossless by design. Thus, for trading off the class-conditional information with den- sity estimation capabilities,
adapt the approach proposed by Ardizzone al. [18] for our cRSB. Specifically, we inject small amount of noise into the input U and hence Z. T (U + e). Further we define an asymptotically exact version of MI, namely the Mutual croos-Information (CI) (more details in appendix):
LIBE = CIUU, Z - OCI(Z,,Y)
(4)
CI(U, Z.) Ep(u).
logg Σ
Pp Pp(lzy log det det(Jr (u + c))
(5)
y
Pv Pp(zel))(())
CI(Z.,Y) = Epts)
log
(6)
Σn
yf Pv (u (2)
where 7, T (u+ c), p(e) = NNO (Ia)) is
au (z|y
(z)y 1)
zero-meaned Gaussian with variance o², and |3 trades off class information and generative density estimation. With flexible conditional base distributions defined in Eq. 3, we can train the topology-matching NF's with IB by substituting cRSB into the conditional base prob- ability (zly) in Eq. 5 and 6. More noteworthy, we observed that the is able to regularize the acceptance rate learning for cRSB better assimilate the topolog- ical structure of the target distribution, leading an overall improved performance accurately approxi- mating the complex target distribution (see Figure 4).
w/o IB
IB
Figure 4: cRSB acceptance rate ay (z) w/o and w/ IB training for Two Moons.
2.3 Detecting OOD Objects
During test time, we detect the OOD data based on the predicted Log-Likelihood (LL.). To note that, only one forward pass is required evaluate the acceptance function in cRSB. Practically, Monte Carlo sampling estimate the normalization factor Z offline so that no additional computation required for this during inference. We marginalize the density over classes for the base distribution defined in Eq. 3 and compute the final LL given the logits u' from the test image:
LLtest (u') log (TT (u')l))) + log det(J) (u')))
y¹ We then expect LL for ID objects be higher than OOD ones.
3 Related Work
Normalizing Flows NFs [28] are a popular class of deep generative models. NFs have shown appli- cability in a variety of areas such as image generation [29, 30], uncertainty estimation [31, 32, 33] and OOD detection [6, 34, 35). For NFs, one trend has been designing expressive flow-based ar- chitectures. Notable examples are affine coupling flows [29, 30], auto-regressive flows [36, 37], invertible ResNet blocks [38] and ODEs-based maps [39]. The major focus of these works is on reducing computing requirements for Jacobian computations while ensuring that each mapping is
5

---

invertible. Another research direction, currently emerging, is on addressing the topological mis- match [28, 10] of NFs. Targeting this problem, some existing works attempt to increase the learning capacity of the transformation via mixture models [26], latent variable models [11, 40] or inject- ing carefully specified randomness [41, 12]. These methods may be limited in their applicability to robotics because they either increase memory consumption by expanding the width of transfor- mations or approximate the exact likelihood. Recently, these constraints have been addressed by improving the expressivity of the base distribution [13, 17]. In this paper, we build upon this class of methods since they only add slight computation overheads and thus are well suited for applications in robotics.
Normalizing Flows for OOD Detection NFs have been widely adapted for OOD detection due to its superior density estimation [42]. For example, though with some counter-intuitive obser- vations
data space [34), NFs have demonstrated encouraging OOD detection results with additional refinements for raw data [43, 44, 45] directly based on task-relevant feature embed- dings [6. 7, 46, 47]. In this work, we directly apply NFs on the feature space. To note that, another principle direction is to estimate the error bound for this task [48]. Recently hybrid models [49, 7, 50] have shown remarkable performance gain on OOD detection by modeling the joint distribution of both data and its class labels. Such works suggest that class labels can provide useful information. However, directly performing class conditional modeling with NFs for OOD detection results in performance degradation. Tishby et al. [19], Ardizzone et al. [18] mitigate such performance degra- dation by utilizing IB for training NFs. This explicitly controis the trade-off between generative and discriminative modeling [9]. However, these works on OOD detection utilize NFs without much concern for the fundamental topological problem as the first citizen. Therefore, complementary to these approaches, we examine the problem of topological mismatch of NFs for OOD detection.
OOD Detection in Object Detectors OOD detection research has focused image classifica- tion [42], which may be limited in relevance to robotic vision. In roboties, we may often need both categorization and localization of objects of interest. Therefore, we focus on object detection in open-set conditions here. In this domain, uncertainty estimation [51] has been considered pro- pitious for OOD detection but suffered from computation burdens on runtime [52, 53, 54, 55] or memory costs [56]. To address this, instead of directly applying uncertainty estimation techniques for object detection [54, 21, another popular approach is to explicitly formulate the problem as OOD detection tasks [23, 57, 8, 58, 59]. Amongst them, NFs has been utilized as an expressive density estimator [8, 58). However, despite the encouraging results, these approaches have not examined the problem of topological mismatch in NFs. As this might prevent additional performance improve- ments, this work examines the oopology-matching NFs for OOD detection in object detectors.
Experiments
We next demonstrate the efficacy of our method. First, we evaluate on synthetic density estimation for distributions with distinct topological properties. We then evaluate the OOD detection perfor- mance on two object-detection data-sets adapted from their public counterparts [60, 61] for open- set (OS) experiments: Pascal-VOC-OP and MS-COCO-OS based on Glow [30] and pre-trained Faster-RCNN [20] provided by Miller et al. [23] for fair comparison. To showcase the practicality, we deploy the one-stage object detector Yolov7 [21] equipped with the proposed method on real acrial manipulation robot along with the run-time and memory analysis. We empirically found that, to parameterize the acceptance function in LARS, a simple multi-layer perceptron (MLP) (2x 1 28 for density estimation and 3x 128 for object detection) is sufficient. We select the hyper-parameters (e.g., T. e, o. () based on the validation set. More details can be found in the supplementary materials.
Datasets and Metrics For density estimation, there are three synthetic datasets: two moons, two rings, and circle of Gaussians. We We employ the KLD between the target and the model distributions to measure the performance. For OOD detection, since existing object detection datasets are not ready for fair evaluation [4], we strictly follow the experimental protocol in [23]. For real robot deployment, we generate 2k synthetic images of two objects (a valve and crawler robot) rendered

---

Figure 5: 1-SNE visualization for (a) feature em- beddings from the object detector (b) latents of the proposed learned base distribution cRSB and based on their CAD models and additionally labeled 2k real images. 1 synthetic images are used for training and another 1 for testing with all real images. We use the Area Under Receiver Operation Curve (AUROC) and the True Positive Rate( at different False Positive Rate (FPR) (5%, 10%, 20%) as metrics for this task, as they represent the performance of the potential operating points for safety-critical applications, which requires the FPR be sufficiently low.
4.1 Density Estimation
Table 1: Performance density estimation for different flow architectures w.r.. KLD, i.c., DRL. (p(u, v) Pa. ( (u,y)), Better base distribution highlighted in bold.
We compare the density estimation perfor- mance in Table and provide qualitative sults in Figure 3. We find that the cRSB base distribution consistently outperforms the class-conditional Mixture of Gaussians (MoG). The performance improvement by cRSB can generalized across two different NFs architec- tures, i.e. Real NVP and NSFs.
Flow architecture
Real NVP
Base distribution
MoG 18
cRSB 18
MoG IB
cRSB IB
Two Morns
0.909
Two Rings
2.032
1.704
1.647
1.602
Circle of Gaussians
2.335
1.667
1.766
1,653
4.2 OOD Detection in Object Detection
We compare our method (cRSBIIB) with both flow-based and non-flow-based approaches. The latter consists of Mahalanobis Distance (MD) [62]. Relative Mahalanobis Distance (RMD) [63], GMMDet [23], Softmax, Entropy and, their Deep Ensemble variants with five models [56]. Among flow-based approaches, have six different base distributions, in- cluding unconditional ones (uni-modal Gaus- sian, MoG, RSB) and their conditional variants (MoG CLS, cRSB CLS) [25] and MoG trained with IB (MoG IB) [8, 18]. From Table 2, we can observe that flows with uni-modal Gaussian are able to provide satisfactory performance, i.e., better than most of non flow-based baselines, while flows with more expressive base distributions such MoG and RSB can bring more benefits on Pascal-VOC-OS than MS-COCO-OS. When trained with IB, the more flexible conditional base distribution (cRSB IB) mostly have greater per- formance gains (on both Pascal VOC and COCO) than its strong competitor (MoG (only on COCO) in comparison with their counterparts without IB McG.CLS). These results demonstrate the effectiveness of cRSB with IB for OOD detection in complicated 2D object detection tasks. We further provide the visualization from data before and after the flow transformation with different base distributions in Figure 5, evidencing the ability of matching complex topology the target data distribution with cRSB.
(a)
(b)
(c) the uni-modal Gaussian on the training set of Pascal-VOC-OS.
4.3 Real Robot Deployment
Next, we validate the applicability an application of robotic inspection and maintenance, where crucial avoid false positives of OOD objects that appear routinely in outdoor environments. In this experiment, we train Yolov7 with only synthetic images two objects (a valve and a crawler robot) and deploy on the robot around only real objects. The task is to identify the falsely detected real objects as OOD since they are from a distribution different to the synthetic ones. Besides, the performance drop when compared with Table 2 is potentially attributed to the "closer" OOD data because the synthetic images are rendered in a highly photorealistic manner. However, our method still outperform other baseline approaches in Figure 6c, where ours can notably achieve higher TPR around the low FPR region, which are commonly used as operating points for the robot. Computational efficiency is another important requirement. We compare the runtime and space memory consumption against vanilla Yolov7 using the NVIDIA's embedded GPU called Jetson Orin in Figure 6. The results indicate that the computational overhead of having an OOD detector is
7

