{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,20]],"date-time":"2026-10-20T16:20:07Z","timestamp":1792513207382,"version":"4.5.0"},"reference-count":25,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,12,21]],"date-time":"2021-12-21T00:00:00Z","timestamp":1640044800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we propose a new approach to train a deep neural network with multiple intermediate auxiliary classifiers, branching from it. These \u2018multi-exits\u2019 models can be used to reduce the inference time by performing early exit on the intermediate branches, if the confidence of the prediction is higher than a threshold. They rely on the assumption that not all the samples require the same amount of processing to yield a good prediction. In this paper, we propose a way to train jointly all the branches of a multi-exit model without hyper-parameters, by weighting the predictions from each branch with a trained confidence score. Each confidence score is an approximation of the real one produced by the branch, and it is calculated and regularized while training the rest of the model. We evaluate our proposal on a set of image classification benchmarks, using different neural models and early-exit stopping criteria.<\/jats:p>","DOI":"10.3390\/e24010001","type":"journal-article","created":{"date-parts":[[2021,12,21]],"date-time":"2021-12-21T04:35:57Z","timestamp":1640061357000},"page":"1","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Probabilistic Re-Intepretation of Confidence Scores in Multi-Exit Models"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3236-3941","authenticated-orcid":false,"given":"Jary","family":"Pomponi","sequence":"first","affiliation":[{"name":"Department of Information Engineering, Electronics and Telecommunications (DIET), Sapienza University of Rome, 00139 Rome, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0881-8344","authenticated-orcid":false,"given":"Simone","family":"Scardapane","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, Electronics and Telecommunications (DIET), Sapienza University of Rome, 00139 Rome, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5793-0917","authenticated-orcid":false,"given":"Aurelio","family":"Uncini","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, Electronics and Telecommunications (DIET), Sapienza University of Rome, 00139 Rome, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2368","DOI":"10.1109\/TIP.2017.2787612","article-title":"Deep visual attention prediction","volume":"27","author":"Wang","year":"2017","journal-title":"IEEE Trans. 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