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0 g 0 G
0.992 0 0 1 250.084 602.441 Tm [(])-253(learns)-253(a)]TJ 1 0 0 1 50.112 590.486 Tm [(temporal)-250(graph)-250(in)-250(sliding)-250(windo)25(w)65(.)]TJ/F120 11.9552 Tf 0 -25.225 Td [(3.)-250(Pr)18(oblem)-250(F)25(ormulation)]TJ/F123 9.9626 Tf 0.98 0 0 1 62.067 545.894 Tm [(W)82(e)-204(start)-204(by)-204(de\002ning)-204(re)15(gular)-204(graph)-203(learning)-204(before)-204(lifelong)]TJ 0.98 0 0 1 50.112 533.939 Tm [(graph)-208(l)1(earning)-208(for)-207(completeness.)-301(An)-207(attrib)20(ute)-207(\(re)15(gular\))-208(graph)]TJ 1.02 0 0 1 50.112 521.984 Tm [(is)-291(de\002ned)-292(as)]TJ/F25 9.9626 Tf 1 0 0 1 104.152 521.984 Tm [(G)]TJ/F19 9.9626 Tf 10.154 0 Td [(=)-365(\()]TJ/F25 9.9626 Tf 15.26 0 Td [(V)]TJ/F22 9.9626 Tf 6.924 0 Td [(;)]TJ/F25 9.9626 Tf 4.428 0 Td [(E)]TJ/F19 9.9626 Tf 6.149 0 Td [(\))]TJ/F123 9.9626 Tf 1.02 0 0 1 150.941 521.984 Tm [(,)-303(where)]TJ/F25 9.9626 Tf 1 0 0 1 184.345 521.984 Tm [(V)]TJ/F123 9.9626 Tf 1.02 0 0 1 194.229 521.984 Tm [(is)-291(the)-292(set)-291(of)-291(nodes)-292(and)]TJ/F25 9.9626 Tf 1 0 0 1 50.112 510.029 Tm [(E)-577<12>]TJ/F12 9.9626 Tf 23.605 8.07 Td [(\b)]TJ/F25 9.9626 Tf 5.812 -8.07 Td [(f)]TJ/F22 9.9626 Tf 4.981 0 Td [(v)]TJ/F21 6.9738 Tf 4.829 -1.494 Td [(a)]TJ/F22 9.9626 Tf 4.82 1.494 Td [(;)-167(v)]TJ/F21 6.9738 Tf 9.257 -1.494 Td [(b)]TJ/F25 9.9626 Tf 4.002 1.494 Td [(g)-167(j)]TJ/F19 9.9626 Tf 9.409 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [(v)]TJ/F21 6.9738 Tf 4.829 -1.494 Td [(a)]TJ/F22 9.9626 Tf 4.82 1.494 Td [(;)-167(v)]TJ/F21 6.9738 Tf 9.257 -1.494 Td [(b)]TJ/F19 9.9626 Tf 4.001 1.494 Td [(\))]TJ/F25 9.9626 Tf 6.642 0 Td [(2)-278(V)]TJ/F18 6.9738 Tf 16.333 3.615 Td [(2)]TJ/F12 9.9626 Tf 4.47 4.455 Td [(\t)]TJ/F123 9.9626 Tf 1.02 0 0 1 180.482 510.029 Tm [(is)-356(the)-356(set)-356(of)-356(edges.)-636(Each)]TJ 0.98 0 0 1 50.112 498.074 Tm [(node)]TJ/F22 9.9626 Tf 1 0 0 1 71.496 498.074 Tm [(v)]TJ/F25 9.9626 Tf 7.954 0 Td [(2)-278(V)]TJ/F123 9.9626 Tf 0.98 0 0 1 98.187 498.074 Tm [(is)-246(associated)-246(with)-247(a)-246(multi-channel)-246(feature)-246(v)15(ector)]TJ/F217 9.9626 Tf 1 0 0 1 49.814 486.119 Tm [(x)]TJ/F21 6.9738 Tf 6.047 -1.495 Td [(v)]TJ/F25 9.9626 Tf 8.302 1.495 Td [(2)-358(X)-505<1a>]TJ/F77 9.9626 Tf 33.66 0 Td [(R)]TJ/F21 6.9738 Tf 7.195 3.615 Td [(F)]TJ/F24 6.9738 Tf 6.125 0 Td [<02>]TJ/F21 6.9738 Tf 6.227 0 Td [(C)]TJ/F123 9.9626 Tf 1.02 0 0 1 126.994 486.119 Tm [(and)-288(a)-287(tar)17(get)]TJ/F217 9.9626 Tf 1 0 0 1 177.908 486.119 Tm [(z)]TJ/F21 6.9738 Tf 5.092 -1.495 Td [(v)]TJ/F25 9.9626 Tf 8.302 1.495 Td [(2)-358(Z)]TJ/F123 9.9626 Tf 1.02 0 0 1 209.524 486.119 Tm [(.)-432(Each)-287(edge)]TJ/F22 9.9626 Tf 1 0 0 1 261.796 486.119 Tm [(e)]TJ/F25 9.9626 Tf 8.207 0 Td [(2)-358(E)]TJ/F123 9.9626 Tf 1.02 0 0 1 50.112 474.163 Tm [(is)-350(associated)-349(with)-350(a)-350(v)15(ector)]TJ/F217 9.9626 Tf 1 0 0 1 164.251 474.163 Tm [(w)]TJ/F21 6.9738 Tf 8.275 -1.494 Td [(e)]TJ/F25 9.9626 Tf 9.015 1.494 Td [(2)-476(W)-557<1a>]TJ/F77 9.9626 Tf 39.263 0 Td [(R)]TJ/F21 6.9738 Tf 7.195 3.616 Td [(W)]TJ/F123 9.9626 Tf 1.02 0 0 1 237.063 474.163 Tm [(.)-618(In)-350(re)15(gular)]TJ 1.02 0 0 1 50.112 462.208 Tm [(graph)-285(learning,)-296(we)-285(learn)-286(a)-285(predictor)]TJ/F22 9.9626 Tf 1 0 0 1 199.954 462.208 Tm [(f)]TJ/F123 9.9626 Tf 1.02 0 0 1 208.804 462.208 Tm [(to)-285(associate)-286(a)-285(node)]TJ/F217 9.9626 Tf 1 0 0 1 49.814 450.253 Tm [(x)]TJ/F21 6.9738 Tf 6.047 -1.494 Td [(v)]TJ/F22 9.9626 Tf 4.733 1.494 Td [(;)-167(v)]TJ/F25 9.9626 Tf 12.386 0 Td [(2)-278(V)]TJ/F24 6.9738 Tf 16.337 3.615 Td [(0)]TJ/F123 9.9626 Tf 0.988 0 0 1 94.604 450.253 Tm [(with)-253(a)-254(ta)1(r)18(get)]TJ/F217 9.9626 Tf 1 0 0 1 146.187 450.253 Tm [(z)]TJ/F21 6.9738 Tf 5.092 -1.494 Td [(v)]TJ/F123 9.9626 Tf 0.988 0 0 1 156.012 450.253 Tm [(,)-253(gi)25(v)15(en)-253(graph)]TJ/F25 9.9626 Tf 1 0 0 1 209.837 450.253 Tm [(G)]TJ/F123 9.9626 Tf 0.988 0 0 1 216.354 450.253 Tm [(,)-253(node)-254(features)]TJ/F25 9.9626 Tf 1 0 0 1 276.581 450.253 Tm [(X)]TJ/F123 9.9626 Tf 0.988 0 0 1 285.146 450.253 Tm [(,)]TJ 1 0 0 1 50.112 438.298 Tm [(edge)-250(v)15(ectors)]TJ/F25 9.9626 Tf 52.413 0 Td [(W)]TJ/F123 9.9626 Tf 10.66 0 Td [(,)-250(and)-250(part)-250(of)-250(the)-250(tar)18(gets)]TJ/F217 9.9626 Tf 94.166 0 Td [(z)]TJ/F21 6.9738 Tf 5.092 -1.494 Td [(v)]TJ/F22 9.9626 Tf 4.733 1.494 Td [(;)-167(v)]TJ/F25 9.9626 Tf 12.382 0 Td [(2)-278(V)-304(n)-222(V)]TJ/F24 6.9738 Tf 32.666 3.615 Td [(0)]TJ/F123 9.9626 Tf 2.796 -3.615 Td [(.)]TJ 0.98 0 0 1 62.067 425.905 Tm [(In)-227(lifelong)-227(graph)-226(learning,)-233(we)-227(ha)21(v)15(e)-227(the)-227(same)-227(objecti)26(v)15(e)-227(b)21(ut)]TJ 0.981 0 0 1 50.112 413.95 Tm [(can)-255(only)-254(obtain)-255(the)-255(graph-structured)-254(data)-255(from)-255(a)-255(dat)1(a)-255(contin-)]TJ 1.02 0 0 1 50.112 401.994 Tm [(uum)]TJ/F25 9.9626 Tf 1 0 0 1 70.968 401.994 Tm [(G)]TJ/F21 6.9738 Tf 5.926 -1.494 Td [(L)]TJ/F19 9.9626 Tf 9.283 1.494 Td [(=)]TJ/F25 9.9626 Tf 11.067 0 Td [(f)]TJ/F19 9.9626 Tf 4.981 0 Td [(\()]TJ/F217 9.9626 Tf 3.875 0 Td [(x)]TJ/F21 6.9738 Tf 6.046 -1.494 Td [(i)]TJ/F123 9.9626 Tf 1.02 0 0 1 115.463 401.994 Tm [(,)]TJ/F22 9.9626 Tf 1 0 0 1 120.866 401.994 Tm [(t)]TJ/F21 6.9738 Tf 3.598 -1.494 Td [(i)]TJ/F123 9.9626 Tf 1.02 0 0 1 127.781 401.994 Tm [(,)]TJ/F217 9.9626 Tf 1 0 0 1 133.184 401.994 Tm [(z)]TJ/F21 6.9738 Tf 5.092 -1.494 Td [(i)]TJ/F123 9.9626 Tf 1.02 0 0 1 141.593 401.994 Tm [(,)]TJ/F25 9.9626 Tf 1 0 0 1 146.996 401.994 Tm [(N)]TJ/F21 6.9738 Tf 8.174 -1.494 Td [(k)]TJ/F18 6.9738 Tf 4.404 0 Td [(=1:)]TJ/F21 6.9738 Tf 12.342 0 Td [(K)]TJ/F19 9.9626 Tf 7.681 1.494 Td [(\()]TJ/F217 9.9626 Tf 3.875 0 Td [(x)]TJ/F21 6.9738 Tf 6.046 -1.494 Td [(i)]TJ/F19 9.9626 Tf 3.317 1.494 Td [(\))]TJ/F123 9.9626 Tf 1.02 0 0 1 196.71 401.994 Tm [(,)]TJ/F25 9.9626 Tf 1 0 0 1 202.113 401.994 Tm [(W)]TJ/F21 6.9738 Tf 9.841 -1.494 Td [(k)]TJ/F18 6.9738 Tf 4.403 0 Td [(=1:)]TJ/F21 6.9738 Tf 12.343 0 Td [(K)]TJ/F19 9.9626 Tf 7.681 1.494 Td [(\()]TJ/F217 