---

Table 2: OOD detection performance on Pascal- and MS- AIS-COC--O datasets for different methods based on the Faster-RCNN from 3 random runs. The highest values are marked in bold and the second highest in italics.
Pasel-VOC-OS VOC-OS
MS-COCI-OS
ALROX:
TPR JORFPR
AUROX:
TPR 10%ERR
SAEPR
20/EPR
SXSPPR
20%BPR
Soltmax
0.901
00.1
72.8
88.1
0.882
01.3
70.6
78.1
Entropy
0.905
50.8
72.9
82.9
0.903
61.2
70.6
80.2
MD [62]
0.9
54.1
68.8
81.3
0.902
57.2
71.4
85.5
RMD [63]
0.839
15.2
28.4
77.4
0.531
1.7
2.6
7.1
Ensemble Softmax [56]
0.885
47.8
72.6
83.1
0.898
08.2
73.5
82.3
Entropy [56]
0.887
83.1
73.5
GMMDet
Gaussian
68.2
Flows MoGi
2.4
2.5
68.3 0.30
Floss RSB [13]
Flows MoG CLS
0.923 0.001
69.2 1.5
76.2 1.3
88.5 0.82
0,930 0.001
68.5 0.73
82.2 0.31
89.7 0.30
Flows MoG JB [8]
0.984 /002
73.1 1,3
79.6 0.66
87.8 0.2
0.924 1: 0.002
75.1 1:
79.6
68.6 $..6.100 0.63
Flows cRSB_CLS CLS
0.919 0.001
72.5 + 0:37
78.8 - 0.27
86.8 0.42
0.924 + 0.001
68.3 0.14
81.1 + 0.30
89.3 0.18
Flows cRSB IB (ours)
0.946 0.003
78.5 0.57
84.0 =: 0.83
90.8 0.76
0.934 0.002
73.3 2.0
84.3 0.40
91.3 =: 0.28
relatively small when compared to the vanilla Yolov7. Overall, these experiments validate our claim
that our method features efficient runtime inference and cost-effective memory consumption.
(bytes)
Comperison Run time
_.Comprriionn of Memory Consumption
ROC Curve
%olo
Ours
Pun-time per fromee
Thue Pocctrve
Ours (AUI:: 0.71)
Seftmax (AUC: 0.64)
0.13
0.66)
RMD (AUC: 0.34)
(AUC: 0.70)
Storage
Ours
Mods Ju (AUC: 0.88)
Inpul Size
Ingut Image Size
False Positive Rate
(c) Figure 6: Results from experiments a real robot. Run-time, memory consumption, and ROC curve are reported. Compared to the vanilla Yolov7, the proposed method does not yield significant computational costs, while providing performance gains in OOD detection.
(a)
(b)
5 Limitations
The proposed method is envisioned to work feature embeddings instead of raw data to counteract the NFs artifacts of assigning higher likelihoods to OOD data [10]. This leads to two limitations. First, it's can't directly applied to the tasks/models that could not provide useful feature embeddings extracted from the raw data. Second, its performance is restricted to the quality features. As reported by previous work [23, 8]. learning more compact and centralized features can often lead to increased performance for OOD detection while feature collapse can be harmful to OOD detection. Besides, there two limitations during deployment. The first is the prolonged initialization time for calculating the normalization factor in LARS based on Monte Carlo sampling. This might not be friendly for applications that require instant response at the beginming. Moreover, the current version of the proposed method does not consider the sequential nature of observations at deployment.
6 Conclusion
To endow robots with introspective awareness against OOD data, we propose the NFs equipped with effective yet lightweight cRSB and train with IB objective. Such NFs are able to mitigate the fun- damental topological mismatch problem, facilitating more effective OOD detection capabilities. We present empirical evidence that the proposed method achieves superior performance both quantita- tively and qualitatively. To demonstrate the run-time efficiency and minimum memory overheads, deployed real-robot system. Overall, hope that the results of our work stemming from an enriched base distribution can push forward the direction of Nas-based OOD detection in robot learning.

---

Acknowledgments
We thank the anonymous reviewers for their thoughtful feedback. Jianxiang Feng and Simon Geisler supported by the Munich School for Data Science (MUDS). Rudolph Triehel and Stephan Gun- nemann members of MUDS.
References
[1] J. Nitsch, M. Itkina, R. Senanayake, J. Nieto, M. Schmidt, R. Siegwart, M. J. Kochenderfer, and C. Cadena. Out-of-distribution detection for automotive perception. In 2021 IEFE In- ternational Intelligent Transportation Systems Conference (ITSC), pages 2938-2943, IEEE, 2021.
[2] Lee, J. Feng, M. Humt, G. Müller, and R. Triebel. Trust your robots! predictive uncer- tainty estimation of neural networks with sparse gaussian processes. Conference on Robot Learning, pages 1 1168-1179. PMLR, 2022.
[3] J. Feng, J. Lee, M. Durnrr, and R. Triebel. Bayesian active learning for sim-to-real robotic perception. In 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 10820-10827. IEEF, 2022.
[4] A. Dhamija, Gunther, J. Ventura, and T. Boult. The overlooked elephant of object detection: Open In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision (WACV), March 2020.
[5] R. Sinha, A. Sharma, S. Banerjee, T. Lew, R. Luo, S. M. Richards, Y. Sun, E. Schmerling, and M. Pavone. A system-level view on out-of dutto--distrbuution data in robotics. arXiv preprint ar arXiv:2212. /4020, 2022.
[6] Kirichenko, P. Izmailov, and A. G. Wilson. Why normalizing flows fail to detect out-of- distribution data. Advances neural information processing systems, 33:20578-20525 2020.
[7] H. Zhang, A. Li. J. Guo, and Y. Guo. Hybrid models for open set recognition. In Computer Vision-ECCC 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceed- ings, Part III 16, pages 102-117. Springer, 2020.
[8] R. Li, C. Zhang, H. Zhou, C. Shi, and Y. Luo. cut-of-distribution identification: Let detector tell which i am not sure. In Computer Vision-ECCV 2022: 17th European Conference, Aviy Israel, October 23-27, 2022, Proceedings, Part X. pages 338-654. Springer, 2022.
[9] R. Mackowiak, L. Ardizzone, U. Kothe, and C. Rother. Generative classifiers basis for trustworthy image classification. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition, pages 2971-2991 2981, 2021.
[10] G. Papamakarios, Nalisnick, D. Rezende, Mohamed, and B. Lakshminarayanan. Nor- malizing flows for probabilistic modeling and inference. The Journal of Machine Learning Research, (211):667,-6880 2021.
[11] R. Comish, A. Caterini, G. Deligiannidis, and A. Doucet. Relaxing bijectivity constraints with continuously indexed normalising flows. In International conference machine learning. pages 2133-2143. PMLR, 2020.
[12] H. Wu, Köhler, and F. Noé. Stochastic normalizing flows. Advances in Neural Information Processing Systems, 33:5933-5944, 2020.
[13] V. Stimper, B. Schölkopf, and J. M. Hernández-Lobate Resampling base distributions of normalizing flows. In International Conference Artificial Intelligence and Statistics, pages 4915-4936. PMLR, 2022.

