Scalable Ensemble Diversification for OOD Generalization and Detection

Venue: NeurIPS_cc_2024_Conference
Published: 2024-05-01 12:52:13

Abstract: Training a diverse ensemble of models has several practical application scenarios, such as model selection for out-of-distribution (OOD) generalization and the detection of OOD samples via Bayesian principles. Previous approaches to diverse ensemble training have relied on the framework of letting the models make the correct predictions for the given in-distribution (ID) data while letting them come up with different hypotheses for the OOD data. As such, they require well-separated ID and OOD datasets to ensure a performant and diverse ensemble and have only been verified in smaller-scale lab environments where such a separation is readily available. In this work, we propose a framework, Scalable Ensemble Diversification (SED), for scaling up existing diversification methods to large-scale datasets and tasks (e.g. ImageNet), where the ID-OOD separation may not be available. SED automatically identifies OOD samples within the large-scale ID dataset on the fly and encourages the ensemble to make diverse hypotheses on them. To make SED more suitable for large-scale applications, we propose an algorithm to speed up the expensive pairwise disagreement computation. We verify the resulting diversification of the ensemble on ImageNet and demonstrate the benefit of diversification on the OOD generalization and OOD detection tasks. In particular, for OOD detection, we propose a novel uncertainty score estimator based on the diversity of ensemble hypotheses, which lets SED surpass all the considered baselines in OOD detection task. Code will be available soon.

