{"title": "H\u221e Optimal Training Algorithms and their Relation to Backpropagation", "book": "Advances in Neural Information Processing Systems", "page_first": 191, "page_last": 198, "abstract": "", "full_text": "oqp\n\n\u0002\u0004\u0003\u0006\u0005\b\u0007\n\n\u001b\u0006\"#\u0007\n\n\t\u000b\n\n\f\u000e\r\u0010\u000f\n\"%\r\u0018\f%\u0005\b\u0007\n\n\u0019&\u0013\n\n\f\u0012\u0011\n\n\t\u0014\u0013\n\n\t\u0014\u0013\u0016\u0015\n\n\u0018\u0015\u000e\u0019\u000e\u001a\n\n\f)(+*,\u0003\u0006\u001a\n\n\u0005\u001c\u001b\u001d\n\n\u0003\u001d\f#\u0015\u000e\f\n\n\f\u000e\u0013 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W\t&\u0004=\nW\u000b25Dz=\n=K.\u0086E\nu\u0002\u00c7\u0011E\n\u00c7\u0011o\nW\u00102\u0004.\u0013=\nd\u0004=\nDi&\u0004=\u0080G\n\u0087Z\u00c6\nC\u00davYE\n&\u000bG\u0011.\u00baG'W)=K.\u0013G\u00110\nGZ=\u00a2X\u0011H\t=\ntm\u00d7\nuy\u00c7\nDzGb=\n&\u0004=\nE\u000bD5&\u0004=\u0080G\nH\u0004=\u0086dyE\nu\u0004\u00c7\nu\u0004G\nH\u0004=Te\u009b0\n=-W\n13.\u0013G'\u0083\nn\u0080\u00c7\n\u00af\u009avfE\n.\u0013a\nDz0\n=\u0095W\u001ap5G\u0011\u00f8\n1#X'=\nn\u0080E\n.\u0011=\u0098.\n\n\u00fa\u00fc\u00fb \u00fd\u0086\u00fe\u000e\u00ff\u0001\u0003\u0002\u00be\u00ff\nG\u0011\u00edy=\u001b\u0012\u0018%\n\u00ce! \u0010 #\"\u001d$&%('*)*+-,\u00a2E\u000b2\n3547698\u000e:\n.0/21\n;=<>6\u001d?\u000b@BA5?DCE6\n`HG\nRTS\nikj\ndfehg\u000bN\nV\u0005N\nV\u0005N\nacb\n^`_\nd\u0001t\nuwv\nGqpsr\nL\u001dx\u000b\u0094yLDe\nL\u0001N\n^oP\nJ!V|{o}~P\u0090E\nG\u0013p\t\u0083yG\u0011.\u0080\u007f\u0081L\u0081{\nps\u0089\n\u008b\u001f\u008c\u008e\u008d\ne!\u008f\nP\u0010\u00a4\u0007P\n\u00ce-\u00aa\u0081\u00ab\nH\u0004=\u00a8\u00a7E\u00a9\nJ\u000bJ\u0007\u00d4\u00b2\u00b1\n\u0092w\u00b8\u0081\u00b9\n\u00b7>e\n\nN\u00c5H\nH\u0004G\nN\u00a0=\u00980\n.'=\u0080\u0092\t\u0083y=\u0080&\nG\u0011H\u0004=-0\nW\u001c.