{"title": "Absence of Cycles in Symmetric Neural Networks", "book": "Advances in Neural Information Processing Systems", "page_first": 372, "page_last": 378, "abstract": null, "full_text": "\u0001\u0003\u0002\u0005\u0004\u0007\u0006\u0003\b\t\u0004\n\n\f\u000b\u000e\r\u000e\u000f\u0010\b\t\u0011\u0012\u0004\u0007\u0002\n\n\u0014\u0015\u0006\n\n\u0004%\u0019'&\n\n\u0016\u0017\u000f\u0010\u0018\n\u001b!(\n\n\u0004\u001a\u0019\u0005\u001b\u001d\u001c\n\n\u0004\u0007\u001f\n\n\u001b! 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21\nH\n\n1\u0012\u00f8\n8\u008c=\ngE-\n\n\u0005\n\u000b\n&\n)\n-\n/\n1\nK\n-\n/\n1\nZ\n1\nB\nf\n)\ng\n\\\n\\\n6\n8\n]\nB\no\nM\n6\nn\n1\n|\n]\n\\\n+\nw\n]\n=\n\\\n\u0084\nD\n-\n_\nF\n8\n3\n/\n<\n1\nn\n\u0090\n\u008b\n]\n\u0090\n{\n3\n@\n\u0084\n3\n/\n\u008a\n\u008a\n\u0094\nZ\nd\n\u0095\n5\nn\nd\n\u008a\n8\n\u00a3\n\u007f\n]\n1\n@\n\u00a1\n\u0084\n/\n3\n=\n\u0089\n1\n6\n-\n8\n5\n8\n3\n/\n1\n\u0090\n1\n\u0087\n\u0084\n\u00a7\n\u0084\nB\n*\n\u0090\n\u0084\n\u00a8\n1\ng\nd\n8\n\u008b\n3\n1\n+\nd\n\u009a\n\u0096\nZ\nH\n1\n1\n=\n\u008a\n\u0097\n\u009f\nZ\n5\n\u0084\n\u00bc\n6\n\u008a\n\u0082\n=\n1\n+\n-\n+\n8\n6\n\u00a8\n8\n6\n\u008b\n+\n1\n1\n\u00a8\n\u0090\n5\n\u0084\nD\n+\n8\n3\n\u008b\n3\n1\n-\n\u0087\nX\n=\n1\n-\n6\n1\n3\n:\n8\n=\n\u0084\n\u00c4\nv\n\u008b\n+\n\u008b\n]\n]\n1\na\n3\n\u008a\n+\n=\n5\n\u0096\n\u0096\n\u00c9\n\u00c7\n=\nH\nZ\n\u00c9\n\u00b1\n5\n+\n\u00c9\n\u0082\n\u0096\n\u00be\ng\n\u00ce\n\u0089\n\u0084\nj\n6\n+\n\u008b\n1\n*\n1\n\u00ca\nd\nf\n\u00d3\n\u00d2\n\u00d5\n:\n1\n\u00d7\n1\n1\n\u0090\n\u00d8\n\u00ae\n3\n+\n\u0084\n*\n6\nB\n|\n1\n-\n1\n\u00ae\n1\n5\n\u0090\n1\n=\n\u0084\nD\n]\n1\n-\n\u0084\n\u00c8\n]\n1\n5\nH\nr\nv\n1\n\u00ae\nh\n8\n6\n\u00c9\n1\n+\n\u0090\n1\n\u0095\n\u008b\n\u0084\nj\n]\n^\n\u008b\n8\n6\n1\nH\n=\n*\n\u00e4\n\u0099\n8\n6\n8\ny\n\u0084\n|\n5\n@\n\u008b\n\u009e\n<\n1\nn\n\u0090\n=\n1\nH\n+\n1\nn\