---

[14] J. Behrmann, P. Vicol, K.-C. Wang, R. Grosse, and J.-H. Jacobsen. Understanding and mitigat- ing exploding inverses invertible neural networks. In International Conference on Artificial Intelligence and Statistics, pages 1792-1800. PMLR, 2021.
[15] Hagemann and S. Neumayer. Stabilizing invertible neural networks using mixture models. Inverse Problems, 37(8):08500,, 2021.
[16] V. Runde. A taste of topology/ Springer, New Delhi:, 2005. Includes bibliographical refer- ences and index.
[17] P. Jaini, I. Kobyzev, Y. Yu, and M. Brubaker. Tails of lipschitz triangular flows. In International Conference on Machine Learning, pages 4673-4681. PMLR, 2020.
[18] L. Ardizzone, R. Mackowiak, C. Rother, and U. Köthe. Training normalizing flows with the information bottleneck for competitive generative classification. Advances in Neural Informa- tion Processing Systems, 33:7828-7840, 2020.
[19] N. Tishby, F. C. Pereira, and W. Bialek. The information bottleneck method. arXiv preprint physics/0000577, 2000.
[20] S. Ren, K. He, R. Girshick, and Sun. Faster r-enn: Towards real-time object detection with region proposal networks. Advances in neural information processing systems, 28, 2015.
[21] C.-Y. Wang. A. Bochkovskiy, and H.-Y. M. Liao. Yolov7: Trainable bag-of-freebies sets new state-of-the-art for reml-time object detectors. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7464-7475, 2023.
[22] H. Wei, R. Xie, H. Cheng, L. Feng, B. An, and Y. Li. Mitigating neural network overconfidence with logit normalization. International Conference on Machine Learning (ICML), 2022.
[23] D. Miller, N. Sünderhauf, M. Milford, and F. Dayoub. Uncertainty for identifying open-set errors in visual object detection. IEEE Robotics and Automation Letters, 7(1):215-222, 2021,
[24] V. I. Bogachev and M. A. S. Ruas. Measure theory, volume 1. Springer, 2007.
[25] E. Fetaya, J.-H. Jacobsen, W. Grathwohl, and R. Zemel. Understanding the limitations of conditional generative models. arXiv preprint arXiv:/906.0117/ 2019.
[26] J. Postels, M. Liu, R. Spezialetti, L. Van Gool, and F. Tombari. Go with the flows: Mixtures of normalizing flows for point cloud generation and reconstruction. In 2021 International Conference on 3D Vision (3DV), pages 1258. IEEE, 2021.
[27] M. Bauer and Mnih. Resampled priors for variational autoencoders. The 22nd Interna- lional Conference on Artificial Intelligence and Statistics, pages 66-75. PMLR, 2019.
[28] I. Kobyzev, S. J. Prince, and M. A. Brubaker. Normalizing flows: An introduction and review of current methods. IEEE transactions pattern analysis and machine intelligence, 43(11): 3964 3979, 2020.
[29] L. Dinh, J. Sohl-Dickstein, and S. Bengio. Density estimation using real nvp. arXiv preprint arXiv:1605.0880: 2016.
[30] D. Kingma and Dhariwal. Glow: Generative flow with invertible Ixl convolutions. Ad- vances in neural information processing systems, 31, 2018.
[31] B. Charpentier, D. Zügner, and S. Günnemann. Posterior network: Uncertainty estimation without ood samples via cansity-basee pseudo-counts. Advances in Neural Information Pro- cessing Systems, 101111351666 2020.
10

---

[32] B. Charpentier, O. Borchert, D. Zügner, S. Geisler, and S. Günnemann. Natural posterior network: Deep bayesian uncertainty for exponential family distributions. arXiv preprint arXiv:2105.04471. 2021.
[33] Postels, H. Blum, Y. Strümpler, C. Cadena, Siegwart, L. Van Gool, and F. Tombari. The hidden uncertainty neural networks activations. arXiv preprint arXiv:2012.03082, 2020.
[34] E. Nalisnick, A. Matsukawa, Y. W. Teh, D. Gorur, and B. Lakshminarayanan. Do deep gener- ative models know what they don't don't know? arXiv preprint arXiv:1810.0911: 2018.
[35] S. K. Lind, R. Triebel, L. Nardi, and V. Krueger. Out-of-distribttin detection for adaptive computer vision. arXiv preprint arXiv:2305.092 00999,9,, 2023.
[36] C.-W. Huang, D. Krueger, A. Lacoste, and A. Courville. Neural autoregressive flows. In International Conference on Machine Learning, pages 2078-2087. PMI.R 2018.
[37] C. Durkan, A. Bekasov, Murray, and G. Papamakarios. Neural spline flows. Advances in neural information processing systems, 32, 2019.
[38] R. T. Chen, J. Behrmann, D. K. Duvenaud, and J.-H. Jacobsen. Residual flows for invertible generative modeling. Advances in Neural Information Processing Systems, 32, 2019.
[39] W. Grathwohl, R. Chen, Bettencourt, I. Sutskever, and D. Duvenaud. Ffjord: Free-form continuous dynamics for scalable reversible generative models. arXiv preprint arXiv:1810.01367. 2018.
[40] L. Dinh, Sohl-Dickstein, H. Larochelle, and R. Pascanu. rad approach to deep mixture models, arXiv preprint 1rXXxv9903300714 2019.
[41] D. Nielsen, P. Jaini, F. Hoogeboom, O. Winther, and M. Welling. Survae flows: Surjections to bridge the gap between vaes and flows. Advances in Neural Information Processing Systems, 13:12685-12666 2020.
[42] Yang, K. Zhou, Y. Li, and Z. Liu. Generalized out-of-distribution detection: A survey, arXiv preprint arXiv:21 10. 1334, 2021.
[43] Ren, P. Liu, E. Fertig, Snock, Poplin, M. Depristo, J. Dillon, and B. Lakshmi- narayanan. Likelihood ratios for distri-iist detection. Advances in neural information processing systems, 32, 2019.
[44] E. Nalisnick, A. Matsukawa, Y. W. Teh, and B. Lakshminarayanan. Detecting out-of-distribution inputs to deep generative models using typicality. arXiv preprint 190iv: 029944 2019.
[45] D. Jiang, S. Sun, and Y. Yu. Revisiting flow generative models for out-of-distribution de- tection. In International Conference on Learning Representations, 2022. URL https:
//openreview nett:forumi.d-byykBbte...
[46] B. Charpentier, C. Zhang, and S. Günnemann. Training, architecture, and prior for determin- istic uncertainty methods. arXiv preprint arXiv:2303.0596 2023.
[47] J. Feng, M. Atad, I. V. Rodriguez Brena, M. Durner, and R. Triebel. Density-based feasibility learning with normalizing flows for introspective robotic assembly. 18th Robotics: Science and System 2023 Workshops, 2023. URL https: alr de/195846/
[48] G. Chou, N. Ozay, and D. Berenson. Safe output feedback motion planning from images via learned perception modules and contraction theory. In International Workshop the Algorithmic Foundations of Robotics, pages 349-367. Springer, 2022.

---

[49] E. Nalisnick, A. Matsukawa, Y. W. Teh, D. Gorur, and B. Lakshminarayanan. Hybrid models with deep and invertible features. In International Conference on Machine Learning, pages 4723 4732. PMLR, 2019.
[50] Cao and Z. Zhang. Deep hybrid models for Conference on Computer Vision and Pattern Recognition (CVPR), pages 4723-4733, 2022. 101:1000100// 202...808.22000666
detection. In 2022 IEEE/CVF
[51] J. Gawlikowski, C. R. N. Tassi, M. Ali, Lee, M. Humt, J. Feng, A. Kruspe, R. Triebel, P. Pung, R. Roscher, et al. A survey of uncertainty in deep neural networks. Artificial Intelligence Review, pages 1-77, 2023.
[52] D. Miller, L. Nicholson, F. Dayoub, and N. Sünderhauf. Dropout sampling for robust object detection in open-set conditions. In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages 3243-3249, IEEE, 2018.
[53] Lee, M. Humt, J. Feng, and R. Triebel. Estimating model uncertainty of neural networks in sparse information form. In International Conference on Machine Learning, pages 5702-5713. PMLR, 2020.
[54] A. Harakeh, M. Smart, and L. Waslander. Bayesod: A bayesian approach for uncertainty estimation in deep object detectors. In 2020 IEEE International Conference on Robotics and Automation (ICRA), pages 87-93. IEEE, 2020.
[55] Feng, M. Durner, Z.-C. Márton, F. Bálint-Benczéde and R. Triebel. Introspective robot perception using smoothed predictions from bayesian neural networks. In Robotics Research: The 19th International Symposium ISRR, pages 660-675. Springer, 2022.
[56] B. Lakshminarayanan, A. Pritzel, and C. Blundell. Simple and scalable predictive uncertainty estimation using deep ensembles. Advances in neural information processing systems, 30, 2017.
[57] X. Du, G. Gozum, Y. Ming, and Y. Li. SIREN: Shaping representations for detecting out-of- distribution objects. In A. H. Oh, A. Agarwal, D. Belgrave, and K. Cho, editors, Advances in Neural Information Processing Systems, 2022. URL httppp///pppeeeeeeeeeeeeeeeee fet/formmm id=8E8tgnYImN.
[58] N. Kumar, S. Segvić, A. Eslami, and S. Gumhold. Normalizing flow based feature synthesis for outlier-aware object detection. arXiv preprint arXiv:2302.077 106, 2023.
[59] X. Du, X. Wang, G. Gozum, and Y. Li. Unknown-aware object detection: Learning what you don't know from videos in the wild. In Proceedings of the IEFF/CVF Conference on Computer Vision and Pattern Recognition, pages 1668813688,, 2022.
[60] M. Everingham, L. V. Gool, C. K. I. Williams, J. M. Winn, and A. Zisserman. The pascal visual object classes (voc) challenge. Int. J. Comput. Vis., 88(2):303-335 338, 2010. URL http: //dblp. uni-triers htt.:tterrrrrrreeeeee
jev88. htmm:EEvrringannGWZ110 dw/dd//////////e http////oooraaassjjss////// /ete////v/e//e/e...ee//
[61] T.-Y. Lin, M. Maire, S. Belongie, L. Bourdev, R. Girshick, J. Hays, P. Perona, D. Ramanan, C. L. Zitnick, and P. Dollár. Microsoft coco: Common objects context, 2014. URL http: arxiv. , org/ aaaaaa///1110 0312. cite arxiv:1405 0312Comment 1) updated annotation pipeline description and figures; 2) added new section describing datasets splits; 3) updated author list.
[62] K. Lee, K. Lee, H. Lee, and Shin. A simple unified framework for detecting out-of- distribution samples and adversarial attacks. Advances in neural information processing sys- tems, 31, 2018.
[63] Ren, S. Fort, Liu, A. G. Roy, S. Padhy, and B. Lakshminarayanan. A simple fix to mahalanobis distance for improving near-ood detection. arXiv preprint wrXiv:210.00902.. 2021.
12