\n\nP\u00a5p&\u00a6\n\u00b3\u0001\u00b4\n\nH\u0004P\u00ae\u00ad\u0085\u00af\n\n=\u00c10\nGZ\u00ed\u0004=\u0095W\n\u0081YE\u000bGZP\n\n=\u0080S\u0013Xb4\ney=\u0080d\n=\u00baX\u0011H\n\n\u00c6\u000b=\n\u0083\u0007G\nNQ4\ney=\n\n1#\u008a\u001f\u00b0y\u00d3\n\n.\u0013=\u0013em=K.\u0011G\u00130\n\nW\u001aS\u00110\nD\u0018=?.\n\n&\u0002X\u000eG\u0011H5E\u000bX\n\nC\u009aE\n1#XZ0\nE\u0010\u00b3zr\u000ba\n\nG\u0011HyP\u00c80\n\n1\u0080\u00c9\n&\tG\u0011=\u0080&\n\nW\u001a`)X\n\n`y\u001e\n\n*\rE\n\n;\u0004\u00a1\n\n\u00a6#Gb4\n\nH\u0004E\n\nH\t=\n\nn\u0098G\n\n.VX\n\nX'W\n\nX'=\n\n\u0092\u001a\u0083\n\nW\t\u0081\nG\u00c5.\n\nd\u0002W\nG\u0011H\nXb4\nX'0\n\nOQP\nPKJML\u0001N\n&\u001dI\nUWV\u001dX\nY\u001dZ\\[\u0003]\nEml\nE\u001a&\u001aenJ\n^\u0003\u0096\n\u008e\u0093\u0092\u0095\u0094\n^o\u00a2\npy`H\u001e\n^\u00b2\u00ba\nV\u000bX\n\nG'S\u0090E\nSZW\u000bw\n\n\u00a4\u000bd\n\nXZ0\n\n\u008a'H\n\nG-W\u000b2\u00e7P\n\nHyP\u00bf\u00cd\n\nDz\u00b3|a\u001eN\u00c54\n\n13d\u009bp\n.@E\u000b&\n\u0085#vfE\nGZ=\u00c5W\n=\r=\u0080.\u0013X'4\n=\u0086k\u0090\u0083\nG\u0011a\u00c8E\u000b&\te@0\nDzD\n=\u0080.TXZH\u0004=\u0095\u00cd\n\n.\u00cbG\nW\u001a`\n&yW\u0010N d\nH\u0004G\nG\u0013H\u0004=-N\u00a0=\nDFu\u001ae\u009b4\n&yr\n\u008d\u0084\u008e\n\n^oP\n\nR\u001e=\n\u008a'0\n\u00d2'=\n\n\u00a6\u0083\u0082\n\nz|\u009f\n\nX\u0011W\u00e9X\u0011H\n\n{o\u00a0\n\nd\u0004W\nP\u00c8E\n\nwz=Ke\u009br\u000bP\n2\u007fa\u00a5\u00c6\u001a=\n\n\u008e\u009a\u0099\np\u0098\u0097\np\u001b\u00bb\n\nd5r\n\ndyP\u0080E\n\u008f\u0013I\nu\u0002&yo\nd\u0002a\n\u0083\u0007\u00c7'2\u009bE\u000b&yn\n\u00c7\u00c5r\nXZW\n\u00c6\u000b=<&\nW\u001a&\n\n\u0015o\u0086\u0088\u0087\n\n=\u0085\u0084\n\n(\b\u009b\tM\n(\b\u00bc\n\nD\u00b4W\u001a.\u0011P\n\nX'WfH\u0004a\n\n\u0016\u0013P\n\n\u0014\n\u0015\n\u0014\n&\n0\nN\nE\nI\nE\n`\n0\nC\nW\n`\nX\nE\n]\nn\n>\nl\nN\n4\n\u0015\n>\nP\n>\nE\nq\nD\nr\n\u0015\nE\nX\nR\nP\nD\nn\n1\n>\n=\n`\np\n`\n\u0015\n\u0081\nE\nX\nP\nW\n\u0087\n`\nl\nS\nu\n1\n1\n&\n>\nW\nq\n1\nD\nE\n&\n>\n\u008d\n\u0097\na\nq\nX\n4\n\u0085\nv\nr\nW\n`\n0\n.