Main paper: 
 introduction: 
 Training a diverse ensemble of models is useful in multiple applications. Diverse ensembles are used to enhance out-of-distribution (OOD) generalization, where strong spurious features learned from the in-distribution (ID) training data hinder generalization [30, 31, 28, 23] . By learning multiple hypotheses, the ensemble is given a chance to learn causal features that are otherwise overshadowed by the prominent spurious features [39, 4] . In Bayesian machine learning, diversification of the posterior samples has been studied as a means to improve the precision and efficiency of sample uncertainty estimates [5, 37] .A common strategy to train a diverse ensemble is to introduce two objectives: one for the main task and one for diversification [29, 5, 28, 23] . The main task loss, such as the cross-entropy loss for classification, encourages the hypotheses to solve the task on the labeled ID training set. The diversification loss encourages the hypotheses to diversify the responses on an unlabelled OOD dataset [28, 23] (Figure 1 ). The datasets for the objectives are separated to avoid contradictory objectives: prediction diversification on the ID set will encourage wrong answers if there is only one correct label.Submitted to 38th Conference on Neural Information Processing Systems (NeurIPS 2024). Do not distribute. This strategy, however, requires a separate OOD dataset where the hypotheses may make diverse predictions without harming the main task performance on the ID training samples. Previous work has thus been tested on hypothetical lab settings where the spurious and causal features can easily be controlled to secure separate ID and OOD datasets for diverse ensemble training. It is not clear yet how one could diversify an ensemble of models for realistic, uncontrolled, and large-scale applications (e.g. ImageNet scale) where collecting a separate OOD dataset can be very costly, if not impossible.Existing work assumes existence of ID and OOD datasets. To address the scalability challenge, we propose a novel diversification framework, Scalable Ensemble Diversification (SED, Figure 1 ). We intro- this work, we focus on scaling up the Agree to Disagree (A2D) method [28] .We verify that SEDdiversifies a model ensemble trained on ImageNet. We demonstrate the benefit of diversification on OOD generalization and OOD detection tasks. For the former, we showcase the usage of SED-diversified ensemble in three variants:(a) vanilla ensemble of prediction probabilities [22] , (b) an average of the model weights through model soup [38] , and (c) the oracle selection of the individual models for each OOD test set [23, 30] .In all three cases, SEDachieves a superior generalization to OOD datasets like ImageNet-A/R/C, OpenImages, and iNaturalist.For OOD detection, we seek multiple ways to use the SED-diversified ensemble: (a) treating them as samples of the Bayesian posterior and (b) using our novel OODness estimate of Predictive Diversity Score (PDS) that measures the diversity of predictions from an ensemble. We show that PDS provides a superior detection of OOD samples like ImageNet-A/R/C, OpenImages, and iNaturalist.Our contributions are 1. Scalable Ensemble Diversification (SED) framework that scales up existing ensemble methods;2. Predictive Diversity Score (PDS) that computes the OODness score for samples based on ensemble prediction diversity;3. First demonstration of the ensemble diversification and its application to OOD generalization and detection at ImageNet level.The code will be released with the next versions of the manuscript.Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?Answer: [Yes] Justification: Please refer to § 4Guidelines:• The answer NA means that the abstract and introduction do not include the claims made in the paper.• The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.• The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.• It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper. 
related work: 
 In this section, we give a short overview of ensembling methods. At first, we speak about ensembles in general and the role of diversity in them ( § 2.1), then we focus on ensembling methods for neural networks and separate them into two big groups. The first group includes algorithms that use loss regularizers ( § 2.2) and the second group covers works that do not modify the training loss ( § 2.3).Ensembling is a powerful technique of aggregating the outputs of multiple models to make more accurate predictions and it has been around for decades [12, 21, 18, 2, 3] . It is well known that diversity in ensemble members' outputs leads to better performance of the ensemble compared to the performance of a single model [21] because ensemble members make independent errors [12, 11] .Therefore, one way to reduce DNNs' reliance on spurious correlations is to train multiple models on the same task and make them diverse in terms of errors they make so that their ensemble is less dependent on such correlations.Diversity in models can be induced by supplying training loss with a suitable regularizer.Such regularizers can diversify models' weights [5, 7, 34, 6] , features [39, 4] , input gradients [29, 30, 31, 33] and outputs [25, 5, 28, 23] .Notably, in [5] authors showed that regularizer of a certain structure that repulses ensemble members' weights or outputs leads to ensembles that provide a better approximation of Bayesian Model Averaging. This idea was later extended by works that repulse ensemble members' features [39] and input gradients [33] .Since the ensemble performs better due to the diversity of errors that ensemble members make [21] we want those members to give pairwise different outputs for the same inputs. Unfortunately, diversity in weights space, input gradient space, or features space does not guarantee such property without additional assumptions due to functional symmetry which means that models can be different in terms of their weights or feature maps and input gradients they produce but still give the same outputs for a given input. That is why we are focused on methods that diversify models' outputs, specifically [28, 23] which are state-of-the-art according to [1] and use regularizer of repulsive nature conceptually similar to [5] .In addition to loss regularizers, there were an uncountable number of different ways to induce diversity in ensembles of neural networks that did not modify the training loss. The most straightforward approach of independently training multiple models of the same architecture by changing only random seeds is called Deep Ensemble [22] which was extended from the Bayesian perspective in [37] .Another solution is to construct an ensemble from models trained with different hyperparameters [36] ,augmentations [24] , or architectures [40] . More computationally efficient direction allows training only one base model inducing diversity by ensembling either checkpoints saved in different local minima along the training trajectory of this base model [19] or models produced by the base model after applying dropout [10] or masking [9] to it. The mixture of experts paradigm can also be viewed as an ensemble diversification technique [41] where diversification happens due to assigning different training samples to different ensemble members.Despite their conceptual simplicity Deep Ensembles [22] and ensembles of models trained with different hyperparameters [36] are strong baselines for OOD detection [27] and OOD generalization tasks, especially when combined with model souping techniques [38] . That is why we selected them as baselines for our experiments.Question: Does the paper discuss the limitations of the work performed by the authors?Answer: [Yes]Justification: Please refer to § 5Guidelines:• The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.• The authors are encouraged to create a separate "Limitations" section in their paper.• The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.• The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.• The authors should reflect on the factors that influence the performance of the approach.For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.• The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.• If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.• While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations. 
method: 
