{
  "id": "1907.07904",
  "version": "v1",
  "published": "2019-07-18T06:58:36.000Z",
  "updated": "2019-07-18T06:58:36.000Z",
  "title": "On the relation between Loss Functions and T-Norms",
  "authors": [
    "Francesco Giannini",
    "Giuseppe Marra",
    "Michelangelo Diligenti",
    "Marco Maggini",
    "Marco Gori"
  ],
  "categories": [
    "cs.LG",
    "stat.ML"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-18T06:58:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "loss functions",
      "faster convergence rates",
      "popular cross-entropy loss",
      "novel class",
      "computer vision"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}