\n4\n=\n\u0088\n4\n0\n\u0085\n&\nW\nu\n`\n1\nP\nc\nn\nE\n`\n\u0015\n=\n\u0087\nN\nW\n4\n\u0085\nE\n`\n\u0085\n&\nr\nP\na\n`\nv\nW\n`\n=\n`\n=\nn\n,\n0\n1\n&\n`\nu\n\u00a7\nC\n7\nE\n1\n\u0089\nE\nn\na\nq\nE\nr\n&\ne\nN\n0\nE\np\n2\n4\n\u0015\n\u0085\nd\n.\nu\nn\n>\n0\n\u00b1\nR\n=\n`\n`\nE\n&\nr\n\u00aa\np\n`\nv\n.\n\u00a9\n\u00b2\n\u009c\n\u00b8\nv\nE\n\u00b3\n\u00b0\n\u00ad\nG\np\n`\n0\n\u0015\n\u0015\nv\n\u0015\np\n`\n\u00a7\nv\n0\n\u00b0\n\u00bc\nv\n0\n`\nr\n;\nr\nE\n0\n\u0015\n&\nW\nv\n\u00af\nu\n`\n2\n\u00ae\nW\n\u00a6\nn\n.\n7\nW\n;\n0\nC\n\u00aa\n\u00b0\n\u00bc\nC\nG\n0\n\u0085\nW\nC\nC\nW\n&\n\u00c2\n\u00c4\n.\nn\nu\n`\nu\n=\nN\n\u00c0\nr\nn\n`\nE\n\u00a6\n\u00aa\nP\n\u00a9\nu\n`\n2\n=\n.\n\u00b3\nW\nH\n\u00ad\n\u00c2\nC\n\u00c7\n\u00c7\n0\nC\nr\n\u0089\n\u00b7\nW\nq\n\u0085\n\u00c7\nE\n0\n\u00a6\n\u00a6\nv\n0\n=\n;\nr\n\u00bc\n&\n\u00aa\n\u00c7\nW\nv\nC\n\u00c7\n2\nE\n\u0015\nn\nX\n4\n\u00cc\nW\nW\n0\n\u0015\nn\n\u00c0\n\u00d0\n\u00c9\n\u00c2\n`\n2\n\u009c\n`\nC\n\u0087\nC\n;\n\u009c\n`\nE\nS\nr\n\u0087\nW\nN\n4\nr\n\u0081\n=\nv\nW\n\u00c7\n;\n7\nN\n\u00a6\nn\nH\n`\n=\n`\nE\n.\n\u0089\n1\n\u008c\n1\n1\n\u0085\nd\nn\nP\nu\nE\nX\n0\n\u0085\nX\nc\n\u00c9\nn\n\u00c7\n\u0092\nu\n0\nP\nS\n\u00a1\nN\ne\nr\nP\nW\n1\n1\nr\nH\nX\nX\n0\nu\nd\n\u0091\nr\n>\n\u00de\nE\nN\nN\nE\n\u00a6\nv\n\u0015\nE\n\u0015\n\u0081\nE\n\u00c7\n`\n.\n\u00d7\n\u0015\n\u00a6\nP\n`\n1\n^\nH\nP\nd\n>\n=\n\u0087\n\u00a6\n&\nr\n\u00e2\n\u0085\nE\nP\n\u00c2\n\u00c9\n\u00a6\n4\n=\n0\n\u00a6\nW\nC\nG\n\u00a6\n\u0081\nE\n;\np\n`\n\u00a9\n\u00c0\nE\nn\n\u00a6\np\n\u00a6\nn\n\u00a9\nG\n;\n7\n>\nW\nn\nG\n\u00d7\nC\nC\nv\n\u009d\nE\n\u00c7\n1\nv\n\u0085\nW\nW\n1\nC\nv\n\u00c7\n\u0015\n^\n=\nn\nW\n0\n\u00ac\n\u00c7\nG\n\u00c7\n\u00e0\nv\n0\n\u0085\nW\n\u00c7\n=\nC\nC\nW\n;\n0\n\u00c7\n6\nW\nw\nr\nW\n\u00c7\n0\nH\nE\n\u00c7\n\u00c2\n\u00af\n.\nE\n.\n=\nn\nW\n&\n\u00c7\n4\n\u00c0\nE\nW\nN\n\u0015\nG\n\u0015\nW\n&\n1\n\u009c\n\u00c7\n\u00c7\nW\ne\nN\n0\nC\n\u00c6\nE\n\u00c7\n0\n;\nW\n\u00aa\n`\nE\n\u00c7\n1\nv\n1\n\u0015\nn\nW\nW\n\u00c7\nX\nH\n;\nW\n\u00aa\n\u00aa\n\u00f6\n\u00c7\n.