Daily Papers

Building on the probability-domain distillation framework of Sparse-KD, we develop an axiomatic, operator-theoretic framework for multi-teacher ensemble knowledge distillation. Rather than prescribing a specific aggregation formula, we define five core axioms governing valid knowledge aggregation operators, encompassing convexity, positivity, continuity, weight monotonicity, and temperature coherence. We prove the existence and non-uniqueness of operator families satisfying these axioms, establishing that multiple distinct aggregation mechanisms conform to the same foundational principles. Within this framework, we establish operator-agnostic guarantees showing that multi-teacher aggregation reduces both stochastic variance and systematic supervisory bias under heterogeneous teachers, while providing Jensen-type bounds, log-loss guarantees, and safety attenuation properties. For aggregation operators linear in teacher weights, we further establish classical ensemble variance-reduction results under standard independence assumptions, with extensions to correlated-error regimes. The framework provides theoretical grounding for multi-teacher distillation from diverse frontier models while admitting multiple valid implementation strategies.

The classification of Intangible Cultural Heritage (ICH) images in the Mekong Delta poses unique challenges due to limited annotated data, high visual similarity among classes, and domain heterogeneity. In such low-resource settings, conventional deep learning models often suffer from high variance or overfit to spurious correlations, leading to poor generalization. To address these limitations, we propose a robust framework that integrates the hybrid CoAtNet architecture with model soups, a lightweight weight-space ensembling technique that averages checkpoints from a single training trajectory without increasing inference cost. CoAtNet captures both local and global patterns through stage-wise fusion of convolution and self-attention. We apply two ensembling strategies - greedy and uniform soup - to selectively combine diverse checkpoints into a final model. Beyond performance improvements, we analyze the ensembling effect through the lens of bias-variance decomposition. Our findings show that model soups reduces variance by stabilizing predictions across diverse model snapshots, while introducing minimal additional bias. Furthermore, using cross-entropy-based distance metrics and Multidimensional Scaling (MDS), we show that model soups selects geometrically diverse checkpoints, unlike Soft Voting, which blends redundant models centered in output space. Evaluated on the ICH-17 dataset (7,406 images across 17 classes), our approach achieves state-of-the-art results with 72.36% top-1 accuracy and 69.28% macro F1-score, outperforming strong baselines including ResNet-50, DenseNet-121, and ViT. These results underscore that diversity-aware checkpoint averaging provides a principled and efficient way to reduce variance and enhance generalization in culturally rich, data-scarce classification tasks.

In this paper, we present a pure-Python library called PyPop7 for black-box optimization (BBO). As population-based methods are becoming increasingly popular for BBO, our design goal is to provide a unified API and elegant implementations for them, particularly in high-dimensional cases. Since population-based methods suffer easily from the curse of dimensionality owing to their random sampling nature, various improvements have been proposed to alleviate this issue via exploiting possible problem structures: such as space decomposition, low-memory approximation, low-rank metric learning, variance reduction, ensemble of random subspaces, model self-adaptation, and smoothing. Now PyPop7 has covered these advances with >72 versions and variants of 13 BBO algorithm families from different research communities. Its open-source code and full-fledged documents are available at https://github.com/Evolutionary-Intelligence/pypop and https://pypop.readthedocs.io, respectively.

Deep Q-learning algorithms remain notoriously unstable, especially during early training when the maximization operator amplifies estimation errors. Inspired by bounded rationality theory and developmental learning, we introduce Sat-EnQ, a two-phase framework that first learns to be ``good enough'' before optimizing aggressively. In Phase 1, we train an ensemble of lightweight Q-networks under a satisficing objective that limits early value growth using a dynamic baseline, producing diverse, low-variance estimates while avoiding catastrophic overestimation. In Phase 2, the ensemble is distilled into a larger network and fine-tuned with standard Double DQN. We prove theoretically that satisficing induces bounded updates and cannot increase target variance, with a corollary quantifying conditions for substantial reduction. Empirically, Sat-EnQ achieves 3.8x variance reduction, eliminates catastrophic failures (0% vs 50% for DQN), maintains 79% performance under environmental noise}, and requires 2.5x less compute than bootstrapped ensembles. Our results highlight a principled path toward robust reinforcement learning by embracing satisficing before optimization.

Despite their remarkable effectiveness and broad application, the drivers of success underlying ensembles of trees are still not fully understood. In this paper, we highlight how interpreting tree ensembles as adaptive and self-regularizing smoothers can provide new intuition and deeper insight to this topic. We use this perspective to show that, when studied as smoothers, randomized tree ensembles not only make predictions that are quantifiably more smooth than the predictions of the individual trees they consist of, but also further regulate their smoothness at test-time based on the dissimilarity between testing and training inputs. First, we use this insight to revisit, refine and reconcile two recent explanations of forest success by providing a new way of quantifying the conjectured behaviors of tree ensembles objectively by measuring the effective degree of smoothing they imply. Then, we move beyond existing explanations for the mechanisms by which tree ensembles improve upon individual trees and challenge the popular wisdom that the superior performance of forests should be understood as a consequence of variance reduction alone. We argue that the current high-level dichotomy into bias- and variance-reduction prevalent in statistics is insufficient to understand tree ensembles -- because the prevailing definition of bias does not capture differences in the expressivity of the hypothesis classes formed by trees and forests. Instead, we show that forests can improve upon trees by three distinct mechanisms that are usually implicitly entangled. In particular, we demonstrate that the smoothing effect of ensembling can reduce variance in predictions due to noise in outcome generation, reduce variability in the quality of the learned function given fixed input data and reduce potential bias in learnable functions by enriching the available hypothesis space.

Variance reduction (VR) techniques have contributed significantly to accelerating learning with massive datasets in the smooth and strongly convex setting (Schmidt et al., 2017; Johnson & Zhang, 2013; Roux et al., 2012). However, such techniques have not yet met the same success in the realm of large-scale deep learning due to various factors such as the use of data augmentation or regularization methods like dropout (Defazio & Bottou, 2019). This challenge has recently motivated the design of novel variance reduction techniques tailored explicitly for deep learning (Arnold et al., 2019; Ma & Yarats, 2018). This work is an additional step in this direction. In particular, we exploit the ubiquitous clustering structure of rich datasets used in deep learning to design a family of scalable variance reduced optimization procedures by combining existing optimizers (e.g., SGD+Momentum, Quasi Hyperbolic Momentum, Implicit Gradient Transport) with a multi-momentum strategy (Yuan et al., 2019). Our proposal leads to faster convergence than vanilla methods on standard benchmark datasets (e.g., CIFAR and ImageNet). It is robust to label noise and amenable to distributed optimization. We provide a parallel implementation in JAX.

Deep neural networks are powerful predictors for a variety of tasks. However, they do not capture uncertainty directly. Using neural network ensembles to quantify uncertainty is competitive with approaches based on Bayesian neural networks while benefiting from better computational scalability. However, building ensembles of neural networks is a challenging task because, in addition to choosing the right neural architecture or hyperparameters for each member of the ensemble, there is an added cost of training each model. We propose AutoDEUQ, an automated approach for generating an ensemble of deep neural networks. Our approach leverages joint neural architecture and hyperparameter search to generate ensembles. We use the law of total variance to decompose the predictive variance of deep ensembles into aleatoric (data) and epistemic (model) uncertainties. We show that AutoDEUQ outperforms probabilistic backpropagation, Monte Carlo dropout, deep ensemble, distribution-free ensembles, and hyper ensemble methods on a number of regression benchmarks.

Training deep neural networks--and more recently, large models--demands efficient and scalable optimizers. Adaptive gradient algorithms like Adam, AdamW, and their variants have been central to this task. Despite the development of numerous variance reduction algorithms in the past decade aimed at accelerating stochastic optimization in both convex and nonconvex settings, variance reduction has not found widespread success in training deep neural networks or large language models. Consequently, it has remained a less favored approach in modern AI. In this paper, to unleash the power of variance reduction for efficient training of large models, we propose a unified optimization framework, MARS (Make vAriance Reduction Shine), which reconciles preconditioned gradient methods with variance reduction via a scaled stochastic recursive momentum technique. Within our framework, we introduce three instances of MARS that leverage preconditioned gradient updates based on AdamW, Lion, and Shampoo, respectively. We also draw a connection between our algorithms and existing optimizers. Experimental results on training GPT-2 models indicate that MARS consistently outperforms AdamW by a large margin.

In recent years, diffusion models have emerged as powerful tools for generating ensemble members in meteorology. In this work, we demonstrate that a Denoising Diffusion Implicit Model (DDIM) can effectively control ensemble variance by varying the number of diffusion steps. Introducing a theoretical framework, we relate diffusion steps to the variance expressed by the reverse diffusion process. Focusing on reanalysis downscaling, we propose an ensemble diffusion model for the full ERA5-to-CERRA domain, generating variance-calibrated ensemble members for wind speed at full spatial and temporal resolution. Our method aligns global mean variance with a reference ensemble dataset and ensures spatial variance is distributed in accordance with observed meteorological variability. Additionally, we address the lack of ensemble information in the CARRA dataset, showcasing the utility of our approach for efficient, high-resolution ensemble generation.

In Part I, we created an ensemble based on Spherical Fourier Neural Operators. As initial condition perturbations, we used bred vectors, and as model perturbations, we used multiple checkpoints trained independently from scratch. Based on diagnostics that assess the ensemble's physical fidelity, our ensemble has comparable performance to operational weather forecasting systems. However, it requires orders of magnitude fewer computational resources. Here in Part II, we generate a huge ensemble (HENS), with 7,424 members initialized each day of summer 2023. We enumerate the technical requirements for running huge ensembles at this scale. HENS precisely samples the tails of the forecast distribution and presents a detailed sampling of internal variability. HENS has two primary applications: (1) as a large dataset with which to study the statistics and drivers of extreme weather and (2) as a weather forecasting system. For extreme climate statistics, HENS samples events 4sigma away from the ensemble mean. At each grid cell, HENS increases the skill of the most accurate ensemble member and enhances coverage of possible future trajectories. As a weather forecasting model, HENS issues extreme weather forecasts with better uncertainty quantification. It also reduces the probability of outlier events, in which the verification value lies outside the ensemble forecast distribution.

Deep ensemble methods often improve predictive performance, yet they suffer from three practical limitations: redundancy among base models that inflates computational cost and degrades conditioning, unstable weighting under multicollinearity, and overfitting in meta-learning pipelines. We propose a regularized meta-learning framework that addresses these challenges through a four-stage pipeline combining redundancy-aware projection, statistical meta-feature augmentation, and cross-validated regularized meta-models (Ridge, Lasso, and ElasticNet). Our multi-metric de-duplication strategy removes near-collinear predictors using correlation and MSE thresholds (τ_{corr}=0.95), reducing the effective condition number of the meta-design matrix while preserving predictive diversity. Engineered ensemble statistics and interaction terms recover higher-order structure unavailable to raw prediction columns. A final inverse-RMSE blending stage mitigates regularizer-selection variance. On the Playground Series S6E1 benchmark (100K samples, 72 base models), the proposed framework achieves an out-of-fold RMSE of 8.582, improving over simple averaging (8.894) and conventional Ridge stacking (8.627), while matching greedy hill climbing (8.603) with substantially lower runtime (4 times faster). Conditioning analysis shows a 53.7\% reduction in effective matrix condition number after redundancy projection. Comprehensive ablations demonstrate consistent contributions from de-duplication, statistical meta-features, and meta-ensemble blending. These results position regularized meta-learning as a stable and deployment-efficient stacking strategy for high-dimensional ensemble systems.

Studying low-likelihood high-impact extreme weather events in a warming world is a significant and challenging task for current ensemble forecasting systems. While these systems presently use up to 100 members, larger ensembles could enrich the sampling of internal variability. They may capture the long tails associated with climate hazards better than traditional ensemble sizes. Due to computational constraints, it is infeasible to generate huge ensembles (comprised of 1,000-10,000 members) with traditional, physics-based numerical models. In this two-part paper, we replace traditional numerical simulations with machine learning (ML) to generate hindcasts of huge ensembles. In Part I, we construct an ensemble weather forecasting system based on Spherical Fourier Neural Operators (SFNO), and we discuss important design decisions for constructing such an ensemble. The ensemble represents model uncertainty through perturbed-parameter techniques, and it represents initial condition uncertainty through bred vectors, which sample the fastest growing modes of the forecast. Using the European Centre for Medium-Range Weather Forecasts Integrated Forecasting System (IFS) as a baseline, we develop an evaluation pipeline composed of mean, spectral, and extreme diagnostics. Using large-scale, distributed SFNOs with 1.1 billion learned parameters, we achieve calibrated probabilistic forecasts. As the trajectories of the individual members diverge, the ML ensemble mean spectra degrade with lead time, consistent with physical expectations. However, the individual ensemble members' spectra stay constant with lead time. Therefore, these members simulate realistic weather states, and the ML ensemble thus passes a crucial spectral test in the literature. The IFS and ML ensembles have similar Extreme Forecast Indices, and we show that the ML extreme weather forecasts are reliable and discriminating.

We introduce ensembles within score-based sampling methods to develop gradient-free approximate sampling techniques that leverage the collective dynamics of particle ensembles to compute approximate reverse diffusion drifts. We introduce the underlying methodology, emphasizing its relationship with generative diffusion models and the previously introduced F\"ollmer sampler. We demonstrate the efficacy of ensemble strategies through various examples, ranging from low- to medium-dimensionality sampling problems, including multi-modal and highly non-Gaussian probability distributions, and provide comparisons to traditional methods like NUTS. Our findings highlight the potential of ensemble strategies for modeling complex probability distributions in situations where gradients are unavailable. Finally, we showcase its application in the context of Bayesian inversion problems within the geophysical sciences.