9.9626 Tf 3.874 0 Td [(x)]TJ/F21 6.9738 Tf 6.047 -1.494 Td [(i)]TJ/F19 9.9626 Tf 3.317 1.494 Td [(\)\))]TJ/F21 6.9738 Tf 7.749 -1.494 Td [(i)]TJ/F18 6.9738 Tf 2.818 0 Td [(=1:)]TJ/F21 6.9738 Tf 12.343 0 Td [(N)]TJ/F25 9.9626 Tf 7.556 1.494 Td [(g)]TJ/F123 9.9626 Tf 1.02 0 0 1 285.067 401.994 Tm [(,)]TJ 1.02 0 0 1 49.753 390.039 Tm [(where)-272(each)-272(item)-271(consists)-272(of)-272(a)-272(node)-272(feature)]TJ/F217 9.9626 Tf 1 0 0 1 226.484 390.039 Tm [(x)]TJ/F21 6.9738 Tf 6.047 -1.494 Td [(i)]TJ/F25 9.9626 Tf 6.587 1.494 Td [(2)-328(X)]TJ/F123 9.9626 Tf 1.02 0 0 1 257.595 390.039 Tm [(,)-279(a)-271(task)]TJ 0.98 0 0 1 50.112 378.084 Tm [(descriptor)]TJ/F22 9.9626 Tf 1 0 0 1 91.379 378.084 Tm [(t)]TJ/F21 6.9738 Tf 3.598 -1.494 Td [(i)]TJ/F25 9.9626 Tf 6.084 1.494 Td [(2)-278(T)]TJ/F123 9.9626 Tf 0.98 0 0 1 118.429 378.084 Tm [(,)-233(a)-228(tar)18(get)-227(v)15(ector)]TJ/F217 9.9626 Tf 1 0 0 1 180.455 378.084 Tm [(z)]TJ/F21 6.9738 Tf 5.092 -1.494 Td [(i)]TJ/F25 9.9626 Tf 6.084 1.494 Td [(2)-278(Z)]TJ/F21 6.9738 Tf 16.63 -1.494 Td [(t)]TJ/F20 4.9813 Tf 3.009 -0.997 Td [(i)]TJ/F123 9.9626 Tf 0.98 0 0 1 214.924 378.084 Tm [(,)-233(a)]TJ/F22 9.9626 Tf 1 0 0 1 226.202 378.084 Tm [(k)]TJ/F123 9.9626 Tf 0.98 0 0 1 231.702 378.084 Tm [(-hop)-228(neighbor)]TJ 0.98 0 0 1 50.112 366.129 Tm [(set)]TJ/F25 9.9626 Tf 1 0 0 1 63.403 366.129 Tm [(N)]TJ/F21 6.9738 Tf 8.175 -1.494 Td [(k)]TJ/F18 6.9738 Tf 4.403 0 Td [(=1:)]TJ/F21 6.9738 Tf 12.343 0 Td [(K)]TJ/F19 9.9626 Tf 7.681 1.494 Td [(\()]TJ/F217 9.9626 Tf 3.874 0 Td [(x)]TJ/F21 6.9738 Tf 6.047 -1.494 Td [(i)]TJ/F19 9.9626 Tf 3.317 1.494 Td [(\))]TJ/F123 9.9626 Tf 0.98 0 0 1 113.117 366.129 Tm [(,)-251(and)-251(an)-250(edge)-250(v)15(ector)-251(set)]TJ/F25 9.9626 Tf 1 0 0 1 207.078 366.129 Tm [(W)]TJ/F21 6.9738 Tf 9.841 -1.494 Td [(k)]TJ/F18 6.9738 Tf 4.404 0 Td [(=1:)]TJ/F21 6.9738 Tf 12.342 0 Td [(K)]TJ/F19 9.9626 Tf 7.681 1.494 Td [(\()]TJ/F217 9.9626 Tf 3.875 0 Td [(x)]TJ/F21 6.9738 Tf 6.047 -1.494 Td [(i)]TJ/F19 9.9626 Tf 3.316 1.494 Td [(\))]TJ/F123 9.9626 Tf 0.98 0 0 1 260.903 366.129 Tm [(associ-)]TJ 1.02 0 0 1 50.112 354.174 Tm [(ated)-257(with)-257(the)]TJ/F22 9.9626 Tf 1 0 0 1 105.36 354.174 Tm [(k)]TJ/F123 9.9626 Tf 1.02 0 0 1 110.86 354.174 Tm [(-hop)-257(neighbors.)-339(F)14(or)-257(simplicity)64(,)-260(we)-257(will)-257(use)]TJ 1.015 0 0 1 50.112 342.219 Tm [(the)-245(symbol)]TJ/F25 9.9626 Tf 1 0 0 1 97.212 342.219 Tm [(N)]TJ/F19 9.9626 Tf 9.642 0 Td [(\()]TJ/F217 9.9626 Tf 3.875 0 Td [(x)]TJ/F21 6.9738 Tf 6.047 -1.495 Td [(i)]TJ/F19 9.9626 Tf 3.316 1.495 Td [(\))]TJ/F123 9.9626 Tf 1.015 0 0 1 126.449 342.219 Tm [(to)-245(denote)-246(the)-245(a)19(v)25(ailable)-245(neighbor)-246(set)-245(and)]TJ 1.02 0 0 1 50.112 330.263 Tm [(their)-288(edges.)-432(W)79(e)-288(assume)-288(tha)1(t)-288(e)24(v)15(ery)-288(item)]TJ/F19 9.9626 Tf 1 0 0 1 215.054 330.263 Tm [(\()]TJ/F217 9.9626 Tf 3.874 0 Td [(x)]TJ/F21 6.9738 Tf 6.047 -1.494 Td [(i)]TJ/F22 9.9626 Tf 3.317 1.494 Td [(;)]TJ/F25 9.9626 Tf 4.428 0 Td [(N)]TJ/F19 9.9626 Tf 9.642 0 Td [(\()]TJ/F217 9.9626 Tf 3.874 0 Td [(x)]TJ/F21 6.9738 Tf 6.047 -1.494 Td [(i)]TJ/F19 9.9626 Tf 3.317 1.494 Td [(\))]TJ/F22 9.9626 Tf 3.874 0 Td [(;)-167(t)]TJ/F21 6.9738 Tf 8.026 -1.494 Td [(i)]TJ/F22 9.9626 Tf 3.317 1.494 Td [(;)]TJ/F217 9.9626 Tf 4.427 0 Td [(z)]TJ/F21 6.9738 Tf 5.092 -1.494 Td [(i)]TJ/F19 9.9626 Tf 3.317 1.494 Td [(\))]TJ/F123 9.9626 Tf 1.02 0 0 1 50.112 318.308 Tm [(satis\002es)]TJ/F19 9.9626 Tf 1 0 0 1 84.821 318.308 Tm [(\()]TJ/F217 9.9626 Tf 3.874 0 Td [(x)]TJ/F21 6.9738 Tf 6.047 -1.494 Td [(i)]TJ/F22 9.9626 Tf 3.317 1.494 Td [(;)]TJ/F25 9.9626 Tf 4.428 0 Td [(N)]TJ/F19 9.9626 Tf 9.642 0 Td [(\()]TJ/F217 9.9626 Tf 3.875 0 Td [(x)]TJ/F21 6.9738 Tf 6.046 -1.494 Td [(i)]TJ/F19 9.9626 Tf 3.317 1.494 Td [(\))]TJ/F22 9.9626 Tf 3.874 0 Td [(;)]TJ/F217 9.9626 Tf 4.428 0 Td [(z)]TJ/F21 6.9738 Tf 5.092 -1.494 Td [(i)]TJ/F19 9.9626 Tf 3.317 1.494 Td [(\))]TJ/F25 9.9626 Tf 6.709 0 Td [<18>]TJ/F22 9.9626 Tf 10.584 0 Td [(P)]TJ/F21 6.9738 Tf 6.396 -1.494 Td [(t)]TJ/F20 4.9813 Tf 3.01 -0.996 Td [(i)]TJ/F19 9.9626 Tf 3.654 2.49 Td [(\()]TJ/F25 9.9626 Tf 3.874 0 Td [(X)]TJ/F22 9.9626 Tf 8.565 0 Td [(;)]TJ/F25 9.9626 Tf 4.428 0 Td [(N)]TJ/F19 9.9626 Tf 9.642 0 Td [(\()]TJ/F25 9.9626 Tf 3.875 0 Td [(X)]TJ/F19 9.9626 Tf 8.565 0 Td [(\))]TJ/F22 9.9626 Tf 3.874 0 Td [(;)]TJ/F25 9.9626 Tf 4.428 0 Td [(Z)]TJ/F19 9.9626 Tf 8.012 0 Td [(\))]TJ/F123 9.9626 Tf 1.02 0 0 1 231.568 318.308 Tm [(,)-250(where)]TJ/F22 9.9626 Tf 1 0 0 1 263.997 318.308 Tm [(P)]TJ/F21 6.9738 Tf 6.396 -1.494 Td [(t)]TJ/F20 4.9813 Tf 3.01 -0.996 Td [(i)]TJ/F123 9.9626 Tf 1.02 0 0 1 279.584 318.308 Tm [(is)]TJ 0.98 0 0 1 50.112 306.353 Tm [(a)-215(probability)-216(di)1(strib)20(ution)-215(of)-216(a)-215(single)-215(learning)-215(task.)-303(In)-216(lifelong)]TJ 0.98 0 0 1 50.112 294.398 Tm [(graph)-222(learning,)-229(we)-223(will)-222(observ)15(e,)-229(item)-222(by)-222(item,)-229(the)-223(continuum)]TJ 1 0 0 1 50.112 282.443 Tm [(of)-250(the)-250(graph-structured)-250(data)-250(as)]TJ
ET
/S/Span<>BDC
BT
/F19 9.9626 Tf 73.91 259.649 Td [(\()]TJ/F217 9.9626 Tf 3.874 0 Td [(x)]TJ/F18 6.9738 Tf 6.047 -1.494 Td [(1)]TJ/F22 9.9626 Tf 4.469 1.494 Td [(;)]TJ/F25 9.9626 Tf 4.428 0 Td [(N)]TJ/F19 9.9626 Tf 9.642 0 Td [(\()]TJ/F217 9.9626 Tf 3.875 0 Td [(x)]TJ/F18 6.9738 Tf 6.046 -1.494 Td [(1)]TJ/F19 9.9626 Tf 4.47 1.494 Td [(\))]TJ/F22 9.9626 Tf 3.874 0 Td [(;)-167(t)]TJ/F18 6.9738 Tf 8.025 -1.494 Td [(1)]TJ/F22 9.9626 Tf 4.47 1.494 Td [(;)]TJ/F217 9.9626 Tf 4.428 0 Td [(z)]TJ/F18 6.9738 Tf 5.092 -1.494 Td [(1)]TJ/F19 9.9626 Tf 4.469 1.494 Td [(\))]TJ/F22 9.9626 Tf 3.874 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F19 9.9626 Tf 22.139 0 Td [(\()]TJ/F217 9.9626 Tf 3.875 0 Td [(x)]TJ/F21 6.9738 Tf 6.047 -1.494 Td [(N)]TJ/F22 9.9626 Tf 7.556 1.494 Td [(;)]TJ/F25 9.9626 Tf 4.428 0 Td [(N)]TJ/F19 9.9626 Tf 9.642 0 Td [(\()]TJ/F217 9.9626 Tf 3.874 0 Td [(x)]TJ/F21 6.9738 Tf 6.047 -1.494 Td [(N)]TJ/F19 9.9626 Tf 7.557 1.494 Td [(\))]TJ/F22 9.9626 Tf 3.874 0 Td [(;)-167(t)]TJ/F21 6.9738 Tf 8.025 -1.494 Td [(N)]TJ/F22 9.9626 Tf 7.557 1.494 Td [(;)]TJ/F217 9.9626 Tf 4.428 0 Td [(z)]TJ/F21 6.9738 Tf 5.092 -1.494 Td [(N)]TJ/F19 9.9626 Tf 7.556 1.494 Td [(\))]TJ
