Early Exit (EE) techniques have emerged as a means to reduce inference latency in Deep Neural Networks (DNNs). The latency improvement and accuracy in these techniques crucially depend on the criteria used to make exit decisions. We propose a new decision criterion BEEM where exit classifiers are treated as experts and aggregate their confidence scores. The confidence scores are aggregated only if neighbouring experts are consistent in prediction as the samples pass through them, thus capturing their ensemble effect. A sample exits when the aggregated confidence value exceeds a threshold. The threshold is set using the error rates of the intermediate exits aiming to surpass the performance of conventional DNN inference. Experimental results on the COCO dataset for Image captioning and GLUE datasets for various language tasks demonstrate that our method enhances the performance of state-of-the-art EE methods, achieving improvements in speed-up by a factor 1.5 to 2.1 . When compared to the final layer, its accuracy is comparable in harder Image Captioning and improves in the easier language tasks. The source code for this work is publicly available at. Transformer-based models (Devlin et al., 2018; Radford et al., 2019; Cornia et al., 2020; Luo et al., 2021; Li et al., 2022; 2023) have set new benchmarks in performance across diverse tasks and domains through their prowess in capturing semantic information and dependencies using attention mechanisms (Vaswani et al., 2017).

We present a general method for fitting finite mixture models (FMM). Learning in a mixture model consists of finding the most likely cluster assignment for each data-point, as well as finding the parameters of the clusters themselves. In many mixture models, this is difficult with current learning methods, where the most common approach is to employ monotone learning algorithms e.g. the conventional expectation-maximisation algorithm. While effective, the success of any monotone algorithm is crucially dependant on good parameter initialisation, where a common choice is $K$-means initialisation, commonly employed for Gaussian mixture models. For other types of mixture models, the path to good initialisation parameters is often unclear and may require a problem-specific solution. To this end, we propose a general heuristic learning algorithm that utilises Boltzmann exploration to assign each observation to a specific base distribution within the mixture model, which we call Boltzmann exploration expectation-maximisation (BEEM). With BEEM, hard assignments allow straight forward parameter learning for each base distribution by conditioning only on its assigned observations. Consequently, it can be applied to mixtures of any base distribution where single component parameter learning is tractable. The stochastic learning procedure is able to escape local optima and is thus insensitive to parameter initialisation. We show competitive performance on a number of synthetic benchmark cases as well as on real-world datasets.