 We present our main technical contributions, Scalable Ensemble Diversification (SED, §3.2) and the Predictive Diversity Score (PDS, §3.3).We cover background materials before introducing our main technical contributions. We work with a training set D := {x n , y n } N n=1 , which we refer to as the in-distribution (ID) dataset. For prior diversification methods, we also assume the existence of a separate, unlabeled out-of-distribution (OOD) dataset D ood := {x ood n } N ood n=1 . We write f (•, θ) for a deep neural network classifier parametrized by θ. f (x; θ) ∈ R C indicates the logit outputs for C classes for input x. We write p(x) := Softmax(f (x)) ∈ [0, 1] C for the probability outputs. We consider an ensemble {f 1 , • • • , f M } of M models.We introduce an existing approach for diversifying an ensemble of models [28, 23] . Two objectives are imposed upon the ensemble of models: the main task loss and the diversification regularization.For the main task, the community has focused on the classification task. The cross-entropy lossEQUATIONThis encourages each member of the ensemble to behave similarly on the ID dataset.Different diversification schemes use different diversification regularization loss L div applied on pairs (f m , f l ) of ensemble members. The diversification objective is commonly optimized on the OOD dataset D ood to encourage the training of multiple hypotheses on the OOD samples while avoiding clashes with the main task objective. In this work, we focus on the Agree to Disagree [28] method.The diversification loss for a pair (p m , p l ) is defined as:EQUATIONwhere ŷ := arg max c p m c (x) is the predicted class for the first model p m . One may symmetrically define ŷ to be the prediction for the second model p l ; in practice, it does not make a difference [28] .Note that the diversification loss favors p l to predict a lower likelihood for the prediction by p m , p l ŷ (x), and vice versa. For M models in an ensemble, A2D is applied on the OOD dataset D ood for every pair of models (p m , p l ):EQUATIONWe present Scalable Ensemble Diversification (SED) that addresses the limitation of the existing ensemble diversification framework that requires a separate OOD dataset. We introduce two main components of SED: dynamic selection of OOD samples within the ID dataset ( §3.2.1) and the stochastic selection of pairs to diverge in the optimization iterations ( §3.2.2).If only the ID training dataset is present, it is difficult to induce diversity in ensemble members, as they are uniformly incentivized to solve the main task objective: given x, predict y. Hence, previous approaches have introduced a qualitatively disjoint unlabeled set, which we refer to as the OOD dataset, where the ensemble members are encouraged to disagree with each other. The clear separation of ID and OOD datasets for the two objectives matters for ensuring a good balance between the main task performance and the diversity of hypotheses.Previous works like Pagliardini et al. [28] , Lee et al. [23] have performed experiments on small-scale datasets where factors are well-controlled and clean versions of OOD datasets are readily available.Examples include Waterbirds, Camelyon17, CelebA, MultiNLI, C-MNIST, and the Office-Home datasets. For example, for Waterbirds, the ID dataset is set as the cases where the bird's habitat matches with the visual background and the OOD dataset corresponds to the complementary case.While conceptually desirable, collecting a separate OOD dataset can be highly cumbersome and expensive. For a large-scale dataset like ImageNet, it is highly non-obvious how one could build a corresponding OOD dataset where the underlying feature-label correlations are different from the ID training dataset.To address this challenge, we consider dynamically identifying an OOD subset of the ID dataset and letting the ensemble diverge on this subset. The desiderata for the identification of OOD samples within the ID dataset are twofold: (a) we wish to discriminate samples where the ensemble members make mistakes and (b) we only trust the ensemble prediction for the OOD sample identification when the ensemble is sufficiently trained.We define the sample-wise weight α n on each ID sample (x n , y n ) ∈ D that satisfy the two conditions:EQUATIONwhereCE(f 1 , • • • , f M ; x n , y n ) := CE( 1 M m f m (x n ), y n )is the loss on the logit-averaged prediction and B is a minibatch that contains the sample (x n , y n ). α n is a weight proportional to the ensemble loss on the sample; we thus meet the condition (a). The normalization is designed to handle the condition (b). To see this, consider the batch-wise weightEQUATION)Note that α B is now inversely proportional to the average cross-entropy loss of the ensemble on the batch B. Thus, the overall level of α n for n ∈ B is lower for earlier iterations of the ensemble training, where the predictions from the models are not trustworthy yet.With this definition of sample-wise weight α n for the diversification objective, we define the SED objective with the A2D loss for the diversification kernel:EQUATIONwhere λ > 0 controls the overall weight of the diversification term. Note that, compared to Equation 3, this formulation does not rely on the OOD dataset D ood . Instead, all ID samples are treated as potential OOD samples, where their OODness is softly determined via α n . This enables a seamless adaptation of existing ensemble diversification methods to a relaxed setting where a separate OOD dataset is unavailable. 6is an example of this. This is potentially a hurdle when ensemble diversification is to be applied to M ≥ 10, and the data and parameter sizes are in the order of millions (e.g. ImageNet).We address this computational challenge by computing the summation of pairwise distances as a stochastic sum. For every minibatch B of SGD iterations, we uniformly-iid sample a subset I of {1, • • • , M } to compute the diversification term in Equation 6. The procedure is illustrated in the figure on the right.To further speed up the SED training, we consider diversifying only a subset of layers, while freezing the other layers. In our experiments, ensemble members share the same frozen feature extractor of Deit3b [32] pretrained on ImageNet-21k [8] and we diversify only the last two layers of the models.We demonstrate several benefits of the diversified ensembles in §4. One of them is the possibility of using them for detecting OOD samples through the notion of epistemic uncertainty [13] . Given an ensemble of models, a simple baseline for OOD detection is to compute the predictive uncertainty of the Bayesian Model Averaging (BMA) by treating the ensemble members as samples of the posterior p(θ|D) [22, 37] :EQUATIONThis notion of epistemic uncertainty does not directly exploit the potential diversity in individual models of the ensemble because it averages out the predictions along the model index m.We propose a novel measure for epistemic uncertainty, Predictive Diversity Score (PDS), that directly measures the prediction diversity of the individual members. The formulation is given below:EQUATIONPDS is a continuous relaxation of the number of unique argmax predictions within an ensemble of models. To see this, consider the special case where p m ∈ {0, 1} are one-hot vectors. Then, max m p m c (x) is 1 if any of m predicts c and 0 otherwise. Thus, c max m p m c (x) computes the number of classes that at least one of the ensemble members predicts. We show that, with our diverse ensembles, PDS outperforms the DE baseline for the OOD detection task ( §4.4).Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?Answer: [NA]Answer: [Yes] Justification: Code will be available soon, please refer to § 4.1.Guidelines:• The answer NA means that paper does not include experiments requiring code.• Please see the NeurIPS code and data submission guidelines (https://nips.cc/ public/guides/CodeSubmissionPolicy) for more details.• While we encourage the release of code and data, we understand that this might not be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for a new open-source benchmark).• The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines (https://nips.cc/public/guides/CodeSubmissionPolicy) for more details.• The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.• The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only a subset of experiments are reproducible, they should state which ones are omitted from the script and why.• At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).• Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted. 
experiments: 
