Combining large language models during training or at inference time has shown substantial performance gain over component LLMs. This paper presents LLM-TOPLA, a diversity-optimized LLM ensemble method with three unique properties: (i) We introduce the focal diversity metric to capture the diversity-performance correlation among component LLMs of an ensemble. (ii) We develop a diversity-optimized ensemble pruning algorithm to select the top-k sub-ensembles from a pool of $N$ base LLMs. Our pruning method recommends top-performing LLM subensembles of size $S$, often much smaller than $N$. (iii) We generate new output for each prompt query by utilizing a learn-to-ensemble approach, which learns to detect and resolve the output inconsistency among all component LLMs of an ensemble. Extensive evaluation on four different benchmarks shows good performance gain over the best LLM ensemble methods: (i) In constrained solution set problems, LLM-TOPLA outperforms the best-performing ensemble (Mixtral) by 2.2\% in accuracy on MMLU and the best-performing LLM ensemble (MoreAgent) on GSM8k by 2.1\%. (ii) In generative tasks, LLM-TOPLA outperforms the top-2 performers (Llama70b/Mixtral) on SearchQA by $3.9\mathrm{x}$ in F1, and on XSum by more than $38$ in ROUGE-1. Our code and dataset, which contains outputs of 8 modern LLMs on 4 benchmarks is available at https://github.com/git-disl/llm-topla
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.
Ensemble techniques are frequently encountered in machine learning and engineering problems since the method combines different models and produces an optimal predictive solution. The ensemble concept can be adapted to deep learning models to provide robustness and reliability. Due to the growth of the models in deep learning, using ensemble pruning is highly important to deal with computational complexity. Hence, this study proposes a mathematical model which prunes the ensemble of Convolutional Neural Networks (CNN) consisting of different depths and layers that maximizes accuracy and diversity simultaneously with a sparse second order conic optimization model. The proposed model is tested on CIFAR-10, CIFAR-100 and MNIST data sets which gives promising results while reducing the complexity of models, significantly.
Over the last few years, the Shapley value, a solution concept from cooperative game theory, has found numerous applications in machine learning. In this paper, we first discuss fundamental concepts of cooperative game theory and axiomatic properties of the Shapley value. Then we give an overview of the most important applications of the Shapley value in machine learning: feature selection, explainability, multi-agent reinforcement learning, ensemble pruning, and data valuation. We examine the most crucial limitations of the Shapley value and point out directions for future research.
Meta-learners and ensembles aim to combine a set of relevant yet diverse base models to improve predictive performance. However, determining an appropriate set of base models is challenging, especially in online environments where the underlying distribution of data can change over time. In this paper, we present a novel approach for estimating the conceptual similarity of base models, which is calculated using the Principal Angles (PAs) between their underlying subspaces. We propose two methods that use conceptual similarity as a metric to obtain a relevant yet diverse subset of base models: (i) parameterised threshold culling and (ii) parameterless conceptual clustering. We evaluate these methods against thresholding using common ensemble pruning metrics, namely predictive performance and Mutual Information (MI), in the context of online Transfer Learning (TL), using both synthetic and real-world data. Our results show that conceptual similarity thresholding has a reduced computational overhead, and yet yields comparable predictive performance to thresholding using predictive performance and MI. Furthermore, conceptual clustering achieves similar predictive performances without requiring parameterisation, and achieves this with lower computational overhead than thresholding using predictive performance and MI when the number of base models becomes large.
Random Forests (RF) are among the state-of-the-art in many machine learning applications. With the ongoing integration of ML models into everyday life, the deployment and continuous application of models becomes more and more an important issue. Hence, small models which offer good predictive performance but use small amounts of memory are required. Ensemble pruning is a standard technique to remove unnecessary classifiers from an ensemble to reduce the overall resource consumption and sometimes even improve the performance of the original ensemble. In this paper, we revisit ensemble pruning in the context of `modernly' trained Random Forests where trees are very large. We show that the improvement effects of pruning diminishes for ensembles of large trees but that pruning has an overall better accuracy-memory trade-off than RF. However, pruning does not offer fine-grained control over this trade-off because it removes entire trees from the ensemble. To further improve the accuracy-memory trade-off we present a simple, yet surprisingly effective algorithm that refines the predictions in the leaf nodes in the forest via stochastic gradient descent. We evaluate our method against 7 state-of-the-art pruning methods and show that our method outperforms the other methods on 11 of 16 datasets with a statistically significant better accuracy-memory trade-off compared to most methods. We conclude our experimental evaluation with a case study showing that our method can be applied in a real-world setting.
What is the value of an individual model in an ensemble of binary classifiers? We answer this question by introducing a class of transferable utility cooperative games called \textit{ensemble games}. In machine learning ensembles, pre-trained models cooperate to make classification decisions. To quantify the importance of models in these ensemble games, we define \textit{Troupe} -- an efficient algorithm which allocates payoffs based on approximate Shapley values of the classifiers. We argue that the Shapley value of models in these games is an effective decision metric for choosing a high performing subset of models from the ensemble. Our analytical findings prove that our Shapley value estimation scheme is precise and scalable; its performance increases with size of the dataset and ensemble. Empirical results on real world graph classification tasks demonstrate that our algorithm produces high quality estimates of the Shapley value. We find that Shapley values can be utilized for ensemble pruning, and that adversarial models receive a low valuation. Complex classifiers are frequently found to be responsible for both correct and incorrect classification decisions.
Neural architecture search (NAS) is gaining more and more attention in recent years due to its flexibility and remarkable capability to reduce the burden of neural network design. To achieve better performance, however, the searching process usually costs massive computations that might not be affordable for researchers and practitioners. While recent attempts have employed ensemble learning methods to mitigate the enormous computational cost, however, they neglect a key property of ensemble methods, namely diversity, which leads to collecting more similar sub-architectures with potential redundancy in the final design. To tackle this problem, we propose a pruning method for NAS ensembles called "Sub-Architecture Ensemble Pruning in Neural Architecture Search (SAEP)." It targets to leverage diversity and to achieve sub-ensemble architectures at a smaller size with comparable performance to ensemble architectures that are not pruned. Three possible solutions are proposed to decide which sub-architectures to prune during the searching process. Experimental results exhibit the effectiveness of the proposed method by largely reducing the number of sub-architectures without degrading the performance.
Ensemble pruning, selecting a subset of individual learners from an original ensemble, alleviates the deficiencies of ensemble learning on the cost of time and space. Accuracy and diversity serve as two crucial factors while they usually conflict with each other. To balance both of them, we formalize the ensemble pruning problem as an objection maximization problem based on information entropy. Then we propose an ensemble pruning method including a centralized version and a distributed version, in which the latter is to speed up the former. At last, we extract a general distributed framework for ensemble pruning, which can be widely suitable for most of the existing ensemble pruning methods and achieve less time consuming without much accuracy degradation. Experimental results validate the efficiency of our framework and methods, particularly concerning a remarkable improvement of the execution speed, accompanied by gratifying accuracy performance.