Title: Asymmetric Duos: Sidekicks Improve Uncertainty
Venue: NeurIPS 2025
Accepted: yes
Keywords: Uncertainty Quantification

Ensembles

Deep Learning

Transfer Learning
Abstract: The go-to strategy to apply deep networks in settings where uncertainty informs decisions—ensembling multiple training runs with random initializations—is ill-suited for the extremely large-scale models and practical fine-tuning workflows of today. We introduce a new cost-effective strategy for improving the uncertainty quantification and downstream decisions of a large model (e.g. a fine-tuned ViT-B): coupling it with a less accurate but much smaller "sidekick" (e.g. a fine-tuned ResNet-34) with a fraction of the computational cost. We propose aggregating the predictions of this *Asymmetric Duo* by simple learned weighted averaging. Surprisingly, despite their inherent asymmetry, the sidekick model almost never harms the performance of the larger model. In fact, across five image classification benchmarks, and a variety of model architectures and training schemes (including soups), Asymmetric Duos significantly improve accuracy, uncertainty quantification, and selective classification metrics with only ${\sim}10-20$% more computation. Code is available at: https://github.com/timgzhou/asymmetric-duos

Asymmetric Duos: Sidekicks Improve Uncertainty

Abstract

The go-to strategy to apply deep networks in settings where uncertainty informs decisions-ensembling multiple training runs with random initializations-is illsuited for the extremely large-scale models and practical fine-tuning workflows of today. We introduce a new cost-effective strategy for improving the uncertainty quantification and downstream decisions of a large model (e.g. a fine-tuned ViTB): coupling it with a less accurate but much smaller 'sidekick' (e.g. a fine-tuned ResNet-34) with a fraction of the computational cost. We propose aggregating the predictions of this Asymmetric Duo by simple learned weighted averaging. Surprisingly, despite their inherent asymmetry, the sidekick model almost never harms the performance of the larger model. In fact, across five image classification benchmarks and a variety of model architectures and training schemes (including soups), Asymmetric Duos significantly improve accuracy, uncertainty quantification, and selective classification metrics with only ∼ 10 -20% more computation. Code is available at: https://github.com/timgzhou/asymmetric-duos.

1 Introduction

Deep ensembles [29] have endured as a de facto method in settings that require uncertainty quantification (UQ) for safety or downstream decision making [4, 9, 31]. When models are trained from scratch with different random seeds, this simple strategy yields strong performance across UQ and decision-making benchmarks [22, 39], provides robustness under distribution shifts [42], and requires no modification to model training methodology.

However, as the modern machine learning paradigm increasingly revolves around larger and larger pre-trained models fine-tuned for specific downstream tasks [12, e.g.], deep ensembles become increasingly ineffective and impractical. First, unlike training models from scratch, fine-tuning from a pre-trained model is much less sensitive to hyperparameters and training randomness. While ensembling multiple fine-tuning runs can yield performance increases, it pales in comparison to the gains obtained when ensembling trained-from-scratch models [19, 49]. Second, and more critically, the growing size of modern models makes ensembling more expensive than ever. Even with moderatesized models like ResNet-50 [24], training and inference costs were a concern [1, 13, 26]; with large architectures such as ViT-H [10], these costs become even more prohibitive. Deploying a single one of these models can approach the limit of practical resources. Ensembling with double, triple, or larger multiples of the computation may be out of the question.

The smallest deep ensemble requires two models, which with standard approaches needs 2 × the computation for both training and inference. In this paper, we reduce this cost to a fractional amount (e.g. 10 -20% ) while still obtaining meaningful improvements in accuracy, uncertainty quantification, and downstream decision making. Our Asymmetric Duo framework pairs a base model with a smaller 'sidekick' to make better predictions together. For instance, we can pair a larger ViT-B with a smaller ResNet-34, while fine-tuning each separately, to improve over either alone . As the

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sidekick model requires a fraction of the compute at training and inference time, it only requires minimal computational overhead over the base model, which enables practical use.

Intuitively, an Asymmetric Duo might not help or might even hurt. The smaller model's accuracy can be much lower, and so one might expect that combining predictions from both models could degrade performance. Yet surprisingly, we find that Asymmetric Duos consistently improve performance, even when the base model and sidekick are extremely imbalanced (i.e. the sidekick is 10 × smaller and 80% as accurate as the base model). Across datasets and model families, Asymmetric Duos yield up to 10 -15% improvements in accuracy, uncertainty quantification, and selective classification metrics, while only adding 10 -20% of the computational cost of the base model.

The Asymmetric Duo framework is straightforward to implement: given a working base model, the user adds a second smaller model (by say simply downloading it from a 'model zoo') and fine-tuning it in the same way as the base model. Moreover, Asymmetric Duos are complementary to other compute-efficient model combinations, like Model Soups [60], and apply broadly by incorporating these methods as base or sidekick models. Our experiments show that Duos can improve the uncertainty quantification of both uncertainty-blind pipelines (like standard training) and uncertainty-aware pipelines (like soups), and so offer a practical drop-in addition to existing models.

2 Background

We focus on deep networks fine-tuned for a k -way classification task in some input domain X . However, the key ideas of our Duos could be extended to regression tasks or other problem settings.

We denote deep networks as mappings of the form f : X → R k , where output logits f ( X ) are mapped to the k -class probability simplex via the softmax function σ ( Z ) = [ e Z i / ∑ k j =1 e Z j ] k i =1 . The deep network's class prediction for an input X is the index of the largest logit (i.e. ˆ Y ( X ) = arg max i [ f ( X )] i ). Its predictive uncertainty can be quantified via its associated softmax probability:

(We note that alternative measures of predictive uncertainty, such as the entropy of the categorical distribution defined by σ ( f ( X )) , are common in other works [2, 29, 57]. We explore entropy uncertainty in Appendix C and find no meaningful difference with respect to our main results.)

2.1 Deep Ensembles

A deep ensemble [29] refers to m independently-trained deep networks f 1 , . . . , f m , typically of identical architecture and training procedure. At test time, each input X is passed through each network and the resulting logits are averaged to produce an aggregate prediction ¯ f ( X ) := 1 m ∑ m i =1 f i ( X ) from which a class prediction and uncertainty estimate can be derived. The randomness of initialization and shuffling of training samples is usually sufficient to produce diverse logits that, when averaged together, produce more accurate class predictions and better calibrated

uncertainty estimates than any of the component models in isolation [29, 42]. Deep ensembles have also been shown to be robust to distribution shifts [2, 32, 42] and have thus been adopted across safety-critical and decision-making applications [4, 9, 31].

As stated in the introduction, deep ensembles are often impractical with the modern transfer learning setup [41, 49, 60]. The primary downside is computational cost. It is common for practitioners to fine-tune large pre-trained models, typically downloaded from a 'model zoo', and training or deploying multiple of these large models can be prohibitively expensive [7]. In addition, member models fine-tuned from a shared pre-trained model tend to settle within the same loss basin, preventing the necessary diversity to produce meaningful improvements [40]. Consequently, deep ensembles are often restricted to settings with moderate-sized models trained from scratch [29, 42, 49].

2.2 Alternative Methods

Many methods aim to replicate the benefits of ensembles without the computational overhead.

Model soups [60] average the parameters of independently fine-tuned models, rather than their predictions, yielding a 'weight-space' ensemble with the same inference cost as a single model. This method takes advantage of the fact that models fine-tuned from an identical base model often settle into the same pre-trained loss basin, and thus the loss is approximately locally convex with respect to the parameters. This parameter averaging often yields competitive performance with the prediction averaging of ensembling when the component models are fine-tuned, though the gain is less than ensembling trained-from-scratch models.

Shallow ensembles [30] reduce the multiple model training and inference costs of deep ensembles by instead making multiple predictions from a single model. Specifically, the last layer (or the last ℓ layers) of a deep network are replaced with m copies that each receive the same input. The outputs of the m 'heads' are averaged together and learned jointly. Since only the last layer is duplicated, the computation and parameters added by a shallow ensemble are only a fraction of that of the original deep network. However, the benefits provided by shallow ensembles are weaker and less consistent than those of deep ensembles. In fact, single model baselines sometimes outperform them on selective classification tasks and robustness under distribution shifts [39].

Other methods. Implicit ensembles aim to produce multiple diverse networks at inference that are all derived from a single training run. These networks are derived through Monte Carlo sampling (e.g. when combined with Dropout [13]), checkpoints from the training process [26], or predictions made at early layers [1]. While these approaches have lower training costs than standard deep ensembles, they retain the same inference costs and typically are incompatible with fine-tuning. Weight-sharing ensembles aim to embed multiple models within a single architecture that can be trained simultaneously [11, 55, 58, e.g.]. While some methods incur lower inference-time costs [23], they typically require from-scratch training and bespoke architectures and/or training techniques. Non-ensemble methods often modify architectures, training, or inference; while they can be effective, these modifications may complicate practical use. See [15, 44] for thorough surveys.