Automating machine learning has achieved remarkable technological developments in recent years, and building an automated machine learning pipeline is now an essential task. The model ensemble is the technique of combining multiple models to get a better and more robust model. However, existing automated machine learning tends to be simplistic in handling the model ensemble, where the ensemble strategy is fixed, such as stacked generalization. There have been many techniques on different ensemble methods, especially ensemble selection, and the fixed ensemble strategy limits the upper limit of the model's performance. In this article, we present a novel framework for automated machine learning. Our framework incorporates advances in dynamic ensemble selection, and to our best knowledge, our approach is the first in the field of AutoML to search and optimize ensemble strategies. In the comparison experiments, our method outperforms the state-of-the-art automated machine learning frameworks with the same CPU time in 42 classification datasets from the OpenML platform. Ablation experiments on our framework validate the effectiveness of our proposed method.

Ensembles of independently trained neural networks are a state-of-the-art approach to estimate predictive uncertainty in Deep Learning, and can be interpreted as an approximation of the posterior distribution via a mixture of delta functions. The training of ensembles relies on non-convexity of the loss landscape and random initialization of their individual members, making the resulting posterior approximation uncontrolled. This paper proposes a novel and principled method to tackle this limitation, minimizing an f-divergence between the true posterior and a kernel density estimator (KDE) in a function space. We analyze this objective from a combinatorial point of view, and show that it is submodular with respect to mixture components for any f. Subsequently, we consider the problem of greedy ensemble construction. From the marginal gain on the negative f-divergence, which quantifies an improvement in posterior approximation yielded by adding a new component into the KDE, we derive a novel diversity term for ensemble methods. The performance of our approach is demonstrated on computer vision out-of-distribution detection benchmarks in a range of architectures trained on multiple datasets. The source code of our method is made publicly available at https://github.com/Oulu-IMEDS/greedy_ensembles_training.

Deep Ensembles are a simple, reliable, and effective method of improving both the predictive performance and uncertainty estimates of deep learning approaches. However, they are widely criticised as being computationally expensive, due to the need to deploy multiple independent models. Recent work has challenged this view, showing that for predictive accuracy, ensembles can be more computationally efficient (at inference) than scaling single models within an architecture family. This is achieved by cascading ensemble members via an early-exit approach. In this work, we investigate extending these efficiency gains to tasks related to uncertainty estimation. As many such tasks, e.g. selective classification, are binary classification, our key novel insight is to only pass samples within a window close to the binary decision boundary to later cascade stages. Experiments on ImageNet-scale data across a number of network architectures and uncertainty tasks show that the proposed window-based early-exit approach is able to achieve a superior uncertainty-computation trade-off compared to scaling single models. For example, a cascaded EfficientNet-B2 ensemble is able to achieve similar coverage at 5% risk as a single EfficientNet-B4 with <30% the number of MACs. We also find that cascades/ensembles give more reliable improvements on OOD data vs scaling models up. Code for this work is available at: https://github.com/Guoxoug/window-early-exit.

Control variates are variance reduction tools for Monte Carlo estimators. They can provide significant variance reduction, but usually require a large number of samples, which can be prohibitive when sampling or evaluating the integrand is computationally expensive. Furthermore, there are many scenarios where we need to compute multiple related integrals simultaneously or sequentially, which can further exacerbate computational costs. In this paper, we propose vector-valued control variates, an extension of control variates which can be used to reduce the variance of multiple Monte Carlo estimators jointly. This allows for the transfer of information across integration tasks, and hence reduces the need for a large number of samples. We focus on control variates based on kernel interpolants and our novel construction is obtained through a generalised Stein identity and the development of novel matrix-valued Stein reproducing kernels. We demonstrate our methodology on a range of problems including multifidelity modelling, Bayesian inference for dynamical systems, and model evidence computation through thermodynamic integration.

Probabilistic forecasting is crucial to decision-making under uncertainty about future weather. The dominant approach is to use an ensemble of forecasts to represent and quantify uncertainty in operational numerical weather prediction. However, generating ensembles is computationally costly. In this paper, we propose to generate ensemble forecasts at scale by leveraging recent advances in generative artificial intelligence. Our approach learns a data-driven probabilistic diffusion model from the 5-member ensemble GEFS reforecast dataset. The model can then be sampled efficiently to produce realistic weather forecasts, conditioned on a few members of the operational GEFS forecasting system. The generated ensembles have similar predictive skill as the full GEFS 31-member ensemble, evaluated against ERA5 reanalysis, and emulate well the statistics of large physics-based ensembles. We also apply the same methodology to developing a diffusion model for generative post-processing: the model directly learns to correct biases present in the emulated forecasting system by leveraging reanalysis data as labels during training. Ensembles from this generative post-processing model show greater reliability and accuracy, particularly in extreme event classification. In general, they are more reliable and forecast the probability of extreme weather more accurately than the GEFS operational ensemble. Our models achieve these results at less than 1/10th of the computational cost incurred by the operational GEFS system.

Model selection is a strategy aimed at creating accurate and robust models. A key challenge in designing these algorithms is identifying the optimal model for classifying any particular input sample. This paper addresses this challenge and proposes a novel framework for differentiable model selection integrating machine learning and combinatorial optimization. The framework is tailored for ensemble learning, a strategy that combines the outputs of individually pre-trained models, and learns to select appropriate ensemble members for a particular input sample by transforming the ensemble learning task into a differentiable selection program trained end-to-end within the ensemble learning model. Tested on various tasks, the proposed framework demonstrates its versatility and effectiveness, outperforming conventional and advanced consensus rules across a variety of settings and learning tasks.

Neural networks are known to produce poor uncertainty estimations, and a variety of approaches have been proposed to remedy this issue. This includes deep ensemble, a simple and effective method that achieves state-of-the-art results for uncertainty-aware learning tasks. In this work, we explore a combinatorial generalization of deep ensemble called deep combinatorial aggregation (DCA). DCA creates multiple instances of network components and aggregates their combinations to produce diversified model proposals and predictions. DCA components can be defined at different levels of granularity. And we discovered that coarse-grain DCAs can outperform deep ensemble for uncertainty-aware learning both in terms of predictive performance and uncertainty estimation. For fine-grain DCAs, we discover that an average parameterization approach named deep combinatorial weight averaging (DCWA) can improve the baseline training. It is on par with stochastic weight averaging (SWA) but does not require any custom training schedule or adaptation of BatchNorm layers. Furthermore, we propose a consistency enforcing loss that helps the training of DCWA and modelwise DCA. We experiment on in-domain, distributional shift, and out-of-distribution image classification tasks, and empirically confirm the effectiveness of DCWA and DCA approaches.

Deep Ensembles (DE) are a prominent approach for achieving excellent performance on key metrics such as accuracy, calibration, uncertainty estimation, and out-of-distribution detection. However, hardware limitations of real-world systems constrain to smaller ensembles and lower-capacity networks, significantly deteriorating their performance and properties. We introduce Packed-Ensembles (PE), a strategy to design and train lightweight structured ensembles by carefully modulating the dimension of their encoding space. We leverage grouped convolutions to parallelize the ensemble into a single shared backbone and forward pass to improve training and inference speeds. PE is designed to operate within the memory limits of a standard neural network. Our extensive research indicates that PE accurately preserves the properties of DE, such as diversity, and performs equally well in terms of accuracy, calibration, out-of-distribution detection, and robustness to distribution shift. We make our code available at https://github.com/ENSTA-U2IS/torch-uncertainty.

We consider the problem of Learning from Label Proportions (LLP), a weakly supervised classification setup where instances are grouped into "bags", and only the frequency of class labels at each bag is available. Albeit, the objective of the learner is to achieve low task loss at an individual instance level. Here we propose Easyllp: a flexible and simple-to-implement debiasing approach based on aggregate labels, which operates on arbitrary loss functions. Our technique allows us to accurately estimate the expected loss of an arbitrary model at an individual level. We showcase the flexibility of our approach by applying it to popular learning frameworks, like Empirical Risk Minimization (ERM) and Stochastic Gradient Descent (SGD) with provable guarantees on instance level performance. More concretely, we exhibit a variance reduction technique that makes the quality of LLP learning deteriorate only by a factor of k (k being bag size) in both ERM and SGD setups, as compared to full supervision. Finally, we validate our theoretical results on multiple datasets demonstrating our algorithm performs as well or better than previous LLP approaches in spite of its simplicity.

Data balancing across multiple modalities and sources appears in various forms in foundation models in machine learning and AI, e.g. in CLIP and DINO. We show that data balancing across modalities and sources actually offers an unsuspected benefit: variance reduction. We present a non-asymptotic statistical bound that quantifies this variance reduction effect and relates it to the eigenvalue decay of Markov operators. Furthermore, we describe how various forms of data balancing in contrastive multimodal learning and self-supervised clustering can be better understood, and even improved upon, owing to our variance reduction viewpoint.

In recent times, with the exception of sporadic cases, the trend in Computer Vision is to achieve minor improvements compared to considerable increases in complexity. To reverse this trend, we propose a novel method to boost image classification performances without increasing complexity. To this end, we revisited ensembling, a powerful approach, often not used properly due to its more complex nature and the training time, so as to make it feasible through a specific design choice. First, we trained two EfficientNet-b0 end-to-end models (known to be the architecture with the best overall accuracy/complexity trade-off for image classification) on disjoint subsets of data (i.e. bagging). Then, we made an efficient adaptive ensemble by performing fine-tuning of a trainable combination layer. In this way, we were able to outperform the state-of-the-art by an average of 0.5% on the accuracy, with restrained complexity both in terms of the number of parameters (by 5-60 times), and the FLoating point Operations Per Second (FLOPS) by 10-100 times on several major benchmark datasets.

Deep ensembles (DE) have been successful in improving model performance by learning diverse members via the stochasticity of random initialization. While recent works have attempted to promote further diversity in DE via hyperparameters or regularizing loss functions, these methods primarily still rely on a stochastic approach to explore the hypothesis space. In this work, we present Multi-Symmetry Ensembles (MSE), a framework for constructing diverse ensembles by capturing the multiplicity of hypotheses along symmetry axes, which explore the hypothesis space beyond stochastic perturbations of model weights and hyperparameters. We leverage recent advances in contrastive representation learning to create models that separately capture opposing hypotheses of invariant and equivariant functional classes and present a simple ensembling approach to efficiently combine appropriate hypotheses for a given task. We show that MSE effectively captures the multiplicity of conflicting hypotheses that is often required in large, diverse datasets like ImageNet. As a result of their inherent diversity, MSE improves classification performance, uncertainty quantification, and generalization across a series of transfer tasks.

Deep ensemble is a simple yet powerful way to improve the performance of deep neural networks. Under this motivation, recent works on mode connectivity have shown that parameters of ensembles are connected by low-loss subspaces, and one can efficiently collect ensemble parameters in those subspaces. While this provides a way to efficiently train ensembles, for inference, multiple forward passes should still be executed using all the ensemble parameters, which often becomes a serious bottleneck for real-world deployment. In this work, we propose a novel framework to reduce such costs. Given a low-loss subspace connecting two modes of a neural network, we build an additional neural network that predicts the output of the original neural network evaluated at a certain point in the low-loss subspace. The additional neural network, which we call a "bridge", is a lightweight network that takes minimal features from the original network and predicts outputs for the low-loss subspace without forward passes through the original network. We empirically demonstrate that we can indeed train such bridge networks and significantly reduce inference costs with the help of bridge networks.

Ensembling neural networks is an effective way to increase accuracy, and can often match the performance of individual larger models. This observation poses a natural question: given the choice between a deep ensemble and a single neural network with similar accuracy, is one preferable over the other? Recent work suggests that deep ensembles may offer distinct benefits beyond predictive power: namely, uncertainty quantification and robustness to dataset shift. In this work, we demonstrate limitations to these purported benefits, and show that a single (but larger) neural network can replicate these qualities. First, we show that ensemble diversity, by any metric, does not meaningfully contribute to an ensemble's uncertainty quantification on out-of-distribution (OOD) data, but is instead highly correlated with the relative improvement of a single larger model. Second, we show that the OOD performance afforded by ensembles is strongly determined by their in-distribution (InD) performance, and -- in this sense -- is not indicative of any "effective robustness". While deep ensembles are a practical way to achieve improvements to predictive power, uncertainty quantification, and robustness, our results show that these improvements can be replicated by a (larger) single model.

Automated machine learning (AutoML) systems commonly ensemble models post hoc to improve predictive performance, typically via greedy ensemble selection (GES). However, we believe that GES may not always be optimal, as it performs a simple deterministic greedy search. In this work, we introduce two novel population-based ensemble selection methods, QO-ES and QDO-ES, and compare them to GES. While QO-ES optimises solely for predictive performance, QDO-ES also considers the diversity of ensembles within the population, maintaining a diverse set of well-performing ensembles during optimisation based on ideas of quality diversity optimisation. The methods are evaluated using 71 classification datasets from the AutoML benchmark, demonstrating that QO-ES and QDO-ES often outrank GES, albeit only statistically significant on validation data. Our results further suggest that diversity can be beneficial for post hoc ensembling but also increases the risk of overfitting.

Ensemble-based attacks have been proven to be effective in enhancing adversarial transferability by aggregating the outputs of models with various architectures. However, existing research primarily focuses on refining ensemble weights or optimizing the ensemble path, overlooking the exploration of ensemble models to enhance the transferability of adversarial attacks. To address this gap, we propose applying adversarial augmentation to the surrogate models, aiming to boost overall generalization of ensemble models and reduce the risk of adversarial overfitting. Meanwhile, observing that ensemble Vision Transformers (ViTs) gain less attention, we propose ViT-EnsembleAttack based on the idea of model adversarial augmentation, the first ensemble-based attack method tailored for ViTs to the best of our knowledge. Our approach generates augmented models for each surrogate ViT using three strategies: Multi-head dropping, Attention score scaling, and MLP feature mixing, with the associated parameters optimized by Bayesian optimization. These adversarially augmented models are ensembled to generate adversarial examples. Furthermore, we introduce Automatic Reweighting and Step Size Enlargement modules to boost transferability. Extensive experiments demonstrate that ViT-EnsembleAttack significantly enhances the adversarial transferability of ensemble-based attacks on ViTs, outperforming existing methods by a substantial margin. Code is available at https://github.com/Trustworthy-AI-Group/TransferAttack.