ET
EMC
BT
/F123 9.9626 Tf 274.746 259.649 Td [(\(1\))]TJ 1.02 0 0 1 49.644 236.855 Tm [(While)-282(observing)]TJ 1 0 0 1 120.297 236.855 Tm [(\()]TJ
1 0 0 rg 1 0 0 RG
[(1)]TJ
0 g 0 G
[(\))]TJ 1.02 0 0 1 131.913 236.855 Tm [(,)-292(our)-282(goal)-283(is)-282(to)-282(learn)-283(a)-282(predictor)]TJ/F22 9.9626 Tf 1 0 0 1 264.745 236.855 Tm [(f)]TJ/F21 6.9738 Tf 4.877 -1.494 Td [(L)]TJ/F123 9.9626 Tf 1.02 0 0 1 278.456 236.855 Tm [(to)]TJ 0.98 0 0 1 50.112 224.9 Tm [(associate)-250(a)-249(test)-250(sample)]TJ/F19 9.9626 Tf 1 0 0 1 140.666 224.9 Tm [(\()]TJ/F217 9.9626 Tf 3.874 0 Td [(x)]TJ/F22 9.9626 Tf 6.047 0 Td [(;)]TJ/F25 9.9626 Tf 4.428 0 Td [(N)]TJ/F19 9.9626 Tf 9.642 0 Td [(\()]TJ/F217 9.9626 Tf 3.875 0 Td [(x)]TJ/F19 9.9626 Tf 6.046 0 Td [(\))]TJ/F22 9.9626 Tf 3.875 0 Td [(;)-167(t)]TJ/F19 9.9626 Tf 8.025 0 Td [(\))]TJ/F123 9.9626 Tf 0.98 0 0 1 192.791 224.9 Tm [(with)-250(a)-250(t)1(ar)18(get)]TJ/F217 9.9626 Tf 1 0 0 1 243.852 224.9 Tm [(z)]TJ/F123 9.9626 Tf 0.98 0 0 1 251.383 224.9 Tm [(such)-250(that)]TJ/F19 9.9626 Tf 1 0 0 1 48.946 212.945 Tm [(\()]TJ/F217 9.9626 Tf 3.875 0 Td [(x)]TJ/F22 9.9626 Tf 6.046 0 Td [(;)]TJ/F25 9.9626 Tf 4.428 0 Td [(N)]TJ/F19 9.9626 Tf 9.643 0 Td [(\()]TJ/F217 9.9626 Tf 3.874 0 Td [(x)]TJ/F19 9.9626 Tf 6.047 0 Td [(\))]TJ/F22 9.9626 Tf 3.874 0 Td [(;)]TJ/F217 9.9626 Tf 4.428 0 Td [(z)]TJ/F19 9.9626 Tf 5.092 0 Td [(\))]TJ/F25 9.9626 Tf 7.514 0 Td [<18>]TJ/F22 9.9626 Tf 11.388 0 Td [(P)]TJ/F21 6.9738 Tf 6.396 -1.495 Td [(t)]TJ/F123 9.9626 Tf 1.02 0 0 1 125.059 212.945 Tm [(.)-443(Such)-291(test)-292(sample)-291(can)-292(belong)-291(to)-291(a)-292(task)]TJ 1.02 0 0 1 50.112 200.99 Tm [(observ)15(ed)-335(in)-335(the)-335(past,)-357(the)-335(current)-335(task,)-358(or)-335(a)-334(task)-335(observ)14(ed)]TJ 1.02 0 0 1 49.783 189.034 Tm [(\(or)-254(not\))-254(in)-254(the)-254(future.)-331(The)-254(task)-254(descriptors)]TJ/F22 9.9626 Tf 1 0 0 1 223.329 189.034 Tm [(t)]TJ/F21 6.9738 Tf 3.597 -1.494 Td [(i)]TJ/F123 9.9626 Tf 1.02 0 0 1 232.825 189.034 Tm [(is)-254(de\002ned)-254(for)]TJ 1.004 0 0 1 50.112 177.079 Tm [(compatibility)-248(with)-248(lifelong)-248(learning)-248(that)-248(requires)-248(them)-248([)]TJ
0 1 0 rg 0 1 0 RG
1 0 0 1 273.069 177.079 Tm [(26)]TJ
0 g 0 G
1.004 0 0 1 283.031 177.079 Tm [(])]TJ 1 0 0 1 50.112 165.124 Tm [(b)20(ut)-250(is)-250(not)-250(used)-250(in)-250(the)-250(e)15(xperiments.)]TJ 1.02 0 0 1 62.067 152.731 Tm [(Note)-386(that)-386(samples)-386(are)]TJ/F120 9.9626 Tf 1.02 0 0 1 157.903 152.731 Tm [(not)]TJ/F123 9.9626 Tf 1.02 0 0 1 175.94 152.731 Tm [(dra)15(wn)-386(locally)-386(independent)]TJ 1.02 0 0 1 50.112 140.776 Tm [(and)-303(identically)-304(distrib)20(uted)-304(\(i.i.d.\))-303(from)-304(a)-303<0278>14(ed)-303(probability)]TJ 1.02 0 0 1 50.112 128.821 Tm [(distrib)20(ution,)-397(since)-367(we)-367(don')18(t)-367(kno)25(w)-367(the)-366(task)-367(boundary)64(.)-669(In)]TJ 1.02 0 0 1 50.112 116.866 Tm [(the)-278(continuum,)-286(we)-278(only)-278(kno)24(w)-278(the)-278(label)-278(of)]TJ/F217 9.9626 Tf 1 0 0 1 224.112 116.866 Tm [(x)]TJ/F21 6.9738 Tf 6.047 -1.495 Td [(i)]TJ/F123 9.9626 Tf 1.02 0 0 1 233.476 116.866 Tm [(,)-286(b)19(ut)-278(ha)20(v)15(e)-278(no)]TJ 1.02 0 0 1 50.112 104.91 Tm [(information)-302(about)-302(the)-302(labels)-302(of)-303(its)-302(neighbors)]TJ/F25 9.9626 Tf 1 0 0 1 236.438 104.91 Tm [(N)]TJ/F19 9.9626 Tf 9.642 0 Td [(\()]TJ/F217 9.9626 Tf 3.875 0 Td [(x)]TJ/F21 6.9738 Tf 6.046 -1.494 Td [(i)]TJ/F19 9.9626 Tf 3.317 1.494 Td [(\))]TJ/F123 9.9626 Tf 1.02 0 0 1 263.193 104.91 Tm [(.)-475(The)]TJ 1.02 0 0 1 50.112 92.955 Tm [(items)-391(in)]TJ 1 0 0 1 87.983 92.955 Tm [(\()]TJ
1 0 0 rg 1 0 0 RG
[(1)]TJ
0 g 0 G
[(\))]TJ 1.02 0 0 1 103.572 92.955 Tm [(are)-391(una)20(v)24(ailable)-391(once)-391(the)15(y)-391(are)-391(observ)15(ed)-391(and)]TJ 1.02 0 0 1 50.112 81 Tm [(dropped.)-463(This)-298(is)-298(in)-298(contrast)-298(to)-299(the)-298(settings)-298(in)-298([)]TJ
0 1 0 rg 0 1 0 RG
1 0 0 1 242.485 81 Tm [(45)]TJ
0 g 0 G
1.02 0 0 1 252.448 81 Tm [(],)-311(where)]TJ
0 g 0 G
0 g 0 G
1.02 0 0 1 308.862 710.037 Tm [(all)-284(historical)-283(data)-284(are)-283(a)19(v)25(ailable)-284(during)-283(training.)-420(As)-283(sho)24(wn)]TJ 0.997 0 0 1 308.862 698.082 Tm [(in)-250(the)-250(e)15(xperiments,)-250(lifelong)-250(graph)-249(learning)-250(in)-250(practice)-250(often)]TJ 0.999 0 0 1 308.862 686.127 Tm [(requires)-250(that)-249(the)-250(number)-250(of)-249(GNN)-250(layers)]TJ/F22 9.9626 Tf 1 0 0 1 469.424 686.127 Tm [(L)]TJ/F123 9.9626 Tf 0.999 0 0 1 478.689 686.127 Tm [(is)-250(lar)18(ger)-249(than)-250(the)]TJ 1.02 0 0 1 308.862 674.172 Tm [(a)20(v)24(ailability)-303(of)]TJ/F22 9.9626 Tf 1 0 0 1 368.759 674.172 Tm [(K)]TJ/F123 9.9626 Tf 1.02 0 0 1 377.933 674.172 Tm [(-hop)-303(neighbors,)]TJ/F130 9.9626 Tf 1.02 0 0 1 445.478 674.172 Tm [(i.e)]TJ/F123 9.9626 Tf 1.02 0 0 1 455.355 674.172 Tm [(.,)]TJ/F22 9.9626 Tf 1 0 0 1 463.659 674.172 Tm [(L)-387(>)-386(K)]TJ/F123 9.9626 Tf 1.02 0 0 1 495.066 674.172 Tm [(,)-317(which)-303(also)]TJ 1 0 0 1 308.862 662.217 Tm [(leads)-250(man)15(y)-250(e)15(xisting)-250(graph)-250(models)-250(inapplicable.)]TJ/F120 11.9552 Tf 0 -23.307 Td [(4.)-250(F)25(eatur)18(e)-250(Graph)-250(Netw)10(ork)]TJ/F123 9.9626 Tf 1.01 0 0 1 320.817 619.981 Tm [(T)79(o)-246(better)-247(sho)25(w)-247(the)-246(relationship)-247(with)-247(a)-246(re)15(gular)-247(graph,)-247(we)]TJ 0.98 0 0 1 308.862 608.026 Tm [<02727374>-221(re)25(vie)26(w)-221(GCN)-222([)]TJ
0 1 0 rg 0 1 0 RG
1 0 0 1 380.463 608.026 Tm [(20)]TJ
0 g 0 G
0.98 0 0 1 390.426 608.026 Tm [(].)-305(Gi)25(v)16(en)-222(an)-221(graph)]TJ/F25 9.9626 Tf 1 0 0 1 460.488 608.026 Tm [(G)]TJ/F19 9.9626 Tf 9.285 0 Td [(=)-278(\()]TJ/F25 9.9626 Tf 14.39 0 Td [(V)]TJ/F22 9.9626 Tf 6.924 0 Td [(;)]TJ/F25 9.9626 Tf 4.428 0 Td [(E)]TJ/F19 9.9626 Tf 6.149 0 Td [(\))]TJ/F123 9.9626 Tf 0.98 0 0 1 507.699 608.026 Tm [(described)]TJ 1.02 0 0 1 308.862 596.071 Tm [(in)-338(Section)]TJ