3 Asymmetric Duos

We introduce Asymmetric Duos to augment a large base model f large with a small sidekick model f small , which are both independently pre-trained and fine-tuned, for improving inference at little computational cost. Duos allow many choices of base f large and sidekick f small . It is practical to choose a base that could be deployed by itself for adequate predictive performance and aggregate it with a much smaller sidekick, even if the sidekick cannot satisfactorily address the task on its own.

We contrast our pairing of asymmetric models with deep ensembles. Even the smallest deep ensemble with m = 2 models doubles the training and inference cost. To sidestep this cost, we instead look to combining models of different sizes. At first glance, this strategy may appear to have limits; too much imbalance may produce worse predictions than the base model alone. However, through a carefully designed aggregation strategy, we show that our Asymmetric Duos can improve performance even when the f small uses an order of magnitude less computation than f large .

The Asymmetric Duo framework is architecture-agnostic and compatible with current transferlearning and regularization techniques. This flexibility offers two key advantages. First, Duos can

more readily adjust the amount of computation, compared to standard ensembling, by extending to combinations of models with vastly different sizes, which is relevant given the wide span of pretrained models available today. Second, Duos only add a small sidekick model to a larger base model, and so the additional computation is merely a fraction of that of the larger model.

3.1 Aggregating Predictions from Asymmetric Models

In standard deep ensembles, all models are inherently 'equal' in that they only differ in randomization. By contrast, the two networks in an Asymmetric Duo explicitly differ in size and predictive performance. For example, an Asymmetric Duo might combine a ConvNeXt-Base (89 million parameters, 15 billion FLOPs, 84.1% Top-1 accuracy on ImageNet1K) [35] and a RegNeXt-1.6GF (9 million parameters, 1.6 billion FLOPs, 79.7% Top-1 accuracy on ImageNet1K) [46]. While this asymmetry achieves computational efficiency, the larger model is more likely to be correct than the other. Aggregating predictions with the equal-weighted logit average of deep ensembles could therefore be detrimental.

While many mechanisms could account for the asymmetry between f small and f large when aggregating predictions, we propose a simple weighted average of their logits. Specifically, we include two temperature parameters, T large and T small to weight the logits:

The Duo class predictions and uncertainty measure are based on these weighted logit averages:

Tuning the temperatures. We tune T large and T small to minimize the negative log likelihood on the same set used for hyperparameter selection during fine-tuning. As there are only two parameters, the learned weights will likely generalize even from a small reused validation set. With f large and f small validation outputs saved, this tuning takes only seconds with any standard optimizer. Note that this procedure closely matches temperature scaling for (single-model) calibration [21].

This temperature tuning automatically guards against defective Duos. If f small is too inaccurate, then the Duo can effectively revert to f large through the weighting T large = 1 , T small = 0 . Conversely, any non-trivial weighting (i.e. T small > 0 ) implies that the Asymmetric Duo provides benefit over f large since it improves negative log likelihood on the validation set.

Ablations. To understand how our proposed asymmetric Duo affects performance on downstream tasks, our experiments and analyses consider the following ablations:

Unweighted Duos equally weight the predictions of both models without regard for their asymmetry, similar to deep ensembles. It is equivalent to setting T large = T small = 0 . 5 : This ablation assesses the importance of a weighted average for aggregating logits.

UQ Only Duos only use Duo predictions for the uncertainty estimate, using the base model's class prediction:

This ablation isolates the effects of Asymmetric Duos on correctness prediction and selective classification tasks, demonstrating whether any benefits to performance can be attributed to better uncertainty quantification versus more accurate class predictions.

3.2 Measuring the Computational Cost of Asymmetric Duos

The cost of a Duo versus a single model is dictated by the degree of asymmetry in size. How to measure size is non-trivial, because no one property fully captures a deep network's size or complexity. Parameter count, network depth, floating point operations per forward pass (FLOPs), and throughput each reflect different aspects of model capacity and computational cost [25, 52, 56]. To focus on practical use we measure computation. We profile FLOPs due to their consistency across hardware in Section 4, and we profile throughput as measure of real-world time efficiency in Appendix B. Asymmetric duos deliver efficient improvement for either measure of computational cost.

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4 Experiment Setup

We evaluate Asymmetric Duos in the context of image classification, measuring their effects on accuracy, uncertainty quantification, and downstream decision-making. To demonstrate their 'out-ofthe-box' nature, we focus on Duos that combine models from popular pre-trained models available from the torchvision [37, 43] and timm [59] 'model zoos.'

Datasets. We benchmark ImageNet [8] for large-scale evaluation, and Caltech 256 [20] and iWildCam [3] for measuring transfer to new domains. As accuracy and uncertainty quantification tend to degrade under distribution shifts [42], we further evaluate with ImageNet V2 [48] and iWildCam-OOD [27] to test robustness under such shifts.

Models. For f large architecture and parameters, we consider pre-trained models that 1. consistently achieve high performance on fine-tuning benchmarks [e.g. 18] and 2. are commonly used in practice for various computer vision tasks. We therefore experiment with four strong f large that cover convolution and attention architectures: a ConvNeXt-Base [35] pre-trained on ImageNet, a SwinV2-Base [34] pre-trained on ImageNet, an EfficientNet-V2-L [53] pre-trained on the largerscale ImageNet21K, and a CLIP ViT-B [10, 45] pre-trained on the larger still LAION-2B [50]. These span standard scale (ImageNet) to extremely large scale (LAION). For f small models, we consider smaller architectures from torchvision and timm [24, 33, 46, 52, 54, 61, 62] (see Appendix A for a complete list). Within a given model family (e.g. ResNet), we choose models of varying size (e.g. ResNet-34, ResNet-50, ResNet-101, etc.) to produce Duos with various levels of asymmetry.

Fine-Tuning and Evaluation. For our downstream datasets evaluations, we fine-tune our models following the LP-FT recipe [28] with standard unweighted Cross-Entropy Loss, AdamW [36] optimizer, linear warm-up with cosine annealing learning rate scheduler, and perform hyperparameter tuning for all models over learning rate and weight decay on a withheld validation set.

We calibrate all fine-tuned models by temperature scaling [21], minimizing the negative log likelihood on the validation set using L-BFGS, to improve baseline uncertainty quantification.

The Size-Accuracy Relationship of Large and Small Models. Figure 2 summarizes the class prediction accuracy of all the pre-trained and fine-tuned models that we use to construct Asymmetric Duos. We report accuracy for ImageNet, ImageNet V2, and Caltech 256 and Macro F1 Score for iWildCam2020-WILDS to account for the significant class imbalances present [27].

Consistent with prior work [18, 38], we find a strong correlation between model size (as measured by FLOPs/parameter counts) and in-distribution (InD) and out-of-distribution (OOD) accuracy. In

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the next section, we investigate to what degree combining pairs of models into Asymmetric Duos allow us to practically traverse the size/performance tradeoff.

5 Experiment Results

Here we present the performance of Asymmetric Duos, as measured by accuracy, uncertainty quantification, and selective classification performance, as a function of computation (i.e. Duo FLOPs balance). For each benchmark, we form Asymmetric Duos using all possible combinations of f large and f small architectures outlined in Section 4. For visual clarity, this section only contains results for a single f large on each dataset. (We choose different f large architectures for each dataset for diversity of results within this section.) We note that the results in this section are representative of all f large architectures (see Appendix G for the full set of results).

5.1 Duos as Classifiers - Accuracy & Macro F1 Score

To determine if the addition of f small can enhance class prediction, we compare the accuracy of Asymmetric Duos to that of a single f large model in isolation. We report top-1 accuracy (ImageNet V2 and Caltech 256) and Macro F1 score (iWildCam) in Figure 3 plotted against FLOPs balance.

Overall, we find that Asymmetric Duos can yield significant improvements in accuracy/F1 over f large . We note that the smallest Duos do not provide an accuracy advantage, and occasionally produce minor performance drops. This result is expected, and arguably the lack of major performance degradations is surprising given the significantly lower accuracy of the smallest f small models. However, after the FLOPs balance reaches 10% , which in many settings may be negligible additional computation, Duos provide consistent accuracy improvements across all datasets.

