Out-of-Distribution Learning with Human Feedback
Authors: Haoyue Bai
Xuefeng Du
Katie Rainey
Shibin Parameswaran
Yixuan Li
Venue: Accepted by TMLR ()

Abstract: Out-of-distribution (OOD) learning often relies on strong statistical assumptions or predefined OOD data distributions, limiting its effectiveness in real-world deployment for both OOD generalization and detection, especially when human inspection is minimal. This paper introduces a novel framework for OOD learning that integrates human feedback to enhance model adaptation and reliability. Our approach leverages freely available unlabeled data in the wild, which naturally captures environmental test-time OOD distributions under both covariate and semantic shifts. To effectively utilize such data, we propose selectively acquiring human feedback to label a small subset of informative samples. These labeled samples are then used to train both a multi-class classifier and an OOD detector. By incorporating human feedback, our method significantly improves model robustness and precision in handling OOD scenarios. We provide theoretical insights by establishing generalization error bounds for our algorithm. Extensive experiments demonstrate that our approach outperforms state-of-the-art methods by a significant margin. Code is publicly available at https://github.com/HaoyueBaiZJU/ood-hf.

Published in Transactions on Machine Learning Research (04/2025)
Out-of-Distribution Learning with Human Feedback
Haoyue Bai
bathaoyue www.wssc.cec......cccomm
Department of Computer Sciences University of Wisconsin-Madison
Xuefeng Du
xfdu@cs. wisc. edu
Deportment Computer Sciences University of Wisconsin-Madissnn
Katie Rainey
kmmnney@@nuuc..nagy mil
Naval Information Worfare Center Pacific
Shibin Parameswaran
peramesu@sppuuer.nayy
Naval Information Warfare Center Pacific
Yixuan Li
sharonli@cs. wwwpi/iiisss.i......... edu
Department of Computer Sciences University of Wiscossin-Madison
Reviewed on OpenReview: https: oppp:/evee..........mmmmmm. net/ formm id= 5q08MFQUU1
Abstract
cut-of-distribution (OOD) learning often relies on strong statistical assumptions or prede- fined OOD data distributions, limiting its effectiveness in real-world deployment for both OOD generalization and detection, especially when human inspection minimal. This paper introduces a novel framework for OOD learning that integrates human feedback to enhance model adaptation and reliability. Our approach leverages freely available unlabeled data in the wild, which naturally captures environmental test-time OOD distributions under both covariate and semantic shifts. To effectively utilize such data, propose selectively acquiring human feedback to label small subset of informative samples. These labeled samples are then used to train both a multi-class classifier and an OOD detector. By incor- porating human feedback, our method significantly improves model robustness and procision in handling OOD scenarios. We provide theoretical insights by establishing generalization error bounds for our algorithm. Extensive experiments demonstrate that our approach out- performs stato-of-the-art methods by significant margin. Code is publicly available at
1 Introduction
Modern machine learning models deployed in the wild can inevitably encounter shifts in data distributions. In practice, data shifts often exhibit heterogeneous forms. For example, out-of-distribution (OOD) data
arise either from semantic shifts where the test data comes from novel categories (Yang et al.) 2021
covariate shifts where the data undergoes domain or environmental changes (Chapaneri & Jayaswal 2022 Zhou el al. 2022a Koh el al. 2021 Ye et. al. 2022). The nature of mixed lypes of OOD data poses significant challenges in both OOD generalization and OOD detection necessitating correctly predicting the covariate- shifted OOD samples into one of the known classcs, while rejecting the semantic OOD data. For a model
be considered robust and reliable, must excel in OOD generalization and OOD detection simultancously, to ensure the continued success and safety of machine learning applications in real-world environments.

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Published in Transactions on Machine Learning Research (04/2025)
Previous works on OOD learning often rely heavily on statistical approaches Ye et al. 2023 Haroush et al, 2021) or predefined assumptions (Ye et. al. 2021 Zhang et al. 2024) about OOD data distributions, which may not accurately reflect the complexity and diversity of real-world scenarios. Consequently, they struggle to adapt to unforeseen OOD distributions encountered during deployment effectively. Furthermore, without human input to provide contextual information and guide model adaptation, these approaches may face challenges in accurately distinguishing between in-distribution (TD) and OOD data, leading to suboptimal performance in OOD detection tasks. The absence of human feedback thus restricts the adaptability of previous approaches, hindering their efficacy in addressing the multifaceted challenges of OOD generalization and detection in real-world deployment environments.
To lackle the challenge, we introduce a novel framework for OOD learning with human feedback, which can provide valuable insights into the nature of OOD shifts and guide effective model adaptation. Human feedback offers a unique perspective that complements automated statistical techniques, and remains under- explored in the context of OOD learning. Our framework capitalizes on the abundance of unlabeled data available in the wild, capluring environmental OOD distributions under diverse conditions, which can be characterized as a composite mixture of ID, covariate OOD, and semantic OOD data (Bai et al. (023). Such unlabeled data is ubiquitous in many real-world applications, arising organically and froely in the model's operational environment. To harness the unlabeled data for OOD learning, our key idea is to selectively provide human feedback and label a small number of highly informative samples from the wild data distri- bution, which are then used to train a robust multi-class classifier that generalizes across different covariate OOD samples and reliable OOD detector that can identify the semantic OOD data points. By exploiting human feedback, we can enhance the robustness and reliability of machine learning models, equipping them with the capability to handle OOD scenarios with greater precision.
Our framework employs a gradient- based sample selection mechanism, which prioritizes the most informative samples for human feedback (Section 3.1). The sampling score is calculated based on the projection of its gradient onto the top singular vector of the gradient matrix, defined over all the unlabeled wild data. Specifically, the sampling score measures the norm of the projected vector, which can be used to select informative samples (e.g., ones with relatively large gradient-based scores). The selected samples are then annotated by human, and incorporated into our learning framework. In training, we jointly optimize for both robust classification of samples from the ID and the annotated covariate OOD data, along with reliable binary OOD detector separating between the ID) data and the annotated semantic OOD data (Section 3.2 Additionally, we deliver theoretical insights (Theorem [ into the learnability of the classifier with the gradient- based sampling score, thus formally justifying the framework of OOD learning with human feedback.
Lastly, we provide extensive experiments showing that this human-centered approach can effectively im- prove both OOD generalization and detection under a small annotation budget (Section E Compared to SCONE (Bai et al., 2023), the current statc-of-the-art method, we substantially improve the accuracy of OOD classification by 5. 82% on covariate-shiifeed CIFAR-10 data, while reducing the average error of OOD detection by 15.16% (FPR95). Moreover, we provide comprehensive ablations on the impacts of labeling budgets, different sampling scores, and sampling strategies, which leads to an improved understanding of OOD learning with human feedback.
Our framework extends active learning litcrature (Li ct al. 2024) which focuses on ID classification to joint OOD generalization and detection tasks by leveraging wild unlabeled data. This challenging and heterogeneous mixture of data points requires an effective and tailored gradient-based strategy for sample selection and training, which improves over existing active learning strategies, as shown in our experiments (Section 4.3 To summarize our key contributions:
We propose a new OOD learning framework with human feedbacks for joint OOD generalization and detection. Our method employs a gradient-based sampling procedure, which can select informative semantic and covariate OOD data from the wild data for OOD learning.
We present extensive empirical analysis and ablation studies to understand our learning framework. The results provide insights into using human feedback on the unlabeled wild data for both OOD generalization and detection and justify the efficacy of our algorithm.
We provide a generalization error bound for the model learned under human feedback, theoretically supporting our proposed algorithm.
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Published in Transactions on Machine Learning Research (04/2025)
2 Problem Setup
Labeled in-distribution data. Let X' denote the input space and y = {[,,.., C} denote the label space for ID data. We use Pxy as the ID joint distribution defined over X' x y. Given an ID joint distribution Pxy, the labeled ID data S = {(x,, y=) is drawn independently and identically (ii.d.)) from Pxy.
Unlabeled wild data. Upon deploying a classifier trained on ID, we have access to unlabeled data from the wild, denoted as Swild { which can be used to assist in OOD learning. Following (Bai et al. 2023), Swild is drawn ii.d. from unknown wild distribution Pwild defined below.
Definition 1. The marginal distribulion of the wild dala is defined as:
F wild: = (1- - - in + Te. out
peceariaae + TylP pasmmnntie
where To, Ns. To + To E [0, Pin, Postariate, covariate-shifted OOD, and semantic-shifted OOD data respectively.
out , and Poemantic represent the marginal distributions of ID,
Learning goal. Our learning framework aims to build robust multi-class predictor fw and an OOD detector Dg by leveraging knowledge from labeled ID data S and unlabeled wild data Swila- Moreover, we allow maximum number of k human annotations for samples in the unlabeled data. Let fw X R be multi-class predictor with parameler w E W, where W is the parameter space. The predicted label for an input is
f(: == arg max fW (x), DEY
where f the y-th coordinate of fw: and x can be either ID or covariate OOD, To detect the semantic OOD data, we need to construct a ranking function Ja : X + R with parameter O E O, where O is the parameter space. With the ranking function ge. one can define the OOD detector:
{
ID
go (x if (x x S X,
x > X,
Da(x; A) = OOD
(1)
where À is a threshold, typically chosen so that a high fraction ID data is correctly classified.
3 Proposed Framework
In this section, we introduce novel framework for OOD learning with human feedback for lackling both OOD generalization and OOD detection problems jointly. Our framework is motivated by the fundamental challenge in harnessing unlabeled wild data for OOD learning- the lack of supervision for samples drawn from the wild data distribution Pwild- To address this challenge, our key idea is to selectively label a small number of samples from the wild data distribution to train robust multi-class classifier and an OOD detector. Specifically, the design of our framework constitutes two components revolving around the following unexplored questions:
Q1: How to select informative samples from the unlabeled data for hummnn feedback? (Section 3.1
Q2: How to learn from these newly labeled somples to enhance OOD generalization and OOD detection capabilities? (Section 3.2
3.1 Sample Selection for Human Feedback
The key to OOD learning with human feedback framework lies in sample selection procedure that identifies the most informative samples while reducing labeling costs. With limited labeling budget, it is advantagcous to select samples from wild data that are cither covariate OOD or semantic OOD and will contribute the most to OOD generalization and detection purposes. These samples would be informative for the purpose of OOD generalization and OOD detection. Given a heterogeneous set of wild unlabeled data Swild: our rationale to employ a sampling score that can effectively scparate ID vs. non-ID part. This way, we can accordingly query samples from the non-ID pool that are most likely covariate or semantic OOD. To achieve this, we proceed to describe the sampling score.