n-\n1\n\u0090\n+\n]\n\u008b\n\u0090\n=\n\u00c5\n\u0094\n5\n1\n\u00c9\n\u00a4\n\u0087\n1\nq\n\u0084\n\u00e8\nr\n|\n+\n\u0093\n\u0094\n1\n^\n-\n\u0099\n\u00c9\n\u009d\nZ\n\u0082\n\u00a1\n*\n\u0089\n\u0084\n*\n6\n@\n\u008b\n\u0084\n`\n\u0094\n5\n\u0090\n\u0091\nn\n\u008a\n\u00a4\n\u00be\n8\n-\n\u008b\nF\n1\ng\nn\n\u008b\n6\n8\n\u0081\n\u0084\n/\ny\n\u008b\n1\n=\n8\n\u008b\n3\n/\n5\n+\n1\n6\n6\nH\n\u0090\nn\n8\n-\n1\n-\n8\n-\n1\n8\n6\n\u008b\n-\n\u0084\n\u00e1\n]\n/\n8\nn\nr\n]\n\u0090\nv\n5\n\u008b\n1\n5\n1\n6\n1\n6\n-\nn\n\u008b\n6\nB\n\u00ea\n\u0093\n\u00a4\nk\n-\n\u00a8\n\u0092\n\u008b\n]\n\u0090\n-\nr\n\u0084\n=\n\u0093\n\u00a4\n\u0092\nH\n+\n6\n+\nl\n\u00fd\n6\n1\n+\n\u008b\n]\n]\n1\n\u00ff\n3\n]\n8\ng\n<\nf\n+\n5\n-\n/\n8\n/\n1\n]\n|\nr\n\u0084\n\u00a9\ny\n\u008b\n=\n\u00f4\n-\n\u00a8\n\\\n6\n\u00c3\n]\n)\nj\n\u00b0\n-\nV\n\u0092\nN\n\u00e0\n\u00c4\n?\n\u00c5\n\u00b1\n5\nv\n1\n+\n\u00c9\n\u00c9\n-\n/\nd\nq\n1\n\u00ae\n\u00b3\n|\n\u00f4\n6\nH\n]\nq\nH\n6\n\u00b0\n-\nB\nj\n5\n6\nd\n\u0084\nf\n\u0084\nF\n\u0084\n|\n-\n\u0084\n\u00e1\nw\n:\n\u00a8\n?\n\u0084\n\u00a9\n/\n1\n+\n1\n-\n/\n1\n\u00d6\n1\n\u00c5\n\u00a4\n\u00be\nB\n\u001f\n+\nw\n1\n-\n5\nN\n\u0091\n\u00c1\n1\nn\n\u00e0\n|\n?\n-\n\u0012\n\u0002\n\u00c5\n\u00b6\n8\n=\n\u00b0\nH\n+\n\u00b7\nT\n1\n1\n=\nw\nl\nd\n\u0082\nk\n\u00c9\n|\n]\n\u0084\n\u0002\n \n\u00fe\n{\n:\nN\n?\n\u00f4\n8\n\u0084\n\u0095\n?\n\u0012\nn\n1\n^\n\u0084\n{\nw\n1\n=\n6\n1\n-\nV\n5\n\u00fe\n1\n=\n1\n6\n-\n\u00e0\ng\n(\n\u00c9\n\u0012\n\u00c5\n+\n\u00a6\nv\n\u00b0\nH\n+\nd\n\u00bc\nd\n\u00cb\ng\nd\nT\n\u00c3\nM\n\u0089\n\u00d6\n\u00b7\nT\n1\n1\n=\nw\n1\nv\n-\n\u00be\n-\n/\n1\nq\n8\n3\n1\n]\n8\n-\n-\n+\n\u008b\n1\nB\n1\n\u00b0\n6\n\u00c3\n-\n8\n=\n5\n6\nw\n\u00f4\n1\n|\n \n\u00c5\n+\n0\n5\nV\n-\n0\n\u00c3\n]\n:\n\u0089\n\u008b\n6\n8\n]\n\u0084\nS\n\u00b0\n+\nB\n*\n-\n\u0002\n6\nH\n3\n|\n]\n8\nM\n+\n\u00e0\n\u00c4\nr\n\u0084\n\u008b\nl\n\u00d6\n1\n\u00a3\n\u007f\n]\n5\nn\n\u00c5\n\u00a4\n\u00a1\n\u00e3\ng\n\u008b\n\u00e0\n\u0098\n \n|\n-\n\u00e0\n/\n1\nn\n\u008b\n6\n8\n|\n\u00b0\n+\n-\n/\n1\n]\n:\n8\nH\nN\nq\n8\n-\n=\n\u00a3\n\u007f\n]\n5\nB\nZ\n?