Plant diseases pose a significant threat to global agriculture, causing over $220 billion in annual economic losses and jeopardizing food security. The timely and accurate detection of these diseases from plant leaf images is critical to mitigating their adverse effects. Deep neural network Ensembles (Deep Ensembles) have emerged as a powerful approach to enhancing prediction accuracy by leveraging the strengths of diverse Deep Neural Networks (DNNs). However, selecting high-performing ensemble member models is challenging due to the inherent difficulty in measuring ensemble diversity. In this paper, we introduce the Synergistic Diversity (SQ) framework to enhance plant disease detection accuracy. First, we conduct a comprehensive analysis of the limitations of existing ensemble diversity metrics (denoted as Q metrics), which often fail to identify optimal ensemble teams. Second, we present the SQ metric, a novel measure that captures the synergy between ensemble members and consistently aligns with ensemble accuracy. Third, we validate our SQ approach through extensive experiments on a plant leaf image dataset, which demonstrates that our SQ metric substantially improves ensemble selection and enhances detection accuracy. Our findings pave the way for a more reliable and efficient image-based plant disease detection.

Knowledge Distillation (KD) aims to train a lightweight student model by transferring knowledge from a large, high-capacity teacher. Recent studies have shown that leveraging diverse teacher perspectives can significantly improve distillation performance; however, achieving such diversity typically requires multiple teacher networks, leading to high computational costs. In this work, we propose a novel cost-efficient knowledge augmentation method for KD that generates diverse multi-views by attaching multiple branches to a single teacher. To ensure meaningful semantic variation across multi-views, we introduce two angular diversity objectives: 1) constrained inter-angle diversify loss, which maximizes angles between augmented views while preserving proximity to the original teacher output, and 2) intra-angle diversify loss, which encourages an even distribution of views around the original output. The ensembled knowledge from these angularly diverse views, along with the original teacher, is distilled into the student. We further theoretically demonstrate that our objectives increase the diversity among ensemble members and thereby reduce the upper bound of the ensemble's expected loss, leading to more effective distillation. Experimental results show that our method surpasses an existing knowledge augmentation method across diverse configurations. Moreover, the proposed method is compatible with other KD frameworks in a plug-and-play fashion, providing consistent improvements in generalization performance.

Ensemble learning has proven effective in improving predictive performance and estimating uncertainty in neural networks. However, conventional ensemble methods often suffer from redundant parameter usage and computational inefficiencies due to entirely independent network training. To address these challenges, we propose the Divergent Ensemble Network (DEN), a novel architecture that combines shared representation learning with independent branching. DEN employs a shared input layer to capture common features across all branches, followed by divergent, independently trainable layers that form an ensemble. This shared-to-branching structure reduces parameter redundancy while maintaining ensemble diversity, enabling efficient and scalable learning.

There has long been plenty of theoretical and empirical evidence supporting the success of ensemble learning. Deep ensembles in particular take advantage of training randomness and expressivity of individual neural networks to gain prediction diversity, ultimately leading to better generalization, robustness and uncertainty estimation. In respect of generalization, it is found that pursuing wider local minima result in models being more robust to shifts between training and testing sets. A natural research question arises out of these two approaches as to whether a boost in generalization ability can be achieved if ensemble learning and loss sharpness minimization are integrated. Our work investigates this connection and proposes DASH - a learning algorithm that promotes diversity and flatness within deep ensembles. More concretely, DASH encourages base learners to move divergently towards low-loss regions of minimal sharpness. We provide a theoretical backbone for our method along with extensive empirical evidence demonstrating an improvement in ensemble generalizability.