Ensemble forecasting is crucial for improving weather predictions, especially for forecasts of extreme events. Constructing an ensemble prediction system (EPS) based on conventional NWP models is highly computationally expensive. ML models have emerged as valuable tools for deterministic weather forecasts, providing forecasts with significantly reduced computational requirements and even surpassing the forecast performance of traditional NWP models. However, challenges arise when applying ML models to ensemble forecasting. Recent ML models, such as GenCast and SEEDS model, rely on the ERA5 EDA or operational NWP ensemble members for forecast generation. Their spatial resolution is also considered too coarse for many applications. To overcome these limitations, we introduce FuXi-ENS, an advanced ML model designed to deliver 6-hourly global ensemble weather forecasts up to 15 days. This model runs at a significantly increased spatial resolution of 0.25\textdegree, incorporating 5 atmospheric variables at 13 pressure levels, along with 13 surface variables. By leveraging the inherent probabilistic nature of Variational AutoEncoder (VAE), FuXi-ENS optimizes a loss function that combines the CRPS and the KL divergence between the predicted and target distribution, facilitating the incorporation of flow-dependent perturbations in both initial conditions and forecast. This innovative approach makes FuXi-ENS an advancement over the traditional ones that use L1 loss combined with the KL loss in standard VAE models for ensemble weather forecasting. Results demonstrate that FuXi-ENS outperforms ensemble forecasts from the ECMWF, a world leading NWP model, in the CRPS of 98.1% of 360 variable and forecast lead time combinations. This achievement underscores the potential of the FuXi-ENS model to enhance ensemble weather forecasts, offering a promising direction for further development in this field.

The sliced Wasserstein (SW) distances between two probability measures are defined as the expectation of the Wasserstein distance between two one-dimensional projections of the two measures. The randomness comes from a projecting direction that is used to project the two input measures to one dimension. Due to the intractability of the expectation, Monte Carlo integration is performed to estimate the value of the SW distance. Despite having various variants, there has been no prior work that improves the Monte Carlo estimation scheme for the SW distance in terms of controlling its variance. To bridge the literature on variance reduction and the literature on the SW distance, we propose computationally efficient control variates to reduce the variance of the empirical estimation of the SW distance. The key idea is to first find Gaussian approximations of projected one-dimensional measures, then we utilize the closed-form of the Wasserstein-2 distance between two Gaussian distributions to design the control variates. In particular, we propose using a lower bound and an upper bound of the Wasserstein-2 distance between two fitted Gaussians as two computationally efficient control variates. We empirically show that the proposed control variate estimators can help to reduce the variance considerably when comparing measures over images and point-clouds. Finally, we demonstrate the favorable performance of the proposed control variate estimators in gradient flows to interpolate between two point-clouds and in deep generative modeling on standard image datasets, such as CIFAR10 and CelebA.

Finetuned LLMs often exhibit poor uncertainty quantification, manifesting as overconfidence, poor calibration, and unreliable prediction results on test data or out-of-distribution samples. One approach commonly used in vision for alleviating this issue is a deep ensemble, which constructs an ensemble by training the same model multiple times using different random initializations. However, there is a huge challenge to ensembling LLMs: the most effective LLMs are very, very large. Keeping a single LLM in memory is already challenging enough: keeping an ensemble of e.g. 5 LLMs in memory is impossible in many settings. To address these issues, we propose an ensemble approach using Low-Rank Adapters (LoRA), a parameter-efficient fine-tuning technique. Critically, these low-rank adapters represent a very small number of parameters, orders of magnitude less than the underlying pre-trained model. Thus, it is possible to construct large ensembles of LoRA adapters with almost the same computational overhead as using the original model. We find that LoRA ensembles, applied on its own or on top of pre-existing regularization techniques, gives consistent improvements in predictive accuracy and uncertainty quantification.

While Masked Diffusion Models (MDMs), such as LLaDA, present a promising paradigm for language modeling, there has been relatively little effort in aligning these models with human preferences via reinforcement learning. The challenge primarily arises from the high variance in Evidence Lower Bound (ELBO)-based likelihood estimates required for preference optimization. To address this issue, we propose Variance-Reduced Preference Optimization (VRPO), a framework that formally analyzes the variance of ELBO estimators and derives bounds on both the bias and variance of preference optimization gradients. Building on this theoretical foundation, we introduce unbiased variance reduction strategies, including optimal Monte Carlo budget allocation and antithetic sampling, that significantly improve the performance of MDM alignment. We demonstrate the effectiveness of VRPO by applying it to LLaDA, and the resulting model, LLaDA 1.5, outperforms its SFT-only predecessor consistently and significantly across mathematical (GSM8K +4.7), code (HumanEval +3.0, MBPP +1.8), and alignment benchmarks (IFEval +4.0, Arena-Hard +4.3). Furthermore, LLaDA 1.5 demonstrates a highly competitive mathematical performance compared to strong language MDMs and ARMs. Project page: https://ml-gsai.github.io/LLaDA-1.5-Demo/.

Randomized ensemble classifiers (RECs), where one classifier is randomly selected during inference, have emerged as an attractive alternative to traditional ensembling methods for realizing adversarially robust classifiers with limited compute requirements. However, recent works have shown that existing methods for constructing RECs are more vulnerable than initially claimed, casting major doubts on their efficacy and prompting fundamental questions such as: "When are RECs useful?", "What are their limits?", and "How do we train them?". In this work, we first demystify RECs as we derive fundamental results regarding their theoretical limits, necessary and sufficient conditions for them to be useful, and more. Leveraging this new understanding, we propose a new boosting algorithm (BARRE) for training robust RECs, and empirically demonstrate its effectiveness at defending against strong ell_infty norm-bounded adversaries across various network architectures and datasets. Our code can be found at https://github.com/hsndbk4/BARRE.

Text embeddings are essential components in modern NLP pipelines. While numerous embedding models have been proposed, their performance varies across domains. This variability motivates the use of ensemble techniques to combine complementary strengths. However, most existing ensemble methods operate on deterministic embeddings and fail to account for model-specific uncertainty, limiting their robustness and reliability in downstream applications. To address these limitations, we propose Uncertainty-driven Embedding Convolution (UEC). UEC first transforms deterministic embeddings into probabilistic ones in a post-hoc manner. It then computes adaptive ensemble weights based on embedding uncertainty, grounded in a Bayes-optimal solution under a surrogate loss. Additionally, UEC employs an uncertainty-aware similarity function that directly incorporates uncertainty into the similarity scoring, providing a theoretically grounded and efficient surrogate to distributional distances. Extensive experiments on diverse benchmarks demonstrate that UEC consistently improves both performance and robustness by leveraging principled uncertainty modeling.

The Combined Algorithm Selection and Hyperparameters optimization (CASH) problem is one of the fundamental problems in Automated Machine Learning (AutoML). Motivated by the success of ensemble learning, recent AutoML systems build post-hoc ensembles to output the final predictions instead of using the best single learner. However, while most CASH methods focus on searching for a single learner with the best performance, they neglect the diversity among base learners (i.e., they may suggest similar configurations to previously evaluated ones), which is also a crucial consideration when building an ensemble. To tackle this issue and further enhance the ensemble performance, we propose DivBO, a diversity-aware framework to inject explicit search of diversity into the CASH problems. In the framework, we propose to use a diversity surrogate to predict the pair-wise diversity of two unseen configurations. Furthermore, we introduce a temporary pool and a weighted acquisition function to guide the search of both performance and diversity based on Bayesian optimization. Empirical results on 15 public datasets show that DivBO achieves the best average ranks (1.82 and 1.73) on both validation and test errors among 10 compared methods, including post-hoc designs in recent AutoML systems and state-of-the-art baselines for ensemble learning on CASH problems.

Recent research finds CNN models for image classification demonstrate overlapped adversarial vulnerabilities: adversarial attacks can mislead CNN models with small perturbations, which can effectively transfer between different models trained on the same dataset. Adversarial training, as a general robustness improvement technique, eliminates the vulnerability in a single model by forcing it to learn robust features. The process is hard, often requires models with large capacity, and suffers from significant loss on clean data accuracy. Alternatively, ensemble methods are proposed to induce sub-models with diverse outputs against a transfer adversarial example, making the ensemble robust against transfer attacks even if each sub-model is individually non-robust. Only small clean accuracy drop is observed in the process. However, previous ensemble training methods are not efficacious in inducing such diversity and thus ineffective on reaching robust ensemble. We propose DVERGE, which isolates the adversarial vulnerability in each sub-model by distilling non-robust features, and diversifies the adversarial vulnerability to induce diverse outputs against a transfer attack. The novel diversity metric and training procedure enables DVERGE to achieve higher robustness against transfer attacks comparing to previous ensemble methods, and enables the improved robustness when more sub-models are added to the ensemble. The code of this work is available at https://github.com/zjysteven/DVERGE

Sampling-based algorithms, which eliminate ''unimportant'' computations during forward and/or back propagation (BP), offer potential solutions to accelerate neural network training. However, since sampling introduces approximations to training, such algorithms may not consistently maintain accuracy across various tasks. In this work, we introduce a variance-controlled adaptive sampling (VCAS) method designed to accelerate BP. VCAS computes an unbiased stochastic gradient with fine-grained layerwise importance sampling in data dimension for activation gradient calculation and leverage score sampling in token dimension for weight gradient calculation. To preserve accuracy, we control the additional variance by learning the sample ratio jointly with model parameters during training. We assessed VCAS on multiple fine-tuning and pre-training tasks in both vision and natural language domains. On all the tasks, VCAS can preserve the original training loss trajectory and validation accuracy with an up to 73.87% FLOPs reduction of BP and 49.58% FLOPs reduction of the whole training process. The implementation is available at https://github.com/thu-ml/VCAS .

imbalanced-ensemble, abbreviated as imbens, is an open-source Python toolbox for leveraging the power of ensemble learning to address the class imbalance problem. It provides standard implementations of popular ensemble imbalanced learning (EIL) methods with extended features and utility functions. These ensemble methods include resampling-based, e.g., under/over-sampling, and reweighting-based, e.g., cost-sensitive learning. Beyond the implementation, we empower EIL algorithms with new functionalities like customizable resampling scheduler and verbose logging, thus enabling more flexible training and evaluating strategies. The package was developed under a simple, well-documented API design that follows scikit-learn for increased ease of use. imbens is released under the MIT open-source license and can be installed from Python Package Index (PyPI) or https://github.com/ZhiningLiu1998/imbalanced-ensemble.

Reinforcement learning has demonstrated great potential for performing financial tasks. However, it faces two major challenges: policy instability and sampling bottlenecks. In this paper, we revisit ensemble methods with massively parallel simulations on graphics processing units (GPUs), significantly enhancing the computational efficiency and robustness of trained models in volatile financial markets. Our approach leverages the parallel processing capability of GPUs to significantly improve the sampling speed for training ensemble models. The ensemble models combine the strengths of component agents to improve the robustness of financial decision-making strategies. We conduct experiments in both stock and cryptocurrency trading tasks to evaluate the effectiveness of our approach. Massively parallel simulation on a single GPU improves the sampling speed by up to 1,746times using 2,048 parallel environments compared to a single environment. The ensemble models have high cumulative returns and outperform some individual agents, reducing maximum drawdown by up to 4.17% and improving the Sharpe ratio by up to 0.21. This paper describes trading tasks at ACM ICAIF FinRL Contests in 2023 and 2024.

Deep Ensembles (DEs) demonstrate improved accuracy, calibration and robustness to perturbations over single neural networks partly due to their functional diversity. Particle-based variational inference (ParVI) methods enhance diversity by formalizing a repulsion term based on a network similarity kernel. However, weight-space repulsion is inefficient due to over-parameterization, while direct function-space repulsion has been found to produce little improvement over DEs. To sidestep these difficulties, we propose First-order Repulsive Deep Ensemble (FoRDE), an ensemble learning method based on ParVI, which performs repulsion in the space of first-order input gradients. As input gradients uniquely characterize a function up to translation and are much smaller in dimension than the weights, this method guarantees that ensemble members are functionally different. Intuitively, diversifying the input gradients encourages each network to learn different features, which is expected to improve the robustness of an ensemble. Experiments on image classification datasets and transfer learning tasks show that FoRDE significantly outperforms the gold-standard DEs and other ensemble methods in accuracy and calibration under covariate shift due to input perturbations.

Typical neural network trainings have substantial variance in test-set performance between repeated runs, impeding hyperparameter comparison and training reproducibility. We present the following results towards understanding this variation. (1) Despite having significant variance on their test-sets, we demonstrate that standard CIFAR-10 and ImageNet trainings have very little variance in their performance on the test-distributions from which those test-sets are sampled, suggesting that variance is less of a practical issue than previously thought. (2) We present a simplifying statistical assumption which closely approximates the structure of the test-set accuracy distribution. (3) We argue that test-set variance is inevitable in the following two senses. First, we show that variance is largely caused by high sensitivity of the training process to initial conditions, rather than by specific sources of randomness like the data order and augmentations. Second, we prove that variance is unavoidable given the observation that ensembles of trained networks are well-calibrated. (4) We conduct preliminary studies of distribution-shift, fine-tuning, data augmentation and learning rate through the lens of variance between runs.

Ensembling is among the most popular tools in machine learning (ML) due to its effectiveness in minimizing variance and thus improving generalization. Most ensembling methods for black-box base learners fall under the umbrella of "stacked generalization," namely training an ML algorithm that takes the inferences from the base learners as input. While stacking has been widely applied in practice, its theoretical properties are poorly understood. In this paper, we prove a novel result, showing that choosing the best stacked generalization from a (finite or finite-dimensional) family of stacked generalizations based on cross-validated performance does not perform "much worse" than the oracle best. Our result strengthens and significantly extends the results in Van der Laan et al. (2007). Inspired by the theoretical analysis, we further propose a particular family of stacked generalizations in the context of probabilistic forecasting, each one with a different sensitivity for how much the ensemble weights are allowed to vary across items, timestamps in the forecast horizon, and quantiles. Experimental results demonstrate the performance gain of the proposed method.