 We verify our contributions, Scalable Ensemble Diversification (SED, §3.2) and Predictive Diversity Score (PDS, §3.3), on ImageNet-scale tasks and datasets. We first verify that SED diversifies the ensemble ( §4.2). Then, we demonstrate the application of diversified ensemble to OOD generalization ( §4.3) and OOD detection ( §4.4) tasks.We task the ensemble with the OOD generalization and OOD detection tasks.Training settings. For both tasks, we train an ensemble of models with the SED framework with the A2D [28] diversity regularization using AdamW optimizer [26] . We use the default settings of a batch size of 16, learning rate 10 -3 , weight decay 0.01, and the number of epochs 10. The overall diversity weight λ is set to 0.1 and the stochastic pairing is done for |I| = 2 models for each SGD batch. We use Deit3b [32] network pretrained on ImageNet21k [8] for all the experiments. Following Baselines. For naive ensemble training, we consider the deep ensemble [22] where each ensemble member independently with different random seeds that control the weight initialization and SGD batch shuffling. To match the resource usage of our SED, where we diversify only the last 2 layers of the network, we consider the shallow ensemble variant, which is the deep ensemble where only the last 2 layers are trained. We further consider a viable diversification scheme that performs deep ensemble with varying hyperparameters [36] . In addition to that, we reimplement A2D [28] and DivDis [23] algorithms and apply them without stochastic model sampling to do classification on labeled samples from ImageNet-Train and disagreement on unlabeled samples from ImageNet-R.For A2D we use frozen feature extractor and a parallel variant of their method which means that all ensemble members are trained simultaneously and not sequentially. The computational complexity of both these approaches scales quadratically with ensemble size which is why they are called Naive classes). OpenImages-O (OI [35] , 17k images, unlabeled), and iNaturalist (iNat [20] , 10k images, unlabeled). For OOD detection, we task the ensemble with the detection of the above OOD datasets against the ImageNet validation split.Evaluation metrics. For OOD generalization, we use the accuracy. For OOD detection, we use the area under the ROC curve, following [15] . We start with the question of whether Scalable Ensemble Diversification (SED) truly diversify the ensemble at the ImageNet scale. To measure the diversity of the ensemble, we compute the number of unique predictions for each sample for the committee of models (#unique). The ensemble size M is 5 for all methods; it is the max possible #unique value.Table 1 shows Qualitative results on ImageNet-R further verify the ability of SED to diversify the ensemble (Fig-ure 2 ). As a measure for diversity, we use the Predictive Diversity Score (PDS) in §3.3. We observe that the samples inducing the highest diversity (high PDS scores) are indeed ambiguous: for the first image, where the "cowboy hat" is the ground truth category, we observe that "comic book" is also a valid label for the image style. On the other hand, samples with low PDS exhibit clearer image-to-category relationship.We examine the first application of diversified ensembles: OOD generalization. We hypothesize that the superior diversification ability verified in §4.2 leads to greater OOD generalization due to the consideration of more robust hypotheses that do not rely on obvious spurious correlations.Ensemble aggregation for OOD generalization. As a means to exploit such robust hypotheses, we consider 3 aggregation strategies. (1) Oracle selection: the best-performing individual model is chosen from an ensemble [28, 30] . Final prediction is given by f (x; θ m ⋆ ) where SED improves OOD generalization for ensembles. We show the OOD generalization performances of ensembles in Table 2 , for the three ensemble prediction aggregation strategies described above. We observe that our SED framework (SED-A2D) results in superior OOD generalization performances for all three strategies. SED-A2D is particularly strong in prediction ensemble (e.g. 48.1% for M = 5 and 54.4% for M = 50 on ImageNet-R) and uniform soup (e.g. 46.1% for M = 5 and 46.5% for M = 50 on ImageNet-R). We contend that the increased ensemble diversity contributes to the improvements in OOD generalization. We also remark that the SED framework (SED-A2D) envelops the performance of Naive A2D in this ImageNet-scale experiment. Together with the superiority of computational efficiency (as discussed at the end of § 4.4) of SED-A2D over the Naive A2D, this demonstrates that SED fulfills its purpose of scaling up ensemble diversification methods like A2D.Deep ensemble is a strong baseline. We also note that deep ensemble, particularly with diverse hyperparameters, provides a strong baseline, outperforming dedicated diversification methodologies under the oracle selection strategy when M = 5. It also provides a good balance between ID (ImageNet validation split) and OOD generalization. Impact of diversification parameter λ. We further study the impact of ensemble diversification on the OOD detection with the PDS estimator. In Figure 3 , we observe that strengthening the diversification objective (higher λ) indeed leads to greater diversity (higher PDS), with a jump at around λ ∈ [10 -1 , 10 1 ]. This range corresponds to the jump in the OOD detection performance (higher AUROC).  
conclusion: 
 Ensemble diversification has many implications for treating one of the ultimate goals of machine learning, handling out-of-distribution (OOD) samples. By training a large number of plausible hypotheses on an in-distribution (ID) dataset, an OOD-generalizable hypothesis may appear. Moreover, the diversity of hypotheses lets us distinguish ID samples from OOD samples by measuring the degree of divergence in ensemble members' predictions. Despite conceptual benefits, diverse-ensemble training has previously remained a lab-bound concept for several reasons. First, previous approaches required a separate OOD dataset that may nurture diverse hypotheses. Second, computational complexities of previous pairwise diversification objectives increase quadratically with the ensemble size.We have addressed the challenges through the novel Scalable Ensemble Diversification (SED) framework. SED identifies the OOD-like samples from a single dataset, bypassing the need to prepare a separate OOD dataset. SED also employs a stochastic pair selection algorithm which reduces the quadratic complexity of previous approaches to a constant cost per SGD iteration. We have demonstrated good performances by SED on the OOD generalization and detection tasks, both at the ImageNet scale, a largely underexplored regime in the ensemble diversification community.In particular, for OOD detection, our novel diversity measure of Predictive Diversity Score (PDS) amplifies the benefits of diverse ensembles for OOD detection. The code to reproduce the results of our experiments will provided with the next revision of the manuscript. 
experimental setting/details: 
 Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?Answer: [Yes] Justification: please refer to § 4.1.Guidelines:• The answer NA means that the paper does not include experiments.• The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them.• The full details can be provided either with the code, in appendix, or as supplemental material. 
experiment statistical significance: 
 Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?Answer: [No] Justification: Error bars are not reported because their magnitude was below the rounding error or roughly around it for the majority of experiments.Guidelines:• The answer NA means that the paper does not include experiments.• The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.• The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions).• The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)• The assumptions made should be given (e.g., Normally distributed errors).• It should be clear whether the error bar is the standard deviation or the standard error of the mean.• It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have a 96% CI, if the hypothesis of Normality of errors is not verified.• For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates).• If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text. 
experiments compute resources: 
 Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?Answer: [Yes] Justification: please refer to § 4.1.Guidelines:• The answer NA means that the paper does not include experiments.• The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.• The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.• The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make it into the paper). 
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 Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?Answer: [NA]Justification: We believe that our paper does not pose such risks as we train models for ImageNet classification.Guidelines:• The answer NA means that the paper poses no such risks.• Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.• Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.• We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.12. Licenses for existing assets Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?Answer: [No] Justification: we were unable to find the license for the dataset we used.Guidelines:• The answer NA means that the paper does not use existing assets.• The authors should cite the original paper that produced the code package or dataset.• The authors should state which version of the asset is used and, if possible, include a URL.• The name of the license (e.g., CC-BY 4.0) should be included for each asset.• For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.• If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset.• For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided. 
 
