{
  "id": "1911.08577",
  "version": "v1",
  "published": "2019-11-19T20:50:20.000Z",
  "updated": "2019-11-19T20:50:20.000Z",
  "title": "Representation Learning with Multisets",
  "authors": [
    "Vasco Portilheiro"
  ],
  "comment": "Under review as a conference paper at ICLR 2020. Preliminary version accepted to the NeurIPS 2019 workshop on Sets and Partitions",
  "categories": [
    "cs.LG",
    "cs.AI",
    "stat.ML"
  ],
  "abstract": "We study the problem of learning permutation invariant representations that can capture \"flexible\" notions of containment. We formalize this problem via a measure theoretic definition of multisets, and obtain a theoretically-motivated learning model. We propose training this model on a novel task: predicting the size of the symmetric difference (or intersection) between pairs of multisets. We demonstrate that our model not only performs very well on predicting containment relations (and more effectively predicts the sizes of symmetric differences and intersections than DeepSets-based approaches with unconstrained object representations), but that it also learns meaningful representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-19T20:50:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "representation learning",
      "symmetric difference",
      "measure theoretic definition",
      "learning permutation invariant representations",
      "learns meaningful representations"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}