1 0 0 rg 1 0 0 RG
[-338(3)]TJ
0 g 0 G
[(,)-361(the)-338(stack)10(ed)-338(node)-338(features)-338(can)-338(be)-338(written)-338(as)]TJ/F217 9.9626 Tf 1 0 0 1 308.427 584.116 Tm [(X)]TJ/F19 9.9626 Tf 12.912 0 Td [(=)-427([)]TJ/F217 9.9626 Tf 14.766 0 Td [(x)]TJ/F18 6.9738 Tf 6.046 -1.495 Td [(1)]TJ/F22 9.9626 Tf 4.47 1.495 Td [(;)]TJ/F217 9.9626 Tf 4.428 0 Td [(x)]TJ/F18 6.9738 Tf 6.046 -1.495 Td [(2)]TJ/F22 9.9626 Tf 4.47 1.495 Td [(;)]TJ/F25 9.9626 Tf 4.428 0 Td [<01>-167<01>-166<01>]TJ/F22 9.9626 Tf 14.943 0 Td [(;)]TJ/F217 9.9626 Tf 4.428 0 Td [(x)]TJ/F21 6.9738 Tf 6.047 -1.495 Td [(N)]TJ/F19 9.9626 Tf 7.556 1.495 Td [(])]TJ/F18 6.9738 Tf 2.768 5.009 Td [(T)]TJ/F25 9.9626 Tf 10.435 -5.009 Td [(2)]TJ/F77 9.9626 Tf 10.892 0 Td [(R)]TJ/F21 6.9738 Tf 7.195 3.615 Td [(N)]TJ/F24 6.9738 Tf 7.058 0 Td [<02>]TJ/F21 6.9738 Tf 6.227 0 Td [(F)-154(C)]TJ/F123 9.9626 Tf 1.02 0 0 1 456.368 584.116 Tm [(,)-344(where)]TJ/F217 9.9626 Tf 1 0 0 1 490.516 584.116 Tm [(x)]TJ/F21 6.9738 Tf 6.047 -1.495 Td [(i)]TJ/F25 9.9626 Tf 7.567 1.495 Td [(2)]TJ/F77 9.9626 Tf 10.892 0 Td [(R)]TJ/F21 6.9738 Tf 7.195 3.615 Td [(F)-154(C)]TJ/F123 9.9626 Tf 1.02 0 0 1 538.334 584.116 Tm [(is)]TJ 1.02 0 0 1 308.862 572.161 Tm [(a)-252(v)15(ectorized)-252(node)-252(feature.)-324(The)-252(GCN)-252(tak)10(es)-252(feature)-252(channel)]TJ 1.02 0 0 1 308.862 560.205 Tm [(as)]TJ/F22 9.9626 Tf 1 0 0 1 320.464 560.205 Tm [(C)]TJ/F19 9.9626 Tf 11.799 0 Td [(=)-398(1)]TJ/F123 9.9626 Tf 1.02 0 0 1 348.958 560.205 Tm [(,)-325(so)-308(that)]TJ/F217 9.9626 Tf 1 0 0 1 385.349 560.205 Tm [(x)]TJ/F21 6.9738 Tf 6.047 -1.494 Td [(i)]TJ/F25 9.9626 Tf 7.282 1.494 Td [(2)]TJ/F77 9.9626 Tf 10.607 0 Td [(R)]TJ/F21 6.9738 Tf 7.195 3.616 Td [(F)]TJ/F22 9.9626 Tf 6.623 -3.616 Td [(;)]TJ/F217 9.9626 Tf 4.428 0 Td [(X)]TJ/F25 9.9626 Tf 12.627 0 Td [(2)]TJ/F77 9.9626 Tf 10.607 0 Td [(R)]TJ/F21 6.9738 Tf 7.196 3.616 Td [(N)]TJ/F24 6.9738 Tf 7.058 0 Td [<02>]TJ/F21 6.9738 Tf 6.227 0 Td [(F)]TJ/F123 9.9626 Tf 1.02 0 0 1 477.869 560.205 Tm [(.)-495(The)]TJ/F22 9.9626 Tf 1 0 0 1 504.377 560.205 Tm [(l)]TJ/F123 9.9626 Tf 1.02 0 0 1 507.546 560.205 Tm [(-th)-309(graph)]TJ 1 0 0 1 308.862 548.25 Tm [(con)40(v)20(olutional)-250(layer)-250(is)-250(de\002ned)-250(as)]TJ
ET
/S/Span<>BDC
BT
/F217 9.9626 Tf 369.192 525.187 Td [(X)]TJ/F18 6.9738 Tf 8.662 -1.799 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(+1\))]TJ/F19 9.9626 Tf 16.466 1.799 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [<1b>]TJ/F12 9.9626 Tf 7.711 11.059 Td [<10>]TJ/F19 9.9626 Tf 7.79 -8.513 Td [(^)]TJ/F217 9.9626 Tf -1.84 -2.546 Td [(A)]TJ/F123 9.9626 Tf 10.322 0 Td []TJ/F217 9.9626 Tf 4.151 0 Td [(X)]TJ/F18 6.9738 Tf 8.662 -1.799 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(\))]TJ/F123 9.9626 Tf 5.272 1.799 Td []TJ/F217 9.9626 Tf 4.151 0 Td [(W)]TJ/F12 9.9626 Tf 12.004 11.059 Td [<11>]TJ/F22 9.9626 Tf 7.61 -11.059 Td [(;)]TJ
ET
EMC
BT
/F123 9.9626 Tf 533.496 525.187 Td [(\(2\))]TJ 1.02 0 0 1 308.503 500.845 Tm [(where)]TJ/F22 9.9626 Tf 1 0 0 1 336.03 500.845 Tm [<1b>]TJ/F19 9.9626 Tf 6.05 0 Td [(\()]TJ/F123 9.9626 Tf 5.535 0 Td []TJ/F19 9.9626 Tf 4.151 0 Td [(\))]TJ/F123 9.9626 Tf 1.02 0 0 1 358.342 500.845 Tm [(is)-266(an)-266(acti)25(v)24(ation)-266(f)1(un)-1(c)1(tion,)]TJ/F217 9.9626 Tf 1 0 0 1 461.562 500.845 Tm [(W)]TJ/F25 9.9626 Tf 15.161 0 Td [(2)]TJ/F77 9.9626 Tf 9.8 0 Td [(R)]TJ/F21 6.9738 Tf 7.195 3.652 Td [(F)]TJ/F17 4.9813 Tf 5.053 -1.334 Td [(\()]TJ/F20 4.9813 Tf 2.698 0 Td [(l)]TJ/F17 4.9813 Tf 2.393 0 Td [(\))]TJ/F24 6.9738 Tf 3.196 1.334 Td [<02>]TJ/F21 6.9738 Tf 6.227 0 Td [(F)]TJ/F17 4.9813 Tf 5.052 -1.334 Td [(\()]TJ/F20 4.9813 Tf 2.698 0 Td [(l)]TJ/F17 4.9813 Tf 2.393 0 Td [(+1\))]TJ/F123 9.9626 Tf 1.02 0 0 1 538.334 500.845 Tm [(is)]TJ 1.02 0 0 1 308.862 487.894 Tm [(a)-297(learnable)-298(parameter)39(,)-310(and)]TJ/F19 9.9626 Tf 1 0 0 1 422.124 490.44 Tm [(^)]TJ/F217 9.9626 Tf -1.84 -2.546 Td [(A)]TJ/F25 9.9626 Tf 12.415 0 Td [(2)]TJ/F77 9.9626 Tf 10.394 0 Td [(R)]TJ/F21 6.9738 Tf 7.196 3.615 Td [(N)]TJ/F24 6.9738 Tf 7.058 0 Td [<02>]TJ/F21 6.9738 Tf 6.227 0 Td [(N)]TJ/F123 9.9626 Tf 1.02 0 0 1 474.153 487.894 Tm [(is)-297(the)-298(normalized)]TJ 1.01 0 0 1 308.862 475.939 Tm [(adjacenc)15(y)-248(\(refer)-248(to)-247([)]TJ
0 1 0 rg 0 1 0 RG
1 0 0 1 389.938 475.939 Tm [(20)]TJ
0 g 0 G
1.01 0 0 1 399.9 475.939 Tm [(])-248(for)-248(details\).)-307(A)-248(graph)-248(con)40(v)20(olutional)]TJ 1.02 0 0 1 308.862 463.984 Tm [(layer)-252(doesn')18(t)-252(change)-252(the)-252(number)-252(of)-252(nodes)-252(\(ro)25(ws)-252(of)]TJ/F217 9.9626 Tf 1 0 0 1 517.719 463.984 Tm [(X)]TJ/F123 9.9626 Tf 1.02 0 0 1 526.381 463.984 Tm [(\))-252(b)20(ut)]TJ 1 0 0 1 308.862 452.028 Tm [(changes)-250(the)-250(feature)-250(dimension)-250(from)]TJ/F22 9.9626 Tf 145.254 0 Td [(F)]TJ/F18 6.9738 Tf 6.406 -1.798 Td [(\()]TJ/F21 6.9738 Tf 3.114 0 Td [(l)]TJ/F18 6.9738 Tf 2.559 0 Td [(\))]TJ/F123 9.9626 Tf 6.103 1.798 Td [(to)]TJ/F22 9.9626 Tf 10.241 0 Td [(F)]TJ/F18 6.9738 Tf 6.407 -1.798 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(+1\))]TJ/F123 9.9626 Tf 13.699 1.798 Td [(.)]TJ 1.02 0 0 1 320.817 440.073 Tm [(GCN)-315(has)-314(been)-315(applied)-314(to)-315(man)15(y)-315(graph-structured)-314(tasks)]TJ 1.02 0 0 1 308.862 428.118 Tm [(due)-257(to)-257(its)-257(simplicity)-257(and)-257(good)-258(generalization)-257(ability)64(.)-340(Ho)25(w-)]TJ 1.02 0 0 1 308.862 416.163 Tm [(e)25(v)14(er)39(,)-315(the)-302(problems)-302(of)-301(GCN)-302(are)-302(also)-301(ob)15(vious.)-474(Besides)-302(the)]TJ 1.01 0 0 1 308.862 404.208 Tm [(for)18(getting)-247(problem)-246(in)-246(lifelong)-247(learning,)-247(its)-246(node)-246(features)-247(in)]TJ 1.02 0 0 1 308.862 392.253 Tm [(the)-302(ne)15(xt)-303(layer)-302(is)-302(a)-302(linear)-302(combination)-303(of)-302(the)-302(current)-302(layer)54(.)]TJ 0.98 0 0 1 308.553 380.297 Tm [(Thus,)-239(GCN)-235(and)-235(its)-235(v)25(ariants)-235(cannot)-235(directly)-235(model)-235(the)-235(feature)]TJ 0.98 0 0 1 307.537 368.342 Tm [(\223interaction\224.)