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Published in Transactions on Machine Learning Research (04/2025)
paemanntc
|p
out
(8..
Vil
1.A.A
poovariate
out
V
P
(a) Visualization of the gradient vectors and their projection
(b) Augle between the gradient and the singular vector
Figure 1: Illustration of the gradient vectors and their projections (the blue points denote Pm, the green points represent Pont poovariate and the gray points indicate ouu Paemantic): (a) Visualization the gradient projected onto top singular vector of matrix G for unlabeled data. The gradients of the set Pi. (inliers in the wild) proximate to the origin (reference gradient V), in contrast to the gradients the set Pout pasmantic, which are more distant. (b) The angle f between the gradient of the set peemantic and the singular vector As v is identified to maximize the distance of out
the projected points (denoted by x) from the origin, considering the sum over all the gradients in Fadd, v indicates the direction of OOD data in the wild with small angle 0.
Sampling score. We employ gradient- based sampling score, where the gradients are estimated from classification predictor fwgin trained on the ID data Sin:
W Sia E arg min Rg (fw);
(2)
where Rg (Jw) (x. (X:((x))) vi), l: RC y R the loss function, Wgm the learned parameter and is the size of ID training set. The average gradient V is:
Σ
Ve(fwgn (x.).
(3)
(XL.)ESS
where V acts as reference gradient that allows measuring the deviation of any other points from it.
With the reference gradient defined, we can now represent each point in Swild as gradient vector, relative to the reference gradient V. Specifically, we calculate the gradient matrix (after subtracting the reference gradient V) for the wild data as follows:
Ve(Swgin (21),
T881 V
G =
(4)
ve(lfgro (Xm), Tzx).
V
where denotes the size of the wild dataset, and 0% is the predicted label for wild sample x
For each data point &; in Swild, we now define our gradient-basel sampling score as follows:
= (VL(Swgu (x,).Tx,) - V,v)²
(5)
where ( the dot product operator and v is the top singular vector of G. The top singular vector v can be regarded as the principal component of the matrix G in Eq. 4 which maximizes the total distance from the projected gradients (onto the direction of v) the origin (sum over all points in Swna) (Hotelling 1933). Specifically, is unit-norm vector and can be computed as follows:
V. arg max [|]|2=1 X.ESwad
Σ
(u, Vl(s (xi), 1z.) 7)²
(6)
Essentially, the sampling score To in Eq. measures the lg norm of the projected vector. To help readers better undersland our design rationale, we provide an illustrative example of the gradient vectors and their projections in Figure D
(see caption for details).
The shape of matrix G is cim(W.gi.) x where each entry of G has dimension of dim(w In practice, dim(w equal to the dimension of the penultimate layer embeddings.
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Sampling strategy. Given the gradient-based scores calculated for each sample x; in Swild: need to select subset of h < m examples for manual labeling. Here & is the annotation budget. We consider three sampling strategies, as illustrated in Figure 2
Top-k sampling: select samples from Swild with the largest score т. As shown in Figure 2 (a): these samples deviate mostly from the ID data and are more obviously to be semantic OOD or covariate OOD.
Near-boundary sampling: select samples that are close to the ID boundary, which may en- compass samples with high ambiguity. As shown in Figure (b), we choose the threshold т using labeled ID data S so that captures a substantial fraction (e.g., 95%) of ID samples. Based on the threshold Th, then select samples from Swild that are closest to this threshold.
Mixed sampling: select samples using both top-k and near- near- boundary sampling, and combine the two subsets.
Without loss of generality, we denote the selected set of samples Syelected, with cardinality |S k. For each sample in Selecctd,, we ask the human annotator to choose label from ( where {1} indicates the semantic OOD. For covariate OOD, the returned label belongs to the existing label space y according to the definition. In Section 4.3. we perform comprchensive ablations to understand the efficacy of cach sampling strategy.
3.2 Learning Objective Leveraging Human Feedback
We now discuss our learning objective, which incorporates the human annotated samples from wild data. For notation convenience, we use S Selected and Seleectd denote labeled samples corresponding to covariate OOD and semantic OOD respectively, where Syelected S selected U Selected Our learning framework jointly optimizes for both: (1) robust classification of samples from 8 and covariate OOD Selected: and (2) reliable binary OOD detector scparating data between Sin and semantic OOD S selected Given weighting factor the risk can be formalized as follows:
w, arg min R Sotocted (Sw) + Rgin St Selceted (90)],
Multi-class classifier
OOD detector
where the first term can be empirically optimized using the standard cross-entropy loss. The sccond term can be viewed explicitly optimizing the level-set based on the model output (threshold 0), where the labeled ID data x from S has positive values and vice versa:
Rgin, seeeteed (go)
Ri (90) R
Snlacted (go)
ExEsin
1(go(x) S 0}
(8)
+ ExEs Stscaca 1:g0 (8) 0}.
ID
ID
Covariata 000
Covariate 000
Semantic DOD
5 Semantic 000
Semanic 000
Sudget
Tirssheld 190% ID coreety Casccled
Soussh Thmebst
Budg
(55% ID coconeeyyy chasilee)
(a) Top-k sampling
(b) Near-boundary sampling
(c) Mixed sampling
Figure Illustaatoon of three selection criteria, (1) top-k sampling, (2) hear-boundary sampling, and (3) mixed sampling, The horizontal axis is the sampling score defined in Equation 5 and the vertical axis is the frequency. Note that we color the three different sub-distributions (ID, covariate OOD, semantic OOD) separately for clarity, but in practice the membership is not revealed due to the unlabeled nature of wild data.
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To make the 0/1 loss tractable, replace it with the binary sigmoid loss, smooth approximation of the 0/1 loss. We train so along with the multi-class classifier fw- The training enables generalization to OOD samples drawn from Foutaratee and at the same time, teaches the OOD detector to identify data from o The above process of sample selection, human annotation, and model training can be repeated until the desired performance level achieved or the entire budget. allocated for annotations is exhausted. An end-to-end algorithm is fully specified in Appendix A
Theoretical insights. We now present theory to support our proposed algorithm. Our main Theorem [ provides generalization error bound w.r.t. the empirical multi-class classifier fw, learned on ID data and the selected covariate OOD data by the objective Rgin Rgin, Sidected (fw). We specify several mild assumptions and necessary notations for our theorem in Appendix [ Due to space limitations, we omit unimportant constants and simplify the statements of our theorems. We defer the full formal statements to Appendix J All proofs can be found Appendices K and
Theorem 1. (Informal). Let W be a hypothesis space with a VC-dimension of d. Denote the datasets Stn and S selented as the labeled ID and the selected covariate OOD data by our learning algorillm, and their sizes are and may respectively. If W minimizes the empirical risk Rs=,s, Sugpr (fw) for classifying the ID and covoriate OOD data, and w arg minwew an (fw), then for any 6 E (0, 1), with probability of at least 1 8, we have
R Rposseriats (f²) < R Peoouriaae (fw + sup (S ;Sirtoted)
out
WEW
2dlog((mmc) + log
+4\ m.
27 + 26.
where 5 = V ) log (2n+22m.)) 2m.)) -logd)) + M and =
min R (Sw). M is the upper bound of the loss weW
function for the muulti class classifier,
d' Stetectel (fw: - VRs insueedd (sw. Alp
where f is classifier which returns the closest one-hot vector representation for the probabilistic prediction of fw, te., Rga(Jw. (m--)m((f..) and Rs: Rs: (fw: (fw: Ex- ((sw:
Practical implications. Theorem states that the generalization error of the multi-class classifier is upper bounded. the sizes the labeled ID n and the selected covariate OOD data m. are relatively large, the optimal ID loss 7 is small, and the optimal risk on covariate OOD Rpcorariato (Sw=), (Jw=)) then the upper bound will mainly depend on the gradient discrepancy between the TD and covariate OOD data selected by our learning algorithm. Notably, this bound synergistically aligns with our gradient- score (Equation 5 Empirically, verify these conditions of Theorem and our assumptions in Appendix M which can hold in practice.
4 Experiments
4.1 Settings
Datasets and benchmarks. Following the sotup Bai et al. (2023). we employ CIFAR-10 Krizhevsky
et al. 2009) as In and CIFAR-10-C (Hendrycks & Dietterich 2018) with Gaussian additive noise as the pcovariate For out (Zhou et al. 2017), and LSUN YY et al. 2015). We divide CIFAR-10 training set into 50% labeled as ID and 50% unlabeled. And we mix unlabeled CIFAR-10, CIFAR-10-C, and semantic OOD data to generate the wild dataset. To simulate the wild distribution Pwild, we adopt the same mixture ratio as in SCONE (Bai let al.) 2023), where मe = 0.5 and म. = 0.1. Detailed descriptions of the datasets and data mixture can be found in the Appendix B To demonstrate the adaptability and robustness of our proposed method, we extend the framework to more diverse settings and datasets. Additional results on other types of covariate shifts can be found in Appendix E.
psemantic we leverage SVHN (Netzer al.) 2011 ), Textures (Cimpoi et. al.) 2014), Places365
Liu al. 2020: Katz-Samuels et. al. 2022 we adopt Wide ResNet with 40 layers and widen factor of 2 (Zagoruyko &
Experimental details. To ensure fair comparison with prior works (aai et al. 2023

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Published in Transactions on Machine Learning Research (04/2025)
Bel Sara VOC 903
ID dats Covar ota OCD Semarck DOD
IB dars
44
Semsrrcc 000
Semantic oob
Coveriate ooD
2.0
0.5
000x
(a) Scores of ERM
(b) Scores of Ours
(c) T-SNE of ERM
(d) T-SNE of Ours
Figure 3: (a)-(b) Score distributions for ERM vs. our method. Different colors represent the different types of test. data: C1FAR-10 as Pin (blue), CIFAR-10-C as Poutarite (green), and Textures as Pourantic (gray). (c)-(d): T-SNE visualization the image embeddings using ERM vs. our method.