 Appendix: We do not provide theoretical justification for the method. Our experiments were conducted on models with a frozen feature extractor.NeurIPS Paper Checklist 


Decision: The submission proposes a method for diversifying ensembles for learning problems that rely on ensembles in their methodology. The submission and the rebuttal were carefully considered, and the AC asked for discussion among the reviewers given the ratings. In the end, the submission didn't generate excitement, and none of the reviewers gave a rating stronger than borderline. After the discussion, the consensus of the reviewers was not to support the submission for acceptance in its current form. Their comments during the discussion are copied below since they are not visible to the authors. A basis for acceptance could not be established. 

"I did not find the paper exciting. There is some consensus that the experiments were not comprehensive and the results were not convincing."

"I also did not find the idea to be exciting. I think the premise of diversifying on "OOD" examples within the ID data is interesting, but clearly leads to worse ID performance, so this does not seem very useful in practice. The contributions for speeding up the pairwise disagreement also seems incremental, since it is the exact same formula but sampled stochastically."

"I think the paper is technically solid (i.e. no big flaw) and has made some contribution, but I don't find it particularly interesting or exciting either, so I maintain borderline acceptance.

The main reason why this paper does not quite interest me is probably that it lacks in-depth analyses/discussion. It offers little insight into why the method works---specifically, why would diversifying models' predictions on hard training samples help OOD generalization? Overall, it seems the paper barely deepens our understanding of the subject, so I have reservations about the paper's impact. The authors acknowledged the issue in the rebuttal but the proposed changes are still somewhat vague and therefore insufficient to fully address the issue."

"the authors did a lot of work in the rebuttal to address this, although given the time frame, the new results were sometimes on limited setups. E.g., a main contribution was finding "an OOD subset in the ID dataset", however, simple heuristic augmentations can also introduce OOD examples in a much cheaper way than what they proposed, the authors added these new results in the rebuttal but understandably, on a small scale."

Reviews: review: paper_summary: paper_summary: The paper proposes Scalable Ensemble Diversification (SED) to extend existing diversification methods to large-scale datasets and tasks where ID-OOD separation may not be possible, and also propose Predictive Diversity Score (PDS) as a novel measure for epistemic uncertainty. Extensive analysis and experiments support the effectiveness of the proposed modules.
strength_weakness: strength_weakness: 1. Although the experiments are diverse, I am not sure if the comparison is comprehensive. Can more explanation and discussion be added?

2. The feature extractor used is frozen. Is the proposed method robust enough to different feature extractors? What will the performance be if the feature extractor is also involved in the training?
questions: questions: The proposed framework is interesting, but can it potentially be extended to improve a wide range of OOD tasks?
limitations: limitations: The authors have addressed the limitations.
paper_summary: paper_summary: Ensembles of diverse models have shown promising signs for out-of-distribution (OOD) generalization.
To boost diversity, some methods require a set of OOD examples for measuring the disagreement among models.
The desired OOD examples, however, can be difficult to obtain in practice.
This paper proposes to dynamically draw OOD samples from the training data during training.
This is done by assigning a higher OOD score to examples with a greater loss in each mini-batch.
To make the diversification process across multiple models more efficient, the authors propose a stochastic approach that only diversifies a small sample of models at each iteration.
The resulting diversified models give rise to the notion of a diversity score for uncertainty estimation and can be used for OOD detection.
strength_weakness: strength_weakness: - The notion of “OOD samples” in an ID dataset is confusing. The actual implementation, i.e. assigning a higher “OOD-ness” weight to training examples with a greater loss, is more like identifying “hard” training examples rather than just OOD samples. Calling them “OOD samples” somewhat obfuscate their nature. They are not arbitrary OOD samples but hard samples within the support of the ID dataset. It is not obvious why diversifying models’ predictions on such samples would help. Is such prediction diversification always conducive to OOD generalization? If not, when would the proposed method work or break? These relevant theoretical questions are not answered satisfactorily in the current manuscript.
- The connection between SED and PDS is weak; PDS is not well justified. The A2D diversification loss can also be seen as a measure for prediction diversity, like PDS. Why choose PDS instead for OOD detection? Furthermore, is PDS really a good measure for epistemic uncertainty? Imagine two cases. In the first case, two models confidently (with probability 1) predict the same class for an input example, while in the second case, the two models assign uniform probability to all classes for another example. The PDS for these two examples are exactly the same, yet the models are much less confident (or more uncertain) in the second case. Meanwhile, BMA does not have this issue.
- The baselines are relatively limited. There are many other diversification methods which do not require a separate OOD dataset [1, 2, 3]. How does the proposed method compare with these methods? Can the authors also comment on why BMS is the only considered baseline for OOD detection?
- The definition of #unique values is not very clear. Table 1 shows SED-A2D has extremely large #unique values. On C-1 dataset, the value is 5, the maximum possible value. If my understanding is correct, does this suggest that all the 5 models disagree with each other on every C-1 example? If so, this suggests that for many examples, 4 out of 5 models are probably wrong. Why is this more of a good sign than a bad one?