\n-\n/\nB\nF\n8\nF\n1\n=\n\u0084\n;\n\u00b0\n/\n\u00f4\n1\n?\n:\nB\n7\n\u0099\n:\n\u0012\n\u00c5\n\u00a4\n\u00be\nV\n\u0084\n*\n \n\u0090\n8\n^\n8\n]\n1\n\u0095\n\u00ce\n5\n\u008b\n:\nl\n^\n\u0084\n\u00bc\n\u00b0\n-\n\u00f8\nN\n+\n/\n\u0084\n\u00d7\n+\n]\n\u0092\n:\n:\n-\n\u008b\nF\n1\n+\n\u0090\n8\n:\n\u00f0\n8\n?\nn\n+\n1\n\f\nH\n\u0098\n\u00e5\n\u008b\n6\n8\n]\n\u0084\n\u00a4\n\u00c7\nH\nH\n1\n]\n1\n\u00b0\nn\n\u0084\nB\n \n+\nN\n?\n-\nm\n\u0090\n8\n^\n8\n]\n1\n-\n+\n\u00c5\n^\n8\n-\n0\n8\n?\nN\n/\nB\n0\n-\n]\n\u00c3\n1\nv\n\u00e1\nv\nl\n0\n1\n\u00e6\n:\n\u00f4\nv\nw\n1\n^\n\u00f4\n1\n\u0090\n8\nv\n\u00a8\n\u008b\n6\n8\n]\nB\nj\n8\n6\n\u00a8\n-\n/\n1\n+\n\u00c3\n]\nN\n\u00b0\n+\n-\n\u00c3\nr\n\u0084\n\u00e4\nv\n\u00e0\n\u008b\n8\n^\nN\nH\n6\n\u00a8\n\u0091\n\u00c1\n1\n|\n \nq\n\u00c5\n\u0082\nk\n7\n\u00b6\n5\nw\nd\nV\n\u0084\n0\n-\n0\n1\n+\n1\n6\n]\n1\n-\n+\n\u0092\nr\n\u0084\no\nq\n8\nl\n\u0084\n 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\n\u00f4\nr\n\u0084\nH\n8\n-\n\u00e0\nJ\n?\n-\n\u0090\n]\n1\n-\n+\n8\n=\n1\nw\n\u00c3\n1\n\u00bf\nB\n\u008b\nd\n\u0084\n|\n-\n0\n\u00fe\nS\n+\n]\n5\n\u00f0\nd\n=\n8\n-\nm\n:\n=\n8\n6\n\u0081\n\u00a4\n\u00be\nB\n8\n-\n\u00e3\nM\n+\n:\nn\n\u00e6\nN\n^\n1\n-\nF\n=\n8\n1\n\u00b0\n1\n\u0092\n8\n\u00e1\n\u0012\n\u00b0\n^\n1\n-\n1\n\u00ae\ng\n\u00e6\n1\n\u0090\n\u00e8\n]\n8\nl\n\u0084\n\u00c4\n5\n\u00c5\n\u0082\n-\nS\n1\nn\n8\n/\nr\n5\nw\n1\n]\n1\nH\n|\n1\nn\n=\n1\n\u0084\n\u00c4\n+\n8\n]\n5\n\u0090\n\u0087\n\u0084\nS\n8\n-\n1\nn\n)\n{\n+\n\u00b0\n-\n1\n\u00ae\n-\n\u0084\n\u00c4\n]\n1\n]\nN\nn\n?