---

Supplementary Materials for the Submission: Topology-Matching Normalizing Flows for Out-of-Distributio Detection in Robot Learning
Jianxiang Feng"
Jongseok 2.e Simon Geisler', Stephan Günnemann' Rudolph Trichel
Department of Informaties, Technical University of Munich (TUM)
2 Institute of Robotics and Mechatronics, German Acrospace Center (DLR)
Department of Informatics, Karlsruhe Institute of Technology (KIT)
jianxiang Seneriaanneengguuum fwwg@tun.gnmmmm de, {jongseok. lee, rudolph. triebel (edlr de, (geisler, guennemann Cin tum.de
Background
1.1 Resampled Base Distribution
Learned Accept/Reeect Sampling (LARS) approximates a d-dimensional distribution ((2) by reweighting proposal distribution. The reweightings are learned through parametrized accep- tance function. The parameter is Φ which determines the shape of the acceptance function. If sample of is given, it is accepted with certain probability, otherwise, it is rejected, and sample is drawn until one of the proposed samples is accepted. This means:
Poo (2) T(2)aa(2) with Z Z
f (2)ag(2)dz.
One can also reduce the reject rates by a truncation parameter. The trick here to accept the T-th sample, the first T-1 samples are rejected. This independent of the value provided by LARS. With this, the sampling distribution becomes, given ar == (1 -)
(o(2)=(2) Pr(2) = aT)
s Σ
+ (z) where
Z = S ad(2)).
(2)
Z
We note that reducing rejection rates are desirable in order reduce the computational overhead. often approximated due to intractability. As parameters of the acceptance function cause changes in 7, needs to be recomputed in every training iteration.
The resample base distributions (RSB) relies on LARS. LARS can be used as a proposal to avoid topological mismatches of the flows. Then, density could become the aforementioned sampling distribution. The likelioodoo using such distributions can be derived as:
(o(2)) logp(x) = (2) + log aT + (1 aT 2
logidet// (z)
(3)
Fg is the flow transformation. The intuition is that by learning the parameters of the base distribution while keeping it computationally feasible with LARS, the base distribution is modified so that the topology mismatch problem can be addressed [1].
7th Conference Robot Learning (CoRL. 2023), Atlanta, USA.

---

1.2 Information Bottleneck for Normalizing Flows
The Information Bottleneck (IB) for Normalizing Flows (NFs) with class conditional base distribu- tion, and its derivation, closely follows Ardizzone et al. [2]. They originally derived this quantity for the class-conditional Mixture of Gaussians (MoG).
Generally, the IB [3] is defined
LB = -U.))(
(4)
with Mutual Information (MI) I and trade-off parameter 8. To derive the learning objective pre- sented in the main part two key steps are required: (1) we substitute MI / with the so-called mutual pross-information CI, and (2) we inject Gaussian noise in the otherwise lossless transformation between U and Z.
The mutual cross-information C' [2] is defined as
g(a, b) q( ((a)g(b)
CI(A, B) = (A log
(5)
where q represents the approximative distribution of the true density p. We then replace both occur- rences of / in Equation (4) with f. Moreover, for simplicity, we assume that g(Y) = p(Y), and in our experiments, we model pYY) uniformly.
The bijection To is loss-less by design and, thus, the joint distributions p(U, Z) and pUU, Z) not valid Radon-Nikodym densities rendering and undefined. circumvent the issue and as indicated above (2), we artificially introduce noise (O I²1) and model Z. T (U + c) instead. Then, dropping all terms that independent of the model vanish for - 0, obtain
(see Ardizzone et al. [2] for full details)
CT(U, 7e) p(())p(()) -log log
E(p log det(Jrr c))1
(6)
yr
Similarly, CI(,, resolves
Pe (T + e)lv)p(y)
CT(Y, 2.) Eptin [- logp(u)) + +B((Y))))))))
log
E (p (Tx
(u + c)(l))((()))
=const.
(z())(())) (pr (z)y (()))
log
+ const.
with z = To (u + c). The overall objective combines Equation (6) and Equation (7) to TiazzTT-la
LINT CTUU, 2) (CI(
(8)
In summary, with CI(U,Z) minimize the marginalized density p(u) subject to the noise term On the other hand, LINE optimizes for predictive performance, again subject to noise
2 Implementation Details
2.1 Synthetic Density Estimation
We follow resource constraint setup to allow for conclusions about practical mobile applications. Specifically, we use a Real NVP [4] with four layers for the cRSB and five layers for the MoG with randomly initialized trainable mean and variance. The difference in layers accounts for the extra compute that is required for the cRSB. For the NSF we use layers each since the cRSB overhead is negligible here. In the MoG's we model class-conditional Gaussian (H,,, or II) with diagonal variance matrix.

---

Table I: Implementation Details for density estimation.
hyper-parane
cRSB
MoG
IB loss
((011); o(0.01)
((0.1); or (0.01)
learning rate
le -
le -
training epoch
10, 000
25, 000
optimizer
Adamax
Adamax
batch_sin
1024
1024
2.2 Out-of-Distribution (OOD) detection for 2D Object Detection
For object detection, we implement method with the Glow [5] architecture based the norm- flows open-sourced package [6]. Besides, we also ablate on this with different ones such as Neural Spline Flows (NSF) [7]. On object detection task, we train our flows based on logits generated by the pre-trained FaNter-RCNN [8] object detectors provided by Miller et al. [9] for fair comparison We summarize the training details for the results presented the main paper Table 2 and Table 3. Regarding the trainability for the base distribution in MoG, we found minor difference between set- ting it trainable and untrainable and the major impacting factor for performance improvement and training stability is the distance between means for initialization. Therefore seek to tune this hyper-parameter and leave the base distribution untrainable.
We compare with the following baseline approaches:
Non Flow-based:
Softmax
Entropy
Mahalanobis Distance (MD)² [10]
Relative Mahalanobis Distance (RMD) [11]
Softmax Ensemble (5) [12]
Entropy Ensemble (5) [12]
GMMDet [9].
Flow-based:
Flows Gaussian
Flows MoG
Flows Resampled Base Distributions (RSB) [1]
Flows MoG.CLS [13]
Flows cRSB CLS [13]
Flows MoG.IB [14, 2].
Table 2: Implementation Details for Glow on Pascal-VOC-OS.
hyperqeams
Deepornth
heu:
1:3
iniitiization
+00.66))
meae in
e0h301) :3
Bow anch
xxx 64]
16
64)
[1
16
64)
16 [1 64)
IB loss Jeuning rate
3050 02: ((0.5)
200000) e(0.5)
Le 4
Ie
Le 4
It
Le 4
In
Le
riiiing spoch
500
400
200
100
200
110)
100
optinizer
Adamn
Adann
Adam
Adam
Adas
Adass
Adam
butchsize
1001
10244
1022
3024
1024
1024
3024
thtps://gtthu..com///a http://gihhh..oommmiiimmmmlooeee https///gthbbboooommmsssaa/rrror www.:hi...iiiitotoooooooo.. _ddtecciin