Komodakis 2016). We use stochastic gradient descent with Nesterov momentum (Duchi et al. 2011 b, with weight decay 0.0005 and momentum 0.09. The model is initialized with a pre-trained network on CIFAR-10, and then trained for 100 epochs using our objective in Equation 7 with a = 10. We use a batch size of 128 and an initial learning rate of 0.1 with cosine learning rate decay. We default to 1000 and provide analysis of different labeling budgets & E {100, 500, 1000, 2000} in Section 4.3 In our experiment, the output of go is utilized as the score for OOD detection. In practice, we find that using one round of human feedback is sufficient to achieve strong performance. Our implementation is based on PyTorch 1.8.1. All experiments are performed using NVIDIA GeForce RTX 2080 Ti.
Evaluation metrics. We report the accuracy of the ID and covariate OOD data, to measure the classifi- cation and OOD generalization performance. In addition, we report false positive rate (FPR) and AUROC for the OOD detection performance. The threshold for the OOD detector selected based on the ID data when 95% of ID test data points are declared as ID.
4.2 Main Results
Competitive performance on both OOD detection and generalization tasks. As shown in Table 1 our approach achieves strong performance for both OOD generalization and OOD detection tasks jointly. For a comprehensive evaluation, we compare our method with three categories of methods: (1) methods developed specifically for OOD detection, (2) methods developed specifically for OOD generalization, and (3) methods that are trained with wild data like ours. We discuss them below.
First, we observe that our approach achieves superior performance compared to OOT) detection baselines, including MSP (Hendryeks & Gimpel, 2016), ODIN (Liang et al. 2018a). Energy (Liu al., 2020), Maha- lanobis (Lec et al.) 2018), VIM (Wang et al.) 2022b). KNN (Sun et al. 2022 and latest baseline ASH (Djurisic al... 2023a). Methods tailored for OOD detection tend to capture the domain-variant information and strug- gle with the covariate distribution shift, resulting in suboptimal OOD accuracy. For example, our method achieves near-perfect FPR95 (0.12%). when evaluating against SVHN as semantic OOD. Secondly, while approaches for OOD generalization, containing IRM (Arjovsky et al. 2019h, ERM, Mixup (Zhang et al. 2018), VREx (Krueger et al. 2021), EQRM (Eastwood et al.) (022a)), and latest bascline SharpDRO (Huang ett al. 2023b), demonstrate improved OOD accuracy, they cannot effectively distinguish between ID) data and semantic OOD data, leading to poor OOD detection performance. Lastly, closest to our setting, we compare with strong baselines trained with wild data, namely Outlier Exposure (Hendrycks et al.] 2018) Energy-rogularized learning (Liu et al.) 2020), WOODS (Katz-Samuels et al. 2022), and SCONE (Bai et al. 2023). These methods emerge as robust OOD detectors, yel display a notable decline in OOD generalization (except for SCONE). In contrast, our method demonstrates consistently better results in terms of both OOD generalization and detection performance. Notably, our method even surpassos the current method SCONE by 32.24% in terms of FPR95 on the Texture OOD dataset, and simultancously improves the OOD accuracy by 4.75% on CIFAR-10-C.
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Table 1: Main results: comparison with competitive OOD generalization and detection methods on CIFAR-10 Results for LSUN-R and Texture datasets are in Appendix D Since all the OOD detection methods the model trained with the CE loss on Pin, they display the same ID and OOD accuracy on CIFAR-10-C. We report the uverage and std of our method based on independent runs. ir denoles the rounded standard OOD Acc. metric refers to the classification accuracy on covoriate OOD data while AUROC and FPR are for OOD detection evaluation.
Note that
SVHN CIFAR-IOC PaRAter
LSUN-C Pistatc CIEAR. I..C....... Pogeriie
TEstur Prreali CIEAR- I&C
OOD Acc.T
ID Acc.
FPR
AUROCI
OOD Acc.T
ID Acc.
FPR.
AUROCI
OOD Acc.
ID Acc.T
FPR.
AUROC
DGD defoction
MSS
75.00*
$4.51
45.49
91.50
75.06
94.84
30.50
55.65
75.05
94.54
19.25
58,50
ODIN
15/15
91.51
35.35
01:54
75.05
91.81
15.52
97.01
75.05
94.54
61.97
EaHrgy
75.05
91.51
35.99
08.00
75.05
91.84
5.20
96.35
75.05
94.54
52.79
65.22
Mabalanobis
01.54
73.05
VIM
01.51
10.
73.05
3.10
KNN
75.00
OGB prammlication
ERM
75.00
75.05
94.84
5.35
75.05
IRM
17.02
98.67
SharpDRO
95.14
79.03
5.07
Energy (W. outller)
10.22
31.55
2.33
94.90
09.52
78.00
95.02
94.63
07.84
84.58
98.78
10.23
27
91.08
0.
99.98,9.e
90.83,210
91. 33gem
88.97 cau
90.31 asur
01.38 o4
28.28
hggorithm
Art painting
Cartoon
Photo
Sketch
Avg (%)
IRM Arjovsky et al.
2019
84.8
76.4
96.7
76.1
83.5
DANN Ganin al.
2016
86.4
77.4
97.3
73.5
83.7
CDANN
Li 2018c
84.6
75.5
96.8
73.5
82.6
GroupDRO Sagawa et
2020
83.5
79.1
96.7
78.3
84.4
MTL Blanchard
87.5
77.1
96.4
77.3
84.6
1-Mixup Wang et al. 220
78.9
97.6
75.8
MMD
et al. 2018b
86.1
79.4
96.6
76.5
84.7
VREx
Krueger et al. 2021
86.0
79.1
96.9
77.7
84.9
MLDG Li cl al. 2018a
85.5
80.1
97.4
76.6
84.9
ARM Zhang et a. 2021
86.8
76.8
97.4
79.3
85.1
RSC HHang et. al. 2020
85.4
79.7
97.6
78.2
85.2
Mixstyle Zhou
2021
86.8
79.0
96.6
78.5
85.2
FRM Vapnik 1999
84.7
80.8
97.2
79.3
85.5
CORAL Sun Saenko
2016
88.3
80.0
97.5
78.8
86.2
SagNet Nam al.
2021
87.4
80.7
80.0
86.3
SelfReg
Kim
2021
87.9
79.4
78.3
85.6
GVRT Min ct al.
2022
78.4
75.7
VNE Kin et al.
2023
88.6
79.9
82.3
Ours
88.1
87.4
98.5
91.3
91.3
Table 2: Comparison with domain generalization methods on the PACS benchmark. All methods are trained ResNet-50. The model selection based on training domain validation set..
Li et al. 2017) from Ded.inBed. We compare our approach with various common OOD generalization baselines. including IRM (Arjovsky et. al., 2019). DANN (Ganin
Additional results on PACS benchmark. In Table 2 we report results on the PACS dataset
al. 2016), CDANN (Li al. 2018c), Group-
DRO (Sagawa al.J al.] 2020). MTL (Blanchard et al.] (002)), I-Mixup (Wang al. 2020 MMD LLi et al.
2018b),
VREx (Krueger al.] 2021)), MLDG (Li et al. 201 8a), ARM (Zhang et al. 2021bb
RSC (Huang
et al.
2020 Mixstyle (Zhou et al. 2021.. ERM [Vapnik 1999). CORAL (Sun & Saenko 2016
SagNet (Nam
ct al.
2021 SelfReg (Kim et al. 2021 GVRT (Min et al. 2022), and the latest bascline VNE (Kim et al.
2023 ).
Our method achieves an average accuracy of 91.3%, which outperforms these OOD generalization
baselines.
Visualization of OOD score distributions. Figure 3 (a) and (b) visualize the score distributions for
ERM (without human feedback) vs. our method. The OOD score distributions between P,, and psemantic are more clearly differentiated using method. This separation leads to improvement in OOD detection
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performance. The enhanced separation be attributed to the effectiveness of the OOD learning with human leedback framework in recognizing semantic-shifted OOD data.
Visualization of feature embeddings. Figure 3 (c) and (d) present t-SNE visualizations (Van der Maaten & Hinton, 2008) of feature embeddings on the test data. The blue points represent the test ID data (CIFAR- 10), green points denote test samples from CTFAR-10-C, and gray points are from the Texture dataset. This visualization indicates that embeddings of In (CIFAR) and out poovariate (CIFAR-C) are more closely aligned using method, which contributes to enhanced OOD generalization performance.
4.3 In- In-Depth Analysis
Impact of labeling budget k. The budget & is central to our OOD learning with human feedback Tramework. In table 3 we conduct an ablation by varying & E {100, 500, 1000, 2000}. We observe that the performance of OOD generalization and OOD detection both increase with larger number of an- notation budgets. For example, The OOD accuracy improves from 86.62% to 91.09% when the budget changes from & = 100 to k = 2000. At the same time, the FPR95 reduces from 22. 16% to 3.60%. Interestingly, we do notice a marginal difference bet ween
Table 3: Ablation on labeling budget & We train
CIFAR-10 as ID, using wild data with Te = 0.5 (CIFAR- 10-C) and n. 0.1 (Texture).
Budget à OOD Acc.1
ID Are.t
FPR.
AUROC1
100
86, 62
95.03
22.16
91.31
500
89. 96
91.70
7.50
97.45
1000
90.31
94.33
4.91
98.28
2000
91.09
94.42
3.60
98.90
= 1000 and & 2000, which suggests that our method suffices to achieve strong performance without excessive labeling budget.