A very simple way to improve the performance of almost any machine learning algorithm is to train many different models on the same data and then to average their predictions. Unfortunately, making predictions using a whole ensemble of models is cumbersome and may be too computationally expensive to allow deployment to a large number of users, especially if the individual models are large neural nets. Caruana and his collaborators have shown that it is possible to compress the knowledge in an ensemble into a single model which is much easier to deploy and we develop this approach further using a different compression technique. We achieve some surprising results on MNIST and we show that we can significantly improve the acoustic model of a heavily used commercial system by distilling the knowledge in an ensemble of models into a single model. We also introduce a new type of ensemble composed of one or more full models and many specialist models which learn to distinguish fine-grained classes that the full models confuse. Unlike a mixture of experts, these specialist models can be trained rapidly and in parallel.

Federated learning algorithms, such as FedAvg, are negatively affected by data heterogeneity and partial client participation. To mitigate the latter problem, global variance reduction methods, like FedVARP, leverage stale model updates for non-participating clients. These methods are effective under homogeneous client participation. Yet, this paper shows that, when some clients participate much less than others, aggregating updates with different levels of staleness can detrimentally affect the training process. Motivated by this observation, we introduce FedStale, a novel algorithm that updates the global model in each round through a convex combination of "fresh" updates from participating clients and "stale" updates from non-participating ones. By adjusting the weight in the convex combination, FedStale interpolates between FedAvg, which only uses fresh updates, and FedVARP, which treats fresh and stale updates equally. Our analysis of FedStale convergence yields the following novel findings: i) it integrates and extends previous FedAvg and FedVARP analyses to heterogeneous client participation; ii) it underscores how the least participating client influences convergence error; iii) it provides practical guidelines to best exploit stale updates, showing that their usefulness diminishes as data heterogeneity decreases and participation heterogeneity increases. Extensive experiments featuring diverse levels of client data and participation heterogeneity not only confirm these findings but also show that FedStale outperforms both FedAvg and FedVARP in many settings.

Recent self-supervised methods for image representation learning are based on maximizing the agreement between embedding vectors from different views of the same image. A trivial solution is obtained when the encoder outputs constant vectors. This collapse problem is often avoided through implicit biases in the learning architecture, that often lack a clear justification or interpretation. In this paper, we introduce VICReg (Variance-Invariance-Covariance Regularization), a method that explicitly avoids the collapse problem with a simple regularization term on the variance of the embeddings along each dimension individually. VICReg combines the variance term with a decorrelation mechanism based on redundancy reduction and covariance regularization, and achieves results on par with the state of the art on several downstream tasks. In addition, we show that incorporating our new variance term into other methods helps stabilize the training and leads to performance improvements.

Machine learning for time-series forecasting remains a key area of research. Despite successful application of many machine learning techniques, relating computational efficiency to forecast error remains an under-explored domain. This paper addresses this topic through a series of real-time experiments to quantify the relationship between computational cost and forecast error using meteorological nowcasting as an example use-case. We employ a variety of popular regression techniques (XGBoost, FC-MLP, Transformer, and LSTM) for multi-horizon, short-term forecasting of three variables (temperature, wind speed, and cloud cover) for multiple locations. During a 5-day live experiment, 4000 data sources were streamed for training and inferencing 144 models per hour. These models were parameterized to explore forecast error for two computational cost minimization methods: a novel auto-adaptive data reduction technique (Variance Horizon) and a performance-based concept drift-detection mechanism. Forecast error of all model variations were benchmarked in real-time against a state-of-the-art numerical weather prediction model. Performance was assessed using classical and novel evaluation metrics. Results indicate that using the Variance Horizon reduced computational usage by more than 50\%, while increasing between 0-15\% in error. Meanwhile, performance-based retraining reduced computational usage by up to 90\% while also improving forecast error by up to 10\%. Finally, the combination of both the Variance Horizon and performance-based retraining outperformed other model configurations by up to 99.7\% when considering error normalized to computational usage.

We employ random matrix theory to establish consistency of generalized cross validation (GCV) for estimating prediction risks of sketched ridge regression ensembles, enabling efficient and consistent tuning of regularization and sketching parameters. Our results hold for a broad class of asymptotically free sketches under very mild data assumptions. For squared prediction risk, we provide a decomposition into an unsketched equivalent implicit ridge bias and a sketching-based variance, and prove that the risk can be globally optimized by only tuning sketch size in infinite ensembles. For general subquadratic prediction risk functionals, we extend GCV to construct consistent risk estimators, and thereby obtain distributional convergence of the GCV-corrected predictions in Wasserstein-2 metric. This in particular allows construction of prediction intervals with asymptotically correct coverage conditional on the training data. We also propose an "ensemble trick" whereby the risk for unsketched ridge regression can be efficiently estimated via GCV using small sketched ridge ensembles. We empirically validate our theoretical results using both synthetic and real large-scale datasets with practical sketches including CountSketch and subsampled randomized discrete cosine transforms.

In modern recommendation systems, the standard pipeline involves training machine learning models on historical data to predict user behaviors and improve recommendations continuously. However, these data training loops can introduce interference in A/B tests, where data generated by control and treatment algorithms, potentially with different distributions, are combined. To address these challenges, we introduce a novel approach called weighted training. This approach entails training a model to predict the probability of each data point appearing in either the treatment or control data and subsequently applying weighted losses during model training. We demonstrate that this approach achieves the least variance among all estimators that do not cause shifts in the training distributions. Through simulation studies, we demonstrate the lower bias and variance of our approach compared to other methods.

It is impossible today to pretend that the practice of machine learning is compatible with the idea that training and testing data follow the same distribution. Several authors have recently used ensemble techniques to show how scenarios involving multiple data distributions are best served by representations that are both richer than those obtained by regularizing for the best in-distribution performance, and richer than those obtained under the influence of the implicit sparsity bias of common stochastic gradient procedures. This contribution investigates the use of very high dropout rates instead of ensembles to obtain such rich representations. Although training a deep network from scratch using such dropout rates is virtually impossible, fine-tuning a large pre-trained model under such conditions is not only possible but also achieves out-of-distribution performances that exceed those of both ensembles and weight averaging methods such as model soups. This result has practical significance because the importance of the fine-tuning scenario has considerably grown in recent years. This result also provides interesting insights on the nature of rich representations and on the intrinsically linear nature of fine-tuning a large network using a comparatively small dataset.

Generating synthetic data through generative models is gaining interest in the ML community and beyond, promising a future where datasets can be tailored to individual needs. Unfortunately, synthetic data is usually not perfect, resulting in potential errors in downstream tasks. In this work we explore how the generative process affects the downstream ML task. We show that the naive synthetic data approach -- using synthetic data as if it is real -- leads to downstream models and analyses that do not generalize well to real data. As a first step towards better ML in the synthetic data regime, we introduce Deep Generative Ensemble (DGE) -- a framework inspired by Deep Ensembles that aims to implicitly approximate the posterior distribution over the generative process model parameters. DGE improves downstream model training, evaluation, and uncertainty quantification, vastly outperforming the naive approach on average. The largest improvements are achieved for minority classes and low-density regions of the original data, for which the generative uncertainty is largest.

Numerous crucial tasks in real-world decision-making rely on machine learning algorithms with calibrated uncertainty estimates. However, modern methods often yield overconfident and uncalibrated predictions. Various approaches involve training an ensemble of separate models to quantify the uncertainty related to the model itself, known as epistemic uncertainty. In an explicit implementation, the ensemble approach has high computational cost and high memory requirements. This particular challenge is evident in state-of-the-art neural networks such as transformers, where even a single network is already demanding in terms of compute and memory. Consequently, efforts are made to emulate the ensemble model without actually instantiating separate ensemble members, referred to as implicit ensembling. We introduce LoRA-Ensemble, a parameter-efficient deep ensemble method for self-attention networks, which is based on Low-Rank Adaptation (LoRA). Initially developed for efficient LLM fine-tuning, we extend LoRA to an implicit ensembling approach. By employing a single pre-trained self-attention network with weights shared across all members, we train member-specific low-rank matrices for the attention projections. Our method exhibits superior calibration compared to explicit ensembles and achieves similar or better accuracy across various prediction tasks and datasets.

Continual learning with an increasing number of classes is a challenging task. The difficulty rises when each example is presented exactly once, which requires the model to learn online. Recent methods with classic parameter optimization procedures have been shown to struggle in such setups or have limitations like non-differentiable components or memory buffers. For this reason, we present the fully differentiable ensemble method that allows us to efficiently train an ensemble of neural networks in the end-to-end regime. The proposed technique achieves SOTA results without a memory buffer and clearly outperforms the reference methods. The conducted experiments have also shown a significant increase in the performance for small ensembles, which demonstrates the capability of obtaining relatively high classification accuracy with a reduced number of classifiers.

We study subsampling-based ridge ensembles in the proportional asymptotics regime, where the feature size grows proportionally with the sample size such that their ratio converges to a constant. By analyzing the squared prediction risk of ridge ensembles as a function of the explicit penalty lambda and the limiting subsample aspect ratio phi_s (the ratio of the feature size to the subsample size), we characterize contours in the (lambda, phi_s)-plane at any achievable risk. As a consequence, we prove that the risk of the optimal full ridgeless ensemble (fitted on all possible subsamples) matches that of the optimal ridge predictor. In addition, we prove strong uniform consistency of generalized cross-validation (GCV) over the subsample sizes for estimating the prediction risk of ridge ensembles. This allows for GCV-based tuning of full ridgeless ensembles without sample splitting and yields a predictor whose risk matches optimal ridge risk.

LLM Ensemble -- which involves the comprehensive use of multiple large language models (LLMs), each aimed at handling user queries during downstream inference, to benefit from their individual strengths -- has gained substantial attention recently. The widespread availability of LLMs, coupled with their varying strengths and out-of-the-box usability, has profoundly advanced the field of LLM Ensemble. This paper presents the first systematic review of recent developments in LLM Ensemble. First, we introduce our taxonomy of LLM Ensemble and discuss several related research problems. Then, we provide a more in-depth classification of the methods under the broad categories of "ensemble-before-inference, ensemble-during-inference, ensemble-after-inference'', and review all relevant methods. Finally, we introduce related benchmarks and applications, summarize existing studies, and suggest several future research directions. A curated list of papers on LLM Ensemble is available at https://github.com/junchenzhi/Awesome-LLM-Ensemble.

As models for nature language processing (NLP), computer vision (CV) and recommendation systems (RS) require surging computation, a large number of GPUs/TPUs are paralleled as a large batch (LB) to improve training throughput. However, training such LB tasks often meets large generalization gap and downgrades final precision, which limits enlarging the batch size. In this work, we develop the variance reduced gradient descent technique (VRGD) based on the gradient signal to noise ratio (GSNR) and apply it onto popular optimizers such as SGD/Adam/LARS/LAMB. We carry out a theoretical analysis of convergence rate to explain its fast training dynamics, and a generalization analysis to demonstrate its smaller generalization gap on LB training. Comprehensive experiments demonstrate that VRGD can accelerate training (1sim 2 times), narrow generalization gap and improve final accuracy. We push the batch size limit of BERT pretraining up to 128k/64k and DLRM to 512k without noticeable accuracy loss. We improve ImageNet Top-1 accuracy at 96k by 0.52pp than LARS. The generalization gap of BERT and ImageNet training is significantly reduce by over 65%.

Recent work has shown that models trained to the same objective, and which achieve similar measures of accuracy on consistent test data, may nonetheless behave very differently on individual predictions. This inconsistency is undesirable in high-stakes contexts, such as medical diagnosis and finance. We show that this inconsistent behavior extends beyond predictions to feature attributions, which may likewise have negative implications for the intelligibility of a model, and one's ability to find recourse for subjects. We then introduce selective ensembles to mitigate such inconsistencies by applying hypothesis testing to the predictions of a set of models trained using randomly-selected starting conditions; importantly, selective ensembles can abstain in cases where a consistent outcome cannot be achieved up to a specified confidence level. We prove that that prediction disagreement between selective ensembles is bounded, and empirically demonstrate that selective ensembles achieve consistent predictions and feature attributions while maintaining low abstention rates. On several benchmark datasets, selective ensembles reach zero inconsistently predicted points, with abstention rates as low 1.5%.

A range of recent optimizers have emerged that approximate the same "matrix-whitening" transformation in various ways. In this work, we systematically deconstruct such optimizers, aiming to disentangle the key components that explain performance. Across tuned hyperparameters across the board, all flavors of matrix-whitening methods reliably outperform elementwise counterparts, such as Adam. Matrix-whitening is often related to spectral descent -- however, experiments reveal that performance gains are *not explained solely by accurate spectral normalization* -- particularly, SOAP displays the largest per-step gain, even though Muon more accurately descends along the steepest spectral descent direction. Instead, we argue that matrix-whitening serves two purposes, and the variance adaptation component of matrix-whitening is the overlooked ingredient explaining this performance gap. Experiments show that variance-adapted versions of optimizers consistently outperform their sign-descent counterparts, including an adaptive version of Muon. We further ablate variance adaptation strategies, finding that while lookahead style approximations are not as effective, low-rank variance estimators can effectively reduce memory costs without a performance loss.

Recent studies have shown that reducing symmetries in neural networks enhances linear mode connectivity between networks without requiring parameter space alignment, leading to improved performance in linearly interpolated neural networks. However, in practical applications, neural network interpolation is rarely used; instead, ensembles of networks are more common. In this paper, we empirically investigate the impact of reducing symmetries on the performance of deep ensembles and Mixture of Experts (MoE) across five datasets. Additionally, to explore deeper linear mode connectivity, we introduce the Mixture of Interpolated Experts (MoIE). Our results show that deep ensembles built on asymmetric neural networks achieve significantly better performance as ensemble size increases compared to their symmetric counterparts. In contrast, our experiments do not provide conclusive evidence on whether reducing symmetries affects both MoE and MoIE architectures.