-309(T)82(o)-234(t)1(his)-234(end,)-237(we)-233(introduce)-234(the)-233(feature)-233(graphs)-233(by)]TJ 1 0 0 1 308.862 356.387 Tm [(de\002ning)-250(feature)-250(nodes)-250(and)-250(feature)-250(adjacenc)15(y)-250(matrix.)]TJ/F120 10.9589 Tf 0 -19.321 Td [(4.1.)-250(F)25(eatur)18(e)-250(Nodes)]TJ/F123 9.9626 Tf 1.02 0 0 1 320.817 319.133 Tm [(Recall)-315(that)-315(each)-315(node)]TJ/F22 9.9626 Tf 1 0 0 1 413.205 319.133 Tm [(v)]TJ/F123 9.9626 Tf 1.02 0 0 1 421.594 319.133 Tm [(in)-315(a)-315(re)14(gular)-315(graph)]TJ/F25 9.9626 Tf 1 0 0 1 498.59 319.133 Tm [(G)]TJ/F19 9.9626 Tf 10.603 0 Td [(=)-410(\()]TJ/F25 9.9626 Tf 15.709 0 Td [(V)]TJ/F22 9.9626 Tf 6.924 0 Td [(;)]TJ/F25 9.9626 Tf 4.428 0 Td [(E)]TJ/F19 9.9626 Tf 6.149 0 Td [(\))]TJ/F123 9.9626 Tf 1.02 0 0 1 308.862 307.178 Tm [(is)-481(associated)-481(with)-481(a)-481(multi-channel)-481(feature)-481(v)14(ector)]TJ/F217 9.9626 Tf 1 0 0 1 524.108 307.178 Tm [(x)]TJ/F19 9.9626 Tf 13.255 0 Td [(=)]TJ/F12 9.9626 Tf -228.501 -0.897 Td [(h)]TJ/F217 9.9626 Tf 4.704 -11.058 Td [(x)]TJ/F18 6.9738 Tf 6.047 3.615 Td [(T)]TJ 0 -6.824 Td [([1)]TJ/F21 6.9738 Tf 6.227 0 Td [(;)]TJ/F18 6.9738 Tf 2.366 0 Td [(:])]TJ/F22 9.9626 Tf 5.009 3.209 Td [(;)]TJ/F25 9.9626 Tf 4.428 0 Td [<01>-167<01>-166<01>]TJ/F22 9.9626 Tf 14.944 0 Td [(;)]TJ/F217 9.9626 Tf 4.427 0 Td [(x)]TJ/F18 6.9738 Tf 6.047 3.615 Td [(T)]TJ 0 -6.824 Td [([)]TJ/F21 6.9738 Tf 2.256 0 Td [(F)-31(;)]TJ/F18 6.9738 Tf 7.633 0 Td [(:])]TJ/F12 9.9626 Tf 5.009 14.267 Td [(i)]TJ/F25 9.9626 Tf 7.675 -11.058 Td [(2)]TJ/F77 9.9626 Tf 9.612 0 Td [(R)]TJ/F21 6.9738 Tf 7.195 3.615 Td [(F)]TJ/F24 6.9738 Tf 6.125 0 Td [<02>]TJ/F21 6.9738 Tf 6.227 0 Td [(C)]TJ/F123 9.9626 Tf 1.02 0 0 1 421.494 295.223 Tm [(,)-259(where)]TJ/F217 9.9626 Tf 1 0 0 1 454.088 295.223 Tm [(x)]TJ/F18 6.9738 Tf 6.047 -1.799 Td [([)]TJ/F21 6.9738 Tf 2.255 0 Td [(i;)]TJ/F18 6.9738 Tf 5.185 0 Td [(:])]TJ/F123 9.9626 Tf 1.02 0 0 1 475.184 295.223 Tm [(is)-256(the)]TJ/F22 9.9626 Tf 1 0 0 1 499.581 295.223 Tm [(i)]TJ/F123 9.9626 Tf 1.02 0 0 1 503.013 295.223 Tm [(-th)-256(feature)]TJ 0.988 0 0 1 308.533 280.996 Tm [(\(ro)25(w\))-253(of)]TJ/F217 9.9626 Tf 1 0 0 1 343.328 280.996 Tm [(x)]TJ/F123 9.9626 Tf 0.988 0 0 1 349.375 280.996 Tm [(.)-314(An)-253(attrib)20(ute)-253(feature)-253(graph)-253(tak)10(es)-253(the)-254(featur)1(es)-254(of)-253(a)]TJ 0.98 0 0 1 308.862 269.041 Tm [(re)15(gular)-225(graph)-225(as)-226(nodes.)-306(It)-225(can)-225(be)-226(de\002ned)-225(as)]TJ/F25 9.9626 Tf 1 0 0 1 478.142 269.041 Tm [(G)]TJ/F24 6.9738 Tf 6.517 3.615 Td [(F)]TJ/F19 9.9626 Tf 9.675 -3.615 Td [(=)-278(\()]TJ/F25 9.9626 Tf 14.391 0 Td [(V)]TJ/F24 6.9738 Tf 6.924 3.615 Td [(F)]TJ/F22 9.9626 Tf 6.908 -3.615 Td [(;)]TJ/F25 9.9626 Tf 4.428 0 Td [(E)]TJ/F24 6.9738 Tf 6.149 3.615 Td [(F)]TJ/F19 9.9626 Tf 6.908 -3.615 Td [(\))]TJ/F123 9.9626 Tf 0.98 0 0 1 543.916 269.041 Tm [(,)]TJ 0.989 0 0 1 308.503 257.086 Tm [(where)-253(each)-253(node)]TJ/F22 9.9626 Tf 1 0 0 1 377.252 257.086 Tm [(v)]TJ/F24 6.9738 Tf 5.187 3.615 Td [(F)]TJ/F25 9.9626 Tf 9.676 -3.615 Td [(2)-278(V)]TJ/F24 6.9738 Tf 16.334 3.615 Td [(F)]TJ/F123 9.9626 Tf 0.989 0 0 1 417.848 257.086 Tm [(is)-253(associated)-253(with)-252(a)-253(feature)]TJ/F217 9.9626 Tf 1 0 0 1 526.616 257.086 Tm [(x)]TJ/F18 6.9738 Tf 6.047 3.615 Td [(T)]TJ 0 -6.824 Td [([)]TJ/F21 6.9738 Tf 2.255 0 Td [(i;)]TJ/F18 6.9738 Tf 5.185 0 Td [(:])]TJ/F123 9.9626 Tf 0.995 0 0 1 308.862 242.756 Tm [(and)-252(will)-251(be)-252(denoted)-252(as)]TJ/F217 9.9626 Tf 1 0 0 1 400.075 242.756 Tm [(x)]TJ/F24 6.9738 Tf 6.047 3.616 Td [(F)]TJ/F21 6.9738 Tf 0 -6.209 Td [(i)]TJ/F123 9.9626 Tf 0.995 0 0 1 413.03 242.756 Tm [(.)-313(Intuiti)25(v)15(ely)66(,)-252(the)-252(number)-252(of)-251(nodes)]TJ 1.02 0 0 1 308.862 230.801 Tm [(in)-256(the)-257(feature)-256(graph)-256(is)-257(the)-256(feature)-256(dimension)-256(in)-257(the)-256(re)15(gular)]TJ 1.008 0 0 1 308.862 218.846 Tm [(graph,)]TJ/F130 9.9626 Tf 1.008 0 0 1 336.721 218.846 Tm [(i.e)]TJ/F123 9.9626 Tf 1.008 0 0 1 346.482 218.846 Tm [(.,)]TJ/F12 9.9626 Tf 1 0 0 1 353.985 227.314 Tm [(\f)]TJ 0 -5.978 Td [(\f)]TJ/F25 9.9626 Tf 3.321 -2.49 Td [(V)]TJ/F24 6.9738 Tf 6.924 3.615 Td [(F)]TJ/F12 9.9626 Tf 6.908 4.853 Td [(\f)]TJ 0 -5.978 Td [(\f)]TJ/F19 9.9626 Tf 6.089 -2.49 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(F)]TJ/F123 9.9626 Tf 1.008 0 0 1 395.533 218.846 Tm [(,)-247(and)-247(the)-247(feature)-247(dimension)-247(in)-247(feature)]TJ 0.98 0 0 1 308.862 206.891 Tm [(graph)-202(is)-202(the)-201(feature)-202(channel)-202(in)-202(a)-201(re)15(gular)-202(graph,)]TJ/F130 9.9626 Tf 0.98 0 0 1 488.941 206.891 Tm [(i.e)]TJ/F123 9.9626 Tf 0.98 0 0 1 498.431 206.891 Tm [(.,)]TJ/F217 9.9626 Tf 1 0 0 1 505.387 206.891 Tm [(x)]TJ/F24 6.9738 Tf 6.047 3.615 Td [(F)]TJ/F21 6.9738 Tf 0 -6.209 Td [(i)]TJ/F25 9.9626 Tf 9.675 2.594 Td [(2)]TJ/F77 9.9626 Tf 9.409 0 Td [(R)]TJ/F21 6.9738 Tf 7.196 3.615 Td [(C)]TJ/F123 9.9626 Tf 0.98 0 0 1 544.415 206.891 Tm [(.)]TJ 1 0 0 1 308.553 194.935 Tm [(Therefore,)-250(we)-250(de\002ne)-250(the)-250(feature)-250(nodes)-250(for)-250(feature)-250(graph)-250(as)]TJ
ET
/S/Span<>BDC
BT
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1 0 0 rg 1 0 0 RG
[(5)]TJ
0 g 0 G
[(\))-250(so)-250(that)-250(\()]TJ
1 0 0 rg 1 0 0 RG
[(1)]TJ
0 g 0 G
[(\))-250(is)-250(con)40(v)15(erted)-250(to)-250(a)-250(continuum)-250(of)-250(graphs:)]TJ
ET
/S/Span<>BDC
BT