---

Table 3: Implementation Details for Glow on MS-COCO-OS.
Toper parans
<RSBJJB
GMMJI
ORSICCLS
GMMALS
RSB
GMM
Ganssion
dicomoo-epllc for meens inttciittion..
Dmppontd 1181: <(0.00): ( 1.3x 125,
desieco-esdii for means intiallation1o
Dmpoet/ 21 1001 <00.00); of 1:33 125.
chsienc--ccii for meean intialintion110
base
c100003; of) ) x 126;
anch
x (1 128]
x H 198]
x f1 178]
x [4 128]
8 175]
x
x 11 128)
J930 -
((AAA) e(0.5)
losning nuc
mrninng spoch
200
200
optinierr
buch
612
1024
1024
1024
2.3 Real Robot Deployment
We used the open-sourced implementation 3 for training and testing the object detector yolov7 [15] based on datasets described in Section 3.3. Specifically, we trained the architecture of yolov7-e6e with learning rate 1e-2, weight decay 5e 5e-1, batch size 2, image size 720 720 and SGD optimizer for 50 epochs. The detector was then deployed on the embedded computing module NVIDIA Jetson Orin aerial manipulation robot.
An aerial manipulation system is composed of a mobile platform, capable of moving in the 3D world. Carrying a robotic manipulator, such systems extend the mobility of robotic manipulators. Several applications are envisioned. Amongst them, in this paper, we ground our method in applications of robotic inspection and maintenance. The perception system has understand its surroundings se- mantically, and here, deep learning-basee methods are the current golden standards. Unfortunately, learning- based methods often assume that the test samples generated from the same distribution as the training data. This assumption is routinely violated in the real world, and out-o--distribution detectors aim to identify such failure cases of learning-based methods.
For the implementation details, our in-house developed robot consists one stereo camera, one monocular camera, one RBG-D camera, and a LiDAR sensor. In this work, since the semantics of the scenes may rely vision its main modalities, we utilize monocular camera detect the objects of interest, which are an industrial valve, and an inspection robotic crawler for oil and gas pipes in refineries. For computing, the robot is equipped with two NVIDIA Jetson Orin. In the experiments adapted, the real images were captured in mock-up facility, and tested with the NVIDIA Jetson ORIN on the robot. The experimental data were collected with 30W mode with JETPACK 5.1.1. Auvidea carrier board is used.
3 Datasets
In this section, we provide more details the datasets used in the experiments.
3.1
2-D Density Estimation
In each training epoch, we sample new batch according to the subsequent unnormalized log den- sities following Stimper et al. [1]. For Two Moons, we use
|||| - 1)2 (luol - 2)² + log ( (1ee*
4ug
0.08
0.18
and define the class assignments in y (0, via ply u) i In words, the class is 1 for positive y-values and 0 otherwise. The Two Rings distribution is defined
log
Σ
2
32
exp { 32( - - ]
(10)
π

---

Table 4: Implementation Details for Glow on Yolov7 on the Robot.
hyper-params
cRSB_IB
GMMJIB
Gaussian
(011:; T(100); <(0.05); a(-) x 128;
distance-scale for means initialization:O..
base
flow arch
2 [4 64]
2 x [4 x 64]
2 x [4 x 64)
IB loss
(10.0); (0.01)
(1.0)): (11.0):((0001) (0.01)
learning rate
-
1e 4
1e - 4
training epoch
200
200
200
optimizer
Adamax
Adamax
Adamax
batch size
128
128
128
where p(y(u) = Uo > 0. Here we split classes along the y-axis. Last, the Circle of Gaussians is given by
9 ((u0 - 2sin (2)1)) + (u1 - cos
2x 8
2)))
9
log
exp
(11)
(2
22)
2v/2
where we assign each Gaussian plot in an alternating scheme to the classes y E (0, 1}. Concretely, we split the classes according to sin(4: (attat2(22() +)) > O. For this, we use the atan2 (u,, uo)
function that is available many programming environments. We follow the IEEE convention for value combinations like ug = U1 = O.
3.2 OOD detection for 2D Object Detection
Following the experimental protocol used in [9], we first construct the open-set object detection data set they did for Pascal-VOG [16] and MS-COCO [17], dubbed as COCO-OS. In this setting, the first 15 classes and 50 classes are selected as known classes from the Pascal-VOO VOC and MS-COCO datasets respectively, while the remaining classes are set as unknown classes. Therefore, the training sets are then filtered to keep only known classes. The original test sets are used for testing as they have both known and unknown classes. The idea behind to exclude the effects of the unknown objects in the backgrounds for object detector training, since the object detector is inherently trained ignore the background objects seen during training. We summarize the detailed information regarding the training, validation and test set of the adapted object detection datasets in Section 3.2. It contains the sizes of correct and false predictions from the detector, i.e. True Positives (TP) and False Positives (FP). The FP here are from the OOD data which should not be detected by the detector.
and MS-
For convenience in training NFs, we further extract the features (logits in our case) from all the detections predicted from the object detector. We then filter out the detections with low quality and keep the meaningful detections by setting thresholds for the Intersection -aaan---ve-nnon (0.5) and confidence score (0.2). The purpose behind is to simplify the problem and focus on only meaningful False Positive (FP) predictions predicted by the detector.
In this task, we want to identify the OOD objects that are falsely detected and classified as known objects by the detector. To evaluate this ability, we use the Area Under Receiver Operation Curve (AUROC) metric with varying thresholds. To note that set the true positives the correct predictions and false positives the incorrect predictions.
5

---

Table Information of Pascal- Pascal-VOC-OS and MS-COCO-OS
MS- MS-COCO-OS
ID train set
first 15 classes from
train val
firtt 50 classes from MS-COCO20) train
ID val set
first 15 classes from
first 50 classes from MS-COC02017 val
Test set #TP in training set
20 classes from Pascal-Voc2000 test
80 classes from MS-COC02017 test
18318
251202
#TP val set
7601
55593
set #ID FP
2287
test set
16148
FP in
213
784
#OOD FP test set
660
1068
Sim- Valve
Sim- Crawler
Real-
Valve
Real- Crawler
Figure 1: Exemplar images from training and test set used in the real robot experiment.
3.3 OOD detection on Real Robot
The synthetic images used for training in this part were generated by BlenderProc [18]. The test set contains real images collected in our lab. Some examplar images are shown in Figure 1. We summarize the sizes of the used training and test data in Section 3.3.
Table 6: Training and test data for real robot experiments
Wimages in Sim train set #images Sim test set
907
#images in Real
2078
#ID Truc Positives in test set #OOD False Positives in test set
1326
1898

---

aa) p = 0). ground truth
(b) y = 1), ground truth
(c) Po.e MoG w/o IB
(d) Pa.c (u), MoG w/ IB
(c) Po.e (u). cRSB w/o IB
(f) Pa. (u), cRSB w/ IB
( p 0), ground truth
(h) p 1). ground truth
① (u). MoG w/o IB
i Poue (u). MoG w/ IB
(k) Pe.w (u). cRSB w/o IB
(I) Pe. (u). cRSB w/ IB
(m) p(uly 0). (n) puu 1). ground truth
(0) Pa.o (u).
(p) Pa.y (u).
(g) (u). cRSB w/o
(1) Pa. (u).
ground truth
MoG
MoG IB
cRSB w/
Figure 2: Comparison of generative modeling capabilities Pa.v (u) including training w/o and w/
IB.
4 Density Estimation
In Figure provide comparison of the (marginal) density estimation capabilities for the three density estimation datasets of NFs with MoG as well as Conditional Resampled Base Distributions (cRSB) base distributions, trained w/o well as w/ IB. In Figure 3-6, we illustrate the marginal and class-conditional feature as well as base distributions.
The main conclusions are (1) training with IB objective results in better modeling capabilities of the marginal distribution P (u): (2) training w/o IB objective not only results in more filaments between the modes but also causes spiky tendrils areas where the class conditional distributions touching; (3) results with our cRSB base distributions are essentially filament free; (4) training with IB allows for slight overlaps in the class conditional densities (uly) as well as Pe.v (zly)- In other words, here we improve the modeling capabilities of the marginal distribution Pe. (u) at the cost imperfect modeling of the class-conditional structure.

---

Po.s (u)
(b) Po.v (ulv=0) (c) (u. 1)
(d) (z
(c) pz 0)
pz 1)
(g) (u)
(h) Po.e (uly=-) (ul 1)
ii Pe
(k) po (zly = 0)
Pe (zly 1)
(m) P
(n) Po.e (uly=0) (0) (ul 1)
(p) (z(
(g) po = 0) pe (z 1)
Figure 3: Marginalized and class-conditional feature as well as base distributions for MoG trained w/o IB.
(a) Pa. (u)
(b) Po.v (ulv=0)
(c) (u. 1)
(d) (x)
(c) (zly 0)
pz 1)
(u)
(h) Po.v Po.v (uly=0) (o (ul 1)
(i) (z)
(k) (o 0)
Ph (z/y 1)
(u)
(n) Po.v (uly=0) (ul
(p) (x)
pz)yy = 0) (r) px 1)
Figure 4: Marginalized and class-conditional feature as well as base distributions for MoG trained
w/ IB.