[1] Rame, Alexandre, et al. "Diverse weight averaging for out-of-distribution generalization." Advances in Neural Information Processing Systems 35 (2022): 10821-10836.  
[2] Chu, Xu, et al. "Dna: Domain generalization with diversified neural averaging." International conference on machine learning. PMLR, 2022.  
[3] Lin, Yong, et al. "Spurious feature diversification improves out-of-distribution generalization." arXiv preprint arXiv:2309.17230 (2023).
questions: questions: Please see the weaknesses.
limitations: limitations: The authors only briefly mentioned two limitations of the work. I don't notice any potential negative societal impact.
paper_summary: paper_summary: The paper aims to train a diverse ensemble of models via a framework called Scalable Ensemble Diversification. This framework does not require an additional dataset of OOD inputs, as it identifies OOD samples from a given ID dataset. It then encourages the ensemble to return diverse predictions (disagreement) on these OOD samples. Furthermore, the framework makes use of stochastic summation to speed up the disagreement computation. Results are shown for different tasks like generalisation, OOD detection on different OOD datasets.
strength_weakness: strength_weakness: 1. It is not clear why the method works, additional ablations studies would be useful.   
    - Naive A2D (and DivDis) uses IN-R data to compute the disagreement loss, which could give the method an advantage as it has access to the OOD data. However, it has a lower accuracy on IN-R. There seems to be two methodological differences between A2D and SED-A2D, the OOD data and use of stochastic sum. Given that A2D computes the full pairwise disagreement and stochastic sum is meant to reduce cost rather than improve performance, why does SED-A2D perform better? It would have been useful to compare two methods that only differs on the OOD data used. E.g., SED-A2D without the stochastic sum.   
    - From eqn 6, it looks like the two terms have contradicting objectives. For a “OOD” point, the first term encourages all models to classify the point correctly, but the second term encourages models to have different predictions on the same point. These objectives can be challenging to balance.   
2. The writing clearly explains the method or setup, but sometimes stops short of giving further insights. For example,  
    - Further analysis of experimental results   
        - Table 2 why does having more ensemble component (5→50) make the SED-A2D results worse? Similar trends can also be seen in Tab 4 for C-1 or C-5. Could it be because the stochastic sum does not scale with more models?   
        - Why was #unique used in Tab 1 to measure diversity when the Predictive Diversity Score was just introduced?  
        - Why does oracle selection perform worse compared to simple average in Tab 2? I would expect otherwise given that there is privilege information.   
    - Components of the method can be better motivated   
        - Why was the A2D loss chosen instead of other losses e.g. DivDis?   
        - Why is optimizing Eqn 6 preferable to e.g., forming an OOD dataset from the ID data based on the errors of DeiT or even from the errors from an ensemble of models, similar to imagnet-a, and using existing techniques like [23,28].   
    - “collecting a separate OOD dataset can be very costly, if not impossible”. 
        - There are cheap ways to introduce OOD samples to an ID dataset, e.g., simple augmentations/transformations to the input. Why are these methods not preferable?  
4. One of the main contributions involves speeding up the disagreement computation. There does not seem to be experimental details or results on this. E.g., a subset of models is chosen, what is the size of this subset? How does performance for generalization/detection change with and without this speedup?
questions: questions: 1. It would be interesting to see if using eval datasets other than IN-R as OOD data results in similar trends in Tab 2. It seems like deep ensemble and its variant and SED-A2D, i.e., the methods that do not make use of external OOD data, tend to perform better. 
2. Instead of computing the detection scores, how does the proposed diversity measure correlate with correct predictions? 
3. In table 1, what is the IN-Val #unique?
limitations: limitations: Yes the limitations were adequately addressed.
paper_summary: paper_summary: This paper presents a new method which directly encourages ensemble diversification on selected ID datapoints without the need for a separate OOD dataset. They also introduce a new measure of epistemic uncertainty which measures the diversity of the final predictions of each model, and suggest a speedup of comparing pairwise disagreement via random sampling.
strength_weakness: strength_weakness: - It appears that utilizing this new training objective leads to a loss in ID accuracy, since it encourages members of the ensembles to diverge. This tradeoff between ID accuracy and OOD accuracy may not be desirable in many settings. Overall, the paper emphasizes the improved OOD performance but does not show its impact on ID data for many experiments, such as the ablation studies for OOD detection, model diversity, etc.
- The stochastic computation of pairwise disagreement seems incremental, and there is no work comparing this stochastic implementation with the traditional expensive one. It would be helpful to include an ablation study to understand the accuracy vs performance tradeoff.
- There are many other methods for OOD detection beyond MSP with BMA (eg [1]). How PDS does compare against other baselines?
- Deep ensembles remain competitive in many settings, and the best values for C-1 and C-5 OOD generalization are still achieved using ensembles. 

[1] Xia and Bouganis: On the Usefulness of Deep Ensemble Diversity for Out-of-Distribution Detection https://arxiv.org/abs/2207.07517
questions: questions: - The selection of OOD samples does not appear to be tied to a specific method. Have you tried applying this method to other like DivDis?
- It's interesting that diversifying on ID samples improves OOD generalization compared to diversifying on ImageNet-R (Table 2). What was the setup for these experiments? Did the ensembles see fewer "OOD" datapoints in the latter?
- In Table 1, I'm surprised that SED-A2D has each model giving a different prediction for C-1, but OOD detection AUROC using PDS is quite low. Does this imply that SED-A2D also has very high disagreement on ID data?
limitations: limitations: - The approach sacrifices ID accuracy for OOD generalization/detection.
- The experiments only showed the result of finetuning the last two layers.
paper_summary: paper_summary: The paper presents SED, a method for scaling up existing diversification methods to large-scale datasets and tasks. SED identifies the OOD-like samples from a single dataset, bypassing the need to prepare a separate OOD dataset. Experimental results demonstrated good performances by SED on the OOD generalization and detection tasks.
strength_weakness: strength_weakness: 1. I am very confused about the dataset division for OOD detection task in the paper. The distribution should refer to “label distribution” in OOD detection [1], which means that OOD samples should not have overlapping labels w.r.t. training data. In the paper, the ID dataset is ImageNet-1K, while the OOD dataset for the OOD detection task includes ImageNet-C (Table 3). Their label spaces overlap, which is clearly incorrect. I don't believe the experiments conducted in this paper fall under the category of OOD detection. I suggest the authors refer to relevant literature on OOD detection, such as OpenOOD [1].