Impact of different sampling scores. Our main results are based on the gradient- based sam- pling score (c.f. Section 3.1 Here we pro- vide additional comparison using different sampling scores, including least-confidence sampling (Wang
Table 4: Impact of sampling scores. We use budget = 1000 for all methods. We train on CIFAR-10 as ID, using wild data with = 0.5 (CIFAR-10-C) and 0.1 (Texture).
& Shang 2014), entropy-based sampling (Wang
Sampling score
OOD Acc.t
ID Acc.t
FPR.
AUROCI
& Shang 2014], margin-based sampling (Roth
Loast confidence
90.22
94.73
5.44
96.45
Eatropy
& Small 2006). energy score (Liu et al. 2020),
Margin
90.31
94.56
6.37
97.68
BADGE (Ash ct al.) 2019). and random sampling.
BADGE
88.68
91.56
8.77
96.39
Detailed description for each method is provided in
Random
Euergy
88.75
94.78
10.89
95.19
Appendix C We observe that the gradient-basee
Gradient-based
90.31
91:33
1.91
98.28
score demonstrates overall strong performance in terms of OOD generalization and detection.
Impact of different sampling strategies. In Table 5 we compare the performance of using three different sampling strategies (1) top-k sampling, (2) near-boundary sampling, and (3) mixed sampling. For all three strategies, we employ the same labeling budget & = 100 and the same gradient- basde scoring function (e.f. Section 3.1). We observe that the top-k sampling achieves the best OOD generalization performance. This because the selected samples are furthest away from the ID data, presenting challenging cases of covariate-shifted OOD data. By labeling and learning from these hard cases, the multi-class classifier acquires stronger generalization to OOD data. Moreover, near-boundary sampling displays the lowest performance in both OOD generalization and OOD detection. To reason for this, we provide the number of samples (among 100) belonging to ID, covariate OOD, and semantic OOD respectively. As seen in Table 5 the majority of the samples appear to be either ID or covariate OOD (easy cases), whereas only out of 100 samples are semantic OOD. As a result, this sampling strategy does not provide sufficient informative samples needed for the OOD detector. Lastly, the mixed sampling strategy achieves performance somewhere in between top-k sampling and near-boundary sampling, which aligns with expectations.
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Table 5: Impact of sampling strategy (k 100).
We train CIFAR-10 as ID, using wild data with me 0.5
(CIFAR-10-C) and T. = 0.1 (Texture).
Sampling Strategies OOD Acc.t
ID Acc.t
FPR.
AUROCT
#ID
# #Covariate 0OD
Semantic OOD
Top-k sampling
86.62
95.03
22.16
91.31
43
Near-boundary sampling
85.12
95.18
41.72
76.56
44
50
6
Mixed sampling
85.36
95.10
36.24
85.37
25
51
24
5 Related Works
distributiiin generalization is a crucial problem in machine learning when training and test data
are sampled from diffcrent distributions. Compared to domain adaptation task (You et al. 2019
Kumar
et al.
2020 Wang et al.) 2022c Prabhu et al. 2021 Su et al. 2020
Kothandaraman et al. 2023
OOD
general ization is more challenging as it focuses on adapting to wnseen
covariate-shited data without access
to any sample from the target domain [Gulrajani & Lopez-Pazz 2020
Bai et al. 2021 Koh et al. 2021 Ye
iet al.
2022
Cho et al.] 2023 Bai et al.) 2024a b). Existing theoretical work on domain adaptation Manssurr
jet al.
2009 Blitzer et al.] 2007 Ben-David et al. 2006 2010 Gui et al.] 2024) discusses the genera lization
error bound with access to target domain data. Our analysis presents several key distinctions: (1) Our focus
is on the wild setting, necessitating an additional step of selection and human annotation to acquire selected covariate OOD data for retraining; (2) Our OOD generalization error bound differs in that it is based on
gradient-based discrepancy between ID and OOD data. This diverges from classical domain adaptation literature and synergistically aligns with our pradient-based sampling score.
A prevalent approach in the OOD generalization area is to learn a domain domain-invariane invariant data representation across training domains. This involves various strategics like invariant risk minimization (Arjovsky et al.
2019
Ahuja et al.
2020
Krueger et al. 2021 Eastwood et al. 2022b), robust optimization (Sagawa et al.
2020
Dai et al.]
2023
Huang al., 2023a) domain adversarial learning (Li et al. 2018b |Wann et al.
2022d
Dayal et al.
2023)
meta-learning Li et al. 2018a Zhang et al. 2021a), and gradient alignment (Shi
ct al.
2021 Rame et al.
2022 Guo et al.) 2023). Some OOD algorithms do not require multiple training
domains (Tong et al.) 2023). Other approaches include model ensembles (Chen et al. 2023c; Ramé el al.
2023), graph learning (Gui et al. 2023 Yuan et al. 2023), and test-time adaptation Chen et al. 2023a;
Park et al. 2223: Samadh et al. 2023 Chen et al.J 2022bb). SCONE (Bai et al. 2023) aims to enhance OOD
robustness and detection by utilizing wild data from the open world. Building on SCONE's problem setting, we leverage human feedback to train robust classifier and OOD detector, supported by theoretical analysis.
Out-of-distribution detection has garnered increasing interest in recent years (Yang et al. 2021
2022
Zhang et al.
2023b Du al. 2024b). Recent methods can be broadly classified into post hoc and regularized
based algorithms.
Post hoc methods, which include confidence-based methods (Hendrycks & Gimpel 2016
Liang ct al.
2018b), energy-based scores [Liu et al.) 2020 Wang et al. 2021 Sun et al. 2021
Djurisic
el al.] 2023b Zhang el al. 2023c Lafon el al.) 2023). gradient- score (Huang el al.] 2021
Be Behpour
et al. 2023). Bayesian approaches [Gal & Ghahramani 2016 Maddox et al. 2019 Kristiadi et al. 2020
and bistanco-basod methods (Lee ct al. 2018 Sun et al.,
2022 Du et al.) 2021 2022a Ming et al.
2022b
perform OOD detection by devising OOD scores at test time. On the other hand, another line of work
addresses OOD detection through training-time regularization (Hendrycks et al. 2018 Hein et al. 2019:
Du et al.] 2022c b)
Ming et al.) 2022a Wang et al. 2023 Du et al. [023] [Ta et al. 2023 ; which typically
relies on a clean set of auxiliary semantic OOD data. WOODS [Katz-Samuels et al. 2022) and SAL Du
et al. 2024a address this issue by utilizing wild mixture data, comprising both unlabeled ID and semantic OOD data. While SAL also employs a mradicnt-basee score, it does not consider OOD gencralization or leveraging human feedback, which is our main focus. Our work builds upon the setting in SCONE (Bai et al. 2023) and introduces novel OOD learning with human feedback framework aimed at enhancing both OOD generalization and detection jointly.
Active learning emphasizes the selection of the most informative data points for labeling (Conn el al. 1994 Balcan et al.] (2066] /Setlles] 2009] [Wang & Shang] 2014 [en et al.) 2021 Karzand & Nowak 2020: Xie et al.) 2024). Well-known sampling strategics include disagroement- basedd sampling, diversity sampling,
and uncertainty sampling. Disagroement- based sampling (Seung et al. 1992 Hanneke et al. 2014 Zhu &
Nowak 2022 focuses on selecting data points that elicit disagreement among multiple models. Diversity
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sampling, explored in (Du et al.
2015 Zhdanov 2019
Citovsky et al. 2021 aims to select data points
that are both diverse and representative of the data's s overall distribution. U Uncertainty sampling [Lewis.
1995
Scheffer et al. 2001 Shannon
2001
Lu et al.
2016
Wang & Shang 2014 Ducoffe & Precioso 2018
Boluch et al. 2018 seeks to identify data points where model confidence is lowest, thus reducing uncertainty.
More advanced methods (Ash al.
2019 Wang et al.
2022a
Elenter el al. 2022 Mohamadi et al. 2022)
incorporate mix of uncertainty and
diversity sampling techniques. Another rescarch direction involves deep
active learning under data imbalance (Kothawade al. 2021
Emam et al. 2021 1 Zhang al. 2022 Coleman
et al. 2022 Zhang et al., 2023a Kothawade et al. 2022
Aggarwal et al. 2020 The work of (Das et al,
2023
Deng et al. 2023 Zhan et al. 2023 Shayovitz et al.
2024 Benkert et al. 2022 considers distribution
shifts in the context of active learning. However, previous approaches usually focus on selecting informative samples for improving ID classification, which do not consider OOD robust.ness and the challenges posed by realistic scenarios involving wild data. In our work, we introduce a novel framework tailored for both OOD gencralization and detection challenges. This framework further supported by thcorctical justification of our learning approach.
6 Conclusion
This paper introduces new framework leveraging human feedback for both OOD generalization and OOD detection. Our framework tackles the fundamental challenge of leveraging the wild data- the lack of super- vision for samples from the wild distribution. Specifically, we employ a gradient-based sampling score selectively label informative OOD samples from the wild data distribution and then train robust multi-class classifier and an OOD detector. Importantly, performs competitively compared to various baselines, which offers practical advantages. We further provide theoretical analysis of the learnability of the classifier. We hope our work will inspire future research on both empirical and theoretical understanding of OOD generalization and detection in a synergistic way.
algorithm only requires small annotation budget and
7 Acknowledgement
This work is supported by the Office of Naval Research under grant number N00014-23-1-2643, AFOSR Young Investigator Program under award number FA9550-23-1-0184, National Seience Foundation (NSF) Award No. IIS-2237037 and IIS-2331669. The authors would also like to thank TMLR reviewers for the helpful suggestions and feedback.