/F19 9.9626 Tf 66.839 368.503 Td [(\()]TJ/F25 9.9626 Tf 3.875 0 Td [(G)]TJ/F24 6.9738 Tf 6.517 4.113 Td [(F)]TJ/F18 6.9738 Tf -0.591 -6.576 Td [(1)]TJ/F22 9.9626 Tf 7.499 2.463 Td [(;)-167(t)]TJ/F18 6.9738 Tf 8.026 -1.494 Td [(1)]TJ/F22 9.9626 Tf 4.469 1.494 Td [(;)]TJ/F217 9.9626 Tf 4.428 0 Td [(z)]TJ/F18 6.9738 Tf 5.092 -1.494 Td [(1)]TJ/F19 9.9626 Tf 4.469 1.494 Td [(\))]TJ/F22 9.9626 Tf 3.874 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F19 9.9626 Tf 22.139 0 Td [(\()]TJ/F25 9.9626 Tf 3.875 0 Td [(G)]TJ/F24 6.9738 Tf 6.517 4.113 Td [(F)]TJ/F21 6.9738 Tf -0.591 -6.576 Td [(i)]TJ/F22 9.9626 Tf 7.499 2.463 Td [(;)-167(t)]TJ/F21 6.9738 Tf 8.026 -1.494 Td [(i)]TJ/F22 9.9626 Tf 3.316 1.494 Td [(;)]TJ/F217 9.9626 Tf 4.428 0 Td [(z)]TJ/F21 6.9738 Tf 5.092 -1.494 Td [(i)]TJ/F19 9.9626 Tf 3.317 1.494 Td [(\))]TJ/F22 9.9626 Tf 3.874 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F19 9.9626 Tf 22.139 0 Td [(\()]TJ/F25 9.9626 Tf 3.875 0 Td [(G)]TJ/F24 6.9738 Tf 6.517 4.113 Td [(F)]TJ/F21 6.9738 Tf -0.591 -6.576 Td [(N)]TJ/F22 9.9626 Tf 7.557 2.463 Td [(;)-167(t)]TJ/F21 6.9738 Tf 8.025 -1.494 Td [(N)]TJ/F22 9.9626 Tf 7.557 1.494 Td [(;)]TJ/F217 9.9626 Tf 4.427 0 Td [(z)]TJ/F21 6.9738 Tf 5.092 -1.494 Td [(N)]TJ/F19 9.9626 Tf 7.557 1.494 Td [(\))]TJ
ET
EMC
BT
/F123 9.9626 Tf 274.746 368.503 Td [(\(6\))]TJ -224.993 -17.686 Td [(where)]TJ/F25 9.9626 Tf 26.818 0 Td [(G)]TJ/F24 6.9738 Tf 6.517 3.615 Td [(F)]TJ/F21 6.9738 Tf -0.591 -6.208 Td [(i)]TJ/F19 9.9626 Tf 10.267 2.593 Td [(=)]TJ/F12 9.9626 Tf 10.516 8.07 Td [<00>]TJ/F25 9.9626 Tf 4.566 -8.07 Td [(V)]TJ/F24 6.9738 Tf 6.924 3.615 Td [(F)]TJ/F21 6.9738 Tf -0.819 -6.208 Td [(i)]TJ/F22 9.9626 Tf 7.727 2.593 Td [(;)]TJ/F217 9.9626 Tf 4.428 0 Td [(A)]TJ/F24 6.9738 Tf 8.662 3.615 Td [(F)]TJ/F19 9.9626 Tf 6.908 -3.615 Td [(\()]TJ/F217 9.9626 Tf 3.874 0 Td [(x)]TJ/F21 6.9738 Tf 6.047 -1.494 Td [(i)]TJ/F19 9.9626 Tf 3.317 1.494 Td [(\))]TJ/F12 9.9626 Tf 3.874 8.07 Td [<01>]TJ/F123 9.9626 Tf 4.567 -8.07 Td [(.)-310(This)-248(means)-249(that)-249(our)-249(objecti)25(v)15(e)]TJ 1.02 0 0 1 50.112 338.862 Tm [(of)-244(learning)-244(a)-244(node)-244(predictor)-244(becomes)-244(learning)-244(a)-244(graph)-244(pre-)]TJ 1.02 0 0 1 50.112 326.907 Tm [(dictor)]TJ/F22 9.9626 Tf 1 0 0 1 76.943 326.907 Tm [(f)]TJ/F24 6.9738 Tf 5.95 3.615 Td [(F)]TJ/F123 9.9626 Tf 1.02 0 0 1 92.924 326.907 Tm [(that)-307(predicts)-308(tar)18(get)]TJ/F217 9.9626 Tf 1 0 0 1 172.668 326.907 Tm [(z)]TJ/F123 9.9626 Tf 1.02 0 0 1 180.884 326.907 Tm [(for)-307(test)-308(sample)]TJ/F19 9.9626 Tf 1 0 0 1 245.005 326.907 Tm [(\()]TJ/F25 9.9626 Tf 3.875 0 Td [(G)]TJ/F24 6.9738 Tf 6.517 3.615 Td [(F)]TJ/F22 9.9626 Tf 6.908 -3.615 Td [(;)-167(t)]TJ/F19 9.9626 Tf 8.025 0 Td [(\))]TJ/F123 9.9626 Tf 1.02 0 0 1 277.328 326.907 Tm [(so)]TJ 1.02 0 0 1 50.112 314.951 Tm [(that)]TJ/F19 9.9626 Tf 1 0 0 1 68.445 314.951 Tm [(\()]TJ/F25 9.9626 Tf 3.874 0 Td [(G)]TJ/F24 6.9738 Tf 6.517 3.616 Td [(F)]TJ/F22 9.9626 Tf 6.908 -3.616 Td [(;)-167(t;)]TJ/F217 9.9626 Tf 12.454 0 Td [(z)]TJ/F19 9.9626 Tf 5.092 0 Td [(\))]TJ/F25 9.9626 Tf 7.751 0 Td [<18>]TJ/F22 9.9626 Tf 11.626 0 Td [(P)]TJ/F24 6.9738 Tf 7.78 3.616 Td [(F)]TJ/F21 6.9738 Tf -1.383 -6.078 Td [(t)]TJ/F123 9.9626 Tf 1.02 0 0 1 137.355 314.951 Tm [(.)-481(Note)-304(that)-304(the)-304(feature)-304(graphs)-304(in)-304(the)]TJ 1 0 0 1 50.112 302.996 Tm [(ne)25(w)-250(continuum)-250(\()]TJ
1 0 0 rg 1 0 0 RG
[(6)]TJ
0 g 0 G
[(\))-250(are)-250(still)-250(non-i.i.d.)]TJ 1.02 0 0 1 62.067 291.041 Tm [(In)-252(this)-252(w)10(ay)63(,)-254(a)-252(gro)25(wing)-252(adjacenc)14(y)-252(matrix)-252(is)-252(con)39(v)15(erted)-252(to)]TJ 1.007 0 0 1 50.112 279.086 Tm [(multiple)-247(small)-247(adjacenc)15(y)-248(matrices.)-307(Hence,)-247(a)-248(lifelong)-247(graph)]TJ 1.009 0 0 1 50.112 267.131 Tm [(learning)-249(problem)-249(becomes)-249(a)-249(re)15(gular)-249(lifelong)-249(learning)-249(prob-)]TJ 0.992 0 0 1 50.112 255.176 Tm [(lem)-251(similar)-251(to)-252([)]TJ
0 1 0 rg 0 1 0 RG
1 0 0 1 110.818 255.176 Tm [(26)]TJ
0 g 0 G
0.992 0 0 1 120.781 255.176 Tm [(])-251(and)-251(the)-252(problem)-251(of)-251(increasing)-251(nodes)-251(can)]TJ 1.004 0 0 1 50.112 243.22 Tm [(be)-250(solv)15(ed)-249(by)-250(applying)-250(l)1(ifelong)-250(learning)-250(to)-249(the)-250(graph)-250(conti)1(n-)]TJ 0.984 0 0 1 50.112 231.265 Tm [(uum)]TJ 1 0 0 1 70.026 231.265 Tm [(\()]TJ
1 0 0 rg 1 0 0 RG
[(6)]TJ
0 g 0 G
[(\))]TJ 0.984 0 0 1 81.642 231.265 Tm [(.)-315(T)81(o)-253(be)-253(more)-254(clear)41(,)-254(we)-253(list)-253(their)-254(detailed)-253(relationship)]TJ 0.986 0 0 1 50.112 219.31 Tm [(in)-253(T)81(able)]TJ
1 0 0 rg 1 0 0 RG
[-254(1)]TJ
0 g 0 G
[(,)-253(where)-254(the)-253(arro)25(w)]TJ/F25 9.9626 Tf 1 0 0 1 160.293 219.31 Tm [(7!)]TJ/F123 9.9626 Tf 0.986 0 0 1 172.746 219.31 Tm [(refers)-253(to)-254(the)-253(con)40(v)15(ersion)-253(from)]TJ 1 0 0 1 50.112 207.355 Tm [(a)-250(re)15(gular)-250(graph)-250(to)-250(multiple)-250(feature)-250(graphs.)]TJ/F120 10.9589 Tf 0 -18.233 Td [(4.3.)-250(F)25(eatur)18(e)-250(Graph)-250(Lay)10(ers)]TJ/F123 9.9626 Tf 1.02 0 0 1 62.067 171.19 Tm [(Since)-281(feature)-281(graph)-281(is)-281(a)-282(ne)25(w)-281(topology)-281(gi)24(v)15(en)-281(by)-281(feature)]TJ 0.982 0 0 1 50.112 159.234 Tm [(adjacenc)15(y)-255(matrix,)-255(we)-254(are)-255(able)-255(to)-255(de\002ne)-255(man)15(y)-254(dif)25(ferent)-255(types)]TJ 1 0 0 1 50.112 147.279 Tm [(of)-250(layers.)-310(In)-250(this)-250(section)-250(we)-250(present)-250(three)-250(types)-250(of)-250(layers.)]TJ/F120 9.9626 Tf 0 -25.764 Td [(4.3.1)-1000(F)25(eatur)18(e)-250(Br)18(oadcast)-250(Lay)10(er)]TJ/F123 9.9626 Tf 0 -18.679 Td [(Inspired)-250(by)-250(GCN,)-250(the)]TJ/F22 9.9626 Tf 88.268 0 Td [(l)]TJ/F123 9.9626 Tf 3.169 0 Td [(-th)-250(broadcast)-250(layer)-250(is)-250(de\002ned)-250(as)]TJ
ET
/S/Span<>BDC
BT
/F217 9.9626 Tf 106.149 82.494 Td [(x)]TJ/F24 6.9738 Tf 6.047 4.114 Td [(F)]TJ/F18 6.9738 Tf 0 -6.824 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(+1\))]TJ/F19 9.9626 Tf 16.466 2.71 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [<1b>]TJ/F12 9.9626 Tf 7.71 11.059 Td [<10>]TJ/F19 9.9626 Tf 7.791 -8.512 Td [(^)]TJ/F217 9.9626 Tf -1.841 -2.547 Td [(A)]TJ/F24 6.9738 Tf 8.662 4.114 Td [(F)]TJ/F21 6.9738 Tf 0 -6.576 Td [(k)]TJ/F123 9.9626 Tf 8.569 2.462 Td []TJ/F217 9.9626 Tf 4.151 0 Td [(x)]TJ/F24 6.9738 Tf 6.047 4.114 Td [(F)]TJ/F18 6.9738 Tf 0 -6.824 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(\))]TJ/F123 9.9626 Tf 5.272 2.71 Td []TJ/F217 9.9626 Tf 4.151 0 Td [(W)]TJ/F24 6.9738 Tf 12.003 4.114 Td [(F)]TJ/F12 9.9626 Tf 6.908 6.945 Td [<11>]TJ/F22 9.9626 Tf 7.611 -11.059 Td [(;)]TJ