We find that the proposed temperature weighting scheme is necessary for these improvements in accuracy. In Appendix D we report the learned temperatures of all Duos, finding larger f large weights when f small is smaller, with more even weights as balance increases. Our ablation further confirms this hypothesis. We observe that Duos that equally average the f large and f small predictions (Duo: Unweighted) significantly underperform f large when the balance is near zero.

In Appendix G we also report results for probabilistic measures of accuracy; namely Brier Score and negative log likelihood. The results for these metrics follow similar trends.

5.2 Predictive Uncertainty Separability - Correctness Prediction AUROC

Predictive uncertainty estimates are often judged by their calibration, as measured by Expected Calibration Error (ECE) [e.g. 21, 42]. Because we apply temperature scaling throughout our experiments, the f large models are largely calibrated to begin with, and so Asymmetric Duos provide little improvement. (See Appendix G for results.) We argue that this is not a failure of Duos but rather a success of temperature scaling.

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We instead choose to measure the quality of Duo uncertainty estimates based on their correlation with the correctness of class predictions. Intuitively, a good uncertainty estimate should be able to separate correct versus incorrect class predictions. To that end, we report correctness prediction Area Under the Receiver Operating Characteristic curve (AUROC) for Duos and for single f large as a function of FLOPs balance. Randomly assigned uncertainty measure would yield an AUROC score of 0 . 5 , while a perfectly separable uncertainty measure would yield 1 . 0 .

In Figure 4 we find that Asymmetric Duos consistently yield higher AUROC than f large . Surprisingly, we observe performance improvements even when the FLOPs balance is near 0 . This finding suggests that AUROC can be increased without much additional computation. Performance does not correlate with additional computation (i.e. higher FLOPs balance), but all Duos provide benefit.

Our ablation demonstrates that these AUROC improvements cannot solely be attributed to the increased accuracy afforded by Duos. Recall that the UQ Only Duo variant uses the Duo's uncertainty estimate while retaining the class prediction of f large . Any AUROC benefits must therefore be attributed to improvements in the uncertainty, as accuracy remains unchanged. We observe that UQ Only Duos obtain significantly better AUROC score compared to their base models, showing that the sidekick model is effective at re-ranking uncertainties for the class prediction of f large , confirming that Duos provide meaningful improvements in uncertainty separability in addition to accuracy.

5.3 Duos as selective classifiers - AURC

To study the effect of Duo uncertainty estimates on downstream decision-making tasks, we evaluate Asymmetric Duos in the context of selective classification. Selective classification allows a model to abstain from prediction when the uncertainty is high, deferring uncertain cases to experts in effective human-in-the-loop systems [16]. The proportion of the test set with uncertainty below a given threshold is referred to as coverage, and performance on this subset is measured using the domain-specific loss, which in our case is the 0-1 loss analogous to classification error rate. As the uncertainty threshold decreases, the model becomes more cautious, abstaining from more inputs and reducing coverage while aiming to improve accuracy on this smaller covered subset. We emphasize that high-quality uncertainty estimates are necessary for selective classifiers to work in practice.

We evaluate selective classification performance using the Area Under the Risk Coverage (AURC) metric [17]. AURC accumulates error rates at all coverage levels to measure a model's overall potential as a selective classifier. As with correctness prediction, the AURC metric conflates accuracy and uncertainty quantification, as different predictors achieve different accuracy at full coverage (entire test set accuracy). To that end, we evaluate our UQ Only Duo ablation in addition to the proposed approach to bypass this potential confound.

In Figure 5, we observe that Duos provide substantial boost to AURC at all computation levels, even when the FLOPs balance is fractional. Analogous to our correctness prediction results, UQ Only Duos also achieve improved AURC scores at low FLOPs balance, demonstrating that these improvements cannot be attributed to accuracy alone. This is a direct result of our findings on

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correctness prediction with AUROC. Together, these results also confirm that smaller models can effectively re-rank the uncertainties of larger models. In contrast, many prior methods for selective classification sacrifice non-selective predictive power [14], resulting in unfavorable trade-offs in practical metrics such as AURC.

5.4 Duos as selective classifiers - Selective Accuracy Constraint

To further evaluate Duos in the selective classification context, we report the Selective Accuracy Constraint (SAC) metric for all Duos and f large models. SAC is a practical evaluation metric for risk-sensitive applications with a guarantee. It measures the maximum coverage a predictor can achieve while maintaining a fixed target accuracy, making it well-suited for settings where reliability is critical. Prior work in selective classification has shown that leveraging softmax response uncertainty allows deep networks to achieve high accuracy on a subset of confidently predicted data by abstaining on uncertain cases [14, 16]. Here we show duos boost coverage at the ambitious accuracy levels of 98% across all of our benchmarked datasets.

In Fig 6, we observe that our proposed Asymmetric Duos achieve higher coverage at minimal FLOPs balances. This finding complements our previous results with the AURC metric. Furthermore, the UQ Only ablation almost always match our proposed method, further implying that the improvements in coverage at high accuracy levels stems from re-ranked uncertainties rather than accuracy increases. Altogether, these results suggest that Asymmetric Duos are a practical choice in high-risk decision-making applications.

5.5 Soup with a (Side)kick: Combining Model Soups and Duos

Weshow the Asymmetric Duo framework is agnostic to model type, compatible with other methods, and compounds uncertainty quantification improvements by making a duo with a model soup [60]. For this experiment, we fine-tuned sixteen ConvNeXt Base models on Caltech 256 starting from

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the same torchvision pre-trained model using different training hyperparameters. We then mixed a greedy model soup for use as f large in our Asymmetric Duo. In Figure 7, we observe that Duos are compatible with soups and other methods of making better base and sidekick models.

5.6 Comparisons between Asymmetric Duos and Deep Ensembles

We show that Asymmetric Duos (AD) can match the performance of classic deep ensembles (DE) with a significantly lower compute budget. We construct ensembles of ResNet50s (RN50) trained on the ImageNet dataset following the 'pool-then-calibrate' strategy from [47]. We compare against ADs that pair a RN50 ( f large ) with MNASNet0.75 (MN.75), ShuffleNet V2 2.0× (SN2.0x), and EfficientNet-B2 (ENB2) models, yielding FLOPs Balances (FB) of 0.05, 0.14, and 0.27, respectively.

Table 1 shows that Asymmetric Duos quickly approach performance of m = 5 Deep Ensembles (e.g., m = 5 RN50s) across most metrics, despite using 4 × fewer FLOPs. We attribute this to architectural diversity from heterogeneity [19] and Duos' simple but effective temperature-based aggregation. If we allow Asymmetric Duos to match the computational budget of m = 5 Deep Ensembles, then Duos become even more advantageous. See Appendix E for a FLOPs-controlled comparison.

6 Discussion

In this work, we proposed the Asymmetric Duos framework, which yield consistent improvements across a range of predictive performance, uncertainty quantification, and decision making metrics. While these improvements may also be achievable through deep ensembles, Asymmetric Duos offer a substantially more efficient alternative, requiring only a fraction of the additional computation cost of their larger member model. Moreover, the framework is inherently compatible with fine-tuning workflows, making it a practical and scalable strategy in modern deployment scenarios.

Methods related to Duos in construction. Gontijo-Lopes et al. [19] used a similar construction of heterogeneous m = 2 deep ensembles to study the effect of predictive diversity induced by models pre-trained on different datasets. Our work differs mainly by aggregating deep network pairs of vastly different sizes as opposed to different architectures with similar accuracy, diving deeper into a smaller member model's effects on a Duo's uncertainty, and of course our fine-tuning the pairs on the same data.

Rahaman and Thiery [47] studied the combination of temperature scaling [21] and deep ensembles [29] and found that deep ensembles constructed by pool-then-calibrate or pool-with-calibrate strategies outperform naive deep ensembles and those following a calibrate-then-pool strategy on proper scoring rules. Our proposed Asymmetric Duos follow a similar construction order to a pool-withcalibration strategy, but fundamentally differ in motivation. As shown with our Unweighted Duos ablation, the asymmetry between f large and f small makes a pool-with-calibrate strategy necessary in preventing degradation in accuracy. Whereas Rahaman and Thiery [47] focuses on such constructions' effects on calibration, we put a unique emphasis on uncertainty quantification metrics like correctness prediction and selective classification.

Limitations and future directions. Our experiments are limited to the image classification task. While our findings show strong performance and computational efficiency on a total of five test sets, it remains unexplored how Asymmetric Duos perform in other tasks and modalities, such as image segmentation, regression, and natural language processing. Exploring these extensions could reveal broader applicability of the framework.