\n\u00a6\n&\n;\nC\n\u00f9\n1\n1\n\u00c7\nv\nE\nv\nn\n=\n6\nd\nv\n;\n%\nt\n`\n0\n1\nX\n0\n\u0085\n\u00c6\nP\n\u00d7\n=\n`\n0\nr\n\u00df\nW\n`\nE\nc\na\nM\n\u0094\nn\n\u0087\nu\np\nX\n\u00c6\n=\n\u00c7\nu\nX\nW\n\u0018\n.\nv\nW\n>\nq\nE\n`\nE\n\u0081\n`\nn\n0\n\u00e2\nN\n4\n\u0015\nX\n\u0015\n.\n\u0081\nE\nN\n\u00a6\nr\n\u00aa\n\u00c7\nW\n\u00c7\nc\na\n`\n\u00cc\n1\nv\nE\n\u0085\nW\n0\nv\nv\nP\nW\nX\nG\n\u00aa\nG\n\u00c7\n2\nE\np\n`\nW\nn\n>\n\u00a6\n\u0081\n\u00c7\n\u00e6\nv\n=\n\u00c7\n.\nu\n\u0015\n&\nr\nv\n\u0085\nG\n;\n0\n\u00c7\n0\nC\n\u00af\n\u009c\nW\n\u0089\n=\nv\nW\n\u00c7\nn\n0\n\u00a9\n7\nn\n\u00a7\n\u00c7\n\u00aa\nc\n\u00c2\n\u00af\n&\nr\nG\nN\nW\n\u00c0\nF\n\u0015\nX\nN\na\n\u0083\n\u0015\nP\nP\nE\n;\nS\nX\nW\n\u00a6\nD\n4\n\u00a6\n`\n>\nL\nN\nN\nN\nO\n\u00df\nM\n=\n\u00c7\n=\nV\nX\nN\n^\n\u008e\n\u00a6\n^\n\u001e\n\u00a6\nS\nN\nd\n\u00e5\nu\nG\n\u00c6\nP\nn\nG\n\u0094\nZ\n4\n\u0015\nH\n=\nN\n&\n\u00c0\nr\nG\nN\n1\n>\nG\nW\n\u00a6\n\u0081\nE\n7\n]\nN\n0\n1\n\u0015\n&\no\ne\n\u00b0\n\u00a6\n.\n\u008a\n=\nn\n=\nC\n[\n=\n(\n7\n\u0085\n\u0015\n\u00a6\n\u0094\nz\nM\na\nG\n=\n\u00aa\n0\n\u00c0\nr\nn\n0\n\u0015\n\u00a6\n&\nq\n.\nd\ne\nu\n\u00aa\n\u00c7\n\u0015\nv\nq\n\u00a6\n&\nn\nr\n\u0015\nv\nH\nP\n\u0081\nX\n\u00ad\n\u00b5\n;\nu\n\u0015\n\u008a\n7\n0\n\u0015\n.\nW\n&\nE\nE\n\u0015\n.\n\u00d7\nW\nW\nN\n0\n\u0085\nn\n`\n0\n\u0015\n`\n4\n\u00a6\nv\n0\nC\n&\np\n\u0090\n\u0091\nN\nL\nV\nX\n\u009c\n\u009d\ne\n\u009e\n7\n\u00a1\n{\n\u00a3\nx\nN\n\u00c7\n=\n\u008c\n0\n1\n.\nE\nq\n\u00e0\n\u00c6\n=\nn\nW\nd\nE\n\u0087\nn\n1\nW\n\u00c7\n0\n\u00a7\nl\nN\n,\nN\nn\np\n0\n\u00a7\nS\n\u00d1\n&\n0\n\u00ee\n0\n\u00a7\n\u0081\nE\nG\ne\nC\n\u009c\nu\n\u0015\nn\n`\n0\n1\n\u00c7\n0\n\u00ac\nW\nd\n0\nC\nS\nr\n0\n\u0085\n\u00c6\nP\n&\n\u0089\n;\nX\nF\n(\n4\n\u0085\n\u009f\n\u0094\nI\n\u0018\n\u0085\np\nN\n\u00b5\np\n\u0089\n\u00b6\nN\nz\n(\nL\nN\nN\n\u00a0\np\nM\n\u0094\ne\nl\n\u00bd\n\f\u0001\u0003\u0002\u0005\u0004\u0007\u0006\t\b\u000b\n\n\u000f\u000e\u0011\u0010\u0013\u0012\u0015\u0014\n\n\u000e\u0011\n\n\u0017\u0018\n\n\u0017\u001b\u001a\u0003\u001c\u001e\u001d\n\n\u001a 