Recent innovations on hardware (e.g. Nvidia A100) have motivated learning N:M structured sparsity masks from scratch for fast model inference. However, state-of-the-art learning recipes in this regime (e.g. SR-STE) are proposed for non-adaptive optimizers like momentum SGD, while incurring non-trivial accuracy drop for Adam-trained models like attention-based LLMs. In this paper, we first demonstrate such gap origins from poorly estimated second moment (i.e. variance) in Adam states given by the masked weights. We conjecture that learning N:M masks with Adam should take the critical regime of variance estimation into account. In light of this, we propose STEP, an Adam-aware recipe that learns N:M masks with two phases: first, STEP calculates a reliable variance estimate (precondition phase) and subsequently, the variance remains fixed and is used as a precondition to learn N:M masks (mask-learning phase). STEP automatically identifies the switching point of two phases by dynamically sampling variance changes over the training trajectory and testing the sample concentration. Empirically, we evaluate STEP and other baselines such as ASP and SR-STE on multiple tasks including CIFAR classification, machine translation and LLM fine-tuning (BERT-Base, GPT-2). We show STEP mitigates the accuracy drop of baseline recipes and is robust to aggressive structured sparsity ratios.

Generalization to out-of-distribution (OOD) data is a critical challenge in machine learning. Ensemble-based methods, like weight space ensembles that interpolate model parameters, have been shown to achieve superior OOD performance. However, the underlying mechanism for their effectiveness remains unclear. In this study, we closely examine WiSE-FT, a popular weight space ensemble method that interpolates between a pre-trained and a fine-tuned model. We observe an unexpected phenomenon, in which WiSE-FT successfully corrects many cases where each individual model makes incorrect predictions, which contributes significantly to its OOD effectiveness. To gain further insights, we conduct theoretical analysis in a multi-class setting with a large number of spurious features. Our analysis predicts the above phenomenon and it further shows that ensemble-based models reduce prediction errors in the OOD settings by utilizing a more diverse set of spurious features. Contrary to the conventional wisdom that focuses on learning invariant features for better OOD performance, our findings suggest that incorporating a large number of diverse spurious features weakens their individual contributions, leading to improved overall OOD generalization performance. Empirically we demonstrate the effectiveness of utilizing diverse spurious features on a MultiColorMNIST dataset, and our experimental results are consistent with the theoretical analysis. Building upon the new theoretical insights into the efficacy of ensemble methods, we further identify an issue of WiSE-FT caused by the overconfidence of fine-tuned models in OOD situations. This overconfidence magnifies the fine-tuned model's incorrect prediction, leading to deteriorated OOD ensemble performance. To remedy this problem, we propose a novel method called BAlaNced averaGing (BANG), which significantly enhances the OOD performance of WiSE-FT.

We propose a direct estimation method for R\'{e}nyi and f-divergence measures based on a new graph theoretical interpretation. Suppose that we are given two sample sets X and Y, respectively with N and M samples, where eta:=M/N is a constant value. Considering the k-nearest neighbor (k-NN) graph of Y in the joint data set (X,Y), we show that the average powered ratio of the number of X points to the number of Y points among all k-NN points is proportional to R\'{e}nyi divergence of X and Y densities. A similar method can also be used to estimate f-divergence measures. We derive bias and variance rates, and show that for the class of gamma-H\"{o}lder smooth functions, the estimator achieves the MSE rate of O(N^{-2gamma/(gamma+d)}). Furthermore, by using a weighted ensemble estimation technique, for density functions with continuous and bounded derivatives of up to the order d, and some extra conditions at the support set boundary, we derive an ensemble estimator that achieves the parametric MSE rate of O(1/N). Our estimators are more computationally tractable than other competing estimators, which makes them appealing in many practical applications.

We propose an empirical measure of the approximate accuracy of feature importance estimates in deep neural networks. Our results across several large-scale image classification datasets show that many popular interpretability methods produce estimates of feature importance that are not better than a random designation of feature importance. Only certain ensemble based approaches---VarGrad and SmoothGrad-Squared---outperform such a random assignment of importance. The manner of ensembling remains critical, we show that some approaches do no better then the underlying method but carry a far higher computational burden.

While the transferability property of adversarial examples allows the adversary to perform black-box attacks (i.e., the attacker has no knowledge about the target model), the transfer-based adversarial attacks have gained great attention. Previous works mostly study gradient variation or image transformations to amplify the distortion on critical parts of inputs. These methods can work on transferring across models with limited differences, i.e., from CNNs to CNNs, but always fail in transferring across models with wide differences, such as from CNNs to ViTs. Alternatively, model ensemble adversarial attacks are proposed to fuse outputs from surrogate models with diverse architectures to get an ensemble loss, making the generated adversarial example more likely to transfer to other models as it can fool multiple models concurrently. However, existing ensemble attacks simply fuse the outputs of the surrogate models evenly, thus are not efficacious to capture and amplify the intrinsic transfer information of adversarial examples. In this paper, we propose an adaptive ensemble attack, dubbed AdaEA, to adaptively control the fusion of the outputs from each model, via monitoring the discrepancy ratio of their contributions towards the adversarial objective. Furthermore, an extra disparity-reduced filter is introduced to further synchronize the update direction. As a result, we achieve considerable improvement over the existing ensemble attacks on various datasets, and the proposed AdaEA can also boost existing transfer-based attacks, which further demonstrates its efficacy and versatility.

Classic results establish that encouraging predictive diversity improves performance in ensembles of low-capacity models, e.g. through bagging or boosting. Here we demonstrate that these intuitions do not apply to high-capacity neural network ensembles (deep ensembles), and in fact the opposite is often true. In a large scale study of nearly 600 neural network classification ensembles, we examine a variety of interventions that trade off component model performance for predictive diversity. While such interventions can improve the performance of small neural network ensembles (in line with standard intuitions), they harm the performance of the large neural network ensembles most often used in practice. Surprisingly, we also find that discouraging predictive diversity is often benign in large-network ensembles, fully inverting standard intuitions. Even when diversity-promoting interventions do not sacrifice component model performance (e.g. using heterogeneous architectures and training paradigms), we observe an opportunity cost associated with pursuing increased predictive diversity. Examining over 1000 ensembles, we observe that the performance benefits of diverse architectures/training procedures are easily dwarfed by the benefits of simply using higher-capacity models, despite the fact that such higher capacity models often yield significantly less predictive diversity. Overall, our findings demonstrate that standard intuitions around predictive diversity, originally developed for low-capacity ensembles, do not directly apply to modern high-capacity deep ensembles. This work clarifies fundamental challenges to the goal of improving deep ensembles by making them more diverse, while suggesting an alternative path: simply forming ensembles from ever more powerful (and less diverse) component models.

It is widely recognized that deep learning models lack robustness to adversarial examples. An intriguing property of adversarial examples is that they can transfer across different models, which enables black-box attacks without any knowledge of the victim model. An effective strategy to improve the transferability is attacking an ensemble of models. However, previous works simply average the outputs of different models, lacking an in-depth analysis on how and why model ensemble methods can strongly improve the transferability. In this paper, we rethink the ensemble in adversarial attacks and define the common weakness of model ensemble with two properties: 1) the flatness of loss landscape; and 2) the closeness to the local optimum of each model. We empirically and theoretically show that both properties are strongly correlated with the transferability and propose a Common Weakness Attack (CWA) to generate more transferable adversarial examples by promoting these two properties. Experimental results on both image classification and object detection tasks validate the effectiveness of our approach to improving the adversarial transferability, especially when attacking adversarially trained models. We also successfully apply our method to attack a black-box large vision-language model -- Google's Bard, showing the practical effectiveness. Code is available at https://github.com/huanranchen/AdversarialAttacks.

We study sampling algorithms for β-ensembles with time complexity less than cubic in the cardinality of the ensemble. Following Dumitriu & Edelman (2002), we see the ensemble as the eigenvalues of a random tridiagonal matrix, namely a random Jacobi matrix. First, we provide a unifying and elementary treatment of the tridiagonal models associated to the three classical Hermite, Laguerre and Jacobi ensembles. For this purpose, we use simple changes of variables between successive reparametrizations of the coefficients defining the tridiagonal matrix. Second, we derive an approximate sampler for the simulation of β-ensembles, and illustrate how fast it can be for polynomial potentials. This method combines a Gibbs sampler on Jacobi matrices and the diagonalization of these matrices. In practice, even for large ensembles, only a few Gibbs passes suffice for the marginal distribution of the eigenvalues to fit the expected theoretical distribution. When the conditionals in the Gibbs sampler can be simulated exactly, the same fast empirical convergence is observed for the fluctuations of the largest eigenvalue. Our experimental results support a conjecture by Krishnapur et al. (2016), that the Gibbs chain on Jacobi matrices of size N mixes in O(log(N)).

This paper studies ensembling in the era of Large Vision-Language Models (LVLMs). Ensembling is a classical method to combine different models to get increased performance. In the recent work on Encyclopedic-VQA the authors examine a wide variety of models to solve their task: from vanilla LVLMs, to models including the caption as extra context, to models augmented with Lens-based retrieval of Wikipedia pages. Intuitively these models are highly complementary, which should make them ideal for ensembling. Indeed, an oracle experiment shows potential gains from 48.8% accuracy (the best single model) all the way up to 67% (best possible ensemble). So it is a trivial exercise to create an ensemble with substantial real gains. Or is it?

While fine-tuning of pre-trained language models generally helps to overcome the lack of labelled training samples, it also displays model performance instability. This instability mainly originates from randomness in initialisation or data shuffling. To address this, researchers either modify the training process or augment the available samples, which typically results in increased computational costs. We propose a new mitigation strategy, called Delayed Ensemble with Noisy Interpolation (DENI), that leverages the strengths of ensembling, noise regularisation and model interpolation, while retaining computational efficiency. We compare DENI with 9 representative mitigation strategies across 3 models, 4 tuning strategies and 7 text classification datasets. We show that: 1) DENI outperforms the best performing mitigation strategy (Ensemble), while using only a fraction of its cost; 2) the mitigation strategies are beneficial for parameter-efficient fine-tuning (PEFT) methods, outperforming full fine-tuning in specific cases; and 3) combining DENI with data augmentation often leads to even more effective instability mitigation.

Training dense LLMs requires enormous amounts of data and centralized compute, which introduces fundamental bottlenecks and ever-growing costs for large models. Several studies aim to reduce this dependency on centralization by reducing the communication overhead of training dense models. Taking this idea of reducing communication overhead to a natural extreme, by training embarrassingly parallelizable ensembles of small independent experts, has been shown to outperform large dense models trained in traditional centralized settings. However, existing studies do not take into account underlying differences amongst data domains and treat them as monolithic, regardless of their underlying complexity, size, or distribution. In this paper, we explore the effects of introducing heterogeneity to these ensembles of domain expert models. Specifically, by allowing models within the ensemble to vary in size--as well as the number of training steps taken depending on the training data's domain--we study the effect heterogeneity has on these ensembles when evaluated against domains included in, and excluded from, the training set. We use the same compute budget to train heterogeneous ensembles and homogeneous baselines for comparison. We show that the heterogeneous ensembles achieve the lowest perplexity scores in 20 out of the 21 data domains used in the evaluation. Our code is available at https://github.com/gensyn-ai/hdee.

We analyse linear ensemble sampling (ES) with standard Gaussian perturbations in stochastic linear bandits. We show that for ensemble size m=Θ(dlog n), ES attains tilde O(d^{3/2}sqrt n) high-probability regret, closing the gap to the Thompson sampling benchmark while keeping computation comparable. The proof brings a new perspective on randomized exploration in linear bandits by reducing the analysis to a time-uniform exceedance problem for m independent Brownian motions. Intriguingly, this continuous-time lens is not forced; it appears natural--and perhaps necessary: the discrete-time problem seems to be asking for a continuous-time solution, and we know of no other way to obtain a sharp ES bound.

It is of great significance to estimate the performance of a given model architecture without training in the application of Neural Architecture Search (NAS) as it may take a lot of time to evaluate the performance of an architecture. In this paper, a novel NAS framework called GP-NAS-ensemble is proposed to predict the performance of a neural network architecture with a small training dataset. We make several improvements on the GP-NAS model to make it share the advantage of ensemble learning methods. Our method ranks second in the CVPR2022 second lightweight NAS challenge performance prediction track.

Large multimodal reasoning models have achieved rapid progress, but their advancement is constrained by two major limitations: the absence of open, large-scale, high-quality long chain-of-thought (CoT) data, and the instability of reinforcement learning (RL) algorithms in post-training. Group Relative Policy Optimization (GRPO), the standard framework for RL fine-tuning, is prone to gradient vanishing when reward variance is low, which weakens optimization signals and impairs convergence. This work makes three contributions: (1) We propose Variance-Aware Sampling (VAS), a data selection strategy guided by Variance Promotion Score (VPS) that combines outcome variance and trajectory diversity to promote reward variance and stabilize policy optimization. (2) We release large-scale, carefully curated resources containing ~1.6M long CoT cold-start data and ~15k RL QA pairs, designed to ensure quality, difficulty, and diversity, along with a fully reproducible end-to-end training codebase. (3) We open-source a family of multimodal reasoning models in multiple scales, establishing standardized baselines for the community. Experiments across mathematical reasoning benchmarks demonstrate the effectiveness of both the curated data and the proposed VAS. Comprehensive ablation studies and analyses provide further insight into the contributions of each component. In addition, we theoretically establish that reward variance lower-bounds the expected policy gradient magnitude, with VAS serving as a practical mechanism to realize this guarantee. Our code, data, and checkpoints are available at https://github.com/LengSicong/MMR1.

Bootstrap aggregating (bagging) is an effective ensemble protocol, which is believed can enhance robustness by its majority voting mechanism. Recent works further prove the sample-wise robustness certificates for certain forms of bagging (e.g. partition aggregation). Beyond these particular forms, in this paper, we propose the first collective certification for general bagging to compute the tight robustness against the global poisoning attack. Specifically, we compute the maximum number of simultaneously changed predictions via solving a binary integer linear programming (BILP) problem. Then we analyze the robustness of vanilla bagging and give the upper bound of the tolerable poison budget. Based on this analysis, we propose hash bagging to improve the robustness of vanilla bagging almost for free. This is achieved by modifying the random subsampling in vanilla bagging to a hash-based deterministic subsampling, as a way of controlling the influence scope for each poisoning sample universally. Our extensive experiments show the notable advantage in terms of applicability and robustness.