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Out-of-Distribttion Learning with Human Feedback (Appendix)
A
Algorithm
Algorithm Out-of-Distribution Learning with Human Feedback
In-distribution labeled data S {(x;, 1)))..- Unlabeled wild data Swild {x;) i== Output: Learned classifier fw and OOD detector 9
Input:
Sample section
1. Perform ERM on labeled ID data S and obtain learned weight parameter wg according to Eq. equa-
tion 2
2. Calculate the reference gradient V on S according Eq. equation
3. Generate predicted labels Ds. for X; E Swila-
4. Calculate gradient Vi(hw (R:), ).
5. Calculate the gradient matrix G by Eq. equation and Compute the gradient-basee based score by
Eq. equation 5
6. Given the gradient- based scores Tr for each sample X,, select a subset kt according to the three sampling strategios described in Sec. 3.1
7.nnottte the selected & samples with labels from: U { to obtain S selected and S Selected where {r}
indicates the semantic OOD.
OOD learning with annotated samples
8. Train the robust classifier using samples from S and covariate OOD S seleted Concurrently, train a binary OOD detector using semantic OOD S selected and S by Eq. equation
B Detailed Description of Datasets
CIFAR-10 (Krizhevsky et al. 2009) contains 60, 000 color images with 10 classes. The training set has 50, 000 images and the test set has 10, 000 images.
CIFAR-10-C is algorithmically generated, following the previous leterature (Hendrycks & Dieuterich 2018 The corruptions include Gaussian noise, defocus blur, glass blur, impulse noise, shot noise, snow, and zoom blur.
SVHN Netieer et al. 2011 is a real-world image dataset obtained from house numbers in Google Street View images, with 10 classes. This dataset contains 73, 257 samples for training and 26, 032 samples for testing.
Places365 (Zhou al. 2017 contains scene photographs and diverse types of environments encountered in the world. The semantic categories consist of three macro-classes: Indoor, Nature, and Urban
LSUN-C (Yu al. 2015 and LSUN-R YYu et al. 2015 are large-scale image dalasets that are annotated using deep learning with humans in the loop. LSUN-C is a cropped version of LSUN and LSUN-R is a resized version of the LSUN datasct.
Textures (Cimpoi et al. 2014) refers to the Describable Textures Dataset, which contains images of natterss and textures. The subset we used has no overlap categories with the CIFAR dataset (Krizhevsky et al. 2009).
PACS Li al. 2017) is commonly used in evaluating OOD generalization approaches. This dataset consists of 9, 991 examples of resolution 224 224 and four domains with different image styles including photo, art painting, cartoon, and sketch with seven categories.
Details of data split for OOD datascts. For datasets with standard train-test split (c.g., SVHN),
we use the original test split for evaluation. For other OOD datasets (e.g.. LSUN-C), we use 70% of the data for creating the wild mixture training data as well the mixture validation dataset. We use the
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remaining examples for test-time evaluation. For splitting and the remaining for training.
use 30% for validation
C Description of Sampling Methods
Least confidence Waang& & Shang, 2014) an uncertainty-based algorithm that selects data for which the most probable label possesses the lowest posterior probability. This method focuses on instances where the model's predictions are least certain.
Margin sampling (Roth & Small 2006) elects data points based on the multiclass margin, specifically tar- geting examples where the posterior probabilities of the two most likely labels are closely matched, indicating the minimal difference between them.
Entropy (Wang & Shang, 2014) an uncertainty-based algorithm that chooses data points by evaluating the entropy within the predictive class probability distribution of each example, aiming to maximize the overall predictive entropy.
Energy sampling (Liu et al. 2020) identifies data points using energy score, measure theoretically aligned with the probability density of the inputs.
BADGE (Ash et al. 2019) samples groups of points that are both diverse and exhibit high magnitude in a hallucinated gradient space. This technique combines predictive uncertainty and sample diversity, enhancing the effectiveness of data selection in active learning.
Random sampling serves straightforward baseline method, involving the random selection of k ex- amples to query.
D Results on Additional OOD Datasets
In this section, we provide the main results on more OOD datasets including Places365 Zhou et al. 2017) and LSUN-R (Yu et al. 2015). As shown in Table our proposed approach achieves overall strong performance in OOD generalization and OOD detection these additional OOD datasets. Firstly, we compare our method with post hoc OOD detection methods such MSP (Hendrycks & Gimpel 2016). ODIN [Liang et al. 2018a), Energy (Liu et al. 2020), Mahalanobis (Lee et al. 2018), ViM (Wang et al. 2022b), KNN (Sun et al. 2022). and latest baseline ASH (Djurisic et al., 2023a]). These methods are all based on a model trained with cross-entropy loss, which suffers from limiting OOD generalization performance. However, our mothod achieves an improved OOD generalization performance (e.g., 91.08% when the wild data is a mixture of CIFAR-10, CIFAR-1O-C, and L.UN--)..
Secondly, we also compare our method with common OOD
generalization baseline methods including
IRM (Arjovsky et al. 2019 ERM, Mixup (hang al. 2018
VREx (Kueger et al. 2021). EQRM East-
wood et al. 2002a),, and latest baseline SharpDRO (Huang et al. 2023b Our approach consistently achieves better results compared to these OOD generalization baselines. Lastly, we compare our method with strong OOD basclines using Pwiid such as Outlier Exposure (Hendrycks et al. 2018), Energy-regularize learn- ing (Liu et al.] 2020), WOODS "Katz-Samuel et al.] 2022), and SCONE (Bai et al. 2023). Contrastly, our approach demonstrates strong performance on both OOD generalization and detection accuracy, which shows the effectiveness of our method for making use of the wild data.
E Results on Different Corruption Types
In this section, we provide additional ablation studies of the different. covariate shifts. In Table 7 we evaluate our method under different common corruptions including Gaussian noise, shot noise, glass blur, and etc. To generate images with corruption, we follow the default sctting and hyperparameters as in Henndyykss & Dietterich| (2018). Our approach is robust under different covariate shifts and achieves strong OOD detection performance.
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Table 6: Additional results. Comparison with competitive OOD detection and OOD generalization methods on CIFAR-10. For experiments using wiild we use T. 0.5, _. 0.1. For each semantic OOD dataset, we create corresponding wild mixture distribution wwild (1 T, Te P out psemanticc + out Pecovariat for training. We report the average and std of our method based independent. runs. + denotes the rounded standard error.
Model
OOD Acc.
Plares365 piemastic, CIFAR-IO-C possciate
oour ID Acc.?
FPR.
AUROCT
OOD Acc.t
LSUN-R
picsonatic CIFAR 10-C possuiate
Fou
ID Acc.
FPR.
AUROCT
0OD detection
MSP
76.05
94.84
57.40
84.49
75.05
94.84
52.15
91.37
ODIN
75.05
94.84
57.40
84.49
75.05
94.84
26.62
94.57
Energy
75.05
40.14
$9.80
75.05
94.84
27.58
94.24
Mabalanobis
75.05
94.84
68.37
84.61
76.05
94.84
42.62
93.23
VIM
75.05
91.81
21.95
95.48
75.05
91.81
36.80
93.37
KNN
76.05
91.81
42.67
91.07
75.05
94..4
29.75
91.60
ASH
75.05
94.84
44.07
88.84
75.05
94.84
22.07
95.61
OOD generalization
ERM
Mixup
79.17
93.30
58.21
75.70
79.17
93.30
32.73
88, 86
IRM
77.92
90.85
$3.79
88.15
77.92
90.85
34.50
91.54
VREx
76.90
91.35
56.13
87.45
76.90
91.35
44.20
92.55
EQRM
75.71
92.03
51.00
92.93
31,23
94.94
SharpDRO
79.03
94.91
34.64
91.96
79.03
94.91
13.27
97.44
Learning Paad
OF
35.98
94.75
27.02
94.57
46.89
94.07
0.7
90.78
Energy (w/ outlier)
19.86
90.55
23.89
93.60
32.91
93.01
0.27
99.90 99.94
Woods
51.58
91.88
30.48
93.28
78.75
95.01
0.60
99.87
Scone
37.56
90.90
91..9
0.87
Ours
89.16
94.51g0.11
15.70.0.0z
94.688.0.00
91.08
94.41g0.00
0.07
99.98.0.0
Table 7: Ablation study on different corruption types for covariate OOD data. The budget is 500 for active
learning. We train on CIFAR-10 as ID, using wild data with n. = 0.5 (CIFAR-1O-C) and т, = 0.1 (Texture).
Corruption types for covariate OOD data
OOD Acc.f
ID Acc.t
FPR
AUROCT
Gaussian noise
90.31
94.33
4.91
98.28
Defocus blur
94.54
9-L688
1.38
99.56
Frosted glass blur
82.22
94.45
8.35
96.87
Impulsc noise
91.82
94.38
3.61
98.88
Shot noise
91.98
94.62
3.79
98.85 98.82
Snow
92.51
94.45
2,89
99.04
Zoom blur
92.31
94.65
98.71
Brightness
94.59
94.53
1.56
99.48
Elastic transform
91.12
94.35
2.70
99.09
Contrast
94.15
94.64
1.56
99.50
Fog
94.34
94.67
1.26
99.53
Forst
92.42
98.79
Gaussian blur
94.40
94.69
1.14
99.58
Jpeg compression
89.75
94.52
3.37
98.95
Motion blur
92.44
94.38
2.89
99.14
Pixclate
93.08
94.42
2.28
99.24
Saturate
93.14
94.43
2.10
90.34
Spatter
93.66
94.60
1.98
99.35
Speckle noise
92.19
94.37
3.79
98.55
F Ablations on Mixing Rate A
In the mixed sampling strategy, samples are selected using a combination of the top-k and near-boundary sampling methods. We introduce a mixing rate À to determine the composition the selected samples, where 0 < << Specifically, samples are chosen from Swild- This set consists of k samples from the kj top-k method and k samples from the near-boundary sampling, where k k ky and ty In Table we perform ablation how À affects the performance. We observe that higher generally results
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Table 8: Ablation results on different mixing rate X. The total labeling budget is k 500. We train on CIFAR-10 ID, using wild data with %e 0.5 (CIAR--1--C C) and T, 0.1 (Texture).
Mixing rate
OOD Acc.t
ID Acc.t
FPR.