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>\n\n$\t>6%\u0010N\n\n.\u000b>\n\n1)i\n\n:\u0012N\n\n%\u00107\n\n\t\b\u0006\n\n4\u000b53%\n\n\u00809$\n\nRF\u00d3\nJ\f\u000b\n\n\u00f6\u00c8\u00ff\n\n-B+\u000b>\u0002%\u0012(\n\n(\u0010N\n\n$C\u00aa\n-&.\n\ni&\u0083\n\n+\u0002>F\u00b9\n\n\u0013\n\u0014\n\u0005\n\u0011\n\u001e\n5\n=\nN\nV\n%\n\u0014\n=\n7\nD\n7\nO\n@\n7\nD\n=\nA\n1\ne\nC\n.\ng\n7\nX\nb\n\u0014\nN\nO\n0\nN\n\u0014\na\nV\no\n}\n$\n\u0080\n~\n.\n+\n(\ng\nT\ne\n\u0090\n.\n+\n(\n7\nb\n\u008f\nE\nU\n7\n\u0014\na\n\u0096\n(\n%\n~\nU\na\nb\n$\n+\n\u007f\n$\n)\n0\nN\nC\n$\nc\nb\ng\n7\n\u008d\n@\n:\nU\ng\nU\n%\n=\n$\n+\n%\nA\n>\n+\nb\n+\n(\nO\n~\n\u0014\n(\n0\nV\n>\nC\n\u0088\n\u008f\nC\nX\n%\nR\nV\n\u0080\n%\nO\n:\n@\nV\n>\nC\ng\n@\nb\nE\nC\n~\nX\n%\n\u0014\n(\nA\n>\n+\n\u0091\n0\n+\n~\nN\n8\n\u00bf\nb\n\u008c\nC\ng\n\u009f\nD\n}\n\u00c2\n%\nb\n>\n7\nO\n\u00c6\nW\n\u00bd\n.\n0\n.\nX\nJ\nN\nE\n+\n\u0014\n:\n8\n+\n+\n+\nQ\nb\n=\n\u008f\n5\nC\n.\n%\nN\n\u00b1\nb\nN\nV\n=\ne\nN\nX\n>\nC\nJ\n+\n:\nb\n$\n7\nE\nC\nN\nV\n%\n\u0080\nJ\nW\nV\nC\nb\n$\n7\nD\nC\n8\n+\nb\n$\n~\n=\n\u0014\nQ\nG\n=\n$\nR\n\u00ca\n.\n~\nU\n7\nC\ng\n\u0096\n%\n\u0096\n0\n\u007f\n.\n+\nb\nb\n\u009f\n8\n~\n.\n\u0014\n$\n+\n5\n+\n\u0014\nJ\n.\nO\n+\n>\n\u00a1\n@\n\u009f\n0\n\u007f\n.\n0\n%\nO\n~\n$\n:\n=\n.\n-\nA\n+\nC\n0\nC\n7\n\u0014\n\u0014\n(\n\u00b9\n7\nD\n%\nb\n0\n\u00bf\n7\n8\n>\nC\n%\n+\n\u0096\n%\n\u008f\nQ\nC\nb\n=\n$\n(\nN\n$\nb\n\u0014\nC\ng\nN\n\u0080\nj\nk\n\u009f\nX\ne\nW\n>\n#\n)\nP\n0\nP\ne\nU\nO\n\u00a6\nX\nW\n.\n%\n:\n@\nN\nX\n>\ng\n=\n\u008f\n.\n:\n$\n\u007f\nX\n\u0014\n+\n:\n%\n=\nN\n7\n0\nQ\nC\nC\n.\n\u0014\n(\nO\n\u00d7\n.\n\u0090\nE\n-\n+\n>\n\u0080\n8\n8\nW\n.