Machine learning (ML)-based weather models have rapidly risen to prominence due to their greater accuracy and speed than traditional forecasts based on numerical weather prediction (NWP), recently outperforming traditional ensembles in global probabilistic weather forecasting. This paper presents FGN, a simple, scalable and flexible modeling approach which significantly outperforms the current state-of-the-art models. FGN generates ensembles via learned model-perturbations with an ensemble of appropriately constrained models. It is trained directly to minimize the continuous rank probability score (CRPS) of per-location forecasts. It produces state-of-the-art ensemble forecasts as measured by a range of deterministic and probabilistic metrics, makes skillful ensemble tropical cyclone track predictions, and captures joint spatial structure despite being trained only on marginals.

In this paper, we consider non-convex multi-block bilevel optimization (MBBO) problems, which involve mgg 1 lower level problems and have important applications in machine learning. Designing a stochastic gradient and controlling its variance is more intricate due to the hierarchical sampling of blocks and data and the unique challenge of estimating hyper-gradient. We aim to achieve three nice properties for our algorithm: (a) matching the state-of-the-art complexity of standard BO problems with a single block; (b) achieving parallel speedup by sampling I blocks and sampling B samples for each sampled block per-iteration; (c) avoiding the computation of the inverse of a high-dimensional Hessian matrix estimator. However, it is non-trivial to achieve all of these by observing that existing works only achieve one or two of these properties. To address the involved challenges for achieving (a, b, c), we propose two stochastic algorithms by using advanced blockwise variance-reduction techniques for tracking the Hessian matrices (for low-dimensional problems) or the Hessian-vector products (for high-dimensional problems), and prove an iteration complexity of O(mepsilon^{-3I(I<m)}{II} + mepsilon^{-3}{IB}) for finding an epsilon-stationary point under appropriate conditions. We also conduct experiments to verify the effectiveness of the proposed algorithms comparing with existing MBBO algorithms.

We provide a concise framework for generalized ensemble theory through a matrix-based approach. By introducing an observation matrix, any discrete probability distribution, including those for non-equilibrium steady states, can be expressed as a generalized Boltzmann distribution, with observables and conjugate variables as the basis and coordinates in a linear space. In this framework, we identify the minimal sufficient statistics required for inferring the Boltzmann distribution. Furthermore, we show that the Hadamard and Vandermonde matrices are suitable observation matrices for spin systems and random walks. In master equation systems, the probability flux observation matrix facilitates the identification of detailed balance violations. Our findings provide a new approach to developing generalized ensemble theory for non-equilibrium steady-state systems.

Deep Learning-based image super-resolution (SR) has been gaining traction with the aid of Generative Adversarial Networks. Models like SRGAN and ESRGAN are constantly ranked between the best image SR tools. However, they lack principled ways for estimating predictive uncertainty. In the present work, we enhance these models using Monte Carlo-Dropout and Deep Ensemble, allowing the computation of predictive uncertainty. When coupled with a prediction, uncertainty estimates can provide more information to the model users, highlighting pixels where the SR output might be uncertain, hence potentially inaccurate, if these estimates were to be reliable. Our findings suggest that these uncertainty estimates are decently calibrated and can hence fulfill this goal, while providing no performance drop with respect to the corresponding models without uncertainty estimation.

We propose a deep-learning system -- for the SQuAD2.0 task -- that finds, or indicates the lack of, a correct answer to a question in a context paragraph. Our goal is to learn an ensemble of heterogeneous SQuAD2.0 models that, when blended properly, outperforms the best model in the ensemble per se. We created a stacking ensemble that combines top-N predictions from two models, based on ALBERT and RoBERTa, into a multiclass classification task to pick the best answer out of their predictions. We explored various ensemble configurations, input representations, and model architectures. For evaluation, we examined test-set EM and F1 scores; our best-performing ensemble incorporated a CNN-based meta-model and scored 87.117 and 90.306, respectively -- a relative improvement of 0.55% for EM and 0.61% for F1 scores, compared to the baseline performance of the best model in the ensemble, an ALBERT-based model, at 86.644 for EM and 89.760 for F1.

Empirical risk minimization (ERM) with a computationally feasible surrogate loss is a widely accepted approach for classification. Notably, the convexity and calibration (CC) properties of a loss function ensure consistency of ERM in maximizing accuracy, thereby offering a wide range of options for surrogate losses. In this article, we propose a novel ensemble method, namely EnsLoss, which extends the ensemble learning concept to combine loss functions within the ERM framework. A key feature of our method is the consideration on preserving the "legitimacy" of the combined losses, i.e., ensuring the CC properties. Specifically, we first transform the CC conditions of losses into loss-derivatives, thereby bypassing the need for explicit loss functions and directly generating calibrated loss-derivatives. Therefore, inspired by Dropout, EnsLoss enables loss ensembles through one training process with doubly stochastic gradient descent (i.e., random batch samples and random calibrated loss-derivatives). We theoretically establish the statistical consistency of our approach and provide insights into its benefits. The numerical effectiveness of EnsLoss compared to fixed loss methods is demonstrated through experiments on a broad range of 14 OpenML tabular datasets and 46 image datasets with various deep learning architectures. Python repository and source code are available on GitHub at https://github.com/statmlben/ensloss.

We explore diverse representations of speech audio, and their effect on a performance of late fusion ensemble of E-Branchformer models, applied to Automatic Speech Recognition (ASR) task. Although it is generally known that ensemble methods often improve the performance of the system even for speech recognition, it is very interesting to explore how ensembles of complex state-of-the-art models, such as medium-sized and large E-Branchformers, cope in this setting when their base models are trained on diverse representations of the input speech audio. The results are evaluated on four widely-used benchmark datasets: Librispeech, Aishell, Gigaspeech, TEDLIUMv2 and show that improvements of 1% - 14% can still be achieved over the state-of-the-art models trained using comparable techniques on these datasets. A noteworthy observation is that such ensemble offers improvements even with the use of language models, although the gap is closing.

In modern neural networks like Transformers, linear layers require significant memory to store activations during backward pass. This study proposes a memory reduction approach to perform backpropagation through linear layers. Since the gradients of linear layers are computed by matrix multiplications, we consider methods for randomized matrix multiplications and demonstrate that they require less memory with a moderate decrease of the test accuracy. Also, we investigate the variance of the gradient estimate induced by the randomized matrix multiplication. We compare this variance with the variance coming from gradient estimation based on the batch of samples. We demonstrate the benefits of the proposed method on the fine-tuning of the pre-trained RoBERTa model on GLUE tasks.

We present Synergy Aware Forgetting Ensemble (SAFE), a method to adapt large models on a diverse collection of data while minimizing the expected cost to remove the influence of training samples from the trained model. This process, also known as selective forgetting or unlearning, is often conducted by partitioning a dataset into shards, training fully independent models on each, then ensembling the resulting models. Increasing the number of shards reduces the expected cost to forget but at the same time it increases inference cost and reduces the final accuracy of the model since synergistic information between samples is lost during the independent model training. Rather than treating each shard as independent, SAFE introduces the notion of a shard graph, which allows incorporating limited information from other shards during training, trading off a modest increase in expected forgetting cost with a significant increase in accuracy, all while still attaining complete removal of residual influence after forgetting. SAFE uses a lightweight system of adapters which can be trained while reusing most of the computations. This allows SAFE to be trained on shards an order-of-magnitude smaller than current state-of-the-art methods (thus reducing the forgetting costs) while also maintaining high accuracy, as we demonstrate empirically on fine-grained computer vision datasets.

As the demand for comprehensive evaluations of diverse model capabilities steadily increases, benchmark suites have correspondingly grown significantly in scale. Despite notable advances in redundancy reduction and subset-level performance prediction, a systematic framework that effectively integrates these methods to ensure both prediction accuracy and ranking consistency is still largely elusive. In this paper, we first perform a sample-level analysis of benchmark redundancy and identify several highly similar samples that can be eliminated. Besides, we frame benchmark compression as an optimization problem with the aim of score reconstruction. Building on these, we then propose EssenceBench, a coarse-to-fine framework utilizing an iterative Genetic Algorithm (GA), which takes the advantages of fitness-based subset search and attribution-based sample search. Compared to previous methods, our approach yields superior compression results with lower reconstruction error and markedly higher efficiency. In particular, on the HellaSwag benchmark (10K samples), our method preserves the ranking of all models shifting within 5% using 25x fewer samples, and achieves 95% ranking preservation shifting within 5% using only 200x fewer samples.

We consider in this paper the problem of optimal experiment design where a decision maker can choose which points to sample to obtain an estimate hatβ of the hidden parameter β^{star} of an underlying linear model. The key challenge of this work lies in the heteroscedasticity assumption that we make, meaning that each covariate has a different and unknown variance. The goal of the decision maker is then to figure out on the fly the optimal way to allocate the total budget of T samples between covariates, as sampling several times a specific one will reduce the variance of the estimated model around it (but at the cost of a possible higher variance elsewhere). By trying to minimize the ell^2-loss E [lVerthatβ-β^{star}rVert^2] the decision maker is actually minimizing the trace of the covariance matrix of the problem, which corresponds then to online A-optimal design. Combining techniques from bandit and convex optimization we propose a new active sampling algorithm and we compare it with existing ones. We provide theoretical guarantees of this algorithm in different settings, including a O(T^{-2}) regret bound in the case where the covariates form a basis of the feature space, generalizing and improving existing results. Numerical experiments validate our theoretical findings.

Combining different models is a widely used paradigm in machine learning applications. While the most common approach is to form an ensemble of models and average their individual predictions, this approach is often rendered infeasible by given resource constraints in terms of memory and computation, which grow linearly with the number of models. We present a layer-wise model fusion algorithm for neural networks that utilizes optimal transport to (soft-) align neurons across the models before averaging their associated parameters. We show that this can successfully yield "one-shot" knowledge transfer (i.e, without requiring any retraining) between neural networks trained on heterogeneous non-i.i.d. data. In both i.i.d. and non-i.i.d. settings , we illustrate that our approach significantly outperforms vanilla averaging, as well as how it can serve as an efficient replacement for the ensemble with moderate fine-tuning, for standard convolutional networks (like VGG11), residual networks (like ResNet18), and multi-layer perceptrons on CIFAR10, CIFAR100, and MNIST. Finally, our approach also provides a principled way to combine the parameters of neural networks with different widths, and we explore its application for model compression. The code is available at the following link, https://github.com/sidak/otfusion.

Most bandit algorithms assume that the reward variances or their upper bounds are known, and that they are the same for all arms. This naturally leads to suboptimal performance and higher regret due to variance overestimation. On the other hand, underestimated reward variances may lead to linear regret due to committing early to a suboptimal arm. This motivated prior works on variance-adaptive frequentist algorithms, which have strong instance-dependent regret bounds but cannot incorporate prior knowledge on reward variances. We lay foundations for the Bayesian setting, which incorporates prior knowledge. This results in lower regret in practice, due to using the prior in the algorithm design, and also improved regret guarantees. Specifically, we study Gaussian bandits with {unknown heterogeneous reward variances}, and develop a Thompson sampling algorithm with prior-dependent Bayes regret bounds. We achieve lower regret with lower reward variances and more informative priors on them, which is precisely why we pay only for what is uncertain. This is the first result of its kind. Finally, we corroborate our theory with extensive experiments, which show the superiority of our variance-adaptive Bayesian algorithm over prior frequentist approaches. We also show that our approach is robust to model misspecification and can be applied with estimated priors.

Ensembling multiple models has always been an effective approach to push the limits of existing performance and is widely used in classification tasks by simply averaging the classification probability vectors from multiple classifiers to achieve better accuracy. However, in the thriving open-source Large Language Model (LLM) community, ensembling methods are rare and typically limited to ensembling the full-text outputs of LLMs, such as selecting the best output using a ranker, which leads to underutilization of token-level probability information. In this paper, we treat the Generation of each token by LLMs as a Classification (GaC) for ensembling. This approach fully exploits the probability information at each generation step and better prevents LLMs from producing early incorrect tokens that lead to snowballing errors. In experiments, we ensemble state-of-the-art LLMs on several benchmarks, including exams, mathematics and reasoning, and observe that our method breaks the existing community performance ceiling. Furthermore, we observed that most of the tokens in the answer are simple and do not affect the correctness of the final answer. Therefore, we also experimented with ensembling only key tokens, and the results showed better performance with lower latency across benchmarks.

Prior-data fitted networks (PFNs) were recently proposed as a new paradigm for machine learning. Instead of training the network to an observed training set, a fixed model is pre-trained offline on small, simulated training sets from a variety of tasks. The pre-trained model is then used to infer class probabilities in-context on fresh training sets with arbitrary size and distribution. Empirically, PFNs achieve state-of-the-art performance on tasks with similar size to the ones used in pre-training. Surprisingly, their accuracy further improves when passed larger data sets during inference. This article establishes a theoretical foundation for PFNs and illuminates the statistical mechanisms governing their behavior. While PFNs are motivated by Bayesian ideas, a purely frequentistic interpretation of PFNs as pre-tuned, but untrained predictors explains their behavior. A predictor's variance vanishes if its sensitivity to individual training samples does and the bias vanishes only if it is appropriately localized around the test feature. The transformer architecture used in current PFN implementations ensures only the former. These findings shall prove useful for designing architectures with favorable empirical behavior.

The ability of an architecture to realize permutations is quite fundamental. For example, Large Language Models need to be able to correctly copy (and perhaps rearrange) parts of the input prompt into the output. Classical universal approximation theorems guarantee the existence of parameter configurations that solve this task but offer no insights into whether gradient-based algorithms can find them. In this paper, we address this gap by focusing on two-layer fully connected feed-forward neural networks and the task of learning permutations on nonzero binary inputs. We show that in the infinite width Neural Tangent Kernel (NTK) regime, an ensemble of such networks independently trained with gradient descent on only the k standard basis vectors out of 2^k - 1 possible inputs successfully learns any fixed permutation of length k with arbitrarily high probability. By analyzing the exact training dynamics, we prove that the network's output converges to a Gaussian process whose mean captures the ground truth permutation via sign-based features. We then demonstrate how averaging these runs (an "ensemble" method) and applying a simple rounding step yields an arbitrarily accurate prediction on any possible input unseen during training. Notably, the number of models needed to achieve exact learning with high probability (which we refer to as ensemble complexity) exhibits a linearithmic dependence on the input size k for a single test input and a quadratic dependence when considering all test inputs simultaneously.