This work serves as an initial step toward understanding the aggregation strategies of deep networks of different sizes and capacities. While we focused on a small set of interpretable aggregation strategies for both point prediction and uncertainty quantification, there remains a large space of unexplored methods. Notably, our finding that simple validation-based weighting can yield effective ensembles from models with vastly different accuracies is itself a surprising and underexplored result. Future work may benefit from exploring other learning-based, adaptive weighting schemes for member aggregation, and may even call them Dynamic Duos.

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A Experimental Details

A.1 Model Architectures

We select popular, recent, and performative pre-trained models from torchvision [37] and timm [59] to construct our Duos, to make sure Duos are compatible with various recent architectures. From torchvision , we experiment with EfficientNet [52], EfficientNet V2 [53], MNASNet [54], ConvNeXt [35], ResNet [24], ResNeXt [61], RegNet [46], ShuffleNet-V2, Swin [62], and Swin (V1 & V2) [33, 34]. From timm , we get an Efficientnet-V2-L pre-trained on ImageNet 21k [8], and a ViT-B-16 [10] pre-trained on LAION 2B [50].

A.2 Training Procedure

For all our fine-tuned experiments we follow the LP-FT recipe from Kumar et al. [28]: we first train only the final classification head (also known as Linear Probing, or LP) for a few epochs (8 for both Caltech 256 and iWildCam) using cross-entropy loss and AdamW, then unfreeze the entire network and Fine-Tune (FT) for more epochs (16 on Caltech 256, 12 on iWildCam) under the same loss and optimizer.

Our FT procedure employs a sequential schedule (linear warm-up followed by cosine annealing), and we perform hyper-parameter search over learning rate in [1 × 10 -6 , 3 × 10 -4 ] and weight decay in [1 × 10 -8 , 1 × 10 -5 ] , picking the best trial by validation score. We use a batch size of 128 for Caltech 256 and 16 for iWildCam. All models are trained on NVIDIA L40S GPUs. Random Augmentation [5] is used to augment training samples during the FT phase. The best LP checkpoint initializes FT, and the top FT model by validation performance is carried forward into our Duo evaluations.

A.3 Datasets

Here we provide descriptions of each dataset used and how train-val-test splits are chosen in our experiment.

ImageNet [8] contains 1,000 classes and over a million training samples. All the pretrained models used in our experiment have been trained on ImageNet as a last step. Since ImageNet never released the official test set, researchers split the official validation set into val and test splits. Since we don't need to fine-tune models on ImageNet for our experiment, our only usage of a validation set is to temperature scale single models and to tune temperature weightings for Asymmetric Duos. We use only 5% of the official test split as our validation set to show how data-efficient the temperatureweighting step is.

ImageNet V2 [48] is a careful reproduction of the original ImageNet, but nevertheless showed model performance degradation, indicating distribution shifts. Since this dataset is used solely for evaluation, the entire dataset is treated as an OOD test set for ImageNet models and Duos.

iWildCam (OOD) [3, 27] is a camera-trap dataset with 203,029 training images containing 182 classes of animals. The IND and OOD are determined by distinctive camera traps, since different locations vary largely in vegetation and backgrounds, resulting in poor generalization to new camera traps. We use the official IND val split for iWildCam, which contains 7315 images captured by the same set of camera traps as the training set.

Caltech 256 [20] contains 30,607 images spanning 256 object classes and a clutter class. We use a random 15% split of the dataset as val and another 15% as test. The same validation set was used for both hyper-tuning and temperature tuning.

A.4 Greedy Soup Setup

For our Greedy Soup experiments, we independently fine-tune 16 ConvNeXt-Base models initialized from the same backbone with different hyperparameters over the same search space as our regular tuning procedure on Caltech 256 starting from the same pre-trained weights from torchvision , and greedily average their weights to improve performance on the validation set following the procedure outlined by Wortsman et al. [60]. The greedy soup in Figure 7 averages three of the sixteen trials.

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All m = x DEs in Section 5.6 and Appendix E are constructed by randomly selecting 32 subsets of size x from 10 independently trained ResNet-50 checkpoints from timm and torchvision, following the 'pool-then-calibrate' strategy of Rahaman and Thiery [47]. Because our temperature-based aggregation strategy for Duos naturally incorporates calibration, this setup enables a fair comparison on NLL, Brier, and ECE metrics.

All ADs used for comparison in Section 5.6 are formed by pairing one ResNet-50 checkpoint as f large with a sidekick f small drawn from torchvision.

B Alternative Measure of Computation (Throughput)

As discussed in Section 3.2, deep networks have several reasonable characterizations of size/computational cost, including parameter counts, FLOPs, depth, and throughput. We explore FLOPs in the main text due to its consistency across hardware and the intuitive interpretation of the FLOPs balance as the additional computation cost as a percentage of the larger member model's computation cost. However, FLOPs fail to consider architectures' parallelization differences, which play a factor in a model's speed during deployment. Here we show how our FLOPs balance notion would translate into throughput, on a single NVIDIA V100 Volta GPU. Figure 8 shows a clear linear correlation between throughput and FLOPs, with small variations among architecture families. For single models, the coefficient of determination for both metrics is 0 . 938 ; for Duos it is 0 . 795 . This result implies that the fractional additional FLOPs repeatedly emphasized in our main text translate directly to wall-clock-time efficiency.

C Alternative Measures of Uncertainty-Entropy

Throughout the paper we use softmax response to quantify the predictive uncertainty of single models and Duos. (Eq. 1). Here we demonstrate that our results are robust to this choice. We replicate our main results from Section 5 where we instead measure uncertainty via the entropy of the predictive distribution, another common measure used in practice. Figure 9 shows AUROC, AURC, and SAC@98 performance under entropy-based uncertainty quantification. We observe similar performance trends to our softmax response-based results in Figures 4, 5, and 6.

D Analysis of Temperature Weightings

In Figure 10 we plot the ratio of the temperatures T large /T small for Asymmetric Duos of various FLOPs balances for all f large models on Caltech 256 to study how temperatures are assigned for fine-tuned models. A ratio ≫ 1 implies that f small does not contribute to the Duo prediction and that the Duo functions like a single model. A ratio that is closer to 1 implies that f small and f large both meaningfully contribute to the Duo and that we should expect higher performance than from

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E Asymmetric Duos versus Deep Ensembles

Section 5.6 compares Asymmetric Duos and pool-then-calibrate DEs with the same base model, finding that Duos nearly match the performance of ensembles with a fraction of compute. In this section, we compare ADs and DEs under a fixed computational budget, which allows the Duo to use a much larger f large than the DE base model.

Table 2 shows that ADs (e.g., AD [4 , 5) ) considerably outperform DEs with similar test-time FLOPs cost (e.g., RN50 DE with m = 5 ) on most metrics. Notably, while DE performance tends to saturate as m increases, ADs continue to improve thanks to the stronger base model at higher FLOPs budgets. This suggests a simple and effective strategy: when deploying Asymmetric Duos, choose the most performant f large that your budget allows to maximize both accuracy and uncertainty quantification metrics. The setups on DEs are identical to Table 2 and is described Appendix A

F Evaluating Asymmetric Duos against scalable Bayesian Methods

Bayesian approaches have been prominent for uncertainty quantification tasks, at times performing competitively against deep ensembles. However, similar to deep ensembles, many Bayesian methods still struggle in scalability, making them hard to compare with methods like Asymmetric Duos. Here we evaluate Asymmetric Duos with two practical Bayesian methods, Improved Variational Online Newton (IVON) [51] and Laplace Approximation [6].

F.1 Improved Variational Online Newton (IVON)

The recently proposed IVON [51] was the first variational Bayesian objective optimizer that matched AdamW [36] in Accuracy when applied to large-scale training, in both from-scratch and fine-tuning settings. We benchmark our Asymmetric Duos against a ResNet50 fine-tuned with IVON optimizer on Caltech256.

Table 3 shows that IVON works well out of the box, outperforming standard AdamW with minimal training overhead. Its sampling-based inference further improved over the deterministic version,

though like Deep Ensembles, it introduces an test-time cost with diminishing returns. In contrast, Asymmetric Duos built on ResNet-50 achieve better performance across all metrics with only a fractional increase in compute. Furthermore, similar to the compatibility shown between soup and Asymmetric Duos in Section 5.5, IVON, as a great plug-and-use uncertainty-aware optimizer, would fit nicely with our Asymmetric Duos framework.