---

(a) Po. (u)
(b) Po.v (ulv=0) (c) (ul 1)
(d) (z)
(c) Pa (zlv 0)
( po 1)
(u)
(h) Po.v Po.e (uly=0) (ul 1)
i Pe (x)
(k) (xly 0)
Pe (zly 1)
(m) Po.s (u) (n) Po.e (uly=0) 0) (ul
(p) (z(
(g) po 0) pa (zly 1)
Figure 5: Marginalized and class-conditional feature well as base distributions for cRSB trained w/o IB.
(a) pa. (u)
(b) Pe.v (ulv=0)
(c) Ps.v (ul 1)
(d) (x)
(c) (zlv 0)
( pa (xly 1)
Po.e(u) (u)
(h) Po.v (uly=0) Po.v (ul 1)
ii (z)
(k) po (zly
0)
Par (z/y 1)
(m) (u)
(n) Po.e (uly=0) (ul
(p) (x)
(q) pz 0) pe (xly 1)
Figure 6: Marginalized and class-conditional feature as well as base distributions for cRSB trained w/ IB.

---

(a) p(v), ground truth
(b) MoG wo IB: argmax, (clu)
(c) MoG w/ IB: argmax, (c/u)
(d) cRSB w/o IB: argmax, po.v
(c) cRSB w/ IB:
argmax, Po.o (c/u)
(1) ply). ground truth
2 MoG w/o IB: argmax, (clu)
(h) MoG w/ IB: arguaax (c/u)
cRSB w/o IB: argmax, (c|u)
i cRSB w/ IB: argmax, Po.e (c(u)
(k) ply), ground truth
(I) MoG w/o IB:
(m) MoG w/ IB: argmax, Po. (c(u)
(n) cRSB w/o IB: argmax, (clu)
(0) cRSB w/ IB: argmax, (cluu
argmax, (clu)
Figure 7: Comparison of predictive capabilities argmax, Pa.e (clu) including training w/o and w/ IB for a sample of size 1,024 that was drawn from the target distribution.
5 Generative Classification
In Figure 7, we plot the ground truth assignments for a sample drawn from the respective data distribution along with the most likely class assignment argmax, Po.v (c/u) over varying base dis- tribution and training objectives. Despite the perceptually different results in the density estimation (Section 4), all models classify the input data remarkably well. This highlights the importance of the IB objective since it allows to govern the tradeoff between the quality of density estimation and predictive capabilities.
6 Ablation Study
6.1 Density estimation
In Figure 8, we study the influence of the tradeoff parameter 3 on the density estimation quality. Generally, we observe that for small 33 the class-conditions density is not modeled sufficiently, while too large values for 3 result in a degradation of the quality of the marginal density. An exception the Two Rings dataset, where a too strong emphasis on the class-conditional density degrades marginal and class-conditional density (i.e., too high (3). We also experimented with different values for the noise defined by σ; however, we do not report detailed results here due to the low impact on the density estimation quality.
10

---

1.9
1.9
1.10
KL. dvergence
divergonce
KL. divergence
1.8
1.00
1.7
1.00
1.7
1.6
0.95
1.5
0.90
1.6
0.05
0.1
0.5
0.05
0.1
0.5
0.06
0.1 tradeoff
0.5
tradeoff
tradeoff
(a) Circle Gaussian
(b) Two Moons
(c) Two Rings
Figure 8: Influence of hyperparemter 3 on the marginalized density quality D& (p(u))lpppp and class- condiitonn density quality DKL (p(u, y) ulll y)).
Prcelpiai Pea
MrG IB
2.4
1.15
2.2
1.00
divergeree
divergece
8:05
1.9
2.0
Tointn step
1.00
1.8
1.8
0.90
12
16
Number layora
Number byers (MV,, MoG only)
Number layers (NVP, MoG only)
Namber layer (NVP, MoG only)
(a) Performance comparison
(b) Circle of Gaussian
(c) Two Moons
(d) Two Rings
Figure Performance tradeoff between using the expressive base distribution cRSB simple
MoG. For cRSB we use 4 Real NVP layers. In the other density estimation experiments, we use Real NVP layers with MoG base to account for the additional compute for the cRSB base. In (b),
(c), and (d), we fix the number of layers to 4 if using the cRSB base distribution.
6.2 Computation Trade-off: Memory Costs and Training Runtime
Training Runtime on Density Estimation: In Figure 9, study how easily more expressive flow can compensate for the distribution mismatch. In the other density estimation experiments, we used 4 Real NVP layers with cRSB base and 5 Real NVP layers with MoG base. The different number flow layers was chosen to account for the additional compute for the cRSB base. While more layers substantially impact runtime (see Figure 9a a comparison of training runtime), more layers do not necessarily compensate for the less expressive MoG base distribution. Especially, class-conditional distribution modeling seems to rely heavily on the expressivity of cRSB. Moreover, for many layers, the training shows signs of increased instability.
Memory Costs on OOD detection: We present the ablation study on memory trade-off with Glow on MS-COCO-OS dataset Table The acceptance function is a MLP of 3x128. With this experiment, observe that with mixture of Gaussian, adding more layers escalate the memory costs ( times). On the other hand, using more expressive base distribution such MoG and cRSB is able to yield similar performance but with less memory consumption 20%) than adding more layers. The savings would become more significant when the size of the NFs model is larger and the number of layers is higher.
6.3 B and in Information Bottleneck Loss
We present the ablation study on 8 and in Information Bottleneck Loss in Table 8. We used the Pascal- Voc--S data set for this experiment. The truncation iteration T is set to 100 and running

---

Table 7: Computation Trade-off: Memory Costs on MS-COCO-OS
Base distribution
Gaussian
MoG IB
cRSB IB
2
0.918( 0.55Mb)
0.916( 0.57Mb)
0.921 0.7Mb) 0.934( 2.4Mb)
8
0.924 2.2Mb)
0.924( 2.3Mb)
average decay to 0.05. To note that, during loss computation, the trade-off parameter | is converted to the weights for both terms with the following equations:
beta nll 1./(1 3)
(12)
and
beta.cls = 1. 3
(13)
This means that the larger 3 is, the weights are larger for the class-disriminnaive term and smaller for the generative negative log-likeling ligeliiel term. And controls the magnitude of noise injected the input to induce information loss for a proper definition of mutual-cross muturl-crros-ifformatioo In Table we can observe that first along the vertical dimension of the noisy variance, adding certain level of noise (e.g. 0.5) can improve the performance. But too much noise (e-g 5.0) corrupts the input and degrades the performance probably due to excessive information loss. On the other hand, 8 controls the tribution of the class-conditional term, which includes the task-specific semantic class information. We can see by increasing this value, the performance boosts and gradually plateaus, implying the success of incorporating class-conditional information for more effective OOD detection.
Table 8: Ablation study on 3 and a in Information Bottleneck Loss on Pascal VOC-OS for Glow.
1
5
30
50
0.1
0.930
0.938
0.945
0.944
0.944
0.5
0.937
0.946
0.948
0.951
0.940
1,0
0.929
0.949
0.944
0.940
0.937
5.0
0.702
0.096
0.717
0.118
0.134
6.4 Truncation Iteration 7 and Running Average Decay in LARS
We present the ablation study on the truncation iteration T and running average decay c in LARS in Table 9. We used the Pascal-Voc-OS data set for this experiment. To note the parameters in IB loss: 3 is set to 30 and running average decay a to 0.5. In LARS, the truncation iteration T controls the number samples we need before we accept one and determines the running average decay for the normalization term computation during training. In Table 9, the changes T and lead to minor fluctuates in the final performance. We hypothesize that the minor difference from might be attributed to the re-computation of the normalization factor Z during inference. The results in the table also show that there are only small impacts on the final performance for different values of T and potentially because the acceptance function parameterized by MLP plays dominant role in the base distribution likelihood computation.
Table 9; Ablation study on T and e on Pascal VOC-OS for Glow,
0.001
0.01
0.05
0.1
0.5
50
0.941
0.941
0.950
0.953
0.945
100
0.944
0.948
0.951
0.953
0.947
250
0.945
0.949
0.949
0.946
0.946
500
0.929
0.945
0.948
0.949
0.950
12

---

6.5 ViSua-isualization of Feature Embeddings and Flow Latents
In this section, we provide the t-SNE (T-distributed Stochastic Neighbor Embedding) visualization for inspecting how the proposed topology-matching NFs learn to match the target distribution. We used the Pascal-Voc-Oe data set for this experiment. For this propose, we first visualize the feature embeddings extracted from the object detector in Figure 10a indexed by their class labels and the In in-Distribution (ID) and OOD objects on Figure 10b. It can be observed that the feature embeddings possess well class-separate structure and the OOD data is close the ID data, which can be con- sidered as near OOD data, a more challenging case [19] for OOD detection. Next, we visualize the transformed data in the latent space of the flows with different base distributions, namely cRSB and unimodal Gaussian Figure 12 colored by class labels and Figure colored by log-likelshoods. By comparison, it can be inspected that the latent structure of cRSB with IB can more faithfully resemble the target distribution in Figure 10. In contrast, the latent structure of unimodal Gaussian is fixed with all data points from different classes overlapping. The pieces of empirical evidence provide us the hint that a learnable base distribution cRSB with IB is able to match the complex topology of the target distribution more felicitous than an oversimplified one such as unimodal Gaussian.
300
visualition training data on VDCDatsset (feature embeddrggs)
I5ME visuaiitton litionn
VOCDstaset embesdings)
120 0001
75-
52-
35-
0-
-25
-25-
-50
(a) Feature embeddings: p(u)
(b) Feature embeddings: p(u)
Figure 10: t-SNE visualization for (a) feature embeddings from the object detector on the training set (b) the feature embeddings of both ID and OOD data of POScal-VOC-OS.
ISNE visualiztion for training set on VOCDstaset (flow latent space of LARS)
ISNE visualiztion train on VOCDataset (flow latent space gauss!
60
82.5
60
00.0
40
77.5
28
80.2
75.0
20
72.5
70.0
85.6
67.5
88.4
65.0
-75
-10
-25
50
75
-75
-50
-25
25
50
75
(a) cRSB with IB
Unimodal Gaussian
Figure 11: t-SNE visualization for (a) latent features of the flow with cRSB (b) latent features of the flow with a uni-model Gaussian on the training set Pascal- VOC-OS, valued by the liellhoss,,, respectively.
13