Spurious correlations in the data, where multiple cues are predictive of the target labels, often lead to a phenomenon known as simplicity bias, where a model relies on erroneous, easy-to-learn cues while ignoring reliable ones. In this work, we propose an ensemble diversification framework exploiting Diffusion Probabilistic Models (DPMs) for shortcut bias mitigation. We show that at particular training intervals, DPMs can generate images with novel feature combinations, even when trained on images displaying correlated input features. We leverage this crucial property to generate synthetic counterfactuals to increase model diversity via ensemble disagreement. We show that DPM-guided diversification is sufficient to remove dependence on primary shortcut cues, without a need for additional supervised signals. We further empirically quantify its efficacy on several diversification objectives, and finally show improved generalization and diversification performance on par with prior work that relies on auxiliary data collection.

This paper presents an innovative approach to enhancing few-shot learning by integrating data augmentation with model fine-tuning in a framework designed to tackle the challenges posed by small-sample data. Recognizing the critical limitations of traditional machine learning models that require large datasets-especially in fields such as drug discovery, target recognition, and malicious traffic detection-this study proposes a novel strategy that leverages Generative Adversarial Networks (GANs) and advanced optimization techniques to improve model performance with limited data. Specifically, the paper addresses the noise and bias issues introduced by data augmentation methods, contrasting them with model-based approaches, such as fine-tuning and metric learning, which rely heavily on related datasets. By combining Markov Chain Monte Carlo (MCMC) sampling and discriminative model ensemble strategies within a GAN framework, the proposed model adjusts generative and discriminative distributions to simulate a broader range of relevant data. Furthermore, it employs MHLoss and a reparameterized GAN ensemble to enhance stability and accelerate convergence, ultimately leading to improved classification performance on small-sample images and structured datasets. Results confirm that the MhERGAN algorithm developed in this research is highly effective for few-shot learning, offering a practical solution that bridges data scarcity with high-performing model adaptability and generalization.

Different large language models (LLMs) exhibit diverse strengths and weaknesses, and LLM ensemble serves as a promising approach to integrate their complementary capabilities. Despite substantial progress in improving ensemble quality, limited attention has been paid to the robustness of ensembles against potential erroneous signals, which often arise from heterogeneous tokenization schemes and varying model expertise. Our analysis shows that ensemble failures typically arise from both the token level and the model level: the former reflects severe disagreement in token predictions, while the latter involves low confidence and pronounced disparities among models. In light of this, we propose CoRE, a plug-and-play technique that harnesses model consistency for robust LLM ensemble, which can be seamlessly integrated with diverse ensemble methods. Token-level consistency captures fine-grained disagreements by applying a low-pass filter to downweight uncertain tokens with high inconsistency, often due to token misalignment, thereby improving robustness at a granular level. Model-level consistency models global agreement by promoting model outputs with high self-confidence and minimal divergence from others, enhancing robustness at a coarser level. Extensive experiments across diverse benchmarks, model combinations, and ensemble strategies demonstrate that CoRE consistently improves ensemble performance and robustness.

The computer vision domain has greatly benefited from an abundance of data across many modalities to improve on various visual tasks. Recently, there has been a lot of focus on self-supervised pre-training methods through Masked Autoencoders (MAE) he2022masked,bachmann2022multimae, usually used as a first step before optimizing for a downstream task, such as classification or regression. This is very useful as it doesn't require any manually labeled data. In this work, we introduce Probabilistic Hyper-Graphs using Masked Autoencoders (PHG-MAE): a novel model that unifies the classical work on neural graphs leordeanu2021semi with the modern approach of masked autoencoders under a common theoretical framework. Through random masking of entire modalities, not just patches, the model samples from the distribution of hyper-edges on each forward pass. Additionally, the model adapts the standard MAE algorithm by combining pre-training and fine-tuning into a single training loop. Moreover, our approach enables the creation of inference-time ensembles which, through aggregation, boost the final prediction performance and consistency. Lastly, we show that we can apply knowledge distillation on top of the ensembles with little loss in performance, even with models that have fewer than 1M parameters. While our work mostly focuses on outdoor UAV scenes that contain multiple world interpretations and modalities, the same steps can be followed in other similar domains, such as autonomous driving or indoor robotics. In order to streamline the process of integrating external pre-trained experts for computer vision multi-modal multi-task learning (MTL) scenarios, we developed a data-pipeline software. Using this tool, we have created and released a fully-automated extension of the Dronescapes dataset. All the technical details, code and reproduction steps are publicly released.

The increasing frequency of extreme weather events due to global climate change urges accurate weather prediction. Recently, great advances have been made by the end-to-end methods, thanks to deep learning techniques, but they face limitations of representation inconsistency in multivariable integration and struggle to effectively capture the dependency between variables, which is required in complex weather systems. Treating different variables as distinct modalities and applying a two-stage training approach from multimodal models can partially alleviate this issue, but due to the inconformity in training tasks between the two stages, the results are often suboptimal. To address these challenges, we propose an implicit two-stage training method, configuring separate encoders and decoders for each variable. In detailed, in the first stage, the Translator is frozen while the Encoders and Decoders learn a shared latent space, in the second stage, the Encoders and Decoders are frozen, and the Translator captures inter-variable interactions for prediction. Besides, by introducing a self-attention mechanism for multivariable fusion in the latent space, the performance achieves further improvements. Empirically, extensive experiments show the state-of-the-art performance of our method. Specifically, it reduces the MSE for near-surface air temperature and relative humidity predictions by 28.82\% and 23.39\%, respectively. The source code is available at https://github.com/ShremG/Met2Net.

In this paper, we present an Adaptive Ensemble Learning framework that aims to boost the performance of deep neural networks by intelligently fusing features through ensemble learning techniques. The proposed framework integrates ensemble learning strategies with deep learning architectures to create a more robust and adaptable model capable of handling complex tasks across various domains. By leveraging intelligent feature fusion methods, the Adaptive Ensemble Learning framework generates more discriminative and effective feature representations, leading to improved model performance and generalization capabilities. We conducted extensive experiments and evaluations on several benchmark datasets, including image classification, object detection, natural language processing, and graph-based learning tasks. The results demonstrate that the proposed framework consistently outperforms baseline models and traditional feature fusion techniques, highlighting its effectiveness in enhancing deep learning models' performance. Furthermore, we provide insights into the impact of intelligent feature fusion on model performance and discuss the potential applications of the Adaptive Ensemble Learning framework in real-world scenarios. The paper also explores the design and implementation of adaptive ensemble models, ensemble training strategies, and meta-learning techniques, which contribute to the framework's versatility and adaptability. In conclusion, the Adaptive Ensemble Learning framework represents a significant advancement in the field of feature fusion and ensemble learning for deep neural networks, with the potential to transform a wide range of applications across multiple domains.

The focus of this study is to evaluate the effectiveness of Machine Learning (ML) methods for two-sample testing with right-censored observations. To achieve this, we develop several ML-based methods with varying architectures and implement them as two-sample tests. Each method is an ensemble (stacking) that combines predictions from classical two-sample tests. This paper presents the results of training the proposed ML methods, examines their statistical power compared to classical two-sample tests, analyzes the distribution of test statistics for the proposed methods when the null hypothesis is true, and evaluates the significance of the features incorporated into the proposed methods. All results from numerical experiments were obtained from a synthetic dataset generated using the Smirnov transform (Inverse Transform Sampling) and replicated multiple times through Monte Carlo simulation. To test the two-sample problem with right-censored observations, one can use the proposed two-sample methods. All necessary materials (source code, example scripts, dataset, and samples) are available on GitHub and Hugging Face.

Matrix-based preconditioned optimizers, such as Muon, have recently been shown to be more efficient than scalar-based optimizers for training large-scale neural networks, including large language models (LLMs). On the other hand, recent benchmarks on optimizers for LLM pre-training have demonstrated that variance-reduction techniques such as MARS can achieve substantial speedups over standard optimizers that do not employ variance reduction. In this paper, to achieve the best of both worlds, we introduce MARS-M, a new optimizer that integrates the variance reduction technique in MARS with Muon. Under standard regularity conditions, we prove that Muon-M converges to a first-order stationary point at a rate of mathcal{O}(T^{-1/3}), which improves upon mathcal{O}(T^{-1/4}) rate attained by Muon. Our empirical results on language modeling and computer vision tasks demonstrate that MARS-M consistently yields lower losses and improved performance across various downstream benchmarks. The implementation of MARS-M is available at https://github.com/AGI-Arena/MARS/MARS_M.

Is bigger always better for time series foundation models? With the question in mind, we explore an alternative to training a single, large monolithic model: building a portfolio of smaller, pretrained forecasting models. By applying ensembling or model selection over these portfolios, we achieve competitive performance on large-scale benchmarks using much fewer parameters. We explore strategies for designing such portfolios and find that collections of specialist models consistently outperform portfolios of independently trained generalists. Remarkably, we demonstrate that post-training a base model is a compute-effective approach for creating sufficiently diverse specialists, and provide evidences that ensembling and model selection are more compute-efficient than test-time fine-tuning.

Large climate-model ensembles are computationally expensive; yet many downstream analyses would benefit from additional, statistically consistent realizations of spatiotemporal climate variables. We study a generative modeling approach for producing new realizations from a limited set of available runs by transferring structure learned across an ensemble. Using monthly near-surface temperature time series from ten independent reanalysis realizations (ERA5), we find that a vanilla conditional variational autoencoder (CVAE) trained jointly across realizations yields a fragmented latent space that fails to generalize to unseen ensemble members. To address this, we introduce a latent-constrained CVAE (LC-CVAE) that enforces cross-realization homogeneity of latent embeddings at a small set of shared geographic 'anchor' locations. We then use multi-output Gaussian process regression in the latent space to predict latent coordinates at unsampled locations in a new realization, followed by decoding to generate full time series fields. Experiments and ablations demonstrate (i) instability when training on a single realization, (ii) diminishing returns after incorporating roughly five realizations, and (iii) a trade-off between spatial coverage and reconstruction quality that is closely linked to the average neighbor distance in latent space.

The probabilistic diffusion model has become highly effective across various domains. Typically, sampling from a diffusion model involves using a denoising distribution characterized by a Gaussian with a learned mean and either fixed or learned covariances. In this paper, we leverage the recently proposed covariance moment matching technique and introduce a novel method for learning the diagonal covariance. Unlike traditional data-driven diagonal covariance approximation approaches, our method involves directly regressing the optimal diagonal analytic covariance using a new, unbiased objective named Optimal Covariance Matching (OCM). This approach can significantly reduce the approximation error in covariance prediction. We demonstrate how our method can substantially enhance the sampling efficiency, recall rate and likelihood of commonly used diffusion models.

Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance tradeoffs. We theoretically show that, under some conditions, estimators such as MINE exhibit variance that could grow exponentially with the true amount of underlying MI. We also empirically demonstrate that existing estimators fail to satisfy basic self-consistency properties of MI, such as data processing and additivity under independence. Based on a unified perspective of variational approaches, we develop a new estimator that focuses on variance reduction. Empirical results on standard benchmark tasks demonstrate that our proposed estimator exhibits improved bias-variance trade-offs on standard benchmark tasks.

Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization trick is applicable when we can simulate a random variable by applying a differentiable deterministic function on an auxiliary random variable whose distribution is fixed. For many distributions of interest (such as the gamma or Dirichlet), simulation of random variables relies on acceptance-rejection sampling. The discontinuity introduced by the accept-reject step means that standard reparameterization tricks are not applicable. We propose a new method that lets us leverage reparameterization gradients even when variables are outputs of a acceptance-rejection sampling algorithm. Our approach enables reparameterization on a larger class of variational distributions. In several studies of real and synthetic data, we show that the variance of the estimator of the gradient is significantly lower than other state-of-the-art methods. This leads to faster convergence of stochastic gradient variational inference.

Model order reduction has been extensively studied over the last two decades. Projection-based methods such as the Proper Orthogonal Decomposition and the Reduced Basis Method enjoy the important advantages of Galerkin methods in the derivation of the reduced problem, but are limited to linear data compression for which the reduced solution is sought as a linear combination of spatial modes. Nonlinear data compression must be used when the solution manifold is not embedded in a low-dimensional subspace. Early methods involve piecewise linear data compression, by constructing a dictionary of reduced-order models tailored to a partition of the solution manifold. In this work, we introduce the concept of optimal partition of the solution manifold in terms of normalized Kolmogorov widths, and prove that the optimal partitions can be found by means of a representative-based clustering algorithm using the sine dissimilarity measure on the solution manifold.

Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior sampling methods proposed for solving common BIPs rely on heuristic approximations to the generative process. To exploit the generative capability of DMs and avoid the usage of such approximations, we propose an ensemble-based algorithm that performs posterior sampling without the use of heuristic approximations. Our algorithm is motivated by existing works that combine DM-based methods with the sequential Monte Carlo (SMC) method. By examining how the prior evolves through the diffusion process encoded by the pre-trained score function, we derive a modified partial differential equation (PDE) governing the evolution of the corresponding posterior distribution. This PDE includes a modified diffusion term and a reweighting term, which can be simulated via stochastic weighted particle methods. Theoretically, we prove that the error between the true posterior distribution can be bounded in terms of the training error of the pre-trained score function and the number of particles in the ensemble. Empirically, we validate our algorithm on several inverse problems in imaging to show that our method gives more accurate reconstructions compared to existing DM-based methods.