\n1\nH\n^\n-\nV\n>\n+\nH\n^\n\u0090\n1\n\u00f9\n-\nm\n:\nN\n2\n1\nj\n\u00b0\n8\n\u00f0\n\u0084\n|\n6\nw\n1\n\u00c3\n=\n\u00fe\nU\n\u00b0\n+\n\u00fe\n|\nN\nn\n\u0090\n\u00b0\nW\n\u00b0\nS\n\u00b0\n8\n-\n\u00e0\n 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\n7\n\u0085\ns\ni\ny\nY\nY\n\u00f2\nx\n\u00ee\n\u00bf\n\u00f3\n\u0081\n4\n9\n\u00af\n.\nV\n\u00d4\nV\n9\n\u009a\ns\n5\nm\n@\n\u00d2\n\u00b1\n\u00ca\nj\n.\ns\n9\n\u00ce\nU\n9\n\u0096\na\n/\n4\ni\nu\n\"\n/\n\u0018\nU\n9\n\u0096\nW\n\u008f\nr\n\u008f\n5\nU\n\u00d5\n<\nU\n\u007f\na\ns\ni\n\u00b9\n\u00ba\n\u00bf\n\u00c3\n]\n\u00f9\n\u00de\n\u008a\n\u00b1\n!\na\n4\n\u00fa\n@\n\u00d2\n\u00b1\n\u00ca\nB\n.\nC\ns\n7\nl\n/\n.\nU\n\u007f\na\ns\n\u0089\n\u00d5\n!\nu\n5\n>\n9\n\u00c6\nU\n^\nu\n.\n9\n\"\nb\n.\n\u0084\n\u0006\nU\n7\nU\n9\n\u0091\n_\n9\n\u009a\n\u0085\n9\n\"\nU\n9\n\u00bc\n\u00c1\n\u00f6\n\u008a\n\u00c1\n\u00ba\n\u0093\n\u00c1\n\u00e5\n\u00f6\n\u00bd\n5\nN\n\u00e7\n\u0081\n\u00ba\n\u00e7\n\u00cb\n\u00b8\n\u00f9\n\u00c5\n\u00c5\n\u00ca\n\u0096\n\u00fd\nc\nq\na\n@\n\u00d2\n.\nC\ns\n\u007f\n9\n\u00de\nU\ns\n7\n4\n.\n\u0098\n\u00d8\ny\n.\nv\na\n.\nv\nU\n9\nc\n\u008f\nU\n9\n\u009d\n\u0085\nq\ns\na\nq\n.\ns\nz\n9\np\n\u008c\n\u0089\n.\na\n5\n=\nU\nU\n\u008f\ns\na\n\u001e\n\u00f6\nc\nz\n\u00f3\nl\nY\n\u00e5\n\u00e7\n\u00f6\n3\n4\n\u0019\n\u00ba\n\u00e5\n\u0095\n\u00e7\nf\n\u0013\ni\n\"\n]\n\u00d3\n\u00f9\n\u00d6\n\u00d0\na\n9\n\u0083\ns\n!\nI\n\u00cd\n\u00a4\nu\n5\na\nx\n4\n9\ni\n5\nu\nU\n.\nU\n9\n\u00c4\nu\nU\n\u00d5\n!\n/\n\u008f\nU\n7\nq\n\u008e\na\n\u00d8\nV\n\u00a9\n\u00bc\n\u0080\n2\n\u00bd\n4\n\u00c1\n\u00e5\n\u00ce\n\u00c5\n\u00fc\n^\n\u00ca\n\u0096\nj\n\u009a\n\u00d4\nc\n\u00d4\n7\ns\n5\n\u00ab\nu\n\u009a\n\u00af\n.\n5\n\u00d8\nb\n.\n\u0085\nU\ni\n\u00d3\n\u00ca\n\u00cd\n>\n5\na\n\u0096\nU\n.\ns\n7\nU\n.\n.\n\u008f\ns\n3\nU\n\u0019\n\u007f\na\nn\n6\n\u00f3\n\u00b3\n\u00f6\n\u00bd\n\u00b8\n\u00ba\n\u00fa\n\u0096\n\u00c6\n\u00d0\n.\nU\n.\ns\n5\na\n\u00fd\ni\n_\n/\n4\n\u00d2\n.