We present a theory of ensemble diversity, explaining the nature of diversity for a wide range of supervised learning scenarios. This challenge, of understanding ensemble diversity, has been referred to as the "holy grail" of ensemble learning, an open research issue for over 30 years. Our framework reveals that diversity is in fact a hidden dimension in the bias-variance decomposition of the ensemble loss. We prove a family of exact bias-variance-diversity decompositions, for both regression and classification, e.g., squared, cross-entropy, and Poisson losses. For losses where an additive bias-variance decomposition is not available (e.g., 0/1 loss) we present an alternative approach, which precisely quantifies the effects of diversity, turning out to be dependent on the label distribution. Experiments show how we can use our framework to understand the diversity-encouraging mechanisms of popular methods: Bagging, Boosting, and Random Forests.

Deep neural network ensembles combine the wisdom of multiple deep neural networks to improve the generalizability and robustness over individual networks. It has gained increasing popularity to study deep ensemble techniques in the deep learning community. Some mission-critical applications utilize a large number of deep neural networks to form deep ensembles to achieve desired accuracy and resilience, which introduces high time and space costs for ensemble execution. However, it still remains a critical challenge whether a small subset of the entire deep ensemble can achieve the same or better generalizability and how to effectively identify these small deep ensembles for improving the space and time efficiency of ensemble execution. This paper presents a novel deep ensemble pruning approach, which can efficiently identify smaller deep ensembles and provide higher ensemble accuracy than the entire deep ensemble of a large number of member networks. Our hierarchical ensemble pruning approach (HQ) leverages three novel ensemble pruning techniques. First, we show that the focal diversity metrics can accurately capture the complementary capacity of the member networks of an ensemble, which can guide ensemble pruning. Second, we design a focal diversity based hierarchical pruning approach, which will iteratively find high quality deep ensembles with low cost and high accuracy. Third, we develop a focal diversity consensus method to integrate multiple focal diversity metrics to refine ensemble pruning results, where smaller deep ensembles can be effectively identified to offer high accuracy, high robustness and high efficiency. Evaluated using popular benchmark datasets, we demonstrate that the proposed hierarchical ensemble pruning approach can effectively identify high quality deep ensembles with better generalizability while being more time and space efficient in ensemble decision making.

Deep neural network ensembles hold the potential of improving generalization performance for complex learning tasks. This paper presents formal analysis and empirical evaluation to show that heterogeneous deep ensembles with high ensemble diversity can effectively leverage model learning heterogeneity to boost ensemble robustness. We first show that heterogeneous DNN models trained for solving the same learning problem, e.g., object detection, can significantly strengthen the mean average precision (mAP) through our weighted bounding box ensemble consensus method. Second, we further compose ensembles of heterogeneous models for solving different learning problems, e.g., object detection and semantic segmentation, by introducing the connected component labeling (CCL) based alignment. We show that this two-tier heterogeneity driven ensemble construction method can compose an ensemble team that promotes high ensemble diversity and low negative correlation among member models of the ensemble, strengthening ensemble robustness against both negative examples and adversarial attacks. Third, we provide a formal analysis of the ensemble robustness in terms of negative correlation. Extensive experiments validate the enhanced robustness of heterogeneous ensembles in both benign and adversarial settings. The source codes are available on GitHub at https://github.com/git-disl/HeteRobust.

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.

Error-correcting output codes (ECOC) is an ensemble method combining a set of binary classifiers for multi-class learning problems. However, in traditional ECOC framework, the binary classifiers are trained independently. To explore the interaction between the binary classifiers, we construct an error correction network (ECN) that jointly trains all binary classifiers while maximizing the ensemble diversity to improve its robustness against adversarial attacks. An ECN is built based on a code matrix which is generated by maximizing the error tolerance, i.e., the minimum Hamming distance between any two rows, as well as the ensemble diversity, i.e., the variation of information between any two columns. Though ECN inherently promotes the diversity between the binary classifiers as each ensemble member solves a different classification problem (specified by the corresponding column of the code matrix), we empirically show that the ensemble diversity can be further improved by forcing the weight matrices learned by ensemble members to be orthogonal. The ECN is trained in end-to-end fashion and can be complementary to other defense approaches including adversarial training. We show empirically that ECN is effective against the state-of-the-art while-box attacks while maintaining good accuracy on normal examples.