---

visualiation training VOCDataset space LARS) ISNE visua liztion for training set on VDCDataset ('oo latent space of gauss]
10
40-
20-
-20
-0
-00
(a) cRSB with IB
(b) Unimodal Gaussian
Figure 12: t-SNE visualization for (a) latent features of the flow with cRSB (b) latent features of the flow with uni-model Gaussian the training set of Pascal-VOC-OS, indexed by the class memberships, respectively.
14

---

References
[1] V. Stimper, B. Schölkopf, and J. M. Hernandez-Lobato. Resampling base distributions of normalizing flows. In International Conference Artificial Intelligence and Statistics, pages 4915-4936. PMLR, 2022.
[2] L.. Ardizzone, R. Mackowiak, C. Rother, and U. Köthe. Training normalizing flows with the information bottleneck for competitive generative classification. Advances in Neural Informa- tion Processing Systems, 53:7828-7844 2020.
[3] N. Tishby, F. C. Pereira, and W. Bialek. The information bottleneck method. arXiv preprint physics/0004057, 2000.
[4] L. Dinh, J. Sohl-Dickstein, and S. Bengio. Density estimation using real nvp. arXiv preprint 1r0.::1605.08800 2016.
[5] D. P. Kingma and P. Dhariwal. Glow: Generative flow with invertible 1x1 convolutions. Ad- vances in neural information processing systems, 31, 2018.
[6] V. Stimper, D. Liu, A. Campbell, Berenz, L. Ryll, B. Schölkopf, and M. Hernández-Lobtto normflows: pytorch package for normalizing flows. arXiv preprint arXiv:2302.12014 2023.
[7] C. Durkan, A. Bekasov, I. Murray, and G. Papamakarios. Neural spline flows. Advances in neural information processing systems, 32, 2019.
[8] S. Ren, K. He, R. Girshick, and J. Sun. Faster r-cmn: Towards real-time object detection with region proposal networks. Advances in neural information processing systems, 28, 2015.
[9] D. Miller, N. Sünderhauf, M. Milford, and F. Dayoub. Uncertainty for identifying open-set errors in visual object detection. IEEE Robotics and Automation Letters, 7(1):215-222, 2021.
[10] K. Lee, Lee, H. Lee, and Shin. A simple unified framework for detecting out-of- distribution samples and adversarial attacks. Advances in neural information processing sys- lems, 31, 2018.
[11] J. Ren, S. Fort, J. Liu, A. G. Roy, S. Padhy, and B. Lakshminarayanan. A simple fix to mahalanobis distance for improving near-ood detection. arXiv preprint arXiv:2106.0902,, 2021.
[12] B. Lakshminarayanan, A. Pritzel, and C. Blundell. Simple and scalable predictive uncertainty estimation using deep ensembles. Advances in neural information processing systems, 30, 2017.
[13] E. Fetaya, J. Jacobsen, W. Grathwohl, and R. Zemel. Understanding the limitations of conditional generative models. arXiv preprint arXiv:1906.01177 2019.
[14] R. Li, C. Zhang, H. Zhou, C. Shi. and Y. Luo. Out-of-distribution identification: Let detector tell which i am not sure. In Computer Vision-ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23-27, 2022, Proceedings, Part X, pages 638-654. Springer, 2022.
[15] C.-Y. Wang, A. Bochkovskiy, and H.-Y. M. Liao. Yolov7: Trainable bag ofg-of-freebies sets new state-of-the-arr for real-time object detectors. In Proceedings of the IEEE/CVE Conference on Computer Vision and Pattern Recognition, pages 1464-7477 2023.
[16] M. Everingham, L. V. Gool, C. I. Williams, J. M. Winn, and A. Zisserman. The pascal visual object classes (voc) challenge. Int. J. Compur. Vis., 88(2):303-333 2010. URL http: / //ablp. uni -trierrrr.. htto/jounnass/iin http///vvvve/////eeeeeeeeeeeesse
http://///eaaao.itotaaoeteeaeetn htw.:EEveringgaaaWWZZ
15

---

[17] T.-Y. Lin, M. Maire, S. Belongie, L. Bourdev, R. Girshick, J. Hays, P. Perona, D. Ramanan, C. L. Zitnick, and P. Dollár. Microsoft coco: Common objects in context, 2014. URL http: // arxiv. aarrii.org//bboe wrt//bs//////ee 1405. 0312. cite arxiv:1455.0311 155.0312Comment 1) updated annotation pipeline description and figures; 2) added new section describing datasets splits; 3) updated author list.
[18] M. Denninger, D. Winkelbauer, M. Sundermeyer, W. Boerdijk, M. W. Knauer, K. H. Strobl, M. Humt, and R. Triebel. Blenderproc2: A procedural pipeline for photorealistic rendering. Journal of Open Source Software, 8(82):4901, 2023.
[19] S. Fort, J. Ren, and B. Lakshminarayanan. Exploring the limits of out-of-distribution detection. Advances in Neural Information Processing Systems, 34:7068-7088 2021.
16