F.2 Laplace Approximation

Laplace Approximation(LA) is another practical and competitive Bayesian method, approximating the posterior with a Gaussian distribution centered at any regularly trained model [6]. We benchmark our Asymmetric Duos against Laplace Approximation on a Swin-V2-S trained on Caltech256, as models with larger final feature dimensions are computationally infeasible for LA given our hardware limits. For the Laplace Approximation method, we follow the original authors and use a kron hessian structure to approximate the posterior of the last-layer of the model. We limit FLOPs Balance (FB) to be 0 . 1 < FB < 0 . 3 for Duos to emphasize its computational efficiency.

Table 4 shows that although Laplace Approximation slightly improve upon baseline on metrics such as AUROC and AURC, it falls short in absolute performance gains compared to Asymmetric Duos across most metrics.

G Complete Experimental Results

Here we present full results for all 4 f large models across their benchmarked datasets.

CLIP ViT-B Pretrained on ImageNet 21K is benchmarked as f large on all five datasets.

0

0.25

0.50

0.75

1

FLOPs Balance

85

86

ViT-B Clip

ImageNet Acc

0

0.25

0.50

0.75

1

FLOPs Balance

74

75

76

77

ViT-B Clip

ImageNet V2 Acc

0

0.25

0.50

0.75

1

FLOPs Balance

74

76

78

ViT-B Clip

iWildCam Acc

0

0.25

0.50

0.75

1

FLOPs Balance

70

72

74

76

ViT-B Clip

iWildCam OOD Acc

0

0.25

0.50

0.75

1

FLOPs Balance

95

96

ViT-B Clip

Caltech 256 Acc

Acc scaled by 100 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

84

85

86

ViT-B Clip

ImageNet F1

0

0.25

0.50

0.75

1

FLOPs Balance

74

75

76

77

ViT-B Clip

ImageNet V2 F1

0

0.25

0.50

0.75

1

FLOPs Balance

39

42

45

ViT-B Clip

iWildCam F1

0

0.25

0.50

0.75

1

FLOPs Balance

24

28

32

36

ViT-B Clip

iWildCam OOD F1

0

0.25

0.50

0.75

1

FLOPs Balance

95

96

ViT-B Clip

Caltech 256 F1

F1 scaled by 100 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

5.5

6.0

6.5

ViT-B Clip

ImageNet NLL

0

0.25

0.50

0.75

1

FLOPs Balance

10

11

ViT-B Clip

ImageNet V2 NLL

0

0.25

0.50

0.75

1

FLOPs Balance

10

12

14

ViT-B Clip

iWildCam NLL

0

0.25

0.50

0.75

1

FLOPs Balance

10

12

14

ViT-B Clip

iWildCam OOD NLL

0

0.25

0.50

0.75

1

FLOPs Balance

1.8

2.0

2.2

2.5

ViT-B Clip

Caltech 256 NLL

NLL scaled by 10 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

1.0

2.0

3.0

4.0

ViT-B Clip

ImageNet ECE

0

0.25

0.50

0.75

1

FLOPs Balance

4.0

6.0

8.0

ViT-B Clip

ImageNet V2 ECE

0

0.25

0.50

0.75

1

FLOPs Balance

5.0

10

15

ViT-B Clip

iWildCam ECE

0

0.25

0.50

0.75

1

FLOPs Balance

10

20

ViT-B Clip

iWildCam OOD ECE

0

0.25

0.50

0.75

1

FLOPs Balance

1.0

2.0

3.0

ViT-B Clip

Caltech 256 ECE

ECE scaled by 100 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

20

22

24

ViT-B Clip

ImageNet Brier

0

0.25

0.50

0.75

1

FLOPs Balance

34

36

38

ViT-B Clip

ImageNet V2 Brier

0

0.25

0.50

0.75

1

FLOPs Balance

180

200

220

ViT-B Clip

iWildCam Brier

0

0.25

0.50

0.75

1

FLOPs Balance

175

200

225

ViT-B Clip

iWildCam OOD Brier

0

0.25

0.50

0.75

1

FLOPs Balance

24

27

30

33

ViT-B Clip

Caltech 256 Brier

Brier scaled by 100000 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

87

88

ViT-B Clip

ImageNet AUROC

0

0.25

0.50

0.75

1

FLOPs Balance

84

85

86

ViT-B Clip

ImageNet V2 AUROC

0

0.25

0.50

0.75

1

FLOPs Balance

86

88

90

92

ViT-B Clip

iWildCam AUROC

0

0.25

0.50

0.75

1

FLOPs Balance

92

94

ViT-B Clip

iWildCam OOD AUROC

0

0.25

0.50

0.75

1

FLOPs Balance

93

94

95

ViT-B Clip

Caltech 256 AUROC

AUROC scaled by 100 for legibility.

Duo: Ours

Duo: UQ Only

0

0.25

0.50

0.75

1

FLOPs Balance

3.4

3.6

3.8

ViT-B Clip

ImageNet AURC

0

0.25

0.50

0.75

1

FLOPs Balance

7.5

8.0

8.5

ViT-B Clip

ImageNet V2 AURC

0

0.25

0.50

0.75

1

FLOPs Balance

6.0

7.0

8.0

ViT-B Clip

iWildCam AURC

0

0.25

0.50

0.75

1

FLOPs Balance

6.0

7.0

ViT-B Clip

iWildCam OOD AURC

0

0.25

0.50

0.75

1

FLOPs Balance

0.4

0.5

ViT-B Clip

Caltech 256 AURC

AURC scaled by 100 for legibility.

Duo: Ours

Duo: UQ Only

0

0.25

0.50

0.75

1

FLOPs Balance

54

57

ViT-B Clip

ImageNet SAC@98

0

0.25

0.50

0.75

1

FLOPs Balance

0.0

10

20

ViT-B Clip

ImageNet V2 SAC@98

0

0.25

0.50

0.75

1

FLOPs Balance

0.0

20

40

ViT-B Clip

iWildCam SAC@98

0

0.25

0.50

0.75

1

FLOPs Balance

48

52

56

60

ViT-B Clip

iWildCam OOD SAC@98

0

0.25

0.50

0.75

1

FLOPs Balance

95

96

ViT-B Clip

Caltech 256 SAC@98

SAC@98 scaled by 100 for legibility.

Duo: Ours

Duo: UQ Only

0

0.25

0.50

0.75

1

FLOPs Balance

84

86

ImageNet Acc

0

0.25

0.50

0.75

1

FLOPs Balance

72

74

76

ImageNet V2 Acc

0

0.25

0.50

0.75

1

FLOPs Balance

76

78

iWildCam Acc

0

0.25

0.50

0.75

1

FLOPs Balance

74

76

iWildCam OOD Acc

0

0.25

0.50

0.75

1

FLOPs Balance

92

94

96

Caltech 256 Acc

Acc scaled by 100 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

82

84

86

ImageNet F1

0

0.25

0.50

0.75

1

FLOPs Balance

72

74

76

ImageNet V2 F1

0

0.25

0.50

0.75

1

FLOPs Balance

42

45

48

iWildCam F1

0

0.25

0.50

0.75

1

FLOPs Balance

27

30

33

36

iWildCam OOD F1

0

0.25

0.50

0.75

1

FLOPs Balance

90

92

94

Caltech 256 F1

F1 scaled by 100 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

6.0

7.0

ImageNet NLL

0

0.25

0.50

0.75

1

FLOPs Balance

10

11

12

13

ImageNet V2 NLL

0

0.25

0.50

0.75

1

FLOPs Balance

10

12

iWildCam NLL

0

0.25

0.50

0.75

1

FLOPs Balance

10

12

14

iWildCam OOD NLL

0

0.25

0.50

0.75

1

FLOPs Balance

2.0

3.0

4.0

Caltech 256 NLL

NLL scaled by 10 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

1.0

2.0

3.0

4.0

ImageNet ECE

0

0.25

0.50

0.75

1

FLOPs Balance

5.0

7.5

10

ImageNet V2 ECE

0

0.25

0.50

0.75

1

FLOPs Balance

0.0

5.0

10

iWildCam ECE

0

0.25

0.50

0.75

1

FLOPs Balance

0.0

5.0

10

15

iWildCam OOD ECE

0

0.25

0.50

0.75

1

FLOPs Balance

1.0

2.0

3.0

Caltech 256 ECE

ECE scaled by 100 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

20

22

24

26

ImageNet Brier

0

0.25

0.50

0.75

1

FLOPs Balance

36

39

42

ImageNet V2 Brier

0

0.25

0.50

0.75

1

FLOPs Balance

165

180

195

210

iWildCam Brier

0

0.25

0.50

0.75

1

FLOPs Balance

180

200

220

iWildCam OOD Brier

0

0.25

0.50

0.75

1

FLOPs Balance

30

40

50

Caltech 256 Brier

Brier scaled by 100000 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

86

88

90

ImageNet AUROC

0

0.25

0.50

0.75

1

FLOPs Balance

84

86

88

ImageNet V2 AUROC

0

0.25

0.50

0.75

1

FLOPs Balance

89

90

91

92

iWildCam AUROC

0

0.25

0.50

0.75

1

FLOPs Balance

92

94

iWildCam OOD AUROC

0

0.25

0.50

0.75

1

FLOPs Balance

92

94

96

Caltech 256 AUROC

AUROC scaled by 100 for legibility.