\n\u00c4\n7\nD\n>\nC\n-\nD\n%\nX\n+\n>\nc\n%\n\u0096\n\u0091\n\u00ca\na\n\u007f\n+\n+\n-\nA\n+\nQ\n\u0014\n\u00ef\nU\nA\n\u0091\n.\n5\nP\nN\n\u00d4\n\u0095\n-\nU\n\u0014\nX\n-\n\u00f6\nU\n\u00fc\n\u0095\nP\n>\n\u00bd\n.\n\u0006\n\u007f\ng\nR\n$\n\u00f6\n(\n\n\u00ad\n\u0002\n\u0006\n\n\u0014\n\u001e\n\u00ef\n\u00f4\n%\n\u0014\n\u00f6\n0\n%\n\u0080\n}\n+\n\u00db\nO\n0\nN\nO\n.\n+\n0\nQ\n\u00a2\n0\n%\n:\nO\n/\n=\n?\n\u0080\n\u00c5\n&\nX\n(\n\u00ca\n\u0014\n\u008c\n\u00b9\n\u00f6\n\u00bd\nX\n7\n.\n\u00cf\n\u0097\n+\n5\n%\nU\n0\nN\nV\n\u0014\nV\n.\n.\nC\n.\nD\n+\n>\nV\nG\n+\n.\n5\n.\n(\nN\nX\nD\n=\n\u0086\n\u0084\n_\ne\nd\ne\n:\n0\nD\n0\nO\n\t\n(\nC\n.\n>\n\u008c\nK\n\u00a6\nP\nA\nN\n\u0080\n>\n8\nN\n\u00cf\nr\nY\nd\nt\nD\n1\nD\n\u0084\n_\nA\nX\n@\n$\n(\n>\nC\n'\n$\nb\n+\n+\nN\n:\nc\n-\n%\nX\nC\n+\n>\n$\nA\n\u00af\ne\n\u00a1\nR\n.\n)\nO\nZ\n\u0002\n\u00fd\nN\n\u0094\n\u00db\nC\n7\n\u0088\n\u0089\nN\n\u0080\n>\nC\n\u0014\n\u0080\n\u0080\n\u00a1\nF\n\u0081\nh\n5\n0\n_\n\u0016\nD\n\u0012\n\u0080\n$\n%\n\u0094\ny\n\u00bc\n%\nv\n.\n5\n8\n\n\u0019\nf\n\u0086\n_\n\u0086\n\u0083\n\u0083\n\u0091\nd\n\u0092\n_\nd\n=\n\u0085\n\u0019\nd\n=\n7\nO\nd\n=\n?\nd\nt\nF\nd\nr\nh\n_\n\u0084\nk\n0\n\u0084\n\u0084\n>\n7\nd\nr\nq\nd\n=\nC\n$\nc\nm\n\u00ca\n:\n\u0014\n\u00a1\nv\n\u0080\n&\nO\n}\nN\n+\nb\nm\n\u0094\n(\nc\n%\n(\nO\nZ\n\u00cf\n\n_\n\u00f6\n\u007f\n\u00a6\n5\ng\nN\n$\n:\n@\nC\n-\nN\nV\n(\n@\nV\n%\n:\n\u0014\n\\\n5\nD\nh\n3\n\u00b9\nv\n%\nX\nP\nE\nX\n\n\u00b5\n\u0006\n\u00a8\n\u0014\n\n\u00a2\n.\n-\nA\n7\n.\n0\n\u008d\n\u0080\n~\nN\n\u0014\n%\n0\n1\n(\n@\n:\n8\nW\n\u00c0\n5\n0\n7\n\u0080\ng\n7\nO\n~\nN\n\u008c\nJ\n.\n.\n%\n\u00c4\nN\n~\nO\n`\n\u0080\n3\n\u0084\n0\nd\nt\nh\n5\n\u0084\n\u0097\n\u00d3\n\u00f6\n\u00fe\n\t\n\u0080\n\u0016\n,\n\u0006\n\u0080\n\f", "award": [], "sourceid": 905, "authors": [{"given_name": "Babak", "family_name": "Hassibi", "institution": null}, {"given_name": "Thomas", "family_name": "Kailath", "institution": null}]}