Abstract
Deep learning has been shown to achieve impressive results in several domains like computer vision and natural language processing. A key element of this success has been the development of new loss functions, like the popular cross-entropy loss, which has been shown to provide faster convergence and to reduce the vanishing gradient problem in very deep structures. While the cross-entropy loss is usually justified from a probabilistic perspective, this paper shows an alternative and more direct interpretation of this loss in terms of t-norms and their associated generator functions, and derives a general relation between loss functions and t-norms. In particular, the presented work shows intriguing results leading to the development of a novel class of loss functions. These losses can be exploited in any supervised learning task and which could lead to faster convergence rates that the commonly employed cross-entropy loss.
This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No 825619.
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Giannini, F., Marra, G., Diligenti, M., Maggini, M., Gori, M. (2020). On the Relation Between Loss Functions and T-Norms. In: Kazakov, D., Erten, C. (eds) Inductive Logic Programming. ILP 2019. Lecture Notes in Computer Science(), vol 11770. Springer, Cham. https://doi.org/10.1007/978-3-030-49210-6_4
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