2. The ablation studies are insufficient. For instance, the number of layers being diversified is a hyperparameter. I believe conducting ablation experiments on this would make the paper more solid.

3. I think the experiments in the paper are not comprehensive enough. For example, how does it perform on small-scale datasets? Although it may not be fair to compare with methods using real OOD datasets, this could provide insights into SED's performance from multiple perspectives.

4. The comparative methods in the paper are not comprehensive enough. How does it perform compared to existing OOD generalization and OOD detection methods? If SED is complementary to existing methods, how much improvement can it bring?

5. The paper claims to speed up pairwise divergence computation, but no results are shown. Could authors demonstrate specifically how much speedup was achieved?

6. typos:
6.1 Line 61: "We verify that SEDdiversifies a model..."
6.2 Line 68: "In all three cases, SEDachieves a superior generalization..."

[1] Yang et al, OpenOOD: Benchmarking Generalized Out-of-Distribution Detection, IJCV 2024.
questions: questions: 1. Where is the batch-wise weight $\alpha_B$ used in the method?
limitations: limitations: I think the author should discuss more about the limitations of the method proposed in the article, such as the computational time required for the method proposed in the article compared with other methods.

Comments: comment: We thank the reviewer for raising their score and appreciating our clarifications with additional experiments.
Thanks for the clarifications and additional experiments, they will be useful additions to the paper. I will raise my score.
Thank you for your response, we present below the requested results and clarifications.

## Additional post-hoc OOD detection methods

We have added the results for Energy [1] and Max Logit [2] in Table D below.

Table D - extended OOD detection baselines

|                    | When added    | C-1   | C-5   | iNat      | OI        |
| ------------------ | --- | --------- | --------- | --------- | --------- |
| BMA                |  Manuscript   | 0.641     | 0.845     | 0.960     | 0.915     |
| PDS                | Manuscript    | **0.686** | **0.896** | **0.977** | **0.941** |
| a2d_score          | Author's rebuttal    | 0.685     | **0.896** | 0.962     | 0.917     |
| Average Entropy    | Author's rebuttal    | 0.580     | 0.825     | 0.960     | 0.916     |
| Ens. Entropy       | Author's rebuttal    | 0.580     | 0.826     | 0.960     | 0.916     |
| Mutual Information | Author's rebuttal    | 0.503     | 0.539     | 0.586     | 0.576     |
| Max Logit          | Current comment    |     0.673      |   0.874       |   0.809        |    0.829       |
| Energy     | Current comment     | 0.633     | 0.858     | **0.977** | 0.908     |

## For covariate shift, goal is to improve classification accuracy. For semantic shift, goal is to have the model reject classification.

Thank you for the further clarification of the concern; we understand the viewpoint. However, fundamentally, we do not agree that the subsequent action for covariate-shift samples should always be to improve classification accuracy. The goal of abstained prediction is to reject samples where the model is *likely to be wrong*, regardless of whether the cause of that is due to covariate shift or semantic shift [a]. 

In fact, covariate shifts are often cited as the motivation for abstained prediction. [b] studies the abstained prediction problem from a theoretical point of view where the OOD samples are covariate-shifted samples (§2.2 and throughout the paper). [c] studies the problem from an empirical perspective where the OOD samples are sourced from CIFAR-C (Figure 11) or ImageNet-C (Figure 7), examples of covariate-shifted samples of the respective ID datasets.

In line with this observation, we point to many OOD detection benchmarks that use the covariate shift as the source of OODness. Authors in [d] have measured the sensitivity of epistemic uncertainties against covariate shifts on MNIST like rotation and translation (Figure 1) as well as the shifts on CIFAR and ImageNet defined by the CIFAR-C and ImageNet-C datasets (Figure 2). Mukhoti et al. [e] have used CIFAR vs CIFAR-C (Figure 1) and ImageNet vs ImageNet-O (Table 2) as the OOD detection benchmarks.

We argue that the detection of covariate-shifted samples as an instance of OOD detection task is not only well-motivated but also a widely-adopted practice in the OOD detection community.

[a] Learning with Rejection. ALT 2016.

[b] Towards optimally abstaining from prediction with OOD test examples. NeurIPS 2021.

[c] Uncertainty Estimates of Predictions via a General Bias-Variance Decomposition. AISTATS 2023.

[d] Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift. NeurIPS 2019.

[e] Deep Deterministic Uncertainty: A New Simple Baseline. CVPR 2023.

## How, after detecting both semantic and covariate shift samples, can we determine which samples are covariate shift and need further classification by the model.

Following our previous argument, covariate-shifted samples do not always need to be subsequently classified by the model. In many applications, it benefits to still reject these samples. 

Independent of this, the separation of covariate shift vs semantic shift cases is an interesting topic on its own. However, this is beyond the scope of the paper.
Dear authors

I think adding some post-hoc methods to the comparative approaches for OOD detection tasks would make the paper more comprehensive. Methods like Energy [1] and MaxLogit [2] could be good additions.

More important, I’m confused about the setting of detecting both semantic and covariate shift simultaneously. For covariate shift samples, our goal should be to improve classification accuracy. For semantic shift samples, our goal should be to have the model reject classification to avoid unpredictable behavior. Therefore, I don’t quite understand how, after detecting both semantic and covariate shift samples, we can determine which samples belong to covariate shift and need further classification by the model.

If the above concerns can be resolved, I am willing to raise my rating.

[1] W Liu, et al. Energy-based Out-of-distribution Detection. In NeurIPS, 2020.

[2] D Hendrycks, et al. Scaling Out-of-Distribution Detection for Real-World Settings. In ICML, 2022.