Duo: Ours

Duo: UQ Only

0

0.25

0.50

0.75

1

FLOPs Balance

3.5

4.0

4.5

ImageNet AURC

0

0.25

0.50

0.75

1

FLOPs Balance

8.0

9.0

10

ImageNet V2 AURC

0

0.25

0.50

0.75

1

FLOPs Balance

5.5

6.0

6.5

7.0

iWildCam AURC

0

0.25

0.50

0.75

1

FLOPs Balance

5.0

5.5

6.0

iWildCam OOD AURC

0

0.25

0.50

0.75

1

FLOPs Balance

0.6

0.8

1.0

Caltech 256 AURC

AURC scaled by 100 for legibility.

Duo: Ours

Duo: UQ Only

0

0.25

0.50

0.75

1

FLOPs Balance

40

48

56

ImageNet SAC@98

0

0.25

0.50

0.75

1

FLOPs Balance

0.0

10

20

ImageNet V2 SAC@98

0

0.25

0.50

0.75

1

FLOPs Balance

32

40

48

56

iWildCam SAC@98

0

0.25

0.50

0.75

1

FLOPs Balance

56

58

60

iWildCam OOD SAC@98

0

0.25

0.50

0.75

1

FLOPs Balance

87

90

Caltech 256 SAC@98

SAC@98 scaled by 100 for legibility.

Duo: Ours

Duo: UQ Only

0

0.25

0.50

0.75

1

FLOPs Balance

84

85

86

87

EfficientNet-V2-L

ImageNet Acc

0

0.25

0.50

0.75

1

FLOPs Balance

74

76

78

EfficientNet-V2-L

ImageNet V2 Acc

0

0.25

0.50

0.75

1

FLOPs Balance

76

78

80

EfficientNet-V2-L

iWildCam Acc

0

0.25

0.50

0.75

1

FLOPs Balance

76

78

80

EfficientNet-V2-L

iWildCam OOD Acc

0

0.25

0.50

0.75

1

FLOPs Balance

95

96

97

EfficientNet-V2-L

Caltech 256 Acc

Acc scaled by 100 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

84

85

86

87

EfficientNet-V2-L

ImageNet F1

0

0.25

0.50

0.75

1

FLOPs Balance

74

76

78

EfficientNet-V2-L

ImageNet V2 F1

0

0.25

0.50

0.75

1

FLOPs Balance

45

48

51

EfficientNet-V2-L

iWildCam F1

0

0.25

0.50

0.75

1

FLOPs Balance

33

36

39

EfficientNet-V2-L

iWildCam OOD F1

0

0.25

0.50

0.75

1

FLOPs Balance

95

96

EfficientNet-V2-L

Caltech 256 F1

F1 scaled by 100 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

5.0

6.0

EfficientNet-V2-L

ImageNet NLL

0

0.25

0.50

0.75

1

FLOPs Balance

9.0

10

11

EfficientNet-V2-L

ImageNet V2 NLL

0

0.25

0.50

0.75

1

FLOPs Balance

8.0

10

12

EfficientNet-V2-L

iWildCam NLL

0

0.25

0.50

0.75

1

FLOPs Balance

8.0

10

12

14

EfficientNet-V2-L

iWildCam OOD NLL

0

0.25

0.50

0.75

1

FLOPs Balance

1.5

2.0

EfficientNet-V2-L

Caltech 256 NLL

NLL scaled by 10 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

2.0

4.0

EfficientNet-V2-L

ImageNet ECE

0

0.25

0.50

0.75

1

FLOPs Balance

4.0

6.0

8.0

EfficientNet-V2-L

ImageNet V2 ECE

0

0.25

0.50

0.75

1

FLOPs Balance

5.0

10

EfficientNet-V2-L

iWildCam ECE

0

0.25

0.50

0.75

1

FLOPs Balance

10

20

30

EfficientNet-V2-L

iWildCam OOD ECE

0

0.25

0.50

0.75

1

FLOPs Balance

1.0

2.0

3.0

EfficientNet-V2-L

Caltech 256 ECE

ECE scaled by 100 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

20

22

24

EfficientNet-V2-L

ImageNet Brier

0

0.25

0.50

0.75

1

FLOPs Balance

32

34

36

38

EfficientNet-V2-L

ImageNet V2 Brier

0

0.25

0.50

0.75

1

FLOPs Balance

160

180

200

EfficientNet-V2-L

iWildCam Brier

0

0.25

0.50

0.75

1

FLOPs Balance

150

180

210

240

EfficientNet-V2-L

iWildCam OOD Brier

0

0.25

0.50

0.75

1

FLOPs Balance

20

24

28

32

EfficientNet-V2-L

Caltech 256 Brier

Brier scaled by 100000 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

86

88

EfficientNet-V2-L

ImageNet AUROC

0

0.25

0.50

0.75

1

FLOPs Balance

84

86

EfficientNet-V2-L

ImageNet V2 AUROC

0

0.25

0.50

0.75

1

FLOPs Balance

84

87

90

EfficientNet-V2-L

iWildCam AUROC

0

0.25

0.50

0.75

1

FLOPs Balance

90

92

94

EfficientNet-V2-L

iWildCam OOD AUROC

0

0.25

0.50

0.75

1

FLOPs Balance

94

95

EfficientNet-V2-L

Caltech 256 AUROC

AUROC scaled by 100 for legibility.

Duo: Ours

Duo: UQ Only

0

0.25

0.50

0.75

1

FLOPs Balance

3.5

4.0

EfficientNet-V2-L

ImageNet AURC

0

0.25

0.50

0.75

1

FLOPs Balance

7.5

8.0

8.5

EfficientNet-V2-L

ImageNet V2 AURC

0

0.25

0.50

0.75

1

FLOPs Balance

5.0

6.0

7.0

EfficientNet-V2-L

iWildCam AURC

0

0.25

0.50

0.75

1

FLOPs Balance

4.0

4.5

5.0

5.5

EfficientNet-V2-L

iWildCam OOD AURC

0

0.25

0.50

0.75

1

FLOPs Balance

0.3

0.3

0.4

0.5

EfficientNet-V2-L

Caltech 256 AURC

AURC scaled by 100 for legibility.

Duo: Ours

Duo: UQ Only

0

0.25

0.50

0.75

1

FLOPs Balance

32

40

48

56

EfficientNet-V2-L

ImageNet SAC@98

0

0.25

0.50

0.75

1

FLOPs Balance

0.0

10

20

EfficientNet-V2-L

ImageNet V2 SAC@98

0

0.25

0.50

0.75

1

FLOPs Balance

0.0

20

40

60

EfficientNet-V2-L

iWildCam SAC@98

0

0.25

0.50

0.75

1

FLOPs Balance

56

60

64

EfficientNet-V2-L

iWildCam OOD SAC@98

0

0.25

0.50

0.75

1

FLOPs Balance

96

97

EfficientNet-V2-L

Caltech 256 SAC@98

SAC@98 scaled by 100 for legibility.

Duo: Ours

Duo: UQ Only

ConvNeXt-Base Pretrained on ImageNet-1K is benchmarked as f large on all five datasets.