We introduce Gradient Agreement Filtering (GAF) to improve on gradient averaging in distributed deep learning optimization. Traditional distributed data-parallel stochastic gradient descent involves averaging gradients of microbatches to calculate a macrobatch gradient that is then used to update model parameters. We find that gradients across microbatches are often orthogonal or negatively correlated, especially in late stages of training, which leads to memorization of the training set, reducing generalization. In this paper, we introduce a simple, computationally effective way to reduce gradient variance by computing the cosine distance between micro-gradients during training and filtering out conflicting updates prior to averaging. We improve validation accuracy with significantly smaller microbatch sizes. We also show this reduces memorizing noisy labels. We demonstrate the effectiveness of this technique on standard image classification benchmarks including CIFAR-100 and CIFAR-100N-Fine. We show this technique consistently outperforms validation accuracy, in some cases by up to 18.2\% compared to traditional training approaches while reducing the computation required nearly an order of magnitude because we can now rely on smaller microbatch sizes without destabilizing training.

One-shot Federated Learning (OFL) has become a promising learning paradigm, enabling the training of a global server model via a single communication round. In OFL, the server model is aggregated by distilling knowledge from all client models (the ensemble), which are also responsible for synthesizing samples for distillation. In this regard, advanced works show that the performance of the server model is intrinsically related to the quality of the synthesized data and the ensemble model. To promote OFL, we introduce a novel framework, Co-Boosting, in which synthesized data and the ensemble model mutually enhance each other progressively. Specifically, Co-Boosting leverages the current ensemble model to synthesize higher-quality samples in an adversarial manner. These hard samples are then employed to promote the quality of the ensemble model by adjusting the ensembling weights for each client model. Consequently, Co-Boosting periodically achieves high-quality data and ensemble models. Extensive experiments demonstrate that Co-Boosting can substantially outperform existing baselines under various settings. Moreover, Co-Boosting eliminates the need for adjustments to the client's local training, requires no additional data or model transmission, and allows client models to have heterogeneous architectures.

Nonlinear model order reduction has opened the door to parameter optimization and uncertainty quantification in complex physics problems governed by nonlinear equations. In particular, the computational cost of solving these equations can be reduced by means of local reduced-order bases. This article examines the benefits of a physics-informed cluster analysis for the construction of cluster-specific reduced-order bases. We illustrate that the choice of the dissimilarity measure for clustering is fundamental and highly affects the performances of the local reduced-order bases. It is shown that clustering with an angle-based dissimilarity on simulation data efficiently decreases the intra-cluster Kolmogorov N-width. Additionally, an a priori efficiency criterion is introduced to assess the relevance of a ROM-net, a methodology for the reduction of nonlinear physics problems introduced in our previous work in [T. Daniel, F. Casenave, N. Akkari, D. Ryckelynck, Model order reduction assisted by deep neural networks (ROM-net), Advanced Modeling and Simulation in Engineering Sciences 7 (16), 2020]. This criterion also provides engineers with a very practical method for ROM-nets' hyperparameters calibration under constrained computational costs for the training phase. On five different physics problems, our physics-informed clustering strategy significantly outperforms classic strategies for the construction of local reduced-order bases in terms of projection errors.

Increasingly expensive training of ever larger models such as Vision Transfomers motivate reusing the vast library of already trained state-of-the-art networks. However, their latency, high computational costs and memory demands pose significant challenges for deployment, especially on resource-constrained hardware. While structured pruning methods can reduce these factors, they often require costly retraining, sometimes for up to hundreds of epochs, or even training from scratch to recover the lost accuracy resulting from the structural modifications. Maintaining the provided performance of trained models after structured pruning and thereby avoiding extensive retraining remains a challenge. To solve this, we introduce Variance-Based Pruning, a simple and structured one-shot pruning technique for efficiently compressing networks, with minimal finetuning. Our approach first gathers activation statistics, which are used to select neurons for pruning. Simultaneously the mean activations are integrated back into the model to preserve a high degree of performance. On ImageNet-1k recognition tasks, we demonstrate that directly after pruning DeiT-Base retains over 70% of its original performance and requires only 10 epochs of fine-tuning to regain 99% of the original accuracy while simultaneously reducing MACs by 35% and model size by 36%, thus speeding up the model by 1.44x.

Based on the weight-sharing mechanism, one-shot NAS methods train a supernet and then inherit the pre-trained weights to evaluate sub-models, largely reducing the search cost. However, several works have pointed out that the shared weights suffer from different gradient descent directions during training. And we further find that large gradient variance occurs during supernet training, which degrades the supernet ranking consistency. To mitigate this issue, we propose to explicitly minimize the gradient variance of the supernet training by jointly optimizing the sampling distributions of PAth and DAta (PA&DA). We theoretically derive the relationship between the gradient variance and the sampling distributions, and reveal that the optimal sampling probability is proportional to the normalized gradient norm of path and training data. Hence, we use the normalized gradient norm as the importance indicator for path and training data, and adopt an importance sampling strategy for the supernet training. Our method only requires negligible computation cost for optimizing the sampling distributions of path and data, but achieves lower gradient variance during supernet training and better generalization performance for the supernet, resulting in a more consistent NAS. We conduct comprehensive comparisons with other improved approaches in various search spaces. Results show that our method surpasses others with more reliable ranking performance and higher accuracy of searched architectures, showing the effectiveness of our method. Code is available at https://github.com/ShunLu91/PA-DA.

Score distillation has emerged as one of the most prevalent approaches for text-to-3D asset synthesis. Essentially, score distillation updates 3D parameters by lifting and back-propagating scores averaged over different views. In this paper, we reveal that the gradient estimation in score distillation is inherent to high variance. Through the lens of variance reduction, the effectiveness of SDS and VSD can be interpreted as applications of various control variates to the Monte Carlo estimator of the distilled score. Motivated by this rethinking and based on Stein's identity, we propose a more general solution to reduce variance for score distillation, termed Stein Score Distillation (SSD). SSD incorporates control variates constructed by Stein identity, allowing for arbitrary baseline functions. This enables us to include flexible guidance priors and network architectures to explicitly optimize for variance reduction. In our experiments, the overall pipeline, dubbed SteinDreamer, is implemented by instantiating the control variate with a monocular depth estimator. The results suggest that SSD can effectively reduce the distillation variance and consistently improve visual quality for both object- and scene-level generation. Moreover, we demonstrate that SteinDreamer achieves faster convergence than existing methods due to more stable gradient updates.

Parameter-Efficient Fine-Tuning (PEFT) is increasingly recognized as an effective method in speech processing. However, the optimal approach and the placement of PEFT methods remain inconclusive. Our study conducts extensive experiments to compare different PEFT methods and their layer-wise placement adapting Differentiable Architecture Search (DARTS). We also explore the use of ensemble learning to leverage diverse PEFT strategies. The results reveal that DARTS does not outperform the baseline approach, which involves inserting the same PEFT method into all layers of a Self-Supervised Learning (SSL) model. In contrast, an ensemble learning approach, particularly one employing majority voting, demonstrates superior performance. Our statistical evidence indicates that different PEFT methods learn in varied ways. This variation might explain why the synergistic integration of various PEFT methods through ensemble learning can harness their unique learning capabilities more effectively compared to individual layer-wise optimization.

Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost estimates, and revenue predictions all benefit from being able to quantify the range of possible values accurately. As such, many models have been developed for this problem over many years of research in statistics, machine learning, and related fields. Rather than proposing yet another (new) algorithm for quantile regression we adopt a meta viewpoint: we investigate methods for aggregating any number of conditional quantile models, in order to improve accuracy and robustness. We consider weighted ensembles where weights may vary over not only individual models, but also over quantile levels, and feature values. All of the models we consider in this paper can be fit using modern deep learning toolkits, and hence are widely accessible (from an implementation point of view) and scalable. To improve the accuracy of the predicted quantiles (or equivalently, prediction intervals), we develop tools for ensuring that quantiles remain monotonically ordered, and apply conformal calibration methods. These can be used without any modification of the original library of base models. We also review some basic theory surrounding quantile aggregation and related scoring rules, and contribute a few new results to this literature (for example, the fact that post sorting or post isotonic regression can only improve the weighted interval score). Finally, we provide an extensive suite of empirical comparisons across 34 data sets from two different benchmark repositories.

We consider the reinforcement learning (RL) problem with general utilities which consists in maximizing a function of the state-action occupancy measure. Beyond the standard cumulative reward RL setting, this problem includes as particular cases constrained RL, pure exploration and learning from demonstrations among others. For this problem, we propose a simpler single-loop parameter-free normalized policy gradient algorithm. Implementing a recursive momentum variance reduction mechanism, our algorithm achieves mathcal{O}(epsilon^{-3}) and mathcal{O}(epsilon^{-2}) sample complexities for epsilon-first-order stationarity and epsilon-global optimality respectively, under adequate assumptions. We further address the setting of large finite state action spaces via linear function approximation of the occupancy measure and show a mathcal{O}(epsilon^{-4}) sample complexity for a simple policy gradient method with a linear regression subroutine.

We introduce a multi-fidelity estimator of covariance matrices that employs the log-Euclidean geometry of the symmetric positive-definite manifold. The estimator fuses samples from a hierarchy of data sources of differing fidelities and costs for variance reduction while guaranteeing definiteness, in contrast with previous approaches. The new estimator makes covariance estimation tractable in applications where simulation or data collection is expensive; to that end, we develop an optimal sample allocation scheme that minimizes the mean-squared error of the estimator given a fixed budget. Guaranteed definiteness is crucial to metric learning, data assimilation, and other downstream tasks. Evaluations of our approach using data from physical applications (heat conduction, fluid dynamics) demonstrate more accurate metric learning and speedups of more than one order of magnitude compared to benchmarks.

With the success of deep neural networks, Neural Architecture Search (NAS) as a way of automatic model design has attracted wide attention. As training every child model from scratch is very time-consuming, recent works leverage weight-sharing to speed up the model evaluation procedure. These approaches greatly reduce computation by maintaining a single copy of weights on the super-net and share the weights among every child model. However, weight-sharing has no theoretical guarantee and its impact has not been well studied before. In this paper, we conduct comprehensive experiments to reveal the impact of weight-sharing: (1) The best-performing models from different runs or even from consecutive epochs within the same run have significant variance; (2) Even with high variance, we can extract valuable information from training the super-net with shared weights; (3) The interference between child models is a main factor that induces high variance; (4) Properly reducing the degree of weight sharing could effectively reduce variance and improve performance.

Visual Autoregressive (VAR) models have recently garnered significant attention for their innovative next-scale prediction paradigm, offering notable advantages in both inference efficiency and image quality compared to traditional multi-step autoregressive (AR) and diffusion models. However, despite their efficiency, VAR models often suffer from the diversity collapse i.e., a reduction in output variability, analogous to that observed in few-step distilled diffusion models. In this paper, we introduce DiverseVAR, a simple yet effective approach that restores the generative diversity of VAR models without requiring any additional training. Our analysis reveals the pivotal component of the feature map as a key factor governing diversity formation at early scales. By suppressing the pivotal component in the model input and amplifying it in the model output, DiverseVAR effectively unlocks the inherent generative potential of VAR models while preserving high-fidelity synthesis. Empirical results demonstrate that our approach substantially enhances generative diversity with only neglectable performance influences. Our code will be publicly released at https://github.com/wangtong627/DiverseVAR.

Some classical uncertainty quantification problems require the estimation of multiple expectations. Estimating all of them accurately is crucial and can have a major impact on the analysis to perform, and standard existing Monte Carlo methods can be costly to do so. We propose here a new procedure based on importance sampling and control variates for estimating more efficiently multiple expectations with the same sample. We first show that there exists a family of optimal estimators combining both importance sampling and control variates, which however cannot be used in practice because they require the knowledge of the values of the expectations to estimate. Motivated by the form of these optimal estimators and some interesting properties, we therefore propose an adaptive algorithm. The general idea is to adaptively update the parameters of the estimators for approaching the optimal ones. We suggest then a quantitative stopping criterion that exploits the trade-off between approaching these optimal parameters and having a sufficient budget left. This left budget is then used to draw a new independent sample from the final sampling distribution, allowing to get unbiased estimators of the expectations. We show how to apply our procedure to sensitivity analysis, by estimating Sobol' indices and quantifying the impact of the input distributions. Finally, realistic test cases show the practical interest of the proposed algorithm, and its significant improvement over estimating the expectations separately.

Machine learning is now used in many areas of astrophysics, from detecting exoplanets in Kepler transit signals to removing telescope systematics. Recent work demonstrated the potential of using machine learning algorithms for atmospheric retrieval by implementing a random forest to perform retrievals in seconds that are consistent with the traditional, computationally-expensive nested-sampling retrieval method. We expand upon their approach by presenting a new machine learning model, plan-net, based on an ensemble of Bayesian neural networks that yields more accurate inferences than the random forest for the same data set of synthetic transmission spectra. We demonstrate that an ensemble provides greater accuracy and more robust uncertainties than a single model. In addition to being the first to use Bayesian neural networks for atmospheric retrieval, we also introduce a new loss function for Bayesian neural networks that learns correlations between the model outputs. Importantly, we show that designing machine learning models to explicitly incorporate domain-specific knowledge both improves performance and provides additional insight by inferring the covariance of the retrieved atmospheric parameters. We apply plan-net to the Hubble Space Telescope Wide Field Camera 3 transmission spectrum for WASP-12b and retrieve an isothermal temperature and water abundance consistent with the literature. We highlight that our method is flexible and can be expanded to higher-resolution spectra and a larger number of atmospheric parameters.

Client selection strategies are widely adopted to handle the communication-efficient problem in recent studies of Federated Learning (FL). However, due to the large variance of the selected subset's update, prior selection approaches with a limited sampling ratio cannot perform well on convergence and accuracy in heterogeneous FL. To address this problem, in this paper, we propose a novel stratified client selection scheme to reduce the variance for the pursuit of better convergence and higher accuracy. Specifically, to mitigate the impact of heterogeneity, we develop stratification based on clients' local data distribution to derive approximate homogeneous strata for better selection in each stratum. Concentrating on a limited sampling ratio scenario, we next present an optimized sample size allocation scheme by considering the diversity of stratum's variability, with the promise of further variance reduction. Theoretically, we elaborate the explicit relation among different selection schemes with regard to variance, under heterogeneous settings, we demonstrate the effectiveness of our selection scheme. Experimental results confirm that our approach not only allows for better performance relative to state-of-the-art methods but also is compatible with prevalent FL algorithms.