Best, Review UGvs
We thank the reviewer for the acknowledgement and the score update. However, since the score is still 4, a borderline reject, we would like to understand if there are any remaining issues that need to be addressed. We would be happy to provide any further clarification, elaboration, or even experiments within the next 24 hours.
Dear authors,

Thank you for the response.

Most of the issues have been addressed. I have raised the score.

Best,
Review UGvs
We thank the reviewer for the extended discussion. Since we only have around 24 hours for the discussion period, we would like to ask the reviewer to share any final requests for us to respond in time. Please also reconsider the original scores, if the concerns are adequately addressed.
Thank you for the review. Since we only have around 24 hours for the discussion period, we would like to kindly ask the reviewer to tell whether they acknowledge our rebuttal and share any additional requests for us to respond in time. Please also reconsider the original scores, if the concerns are adequately addressed.
We thank the reviewer for appreciating our rebuttal and raising their score.
We thank the reviewer for the discussion about the role of PDS in measuring epistemic uncertainty and for appreciating our clarifications.
Thank you for the further clarifications. My concerns have mostly been addressed, and thus I have raised my score to borderline accept.
Thank you for providing so many additional experiments and ablations during the rebuttal process! Based on these new results, I am willing to increase my score to a 5.
Thanks for the suggestion. We are keen to include additional comparisons in the final version to strengthen the paper. Suggestions of specific methods are welcome.

We provided results for additional OOD detection methods in the authors' rebuttal (see Table B: Ensemble Entropy, Average Entropy, Mutual Information, Average Energy, and the A2D disagreement as an uncertainty score [k,p]).

The comparison with BMA/deep ensembles (already in the paper) is probably the most important since this is considered state-of-the-art in recent studies [s, v, w].

Summary of results: the proposed PDS proves superior to all compared methods on all covariate and semantic shift datasets, i.e. C-1, C-5, iNaturalist, OpenImages.

[k] Pagliardini et al., *Agree to disagree: Diversity through disagreement for better transferability*, ICLR 2022.

[p] Xia and Bouganis, *On the Usefulness of Deep Ensemble Diversity for Out-of-Distribution Detection*, ICLR 2022.

[s] Ovadia et al., *Can you trust your model's uncertainty? evaluating predictive uncertainty under dataset shift*, NeurIPS 2019.

[v] Mukhoti et al. *Deep deterministic uncertainty: A new simple baseline*, CVPR 2023.

[w] Dusenberry et al. *Efficient and scalable bayesian neural nets with rank-1 factors.* International conference on machine learning, PMLR 2020.
The reviewer thanks the authors for the response.

Regarding weakness 4, the authors' added baselines are all OOD generalization methods. I suggest adding more OOD detection baselines to make the article more complete.
Thank you for the clarification. We show below how the provided example does not invalidate PDS as a metric of epistemic uncertainty. We also clarify our understanding of epistemic uncertainty and the soundness of ensembles in measuring it. The final version of the paper should be clearly improved by including this discussion.

**Definition of epistemic uncertainty**

Epistemic uncertainty is defined by a lack of training data in certain input regions [a,b].

**Ensembles and epistemic uncertainty**

The lack of supervision in OOD regions means that multiple models exist with similar training risk. They agree on training/ID data but disagree in their predictions on OOD examples [c,d,e]. This is the reason why the rate of agreement on OOD data is a valid measure of epistemic uncertainty.

**Example given by the reviewer**

Regardless of how much entropy each ensemble member exhibits, what eventually matters for the epistemic uncertainty is the degree of agreement among the members. It makes sense that both $v$ and $w$ have the identically low epistemic uncertainty as long as $p_1(v)=p_2(v)$ and $p_1(w)=p_2(w)$. The overall entropy of the predictions matters more for predictive uncertainty (concerned with the correctness of predictions) and aleatoric uncertainty (data uncertainty stemming from the entropy of the ground-truth $p(y|x))$. Epistemic uncertainty is thus related to the ensemble agreement rather than entropies [c,d,e].

We prepared a concrete demonstration of case suggested by the reviewer [1/2, 1/2], [1/2, 1/2] to be added to the appendix. We use a combined dataset of ImageNet-Val (ID) and OpenImages-O (OOD). We compute the predictive distribution of our SED ensemble on this data. We retain examples with a highly-similar distribution across ensemble members (i.e. high agreement) then rank them by decreasing entropy of the predictive distribution. As we expected/argued, the top examples (high entropy) do correspond to ID samples (from ImageNet-Val). Entropy thus cannot be used to reliably separate ID from OOD samples.

**Soundness of PDS**

PDS is precisely measuring the agreement among ensemble members. Unlike BMA, PDS disregards the overall entropy and focuses purely on the agreement. Previous studies [c,d,e] and our empirical results (Table 3 in the paper) support that PDS is a more suitable measure to determine the *OODness* of a sample than BMA and entropy.
We thank the reviewer for the response to the rebuttal. We assume that there are some remaining weaknesses of the paper that do not allow to increase the score. Could you please share them as well to improve the final manuscript?
I don't have more problems and I am willing to keep my score.
Thank you for the clarifications and for providing the additional experiment results.

About PDS, I was referring to the following example:
- $p_1(v) = p_2(v) = [1,0]$
- $p_1(w) = p_2(w) = [1/2, 1/2]$

In this case, PDS does not seem to capture the uncertainty in the prediction of $w$ since the PDS of $v$ and $w$ is the same. I see why PDS would do better than BMA in certain cases, but perhaps PDS also has some non-trivial limitations (or assumptions). I don't think they are adequately discussed. It is still not very clear to me why PDS are generally better than BMA as shown by the experiments.