AUROCT
A=0.1
87 .3
94.90
16.08
92.17
0=0.3
88.76
94.86
13.05
94.35
0=0.5
88.08
95.02
12.98
94.41
A=0.7
89.73
94.76
9.36
96.68
0=0.9
89.80
94.70
97.91
in stronger performance in both OOD gencralization and OOD detection. The observation aligns with our expectations and is supported by the detailed quantitative analysis presented in Section 4.3
G Hyperparameter Analysis
In Table we present the performance OOD generalization and detection by varying hyperparameter a, which balances the weight. between two loss terms. We observe that the generalization performance remains competitive and insensitive across wide range of a values. Additionally, our method demonstrates enhanced OOD detection performance when a relatively larger value of is employed in this scenario.
Table 9: Ablation study on the effect of loss weight a. The sampling strategy top-k sampling, with a budget of 1000. We train on CIFAR-10 as ID, using wild data with Te 0.5 (CIFAR-10-C) and nT 0.1 (Texture).
Balancing weights
OOD Acc.
ID Acc.
FPR.
AUROC1
1.0
90.76
94.49
5.29
98.33
a=3.0
90.61
94.43
5.35
98.19
a=5.0
90.52
94.41
5.29
98.16
a=7.0
90.51
94.35
5.41
98,15
a=9.0
90.41
94.33
5.11
98.24
10.0
90.31
94.33
4.91
98.28
H Application to Foundation Models
OOD learning, especially OOD generalization remains a significant challenge even for powerful foundation models like CLIP (Radford et al. 2021), despite their large-scale pretraining. While these models demon- strate impressive zero-shot recognition, they not inherently robust to all types of OOD shifts. Recent studics (Zhou et al.) 2022c b) have shown that CLIP can still struggle with domain shifts (e.g., changes in lighting, lexture, or style) and semantic shifts (e.g., entirely novel categories outside its training distribu- tion). Moreover, spurious correlations learned during large-scale training can degrade performance when encountering unseen real-world variations.
Unlike lask-specific models like Wide ResNet trained CIFAR-10, foundation models are deployed in highly open-ended environments, where the distribution of encountered data is constantly evolving. This makes selective human feedback and adaptive learning strategies, like those proposed in our framework, crucial for improving reliability. Our method can be integrated with CLIP or other foundation models by identifying and adapting to OOD) instances dynamically, ensuring that even large-scale models remain robust and trustworthy in real-world deployments, e.g., biomedical assisting systems for question answering and image analysis. Thus, OOD generalization is still critical research problem, even for state-of the-art vision foundation models.
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Notations, Definitions, and Assumptions
Here we summarize important notations in Table I0 restate necessary definitions and assumptions in Sections
and
L33
1.1
Notations
Please see Table 10
for detailed notations.
Table 10: Main notations and their descriptions.
Notation
Description
Spaces
X, y W. θ
the input space and the label space.
the hypothesis spaces
Distributions
Pwild, Pin poovariate IP semantic P Px
data distribution for wild data, labeled ID data.
data distribution for covariatc-shifted OOD data.
data distribution for semantic-shilted OOD data.
the joint data distribution for ID data.
Data and Models
w, x, V V Sin, Swild Spelected St selected Selected fw and Jo
top-1 right singular vector of G
the average gradients labeled ID data, uncertainty labeled ID data and unlabeled wild data selected data
semantic and covariate OOD in the selected data Sselected predictor on labeled in-distribution and binary predictor for OOD detection label for ID classification
y Vx
Predicted one-hot label for input x size of gin size of Swild, labeling budget Distances
n, m.
dwaw(s))
WAW distance.
and T2 ll2
the radius of the hypothesis spaces W and O, respectively & norm
Loss, Risk and Predictor
:(::))
ID loss function
Rging "omn,tttecee Statecsad (g0)
the overall empirical risk that classifies ID and detects semantic OOD the overall empirical risk that classifies covariate OOD and ID the empirical risk w.r.t. predictor fw over data Sin the empirical risk w..t. predictor fw over covariate OOD St in-distribution accuracy.
Rsin, Ietocted
(fw)
Rig (fw)
Rs (fw)
selected
AD-Acc
OOD-Acc FPR
out-of-distribution accuracy.
OOD detection performance.
Additional Notations in Theory
Wins We
the weight coefficients for ID empirical risk, and covariate OOD empirical risk.
M = 3 + biri + B
the upper bound of loss (xh, y), see Proposition 3
d
VC dimension of the hypothesis space W
1.2 Definitions
Definition 2 (3-smooth). We say a loss function E(fw y) (defined over X D) B-smooth, if for any x X and y V, Ve(f[(x),)) Ve(sw(x) w) & B|[w w'll2
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Definition 3 (WAW-distance (Ben-David et al. 2010)). For two distribulion Pi and F2 over o domain X' and hypothessi class W, the W&W W&W-ddistonee between P1 and P2 w.r.t. W is defined as
P2)
sup Ex-r, (x((x) # fw(( Ex-r, # [w)(
(9)
w.W'WW
Definition 4 seradient-basedd Distribution Discrepancy). Given distributions P and Q defined over N, the Grudient-basel Distribution Discrepancy w.r.t. predictor fw and loss
(P, Q) [V VRe(Sw
(10)
where f a classifier which returns the closest one-hot vector of Swo Ry(fw: Exwpl(fw. f) and Ra(fw, f) = Exnge(fw:F)
1.3 Assumptions
Assumption 1.
The parameter space W C rz) C Rd (l2 ball of radius rı around wo); (fw(x), y) 2 0 and ((f (x), y) is -m-smooth where E(.,)) is the ID loss function;
suP(x,))xxx [[ (x), v) la b1, suP(x,))xxx) ((fw (x), B1.
Remark 1. For neural networks with smooth activation functions and soft max output function, we can check
that the norm of the second derivative of the loss functions (cross-entropp loss and sigmoid loss) is bounded given the bounded parameter space, which implies that the f-smoothness of the loss functions can hold true. Therefore, assumptions reasonable in practice.
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J Main Theorem
In this section, we provide a detailed and formal version of our main thcorems with a complete description of the constant terms and other additional details that are omitted in the main paper.
Theorem 2. Let W be hypolhesss space with VC-dimension of d. Denole the dalasels 8 and seelected the labeled in-distribution and the selected covariate OOD data by human feedback, and their sizes are nt and me, respectively. If W E W minimizes the empirical risk Rs: Rs (Fw) of the multi-class classifier for sebaate classifying the covariale OOD, and w arg wiw Resonvrstt (sw), then for any (0, 1), with probability of at least. 8, we have
2d lollo((2))) (21gm)mmm) + log 2 3 7) 2C,
Rpeenarete (fr) S Rp Rpproorrsst (fw:) ) + in sup dew (8 S Stleected) 2wmn(2 weW
out
me
(dlos (2n (2n+ log(6) + WinMM and y min { Rp (fw) + RE (fw)}. M is the upper bound of the loss functiion for the malli--lass classifier
where S
m
sup sup {(fw(x), M. wEW (X
(11)
Wins We are two weight coefficients such that
RI Peororiat (fw) Win (fw) + We Raoveian (fw)
(12)
Multi-class classifier
and d'w (S S Sitecttdd) is calculated as follows:
(S
S Siceected) = |/ Rf - V Vs sasee (fw: Flll..
where f is classifier which returns the closest one-hot vector representation for the probabilistic prediction of fw, i.e., (f: f) Ex-ssnlff... f) and Rs: ( f) Ex-St Saaeeed Elfw: F). Note that our theoretical analysis primarily focases the OOD generalization error of specific set of covariate data, which is associated with the set S selected. For simplicity, we will continue to use the notation poovariate.
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K Proof of the Main Theorem
In this section, we present the proof of our main Theorem 2 Before we dive into the proof details, we first clarify the analysis framework and the analysis target in our proof techniques.
Specifically, we consider the empirical error of the robust classification of samples from S and covariate OOD 8h selected the following weighted combination:
Rgin, S: solected (fw) wi Rg (fw) + wss selected (fw).
(13)
Multi-class classifier
Let Rr. (fw) represents the error of fw the in distribution (ID) data Pin; and Reeevariaee (fw) denotes the error of fw on the covariate OOD data Fout can define the true risk over the data distributions the same way:
peovariate Win and We denote the weight coefficients. Similarly, we
R peovariuse (Jw) = win Re (Sw) + we Rpsovarinte (Sw).
(14)
Multi-class classifier
Step 1. First, we prove that for any (0,1) and W, with probability of at least 6, have
with +
wā ) me
dlog (2n + 2me) log(6),
P( Rp in out
provariate (fw) - Rsin Sheered (fw)) R S
(15)
2
where n, me are the sizes of datasets S S selected
We first apply Theorem 3.2 of (Kifer et al. 2004) as restated in Lemma
g to get the following equation,
-2R
R
provariate (fw) Rg S selected (fw)l R S (2n + 2m exp( out
2 where d is the VC dimension of the hypothesis space W. Given & E (0, we set the upper bound of the inequality to 8, and solve for R:
wa
m.