Reviews:
[{"review_id": "uI9A_QonAN", "reviewer": "Reviewer_MswT", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "This paper presents a method for performing out-of-distribution (OOD) detection for trained object detection models. The authors use a Normalizing Flow to learn a class conditioned generative model of the object detector class classifier logits, and use the likelihood of this generative model to perform OOD detection. The main contributions of this paper are extending an existing work [13], which uses learned rejection sampling of the base distribution, to class conditioned base distributions. The authors also adapt the method from [18] in order to train this model with an information bottleneck (IB) objective to prevent class information being under-utilized. The authors show in experiments that their method outperforms several baselines on benchmark datasets on a variety of metrics, as well as demonstrate the method in the context of a robotic inspection task. ", "summary_of_recommendation": "I believe this paper tackles an important problem, and shows promising results, though the proposed approach has limited technical novelty. The paper could be further improved with a more comprehensive limitations section and more discussion on the use of likelihood to perform OOD. On this basis I recommend a weak accept. ", "technical_quality": "Very Good:  Convincing.", "clarity_of_presentation": "Very Good:  Well organized and clear.", "potential_impact": "", "robotics_focus": "Sufficient demonstration on hardware", "quality_of_limitations": "Additional details required", "questions_for_rebuttal": "- Add more discussion / justification for the use of likelihood to perform OOD detection. \n- Improve limitations section as mentioned above\n", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "Strengths\n- This paper deals with an important issue for robot learning that is very relevant to the CoRL community\n- The efficacy of the method is demonstrated convincingly by the results, with both benchmark results and a compelling real-robot deployment scenario\n- I found the paper well written and the quality of exposition to be high. \n\nWeaknesses\n- Much of the cited literature, particularly [27, 35, 45] discusses how likelihood is often a poor choice both as training objective and as a means of performing OOD detection. This supports the author's use of the IB objective for training, but the authors still use the likelihood in order to perform OOD detection. I think the authors could engage more with this aspect of the literature. For instance, did the authors try other methods for performing OOD detection such as those in [45] or [46] for instance? Why is likelihood a good metric for OOD detection in their case?\n- The main contributions of the paper are an extension of [13] to class-conditioned priors, and of [18] to the resampled base distribution. The technical contributions of the paper are fairly incremental. \n- Limitations sections could be improved. Other than line 273, the limitations section is mostly justifying the method and arguing that the computational cost is negligible, rather than a frank assessment of the limitations. I would be interested to see the authors outline what tasks their current method is restricted to, or alternatively any limitations that might affect real-robot deployment. For instance, the current method does not consider the sequential nature of observations at deployment. \n\nMisc questions\n- What is the relative increase in computational cost due to the rejection sampling vs MoG flow with the same number of flow layers? \n", "extra_scores": {"impact": "3: The work is incremental and unlikely to have much impact, even though it may be technically correct and well executed."}, "extra_text": {}}, {"review_id": "Td7UTpB7P6", "reviewer": "Reviewer_q52p", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "The paper proposes a new out-of-distribution method using normalizing flows but with a class-conditional base distribution. This enables the new method to ‘topologically match’ the target distribution, thereby enabling better ODD detection. ", "summary_of_recommendation": "The work is good and sound. However, its use in robotics is not very clear. The robotic inspection and maintenance scenario (Sec 4.3) is not clearly explained. It would have helped the paper if either this was the key application explored, or at least two other robotic applications of the proposed ODD method were shown. ", "technical_quality": "Good: Generally convincing, but some additional experiments or analyses needed.", "clarity_of_presentation": "Good: Minor revision needed to improve organization or clarity.", "potential_impact": "", "robotics_focus": "Relevant but unlikely to deploy to hardware in near future", "quality_of_limitations": "Additional details required", "questions_for_rebuttal": "The method seems nice, but its application to robotics is not fully demonstrated. Any comments by authors about this would help. Thanks!", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The paper proposes a novel method for ODD detection. The paper does not fully demonstrate its use in robotics. It is unclear whether the problem being addressed indeed exists in robotic inspection problems, or not. It would have helped if this was made clear right at the beginning of the paper. The paper's readability would have improved if a section on the background covered more details about the prior methods used.\n", "extra_scores": {"impact": "2: Unsure, difficult to assess."}, "extra_text": {}}, {"review_id": "TI5IUfjd_R", "reviewer": "Reviewer_hs3b", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "This paper presents a method for improving the distribution modeling accuracy of normalizing flows when the target distribution has complex topological properties, for the purpose of OOD detection in object classification from images. In particular, a fundamental limitation of normalizing flows is that the learned distribution shares the topological properties of the base distribution; hence, if the base distribution is unimodal (e.g., a Gaussian, which is commonly used), the flow may be unable to accurately model the target distribution. To overcome this, this paper proposes using a more expressive learned base distribution combined with an information bottleneck loss. At test time, the OOD metric used is the predicted likelihood, marginalized over classes. The approach leads to improvements in OOD detection accuracy on pre-existing datasets as well as on images collected on a real robot.", "summary_of_recommendation": "Paper is clear with extensive baseline comparisons, but could use more motivation on design choices in the method, discussion of limitations, and clarifications on the real robot experiment.", "technical_quality": "Good: Generally convincing, but some additional experiments or analyses needed.", "clarity_of_presentation": "Good: Minor revision needed to improve organization or clarity.", "potential_impact": "", "robotics_focus": "Sufficient demonstration on hardware", "quality_of_limitations": "Additional details required", "questions_for_rebuttal": "Please respond to the questions in the review above.", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "Strengths: The paper is generally clear, technically sound, and is extensively compared to baselines. Moreover, the problem of OOD detection is highly relevant for robot learning today. While the paper essentially combines existing techniques (LARS and IB) for application to class-conditioned flows, the paper could still be useful for future normalizing flow practitioners.\n\nWeaknesses and concerns:\n- As a general comment, I am curious how often multimodal distributions with pathologically disconnected supports actually occur in practice for image classification. I ask because the overall OOD accuracy improvement in the real image datasets in Table 2 seems fairly minor. For the purpose of understanding, it would strengthen the paper to analyze the learned acceptance function in these settings: does it actually learn a multimodal base distribution, like in the synthetic examples? How many disconnected modes are there? If the learned base distribution is still unimodal, it would seem that topology is not the bottleneck, but rather that using a modified based distribution may overall improve the training optimization landscape compared to using a standard Gaussian, and maybe the contribution should be stated as such.\n- It is well-known that flows can often assign higher likelihood to OOD data than in-distribution data, and thus may have limited utility as an OOD measure [1]; however, this limitation is not discussed in the paper. Intuitively, this is because while maximum likelihood training encourages high likelihood values for training data, nothing constrains the training to assign low values to unseen data. Thus, flows still may be insufficient for OOD detection requirements in the safety-critical applications mentioned in the paper (one alternative is to use distance to training data and calibrated bounds on perception error, e.g., [2]).\n- I would recommend putting more details on LARS in the paper (perhaps moving some details from the appendix). How is the acceptance function parameterized? How is T selected?\n- In the paper, $p_{\\phi,\\psi}$ is used in the figure subtitles but the notation is never defined?\n- Instead of LARS, what about simply using a mixture of bounded uniform distributions as a base distribution for each class? This would be potentially simpler than LARS, and could capture multimodality without inefficient sampling due to the rejection in LARS?\n- It wasn’t clear to me why a class-conditional setup is required for the OOD detection problem, since in Sec 2.3, the OOD score is just computed by marginalizing over all classes anyway. Why couldn’t one just train a flow with a single class for all training images and use that to compute an OOD score for test-time images? Some discussion in the paper would help.\n- In the information bottleneck loss, how is epsilon chosen, and how sensitive is the performance to the choice of epsilon?\n- It would strengthen the paper to report the accuracy of the other baselines on the real robot experiment.\n- For the real robot experiment, the OOD detection performance is overall much worse compared to the Pascal-VOC and MS-COCO datasets (in Figure 5c, comparing TPR for the FPRs seen in Table 2). It would be good to have discussion in the paper as to why this is; is it due to limited dataset size?\n- What is considered to be an OOD image and ID image for the real robot experiment - this should be described in the results?\n\n[1] Zhang, Goldstein, and Ranganath. Understanding Failures in Out-of-Distribution Detection with Deep Generative Models. ICML’21.\n\n[2] Chou, Ozay, and Berenson. Safe Output Feedback Motion Planning via Learned Perception Modules and Contraction Theory. WAFR’22.", "extra_scores": {"impact": "3: The work is incremental and unlikely to have much impact, even though it may be technically correct and well executed."}, "extra_text": {}}, {"review_id": "KGz-PQ0agp6", "reviewer": "Reviewer_X7BF", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "This work addresses OOD detection based on density modeling with normalizing flows (NFs). Specifically, the authors propose an approach which follows past work in modeling the distribution of logits with a NF. The authors improve on past work aiming to address topology mismatch issues between the logit distribution and base distribution. To do so, they use class conditional distributions, as opposed to a single marginal, and further reshape each class's base distribution using learned accept/reject sampling. They demonstrate their approach on object detection tasks in both simulated and real-robot OOD detection tasks.", "summary_of_recommendation": "Overall, this paper tackles an important problem and presents a solution that performs well on the domains tested, but the approach is a relatively straightforward application of existing work, and the experimental evaluation is missing useful comparisons and lacking details regarding the real-robot experiments.", "technical_quality": "Good: Generally convincing, but some additional experiments or analyses needed.", "clarity_of_presentation": "Very Good:  Well organized and clear.", "potential_impact": "", "robotics_focus": "Sufficient demonstration on hardware", "quality_of_limitations": "Limitations are addressed clearly", "questions_for_rebuttal": "How are hyperparamters optimized? Is the approach sensitive to the value of beta in the IB loss? How was this chosen?\n\nCould you compare to other non-flow based approaches to OOD detection? Specifically, comparing to the Mahalanobis distance (Lee et al. 2018) and Relative Mahalanobis Distance (Ren et al., 2021) approaches would be worthwhile, since they also aim to detect anomalies at the logit level, and could serve as a point on the compute / accuracy tradeoff curve (as they can be thought of as a limit taking the number of flow layers to 0).", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "Strengths:\n- The proposed approach balances computational complexity and performance, yielding good density modeling yet remaining practical to deploy in real-time contexts.\n- The paper is well written, and the authors provide a good amount of background on the prior advances the authors build on in this work.\n\nWeaknesses:\n- The work strikes me as a straightforward application of prior advances for improving the quality of NF density modeling to existing techniques using NFs for OOD detection. With this in mind, the main contribution of the authors is to show that such a technique works well and is efficient enough to run in real-time. Specifically, the authors claim that spending computational budget on resampling base distributions per class is better than just adding more layers to the normalizing flow. This is an interesting claim, and I would have liked to see an empirical evaluation of this tradeoff.\n- The real-robot experiment was not described in sufficient detail: how were the images labeled? how were images classified as being in- or out-of-distribution? Furthermore, the real-world experiment lacked comparison to any baselines other than the base YOLO model.\n\nMinor comments\n- Some claims are contradictory:\n  - Line 106-108: \"This way we get similar benefits...without having to burden the cost on marginalization over classes\"\n  - Line 163: \"We marginalize the density over classes\"", "extra_scores": {"impact": "3: The work is incremental and unlikely to have much impact, even though it may be technically correct and well executed."}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper proposes topology-matching normalizing flows for out-of-distribution detection in robot learning. The reviewers had various concerns about the approach including the novelty however it has many positives. The reviewers appreciate the authors' time and effort in addressing the rebuttal, the paper has improved. Therefore, it is my pleasure to let you know the paper is Accepted (Poster). Authors are encouraged to address the reviewer comments to further improve the paper before the publication.
Decision: Accept (Poster)