\n\u008f\ns\n7\n\u0085\n\u007f\na\ns\n\u0018\n4\n\u009b\nu\na\n\u0087\n\u0006\n\u0085\n\u008e\nq\nU\n9\n\u00a5\n\u0092\n\u0090\nU\n9\n\u00ce\na\n/\nq\nn\na\n_\no\n.\n\u0084\n5\n\u00cc\nq\n=\na\ns\nv\nU\nC\n4\n>\na\n/\nU\nX\n\u00d8\n7\n\u0006\ny\n_\n9\n\"\nU\n\u001a\n)\na\ns\n\u0087\n\u00fa\n\u00e9\n\u00bf\nB\n\u0096\n<\n\u00ca\n\u00d3\ni\n\u00cd\n\u009a\nu\n~\n\u0085\n.\ni\n\u00e0\n\u00be\n\u00ba\n\u00e9\n\u00ba\nw\n-\n\u00f3\n\u001b\n\u00c4\n\u00ba\n\u00bc\n\u00ba\n\u00e5\n\u00c5\n3\n\u00c6\n\u00f6\n\u00c3\n\u00bd\n.\n\u007f\n\u00bd\n.\n\u00e8\ni\n\u001a\n!\ns\n\u008e\n5\n5\n/\nu\n\u00ce\n\u00ad\n\u00b9\n\u00af\n7\n/\n\u0015\nV\n\u00a2\n\u00c6\n\u00aa\n\u00dc\n\u008f\n\u0084\ni\nM\n\u00d3\nB\nF\n\u00cd\n9\ni\n5\nu\ns\n.\n9\ns\n5\n\u008f\n5\nJ\n\u0096\n/\n\u008f\nU\n9\n.\n\u008f\ns\n7\no\n/\n\u0019\n\u00a8\na\ns\nc\n5\ni\nL\n\u008a\n\u00c1\n2\n\u00bc\n\u00e3\n\u00e7\n\u00e7\n\u00c5\n\u00ba\n\u00e5\n\u00b1\n\u009a\nm\n\u00fa\nu\ni\n\u00af\n7\n\u008f\nX\ny\n\u009a\n\u00d4\n\u00ce\n\u00af\nU\n.\ns\n\u009d\n\u0096\n@\n\u0085\na\nX\n~\ns\n.\nU\n\u007f\na\ns\n\u0006\n.\nU\n9\n\u00b7\n\u009a\na\n/\n\u0096\n\u00cd\n>\n\u0084\n9\n5\n7\n/\n\u0098\n_\n9\n\u0094\n\u0085\n\u00b0\n>\n\"\n\n6\n\u0012\n\u00f6\n.\n\u00c4\n\u0096\n\u0096\nB\n\u00fc\n\u00fb\n\u00fc\n=\n<\n\f\u0001\u000b\n\r\f\n\n\u0010\u0012\u0011\n\n\u0001\u0004\u0015\u0017\u0016\n\n\u0003\u0004\u0018\n\n\u0010\u001a\u0019\n\n\u0010\u001a\u001b\n\n\u0019\r\u0014\n\n\u0002\u0001\u0004\u0003\u0006\u0005\n\n\u0007\t\b\n\n\u000e\n\u000f\n\u0013\n\u0014\n\u0001\n\u0011\n\u0007\n\u0018\n\u0003\n\u001c\n\u001d\n\u001e\n\u001f\n \n!\n\"\n#\n\f\f", "award": [], "sourceid": 1090, "authors": [{"given_name": "Xin", "family_name": "Wang", "institution": null}, {"given_name": "Arun", "family_name": "Jagota", "institution": null}, {"given_name": "Fernanda", "family_name": "Botelho", "institution": null}, {"given_name": "Max", "family_name": "Garzon", "institution": null}]}