-2R
(2n + 2m.) exp(
wim
We rewrite the inequality
5
2R /(
(2n + 2m
laking the logarithm of both sides, we get
log (2n + 2m
8
-2R2
2 +
w
me
Rearranging the equation, we then get
R²
win +
w2 )(
dl dlog (2n 2m.) log(0)
me
Therefore, with the probability of at least - 6, we have
w /
wa
d dog (2n + 2m.) log(E)
Re Rowarrii (fw) Rg Se Seteccted (fw)) S
(16)
7
me
2
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Step 2. Based on Equation 16
now prove Theorem 2
For the true error of hypothesis w on the covariate
OOD data Rgeavariate (fw); applying Lemma 7 we get
Equation
16 and suppose w = arg minwew Ryeavariate (fw
out
1
2d log + log 2 + +2)
Recovariate (f S Rs
Peovariate (fx) + win dwaw(S Scclected) +
out
out
me
W
dlog (2n + 2me) - log(d)
< Rgn S ianneed (fz) +
in
11
Me
2
2d Edlog(2n)) (2mm) + log 3
+ Win +win
S selected) + +2V
+ +7)
me
2
w
d doo (2n + 2m.) - log(d)
< R5m Satatted (fw-)+ +/
in
+
me
2
2d (dlog(2m)) (2m.) + log 2/2
+ winl dwaw(s S Selectoa) + 2
7))
me
w
w2
dlog (2n + 2mc) log(d)
< R provertate (fw-) + +2 out
me
2
2d lollo((mm) + log
2
+ Win ( ddwaw(S Spelectea) + +2V
+ 7)
mc
2 S Rporariaca (fw-) + +
Win
w
d log (2n 2mc) - log(d)
n
me
2
1 (dwaa((S Se -Selected) + 2
2d (lgg) + log
2win (
+ 7)
me
Reoovariato (Sw:) + 2win ( 1 (dwaaw(Sh Sc Selected) + +2
2d 2d (2me) log 2 + +7) + 2C1,
me
with probability of at least 1 1-5, where Si ( + m. (
w2
dlog (2n+ log(()) and min Repovoriate (fw) + hew
2
out
Re.. (Jw)
Step 3. In this step, we aim to obtain the upper bound of the term dwaw(S S Scllected) To begin with, recall we have the following definition:
dw Stelected)
sup w.w'EW
Ex [Jw()][(())))))) # Sw Ex Si (lw(x) Sw (x)]]-
(17)
Therefore, it is easy to check that
dSaw(( Se Selected) sup wEW
Rg (fw) V Rgu (Sw: + VRgi(Jww.) Rosseeee (fw)
-RR f) + VRS. Rigittenn (fws
sup Rs (fw) - RRs (fw) + sup WEW
VR (fw: f) V Rse insteee (fwsF)) (18)
weW
sup RRg (Sw)] + sup Rise weW
Schoctod (Sw) + 2 sup &f (Sin ge (selected)
weW
weW
< sup d S (tllectdd) + 2M, wEW
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where is classifier which returns the closest one-hot vector of fw: Rg (fw. Ex [x f) and RSs (Sw. f) Ex [(fw: f).
The last inequality holds because of Proposition 3 and the definition of the Gradient-basse Distribution Discrepancy in Definition Therefore, we prove that:
2d log(2me) log 2/2
Recoratiate (f/) I Recovaziate (fw-) ) 2uin sup (5 Se Selected + 2w0in (4) ous
+7)+ + 2win M.
wEW
me
(19)
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L
Necessary Lemmas, and Propositions
L.1
Boundedness
Proposition 3. Assumption holds,
(V((/((x) 3in + + = /M122
sup sup wEW (xx))xxx
(x)w(x)) S 3ir + bin + B1 M,
sup sup (x.
Proof. One can prove this by Mean Value Theorem of Integrals casily.
Proposition 4. If Assumption I holds, for any w E W,
Ve( w)12 (81((f((x))))
Proof. The details of the self-bounding property can be found in Appendix B of LLe & Ying 2021
Proposition 5. If Assumption holds, for any labeled data S and distribution IP, [Rs(Sw))) ) 11 s 28, Rs(sw), E [p 1 23, Rp(Sw, V.EW.
Proof. Jensen's inequality implies that Rs(sw) and Rr(sw) are 81-smooth. Then Proposition implies the results.
L.2 Necessary Lemmas for Theorem
Lemma (Theorem 3.4 in Kifer al. 2004)). Let A be a collection of subsets of some domain measure space, and assume that the VC-dimension is some finite d. Let Pi and P2 be probability distributions over that domain and S1, S2 finite samples of sizes m1, m2 drawn according to P1. Pa with certain selection criteria respectively. Then
Pmi+mell MattmelloA(SA (S,, -A(P,, RJ ee- mp R2/16 /16 +
m22/0100 R2/16
where Pmitm2 is the ml + m2'th power of P, the probability that P induces over the choice of samples.
This theorem bounds the probability for the relativized discrepancy, and will help bounds the quantified distribution shifts between domains in our Theorem 2
Lemma 7. Let W be hypothesis space with VC-dimension of d. Denote the datasets Sin and Sc Selected the labeled in-distribution and the selected covariate OOD data, and their sizes are and me, respectively. Then for any 8 E (0, 1), for every w E W minimizing Rg Sinnte (Sw) on datasets Sin Se Schected we have
1 R provarlace (Jw)= R Rprovartace (Sw)ll S win dwww St Selectedd + +4 out
2d (2mm) + log 8 + +7),
(20)
Hur out
me
where 7 win Re,,, (Sw) H Rpeaaariate (Jw)). dwaww(Si Se (etected)) is defined according to Definition
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Proof. First, prove that given datasets Sth , selected from two distributions Pin and Pontariae, we have out
2d log (2mg))m log
dwaw(Pin: Ponvariate)
S dwww((Sh Sc selectea) + +4V
(21)
me
We start with Theorem 3.4 Kifer et al. 2004), which is restated in Lemma
Pa Pa ( (S S Selected) ( in, penvariate)
Put
( R S (2n) alt /16 + (2me) m. n//f//16, "
(22)
In this equation, d is the VC-dimension of collection of subsets of some domain measure space A, while in our case, d is the VC-dimension of hypothesis space W. Following [en David et al. (2010), the VC-dimension of WAW is at most twice the VC-dimension of W, and the VC-dimension of our domain mcasure space is thus 2d.
Given 5 E (0,1), 1), we can set the upper bound of the inequality to 6, and solve for R:
(2n)ad 2d ~nR + (2mx)aa )dd R2/6/16
(23)
Let me; we can rewrite the inequality as:
ne2//16 /16,
+ E 2/16
(24)
(2m,) 2d
taking the logarithm of both sides, we get
2²
(1+1 (a-
log
(2m
2d
n
16
+
log
(25)
rearranging the equation and defining a
R I6.
we then get
8
log
= -maa + log
(26)
(2m
which implies
maa + log(6/2) 2d (ollog22)
(27)
Therefore, we have
2d log (2m)) log 3
4= -
11
(28)
Mc
With probability of least 1- 8, we have
2d + log
( Se Solecctaa)
- dh out
peovariste ) <
(29)
me
therefore,
2d logoog22 (og((m.) + log
dwaw
peovariatey Pont
S dwaw(8" Sc Sellected) + 1
(30)
mc
Now in order to prove Lemma
we triangle inequality for classification error in the derivation.
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For the true risk of hypothesis fw on the covariate OOD data Re (fw), given the definition of peavariate (fw):
P out
Rp
provariaze (fw) - Rp Aprorartta (fw)ll Who Rp,, (fw) + We Rpenvariaae (fw) R Reoowsitaee (fw)l
out
S win Rpm. (Jw) Rpennartaaso (fw)l
Win ( RF (fw) Re (fw: Sw- + |R (Fw: Sw-) - R
Recoruciate (fw fw } out
Resuruiss (Swr Sw: Reporariano (fw))
win (R (fw-) ) + [R (Swr Sw Reconaiioe (Sws Sw. )1 + Recovariate (Swr
S win (7 + PP (ww:Sw) - Pepcovariated (Sw, Sw-)));
where 7 minnew (fw) Rpcoraaan (fw)} and sw- classifier that parameterized with the optimal hypothesis fw Pin. And we also have
Re (fw, fw-) = Exwellfwwll fw- (x)]x)]]-
(31)
By the definition of WAW-distance and our proved Equation 30
Ry (w.)wwww) R Reperatiore (fws fw )1l
sup w.w'EW
Ren, (Swr Swi) R Rpcoracione (fwi swi)l
Px PawPia Us + sw- (x)] P Peoperaatatt [S [w(x) # sw (x)) out
sup w.w'EW
ddwaw(Pmm in.
provariate out
2dlog(2m.) + log
2 dwaw(( SSelected) + +2
me
Therefore, we can get
R
penvartate (fw) Reporontae
(fw)) S win + [Re,, (fw, fw-) Rpeovariata (fw, fw: )l
out
aut
I win (r + ddwa ppcovariatey
2d log (2gm) + log 3
I Winl dwawwsin
S Stolocted) + =2
+ +2),
me
with probability of at least - 6, where 7 = min + Reeoraciate (fw)). This completes the proof. oul
Lemma 8. Under the same conditions as Lemma if the empirical risk is denoted as Rg Se Seterged (fw) (as defined in Equation 13). then for any 5 E (0 and w E W, with the probability of at least 0, we have
22R2
R provariato (fw) - Rgg Se Seteected (fw)l R S exp W
(32)
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Proof. We apply Hoeffding's Inequality in our proof. Specifically, denote the true labeling function fw: we have that
P(
Win [xi( (xi) + Σ
We [f((x;) - fm (x,)]]] (win Ex - fw (x)] + we WeBBoreefwe (x))))) fw fw(())]] 2 R)
71
me
2m0
1
2R²
$ 22exp( > (b: a;)²
(33)
where Him (xx)) (x:)] E [0, [im] and de [x,) fw (X;)1 [0, [
me
Considering the weighted empirical error, we get
Rg S Sintecedd (Sw) Win Rggn (fw) we Rs= Rsyncced (Sw)
me
Win [fw - fwo(x)) n
We
(x;) fw(xx))
Mc
which corresponds to the first part of Hoellding's Inequality.