0

0.25

0.50

0.75

1

FLOPs Balance

82

83

84

ConvNext-B

ImageNet Acc

0

0.25

0.50

0.75

1

FLOPs Balance

72

74

ConvNext-B

ImageNet V2 Acc

0

0.25

0.50

0.75

1

FLOPs Balance

76

77

78

ConvNext-B

iWildCam Acc

0

0.25

0.50

0.75

1

FLOPs Balance

75

76

77

ConvNext-B

iWildCam OOD Acc

0

0.25

0.50

0.75

1

FLOPs Balance

92

93

94

ConvNext-B

Caltech 256 Acc

Acc scaled by 100 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

82

83

84

ConvNext-B

ImageNet F1

0

0.25

0.50

0.75

1

FLOPs Balance

72

74

ConvNext-B

ImageNet V2 F1

0

0.25

0.50

0.75

1

FLOPs Balance

42

45

48

ConvNext-B

iWildCam F1

0

0.25

0.50

0.75

1

FLOPs Balance

27

30

33

ConvNext-B

iWildCam OOD F1

0

0.25

0.50

0.75

1

FLOPs Balance

92

93

ConvNext-B

Caltech 256 F1

F1 scaled by 100 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

6.0

6.5

7.0

7.5

ConvNext-B

ImageNet NLL

0

0.25

0.50

0.75

1

FLOPs Balance

11

12

13

ConvNext-B

ImageNet V2 NLL

0

0.25

0.50

0.75

1

FLOPs Balance

10

12

ConvNext-B

iWildCam NLL

0

0.25

0.50

0.75

1

FLOPs Balance

10

12

ConvNext-B

iWildCam OOD NLL

0

0.25

0.50

0.75

1

FLOPs Balance

2.5

3.0

ConvNext-B

Caltech 256 NLL

NLL scaled by 10 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

2.0

3.0

4.0

ConvNext-B

ImageNet ECE

0

0.25

0.50

0.75

1

FLOPs Balance

4.0

6.0

8.0

10

ConvNext-B

ImageNet V2 ECE

0

0.25

0.50

0.75

1

FLOPs Balance

5.0

10

ConvNext-B

iWildCam ECE

0

0.25

0.50

0.75

1

FLOPs Balance

5.0

10

15

ConvNext-B

iWildCam OOD ECE

0

0.25

0.50

0.75

1

FLOPs Balance

1.0

2.0

3.0

ConvNext-B

Caltech 256 ECE

ECE scaled by 100 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

24

26

ConvNext-B

ImageNet Brier

0

0.25

0.50

0.75

1

FLOPs Balance

38

40

42

ConvNext-B

ImageNet V2 Brier

0

0.25

0.50

0.75

1

FLOPs Balance

165

180

195

ConvNext-B

iWildCam Brier

0

0.25

0.50

0.75

1

FLOPs Balance

180

200

220

ConvNext-B

iWildCam OOD Brier

0

0.25

0.50

0.75

1

FLOPs Balance

35

40

45

ConvNext-B

Caltech 256 Brier

Brier scaled by 100000 for legibility.

Duo: Ours

Duo: Unweighted

0

0.25

0.50

0.75

1

FLOPs Balance

85

86

87

88

ConvNext-B

ImageNet AUROC

0

0.25

0.50

0.75

1

FLOPs Balance

82

84

86

ConvNext-B

ImageNet V2 AUROC

0

0.25

0.50

0.75

1

FLOPs Balance

89

90

91

92

ConvNext-B

iWildCam AUROC

0

0.25

0.50

0.75

1

FLOPs Balance

91

92

93

ConvNext-B

iWildCam OOD AUROC

0

0.25

0.50

0.75

1

FLOPs Balance

94

95

ConvNext-B

Caltech 256 AUROC

AUROC scaled by 100 for legibility.

Duo: Ours

Duo: UQ Only

0

0.25

0.50

0.75

1

FLOPs Balance

4.0

4.2

4.5

4.8

ConvNext-B

ImageNet AURC

0

0.25

0.50

0.75

1

FLOPs Balance

9.0

10

11

ConvNext-B

ImageNet V2 AURC

0

0.25

0.50

0.75

1

FLOPs Balance

5.0

5.5

6.0

6.5

ConvNext-B

iWildCam AURC

0

0.25

0.50

0.75

1

FLOPs Balance

4.8

5.0

5.2

5.5

ConvNext-B

iWildCam OOD AURC

0

0.25

0.50

0.75

1

FLOPs Balance

0.6

0.6

0.7

ConvNext-B

Caltech 256 AURC

AURC scaled by 100 for legibility.

Duo: Ours

Duo: UQ Only

0

0.25

0.50

0.75

1

FLOPs Balance

15

30

45

ConvNext-B

ImageNet SAC@98

0

0.25

0.50

0.75

1

FLOPs Balance

0.0

10

20

ConvNext-B

ImageNet V2 SAC@98

0

0.25

0.50

0.75

1

FLOPs Balance

32

40

48

56

ConvNext-B

iWildCam SAC@98

0

0.25

0.50

0.75

1

FLOPs Balance

52

54

56

58

ConvNext-B

iWildCam OOD SAC@98

0

0.25

0.50

0.75

1

FLOPs Balance

89

90

91

ConvNext-B

Caltech 256 SAC@98

SAC@98 scaled by 100 for legibility.

Duo: Ours

Duo: UQ Only

NeurIPS Paper Checklist

1. Claims

Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?

Answer: [Yes]

Justification: Yes, our main contribution is the development of a computationally efficient Asymmetric Duos method that improves upon single models across a wide selections of metrics using only fractional additional computation. This claim was made clear in the abstract, and supported by Figure 1 and Section 5.

2. Limitations

Question: Does the paper discuss the limitations of the work performed by the authors?

Answer: [Yes]

Justification: Limitations of our work is discussed in the Section 6, and specifically the paragraph on Limitations and Future Directions.

3. Theory assumptions and proofs

Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?

Answer: [NA]

Justification: Our work is an empirical study that doesn't include novel theoretical results.

4. Experimental result reproducibility

Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?

Answer: [Yes]

Justification: Details found in Section 4 and Appendix A are sufficient for reproduction of our main experimental results.

5. Open access to data and code

Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?

Answer: [Yes]

Justification: All pre-trained backbones used in our experiments are publically available, and are described in Appendix A. Full experimental code would be made available.

6. 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: We provide detailed descriptions of training procedure in Section 4 and Appendix A

7. 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: [Yes]

Justification: Our scatterplot results in Section 5 display all Duos, so no error bar is needed. Our high-level result in Figure 1 displays clear error bar to show significance.

8. 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: Compute resources are made clear whenever necessary (e.g. for the temperature weights tuning step described in Section 3 and the throughput experiment described in Appendix B).

9. Code of ethics

Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines ?

Answer: [Yes]

Justification: No ethical concerns.

10. Broader impacts

Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?

Answer: [NA]

Justification: Our method aims to improve computational efficiency and effectiveness in deep networks' predictive power and uncertainty quantification quality. We do not perceive any societal impacts beyond those of standard deep networks.

11. Safeguards

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: Our method aims to improve reliability of model uncertainty and has no more risk of being misused than existing methods like deep ensembles.

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: [Yes]

Justification: All pre-trained models used in our paper are open-source and publicly available.

13. New assets

Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?

Answer: [NA]

Justification: Not applicable.

14. Crowdsourcing and research with human subjects

Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?

Answer: [NA]

Justification: Not applicable.

15. Institutional review board (IRB) approvals or equivalent for research with human subjects

Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?

Answer: [NA]

Justification: Not applicable.

16. Declaration of LLM usage

Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.

Answer: [NA]

Justification: LLMs were not used in any important, original, or non-standard capacity.

Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes to build an ensemble of n=2 models, especially when the second model is smaller than the first. The models are combined on the logit level by learning mixture weights (= temperatures) based on validation log likelihood. The authors find that these “Duos” give increased performance, both in terms of accuracy and uncertainty quantification, and that the second model does not have to be big for this to be true. Indeed, if the second model has about 25% of the FLOPs of the first model, the performance already saturates. This indicates that model ensembles can be more efficient than the popular default n=10 deep ensembles.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n\n* The paper is well written and section connect to each other in a logical manner\n* The paper pays attention to detail, such as reporting number of parameters + FLOPS + throughput to give a wholistic picture, adding ablations on metrics and models in the appendices, and making sure comparisons are fair (for example using the UQ-only Duo when comparing AURC)\n* The analysis is very deep in terms of metrics (accuracy, logl, Brier score, ECE, AUROC, AURC, SAC). All of these metrics are grouped nicely and put into perspective correctly, I am not missing anything here.\n* The paper is reproducible. The appendix contains an in-depth description of all hyperparameters and code that reproduces Figure 1-14 is provided.\n\n## Weaknesses\n\n### Major weaknesses (that influence my score)\n\n* The paper only compares duos to single models as a baseline. It would be interesting to compare to deep ensembles of different sizes, if not further modern ensembling approaches. Currently, the paper only supports the hypothesis “Yes, adding a second model improves performance and UQ of the duo, even if the second model is small.”, but comparing to ensembles could help judge if the improvement is already saturating to the performance of the ensemble (showing that deep ensembles are unnecessarily big), or how big the gap is. I would be happy to see experiments on this in the rebuttal. Regardless of whether the outcome is “positive” or not, I think it would strengthen the paper.\n* The novelty of the paper is incremental. In essence, the main message is “Adding a second model helps improve performance slightly, and this second model can be smaller (although bigger = better)”. Since ensembling is already well-known, and also n=2 ensembles were explored in literature, the methodological and insight contribution is limited, and it is also limited in scope to image classification, which is a topic that ages currently.\n\n### Other notes that did not influence my score and need no rebuttal but could help improve the camera-ready:\n\n* Caption of Figure 2, I would replace “littler” with “smaller”\n* “Randomly assigned uncertainty measure would yield an AUROC score of 0.5“ → might want to rewrite to either a measure / estimator that randomly assigns, or randomly assigned estimates. A randomly assigned measure is somewhat unorthodox\n* “We note that the AUROC metric couples accuracy and uncertainty quantification“ I do not believe this is true. The AUROC (Section 5.2) is independent of the marginal of the binary variable, which in your case is the accuracy. (the AURC in section 5.3 does conflate them)\n\n## Justification for score\n\nThe paper is exceptionally well executed both in experiments and in writing. However, its novelty is somewhat incremental. Since I generally support well-executed papers, even if not exactly novel, I recommend to accept the paper. However, I am looking forward to experiments with deep-ensemble and other ensembling baselines, which I believe are somewhat missing with the papers scope of showing that ensembles don’t need to be big. I am willing to increase my score if these experiments can be provided, whether the outcome is “negative” or “positive” for the papers message.\n\nQUESTIONS:\nSee the request for other ensemble baselines.\n\nSince you mix the two models on the logit level (=unnormalized), it could be that one model generally has logit vectors with bigger norms than another, such that there is a confounding factor besides the mixture temperatures. I do not expect this to happen systematically, but could you check whether this is an issue, just in case?\n\nLIMITATIONS:\nThe authors describe limitations and related works that are close to their results.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces Asymmetric Duos, a practical and cost-effective method for uncertainty quantification (UQ) that leverages an ensemble of two models: a large model and a considerably smaller \"sidekick.\" The final prediction is obtained via a simple learned temperature-weighted aggregation of both outputs in logit space. The approach is evaluated in the image classification setting and is shown to improve predictive accuracy and UQ with negligible overhead, making it particularly attractive in large-scale or fine-tuning regimes.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n- **[S1]** The approach is simple and practical, offering improvements in predictive accuracy and UQ with very low computational overhead.\n- **[S2]** Applicable in standard fine-tuning scenarios and scales well to large architectures.\n- **[S3]** The empirical evaluation is thorough within the considered setup, and the paper is clearly written and easy to follow.\n\n## Weaknesses\n\n**Major:**\n\n**[W1]** The study focuses exclusively on very large architectures. However, it is known from theory and practice that deep ensembles of moderate size (e.g., 5–10 models) can offer significant improvements and can themselves even be improved significantly (cf. [1,2,3]). It would be insightful to compare Asymmetric Duos against larger deep ensemble sizes - potentially even other UQ methods see W2 - on smaller-scale problems where these are computationally feasible. This would allow a rough assessment of how large the *cost-quality trade-off* is between DEs with usual ensemble sizes and Asymmetric Duos (and potentially other competing UQ methods). \n\n**Minor:**\n- **[W2]** No comparison is made with scalable approximate Bayesian methods like IVON [4] or Laplace Redux [5]. While not critical, such a comparison could better contextualize the proposed method in the UQ landscape.\n- **[W3]** The aggregation scheme is simplistic—fixed temperature scaling. The paper lacks theoretical development or empirical exploration of even simple data-dependent or more complex adaptive combination strategies. As the simple one seems to work already well this point is minor. A closer look at potentially persistent performance gaps with larger ensemble sizes (see W1) could help in assessing how much room for improvement from more evolved aggregations can be anticipated.\n- **[W4]** The discussion of individual results and metrics is occasionally redundant and could be streamlined for conciseness.\n## References\n\n- [1] Wang, Y., & Wang, X. (2025). Agree to Disagree: Demystifying Homogeneous Deep Ensembles through Distributional Equivalence. In *The Thirteenth International Conference on Learning Representations*.\n- [2] Wild, V. D., Ghalebikesabi, S., Sejdinovic, D., & Knoblauch, J. (2024). A Rigorous Link between Deep Ensembles and (Variational) Bayesian Methods. *Advances in Neural Information Processing Systems*, 36.\n- [3] Sommer, E., Robnik, J., Nozadze, G., Seljak, U., & Rügamer, D. (2025). Microcanonical Langevin Ensembles: Advancing the Sampling of Bayesian Neural Networks. In *The Thirteenth International Conference on Learning Representations*.\n- [4] Shen, Y., Daheim, N., Cong, B., Nickl, P., Marconi, G. M., Raoul, B. C. E. M., Yokota, R., Gurevych, I., Cremers, D., Khan, M. E., & Möllenhoff, T. (2024). Variational Learning is Effective for Large Deep Networks. In *Proceedings of the 41st International Conference on Machine Learning*, *Proceedings of Machine Learning Research*, 235:44665–44686. Available from: https://proceedings.mlr.press/v235/shen24b.html.\n- [5] Daxberger, E., Kristiadi, A., Immer, A., Eschenhagen, R., Bauer, M., & Hennig, P. (2021). Laplace Redux – Effortless Bayesian Deep Learning. In *35th Conference on Neural Information Processing Systems (NeurIPS 2021)*.\n\nQUESTIONS:\n- **[Q1]** How do the learned temperatures behave in practice? Do they consistently emphasize a single model or does the dominance of one model balance out with FLOPS? Are there \"mode-collapses\"? Could the authors quantify how often the sidekick model meaningfully changes the prediction, e.g., via majority class swaps?\n\n\n- **[Q2]** How does the performance (accuracy/UQ) of Asymmetric Duos compare against a standard Deep Ensemble with 5–10 models on smaller datasets (and other scalable UQ methods)? See [W1].\n\n\n- **[Q3]**:  Do the authors see potential connections between the proposed Duos approach and Bayesian Deep Learning—particularly sampling-based inference—which also constructs ensembles of model instances to approximate the Bayesian model average (BMA)? Would you then expect a BMA composed of posterior samples from asymmetric architectures to perform well?\n\n\n$\\rightarrow$ If the authors can satisfactorily address the raised weaknesses and questions, in particular  W1/Q2, I would be inclined to raise my score to an accept.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-14"}

comments: SUMMARY:
The paper presents a combining strategy for a set of two learning models. The althors argue that the proposed model improve upon single models.

STRENGTHS AND WEAKNESSES:
The proposed method is simples but the paper lacks a more robust analysis (theorectical and/or computational) to ensure that the proposed combination scheme presents any advantage when compared to other popular combination strategies

QUESTIONS:
- How does the method compare to dynamic or adaptive combination strategies commonly used in ensemble models?
- How does the proposed method differ from a weighting scheme with weights adjusted via cross validation
- The experiments do not compared the proposed model to state of the art models for the classsification tasks

LIMITATIONS:
The proposal is simple and thus requires an extesive experimental evaluation to support its claims. It that sense, the experimental procedure should be improved by compraing the proposed strategy to state of the art models.
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-01

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper presents \"Asymmetric Duo,\" a novel efficiency-focused approach to uncertainty estimation that challenges conventional ensembling methods. Rather than the computationally prohibitive practice of training multiple large models, the researchers demonstrate how pairing a heavyweight primary model with a lightweight companion model yields remarkable benefits. By implementing a learned weighting mechanism to blend predictions from these mismatched architectures (such as combining a ViT-B with a much smaller ResNet-34), the system achieves enhanced performance across multiple dimensions. Testing across five image classification datasets revealed that this asymmetric pairing not only preserves but actually improves the primary model's accuracy and uncertainty calibration while requiring only fractional additional computational resources. Particularly noteworthy is that this performance boost occurs despite the significant capability gap between the models, working effectively even when applied to sophisticated techniques like model soups. This represents a practical breakthrough for deploying uncertainty-aware deep learning in resource-constrained environments.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths:\n- The paper tackles an important problem. \n- The idea of combining a large model is simple yet smart. \n- The results that combining a large model prediction with a small one can lead to enhanced classification accuracy is pleasantly surprising to me. \n- Extensive experiments were conducted to validate the claims. \n\n## Weaknesses:\n- Though empirically supported, the proposed method is not backed up by any theoretical foundations. It would be better if there are interesting theoretical insights to further support the proposed method. \n- Although most of the Duos lead to performance improvements, the relative improvements can vary given the same FLOPs Balance. It is not immediately clear to me on how we can select the optimal model/configuration to pair up with the large model.\n\nQUESTIONS:\n- Are the large and small models trained on the same set of data? If so, what would happen if the training data is not available to the smaller model? \n- The paper only considered a duo. Does adding more small models further improve the performance?\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-02"}