Due to the lincarity of expectations, we can calculate the sum of expectations as
Win 1xw.r,,,, [x)] we (x) fx win Ri (fw) + We R Rpcovarttto (sw) R P poweariate (fw), out
which corresponds the second part of Hoeffding's Inequality. Therefore, we can apply Hoeffding's Inequal- ity as
22R
R nn provaciate (Sw) - Rgnn Selecttd (Sw)l 2 R] < 2 2exp(
Win + w2
mc
M Verification of Main Theorem
Optimal Loss for Covariate OOD. For training the model, utilized 50,000 covariate OOD data samples. The optimal loss for covariate OOD data, denoted Reeveriave (fw), was evaluated using the CIFAR-10 versus CIFAR-10-C datasets (with Gaussian noise). The results indicated an optimal loss of 0.2383 on the test set, with a corresponding OOD test accuracy of 92.79%. This small optimal loss for covariate OOD data contributes to a tighter upper bound.
out
Optimal Loss for In-Distribution (ID) Data. The training involved 50,000 ID data samples to deter- mine the optimal loss for ID data, represented as Rr., (fw). the CIFAR-10 context, the optimal loss on the test set for ID data was recorded as 0.1792, while the corresponding ID accuracy on test data reached 93.13% The minimal nature of the optimal loss for ID data is consistent with expectations and results in a tighter upper bound.
Gradient Discrepancy. The gradient discrepancy for the ID CIFAR-10, Covariate OOD CIFAR-10- C (Gaussian noise), and Semantic OOD Textures dataset was found be 0.00035. This small gradient discrepancy suggests tighter upper bound.
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Dataset
Gradient Discrepancy. OOD Acc.
CIFAR-10-C (Gaussian noise)
0.00035
90.37
CIFAR-10-C (Shot noise)
0.00030
82.04
CIFAR-10-C (Glass blur)
0.000400
92.41
Table 11: Empirical verification of gradient discrepancy in Theorem
Gradient Discrepancy Versus Covariate OOD Accuracy Across Different Datasets. Table 11
offers a comparative analysis, empirically validating the gradient discrepancy among various datasets. The results show a correlation between gradient discrepancy and OOD accuracy.
N Impact Statements and Limitations
Broader Impact. Our research aims to raise both research and societal awareness regarding the critical challenges posed by OOD detection and gencralization in real-world contexts. On practical level, our study has the potential yield direct benefits and societal impacts by ensuring the safety and robustness of deploying classification models in dynamic environments. This particularly valuable in scenarios where practitioners have access to unlabeled datasets and need to discern the most relevant portions for safety- critical applications, such as autonomous driving and healthcare data analysis. From a theoretical standpoint, our ana lysis contributes to deeper understanding leveraging unlabeled wild data by using gradient-based scoring for selecting the most informative samples for human foodback. In Appendix M we properly verify the necessary conditions of our bound using real-world datasets. Hence, we believe our theoretical framework has broad utility and significance.
Limitations. Our proposed algorithm aims to improve both inttof-distribution detection and generalization results by leveraging unlabeled data. It still requires a small amount of human annotalions and an additional gradient- based scoring procedure for deployment in the wild. Therefore, extending our framework to further reduce the annotation and training costs is a promising next step.
O Software and Hardware
We run all experiments with Python 3.8.5 and Py 1.13.1, using NVIDIA GeForce RTX 2080 Ti GPUs.
35


Reviews:
[{"review_id": "8XO4hXK6EX", "reviewer": "Reviewer_Gme9", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n1. The idea of measuring *informativeness* with the norm of coefficients w.r.t the major principal components of the gradient matrix is intriguing.  It follows the similar idea as PCA, where the major principal components maximally explains the data distribution, which is the loss gradients in this paper.  The loss is calculated with pseudo labels, and thus, is equivalent to \"measurement of confidence\".\n2. The experiment results support the proposition of the paper, showing better OOD generalization and OOD detection performance.\n3. The paper is well written and easy to follow\n\n---\n\nWeaknesses:\n\n1. The problem formulation of incremental annotation is similar to the idea of active learning.  However, the paper does not discuss clearly in the introduction/method section.\n2. The statement of \"Previous works on OOD learning often rely heavily on statistical approaches or predefined assumptions\nabout OOD data distributions, which may not accurately reflect the complexity and diversity of real-world\nscenarios.\" is not supported by any reference.\n3. In Eqn 4, why does the gradient matrix $G$ of the wild data subtracts with the average gradient of the in-distribution data?\n4. In table 1, the OOD Acc. metric does not distinguish semantic and covariate OOD. It's difficult to understand where does the performance gain come from.\n5. The experiments are conducted only on Wide ResNet architecture pre-trained on Cifar-10.  However, there're already performance vision foundation models, e.g. CLIP.  Is the OOD generalization still a research problem in those fantastic foundation models, which are trained on extremely large-scale datasets?", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposes to tackle out-of-distribution (OOD) learning with human feed-back.  Under a limited annotation budget, the proposed method increasingly annotates unlabeled wild data, aiming to address the challenges of OOD generalization and OOD detection.  The core idea is to sample the most informative wild data in each annotation stage, given the current knowledge of labeled data.  The informativeness is measured as the norm of coefficients w.r.t the major principal components of the gradient matrix.  The experiment demonstrates superior OOD classification and OOD detection performance against other strong baselines.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. Please include discussion of active learning in the introduction/method section\n2. Please add the reference according to Weakness 2.\n3. Please address my concern of Weakness 3.\n4. Please distinguish covariate and semantic OOD in the evaluation metric.\n5. Please add discussion about OOD generalization and foundation models.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "Xet5ue0qLs", "reviewer": "Reviewer_FhLH", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "## Strengths\n* The paper is well-written and easy to understand.\n* The experiments are comprehensive, including OOD detection, OOD generalization, and in-depth analysis.\n * The proposed algorithm shows significant improvement over previous methods.\n\n## Weaknesses\n### Major\n* I am confused with the term “human feedback”. It feels like the authors are using some reinforcement learning techniques. For example, given an input, the model generates some output, receive human feedback, and improve itself.  I think this work is more aligned with active learning. It involves selecting a set of informative unlabelled samples, asking humans to label these samples, and retraining / fine-tuning the model. These fields may share similar ideas, so I hope the authors could clarify this.\n* I am not familiar with OOD learning with in-the-wild data, such as Woods and Scone. I am wondering if these previous works use extra labels from humans in wild data to train their model, or if they just use the unlabelled wild data. If the authors collect extra labels from humans but they do not, are Tables 1 & 2 showing fair comparison?\n* How do the authors decide $\\pi_c$ and $\\pi_s$, the mixture ratios of covariate and semantic OOD data in unlabelled wild data? Will these two ratios have large effect on method performance? I notice that the authors fixed them in the experiments, $\\pi_c=0.5$ and $\\pi_s=0.1$. Could the authors clarify this? \n\n### Minor\n* The citation styles need to be improved. For instance, in Page 9, “Impact of different sampling scores.”. The authors use textual citations (\\citet) but these should be parenthetical citations (\\citep). While in Related Works, some sentences like “The work of (Das et al., 2023; …” The authors use parenthetical citations but there should be textual citations.\n* I’m curious about the effect of the top singular vector of gradient matrix. Is it not good if the authors simply calculate the distance between gradient of one sample and the average gradient, or use the average of more singular vectors?\n* After receiving human feedback, do the algorithm use the remaining unlabelled wild data or throw them away? Is it better to utilize the remaining data with some loss functions?", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The authors introduce a framework for OOD learning with human feedback.\n* Following a previous work, they assume that we have access to labelled ID data and unlabelled wild data. The wild data is a mixture of ID, covariate OOD, and semantic OOD data.\n* The proposed framework employs a gradient-based sample selection mechanism, which selects a small number of informative samples from the wild data distribution. \n* The selected samples will be labelled by humans and then used to train a robust ID classifier and an OOD detector.\n\nThe authors also provide theoretical insights on the generalization error bounds to justify their algorithm. The proposed method outperforms previous ones in experiments.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please see the major weaknesses.", "broader_impact_concerns": "The paper tackles significant challenges in OOD detection and generalization with wild data, which are relevance to many applications. There are no concerns regarding ethical implications.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "YWqqMomYo8", "reviewer": "Reviewer_vUE7", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n- The paper proposes an interesting idea to leverage large unlabeled datasets via only a few human labeled samples. \n- The algorithm outperforms previous methods in the designed experiments.\n- The flow of the paper is smooth, and the claims are clear.\n\nWeaknesses:\n- Technical details should be correct and accurate. For example, in Equation (4), the dimension of matrix G seems to be $\\text{dim}(w)m\\times 1$, which contradicts with the fact that its singular vector should has dimension $\\text{dim}(w)$ (from Equation (5)). I believe the dimension of $G$ should be $\\text{dim}\\times m$, and its definition should be changed accordingly. Another example is from Theorem 1, where $\\hat{f}$ is not clearly defined. Maybe I'm missing something here, but it's not clear to me now what \"the closest one-hot vector of $f_w$\" means.\n- More explanation about the theoretical results should be provided. Currently, it seems the term $d_w^l$ doesn't decay as the sample size grows. If so, explanation on how large this term will be helpful, e.g. calculate the term using basis distributions including gaussians.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposes a novel framework for classification tasks with out-of-distribution (OOD) samples (both semantic and covariate). The algorithm learns to cope with the OOD samples with relatively few human labels and a large unlabeled dataset. Superiority of the algorithm is demonstrated via sound empirical experiments and partial theoretical analysis.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "The authors should address the above weaknesses, which are critical for acceptance.", "broader_impact_concerns": "Nnone of those are considered as necessary to be specifically highlighted here.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper received mixed reviews, with most reviewers acknowledging its strengths in tackling OOD learning through a structured human feedback mechanism. 

The primary points of contention revolved around:
- The terminology of “human feedback” and its distinction from traditional active learning approaches.
- The need for clearer explanations regarding key theoretical claims, particularly in Appendix C.
- The evaluation methodology, including how OOD accuracy is measured and the applicability of the method to large-scale foundation models.

While one reviewer leaned toward rejection due to concerns over novelty and methodological clarity, others recommended acceptance with minor revisions. Given the overall positive recommendation and the authors’ willingness to address these concerns, a minor revision is recommended. 

The authors should focus on:
- More explicitly distinguishing their method from active learning in the introduction and related work sections.
- Providing additional theoretical clarifications in Appendix C.
- Addressing specific concerns regarding metric definitions and evaluation fairness.
With these revisions, the paper would be a valuable contribution to the TMLR community.
Decision: Accept (poster)