ET
EMC
BT
/F123 9.9626 Tf 274.746 82.494 Td [(\(7\))]TJ
0 g 0 G
0 g 0 G
1.02 0 0 1 308.503 710.037 Tm [(where)]TJ/F22 9.9626 Tf 1 0 0 1 336.462 710.037 Tm [<1b>]TJ/F19 9.9626 Tf 6.05 0 Td [(\()]TJ/F123 9.9626 Tf 5.535 0 Td []TJ/F19 9.9626 Tf 4.151 0 Td [(\))]TJ/F123 9.9626 Tf 1.02 0 0 1 359.206 710.037 Tm [(is)-308(a)-309(non-linear)-308(acti)24(v)25(ation)-308(function,)]TJ/F19 9.9626 Tf 1 0 0 1 505.92 712.583 Tm [(^)]TJ/F217 9.9626 Tf -1.841 -2.546 Td [(A)]TJ/F24 6.9738 Tf 8.662 3.616 Td [(F)]TJ/F21 6.9738 Tf 0 -6.437 Td [(k)]TJ/F123 9.9626 Tf 1.02 0 0 1 522.783 710.037 Tm [(is)-308(the)]TJ 1.02 0 0 1 308.862 698.082 Tm [(associated)-245(normalized)-244(feature)-245(adjacenc)15(y)-245(matrix,)-245(and)]TJ/F217 9.9626 Tf 1 0 0 1 523.699 698.082 Tm [(W)]TJ/F25 9.9626 Tf 14.771 0 Td [(2)]TJ/F77 9.9626 Tf -229.608 -11.955 Td [(R)]TJ/F21 6.9738 Tf 7.195 3.652 Td [(C)]TJ/F17 4.9813 Tf 5.714 -1.334 Td [(\()]TJ/F20 4.9813 Tf 2.699 0 Td [(l)]TJ/F17 4.9813 Tf 2.392 0 Td [(\))]TJ/F24 6.9738 Tf 3.197 1.334 Td [<02>]TJ/F21 6.9738 Tf 6.226 0 Td [(C)]TJ/F17 4.9813 Tf 5.715 -1.334 Td [(\()]TJ/F20 4.9813 Tf 2.698 0 Td [(l)]TJ/F17 4.9813 Tf 2.393 0 Td [(+1\))]TJ/F123 9.9626 Tf 1.02 0 0 1 362.618 686.127 Tm [(is)-327(a)-327(learnable)-327(parameter)54(.)-550(F)15(or)-327(simplicity)64(,)-348(the)]TJ 1.02 0 0 1 308.862 674.172 Tm [(channel)]TJ/F22 9.9626 Tf 1 0 0 1 343.536 674.172 Tm [(c)]TJ/F123 9.9626 Tf 1.02 0 0 1 350.918 674.172 Tm [(is)-302(left)-302(out)-302(in)]TJ 1 0 0 1 404.417 674.172 Tm [(\()]TJ
1 0 0 rg 1 0 0 RG
[(7)]TJ
0 g 0 G
[(\))]TJ 1.02 0 0 1 419.104 674.172 Tm [(and)-302(the)-302(layer)-302(channel)-303(is)-302(broad-)]TJ 1.02 0 0 1 308.862 662.217 Tm [(casted)-269(independently)63(.)-376(It)-270(is)-269(w)10(orth)-270(noting)-269(that,)-275(although)-270(the)]TJ 1.02 0 0 1 308.862 650.262 Tm [(de\002nition)-272(of)]TJ 1 0 0 1 361.819 650.262 Tm [(\()]TJ
1 0 0 rg 1 0 0 RG
[(7)]TJ
0 g 0 G
[(\))]TJ 1.02 0 0 1 376.202 650.262 Tm [(appears)-272(similar)-272(to)]TJ 1 0 0 1 451.669 650.262 Tm [(\()]TJ
1 0 0 rg 1 0 0 RG
[(2)]TJ
0 g 0 G
[(\))]TJ 1.02 0 0 1 463.285 650.262 Tm [(,)-279(the)15(y)-272(ha)19(v)15(e)-272(dif)24(f)1(erent)]TJ 1 0 0 1 308.862 638.306 Tm [(dimension)-250(and)-250(represent)-250(dif)25(ferent)-250(meanings.)]TJ/F120 9.9626 Tf 0 -26.56 Td [(4.3.2)-1000(F)25(eatur)18(e)-250(T)74(ransf)25(orm)-250(Lay)10(er)]TJ/F123 9.9626 Tf 1.02 0 0 1 308.862 593.054 Tm [(Similar)-246(to)-246(graph)-247(con)40(v)19(olutional)-246(layer)]TJ 1 0 0 1 457.95 593.054 Tm [(\()]TJ
1 0 0 rg 1 0 0 RG
[(2)]TJ
0 g 0 G
[(\))]TJ 1.02 0 0 1 469.566 593.054 Tm [(,)-247(the)-246(feature)-246(broad-)]TJ 0.98 0 0 1 308.862 581.099 Tm [(cast)-252(layer)-253(doesn')19(t)-253(change)-252(the)-253(number)-252(of)-253(feature)-252(nodes.)-316(Ho)26(w-)]TJ 1.01 0 0 1 308.862 569.143 Tm [(e)25(v)15(er)39(,)-246(this)-247(is)-246(not)-247(al)10(w)10(ays)-246(necessary)64(,)-247(as)-246(the)-247(objecti)25(v)15(e)-246(has)-247(been)]TJ 1.007 0 0 1 308.862 557.188 Tm [(turned)-249(into)-249(graph)-249(classi\002cation.)-310(Therefore,)-250(we)-249(de\002ne)-249(a)-249(fea-)]TJ 0.98 0 0 1 308.862 545.233 Tm [(ture)-245(transform)-245(layer)-245(which)-245(can)-245(change)-245(the)-245(number)-246(of)-245(feature)]TJ 0.982 0 0 1 308.862 533.278 Tm [(nodes)-254(and)-254(will)-255(be)-254(helpful)-254(for)-254(further)-255(reducing)-254(the)-254(number)-254(of)]TJ 1.02 0 0 1 308.862 521.323 Tm [(learnable)-245(parameters.)-306(Dif)25(ferent)-245(from)-246(the)-245(feature)-246(broadcast)]TJ 0.984 0 0 1 308.862 509.368 Tm [(layer)41(,)-254(we)-253(need)-253(to)-254(re-calculate)-253(the)-253(feature)-253(adjacenc)15(y)-253(matrices)]TJ 1.02 0 0 1 308.862 497.412 Tm [(from)-291(transformed)-290(neighbors.)-441(Therefore,)-302(gi)24(v)15(en)-291(the)-291(feature)]TJ 0.983 0 0 1 308.862 485.457 Tm [(graph)]TJ/F25 9.9626 Tf 1 0 0 1 333.652 485.457 Tm [(G)]TJ/F24 6.9738 Tf 6.517 3.616 Td [(F)]TJ/F123 9.9626 Tf 0.983 0 0 1 347.077 485.457 Tm [(,)-254(the)]TJ/F22 9.9626 Tf 1 0 0 1 366.474 485.457 Tm [(l)]TJ/F123 9.9626 Tf 0.983 0 0 1 369.642 485.457 Tm [(-th)-254(feature)-255(transform)-254(layer)-254(can)-255(be)-254(de\002ned)-254(as)]TJ
ET
/S/Span<>BDC
BT
/F217 9.9626 Tf 330.924 451.572 Td [(A)]TJ/F24 6.9738 Tf 8.662 4.113 Td [(F)]TJ/F18 6.9738 Tf 0 -6.824 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(\))]TJ/F19 9.9626 Tf 3.612 2.711 Td [(\()]TJ/F217 9.9626 Tf 3.874 0 Td [(x)]TJ/F19 9.9626 Tf 6.047 0 Td [(\))]TJ/F74 9.9626 Tf 6.642 0 Td [(,)]TJ/F217 9.9626 Tf 10.516 0 Td [(A)]TJ/F24 6.9738 Tf 8.662 4.113 Td [(F)]TJ/F21 6.9738 Tf 0 -6.576 Td [(k)]TJ/F12 9.9626 Tf 8.568 10.532 Td [<00>]TJ/F217 9.9626 Tf 4.566 -8.069 Td [(x)]TJ/F18 6.9738 Tf 6.047 -1.799 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(\))]TJ/F22 9.9626 Tf 3.612 1.799 Td [(;)]TJ/F217 9.9626 Tf 4.427 0 Td [(y)]TJ/F18 6.9738 Tf 6.047 -1.799 Td [(\()]TJ/F21 6.9738 Tf 3.114 0 Td [(l)]TJ/F18 6.9738 Tf 2.559 0 Td [(\))]TJ/F12 9.9626 Tf 3.612 9.868 Td [<01>]TJ/F22 9.9626 Tf 6.226 -8.069 Td [(;)]TJ/F25 9.9626 Tf 14.391 0 Td [(8)]TJ/F217 9.9626 Tf 5.535 0 Td [(y)]TJ/F25 9.9626 Tf 8.973 0 Td [(2)-278(N)]TJ/F21 6.9738 Tf 17.583 -1.495 Td [(k)]TJ/F19 9.9626 Tf 4.902 1.495 Td [(\()]TJ/F217 9.9626 Tf 3.874 0 Td [(x)]TJ/F19 9.9626 Tf 6.047 0 Td [(\))]TJ/F22 9.9626 Tf 3.875 0 Td [(;)]TJ/F123 9.9626 Tf 24.829 0 Td [(\(8a\))]TJ/F217 9.9626 Tf -198.148 -19.897 Td [(x)]TJ/F24 6.9738 Tf 6.047 4.114 Td [(F)]TJ/F18 6.9738 Tf 0 -6.825 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(+1\))]TJ/F19 9.9626 Tf 16.466 2.711 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [<1b>]TJ/F12 9.9626 Tf 7.711 11.059 Td [<10>]TJ/F217 9.9626 Tf 5.95 -11.059 Td [(W)]TJ/F24 6.9738 Tf 12.003 4.114 Td [(F)]TJ/F123 9.9626 Tf 8.569 -4.114 Td []TJ/F19 9.9626 Tf 5.991 2.546 Td [(^)]TJ/F217 9.9626 Tf -1.84 -2.546 Td [(A)]TJ/F24 6.9738 Tf 8.662 4.114 Td [(F)]TJ/F18 6.9738 Tf 0 -6.825 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(\))]TJ/F19 9.9626 Tf 3.611 2.711 Td [(\()]TJ/F217 9.9626 Tf 3.875 0 Td [(x)]TJ/F19 9.9626 Tf 6.046 0 Td [(\))]TJ/F123 9.9626 Tf 5.535 0 Td []TJ/F217 9.9626 Tf 4.151 0 Td [(x)]TJ/F24 6.9738 Tf 6.047 4.114 Td [(F)]TJ/F18 6.9738 Tf 0 -6.825 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(\))]TJ/F12 9.9626 Tf 3.612 13.77 Td [<11>]TJ/F22 9.9626 Tf 7.61 -11.059 Td [(;)]TJ/F123 9.9626 Tf 60.009 0 Td [(\(8b\))]TJ/F217 9.9626 Tf -197.59 -21.918 Td [(y)]TJ/F24 6.9738 Tf 6.206 4.114 Td [(F)]TJ/F18 6.9738 Tf -0.159 -6.825 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(+1\))]TJ/F19 9.9626 Tf 16.466 2.711 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [<1b>]TJ/F12 9.9626 Tf 7.711 11.059 Td [<10>]TJ/F217 9.9626 Tf 5.95 -11.059 Td [(W)]TJ/F24 6.9738 Tf 12.003 4.114 Td [(F)]TJ/F123 9.9626 Tf 8.569 -4.114 Td []TJ/F19 9.9626 Tf 5.991 2.546 Td [(^)]TJ/F217 9.9626 Tf -1.84 -2.546 Td [(A)]TJ/F24 6.9738 Tf 8.662 4.114 Td [(F)]TJ/F18 6.9738 Tf 0 -6.825 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(\))]TJ/F19 9.9626 Tf 3.611 2.711 Td [(\()]TJ/F217 9.9626 Tf 3.875 0 Td [(x)]TJ/F19 9.9626 Tf 6.046 0 Td [(\))]TJ/F123 9.9626 Tf 5.535 0 Td []TJ/F217 9.9626 Tf 4.151 0 Td [(y)]TJ/F24 6.9738 Tf 6.206 4.114 Td [(F)]TJ/F18 6.9738 Tf -0.159 -6.825 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(\))]TJ/F12 9.9626 Tf 3.612 13.77 Td [<11>]TJ/F22 9.9626 Tf 7.61 -11.059 Td [(;)]TJ
ET
EMC
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/F120 10.9589 Tf 50.112 710.037 Td [(4.4.)-250(Analysis)-250(and)-250(Computational)-250(Complexity)]TJ/F123 9.9626 Tf 1.02 0 0 1 62.067 689.856 Tm [(W)78(e)-454(ne)14(xt)-454(pro)14(vide)-454(an)-455(intuiti)25(v)14(e)-455(e)15(xplanation)-455(for)-454(feature)]TJ 0.989 0 0 1 50.112 677.901 Tm [(graphs.)-315(A)-254(feature)-253(graph)-254(doesn')18(t)-253(retain)-254(the)-253(ph)5(ysical)-253(meaning)]TJ 0.984 0 0 1 50.112 665.946 Tm [(of)-253(its)-254(re)16(gular)-254(graph.)-315(T)82(ak)10(e)-253(a)-254(social)-253(netw)10(ork)-253(as)-254(an)-253(e)15(xample,)-253(in)]TJ 0.98 0 0 1 50.112 653.99 Tm [(a)-250(re)15(gul)1(ar)-250(graph,)-251(each)-250(user)-250(is)-250(a)-249(node)-250(and)-250(user)-250(connections)-250(are)]TJ 0.982 0 0 1 50.112 642.035 Tm [(edges.)-317(In)-255(feature)-255(graphs,)-255(each)-255(user)]TJ/F130 9.9626 Tf 0.982 0 0 1 188.471 642.035 Tm [(is)]TJ/F123 9.9626 Tf 0.982 0 0 1 197.491 642.035 Tm [(a)-255(graph,)-255(while)-255(the)-255(user)]TJ 1.02 0 0 1 50.112 630.08 Tm [(features,)-331(including)-313(the)-314(users')-314(age,)-330(gender)39(,)]TJ/F130 9.9626 Tf 1.02 0 0 1 225.972 630.08 Tm [(etc)]TJ/F123 9.9626 Tf 1.02 0 0 1 237.821 630.08 Tm [(.,)-331(are)-313(nodes.)]TJ 1.02 0 0 1 49.803 618.125 Tm [(Therefore,)-295(user)-284(beha)19(vior)-285(prediction)-284(becomes)-285(graph)-285(classi-)]TJ 1.02 0 0 1 50.112 606.17 Tm [(\002cation)-310(based)-309(on)-310(node)-309(information)-310(and)-309(ne)24(w)-309(users)-310(simply)]TJ 0.984 0 0 1 50.112 594.215 Tm [(become)-254(multiple)-254(training)-253(samples.)-315(Since)-254(the)-254(number)-254(of)-254(user)]TJ 1 0 0 1 50.112 582.259 Tm [(features)-250(is)-249(more)-250(stable)-250(than)-249(the)-250(number)-250(of)-250(users,)-249(the)-250(size)-250(of)]TJ 1.02 0 0 1 50.112 570.304 Tm [(a)-278(feature)-278(graph)-279(is)-278(more)-278(stable)-278(than)-279(its)-278(re)15(gular)-278(graph.)-404(This)]TJ 1.02 0 0 1 50.112 558.349 Tm [(simpli\002es)-274(the)-275(learning)-274(on)-274(gro)24(wing)-274(graphs)-275(dramatically)-274(by)]TJ 1 0 0 1 50.112 546.394 Tm [(reducing)-250(the)-250(problem)-250(to)-250(the)-250(sample-incremental)-250(learning.)]TJ 1.016 0 0 1 62.067 532.19 Tm [(On)-245(the)-245(other)-245(hand,)-246(a)-245(re)15(gular)-245(graph)-245(usually)-245(assumes)-245(that)]TJ 1.008 0 0 1 50.112 520.235 Tm [(some)-247(useful)-247(information)-248(of)-247(a)-247(node)-247(is)-248(often)-247(encoded)-247(into)-247(its)]TJ 1.02 0 0 1 50.112 508.28 Tm [(neighbors,)-357(thus)-335(graph)-335(propag)5(ation)-335(is)-335(able)-335(to)-335(impro)15(v)14(e)-335(the)]TJ 1.014 0 0 1 50.112 496.325 Tm [(model)-246(performance.)-306(A)-246(feature)-246(graph)-246(has)-247(the)-246(same)-246(assump-)]TJ 1.004 0 0 1 50.112 484.37 Tm [(tion.)-311(Ho)25(we)25(v)15(er)40(,)-250(feature)-250(graph)-249(doesn')18(t)-250(directly)-250(propag)5(ate)-249(the)]TJ 0.997 0 0 1 50.112 472.414 Tm [(neighbor)-251(features,)-250(b)20(ut)-251(encode)-251(t)1(he)-251(neighbors)-251(into)-250(the)-251(feature)]TJ 1.02 0 0 1 50.112 460.459 Tm [(adjacenc)15(y)-308(matrices)]TJ 1 0 0 1 131.268 460.459 Tm [(\()]TJ
1 0 0 rg 1 0 0 RG
[(4)]TJ
0 g 0 G
[(\))]TJ 1.02 0 0 1 142.885 460.459 Tm [(.)-491(Re)14(g)5(ardless)-307(of)-308(the)-307(nonlinear)-308(func-)]TJ 1.013 0 0 1 50.112 448.504 Tm [(tion,)-247(e)15(xisting)-247(methods)-247(propag)5(ate)-247(neighbor)-246(features)-247(as)]TJ/F19 9.9626 Tf 1 0 0 1 269.601 451.05 Tm [(^)]TJ/F217 9.9626 Tf -1.841 -2.546 Td [(AX)]TJ/F123 9.9626 Tf 1.013 0 0 1 285.084 448.504 Tm [(,)]TJ 0.996 0 0 1 49.753 436.549 Tm [(where)]TJ/F217 9.9626 Tf 1 0 0 1 76.493 436.549 Tm [(X)]TJ/F19 9.9626 Tf 11.443 0 Td [(=)-279([)]TJ/F217 9.9626 Tf 13.297 0 Td [(x)]TJ/F18 6.9738 Tf 6.047 -1.495 Td [(1)]TJ/F22 9.9626 Tf 4.47 1.495 Td [(;)]TJ/F25 9.9626 Tf 4.427 0 Td [<01>-167<01>-166<01>]TJ/F22 9.9626 Tf 14.944 0 Td [(;)]TJ/F217 9.9626 Tf 4.428 0 Td [(x)]TJ/F21 6.9738 Tf 6.047 -1.495 Td [(n)]TJ/F19 9.9626 Tf 5.423 1.495 Td [(])]TJ/F123 9.9626 Tf 0.996 0 0 1 149.786 436.549 Tm [(,)-252(meaning)-252(the)15(y)-251(can)-252(only)-252(propag)5(ate)]TJ 0.99 0 0 1 50.112 424.594 Tm [(information)-251(element-wisely)65(,)-251(as)-252(features)-251(in)-252(the)-251(ne)15(xt)-252(layer)-251(are)]TJ 1 0 0 1 49.753 412.639 Tm [(weighted)-250(a)20(v)15(erage)-250(of)-250(the)-250(current)-250(features)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(20)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-250(22)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-250(41)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-250(57)]TJ
0 g 0 G
[(].)]TJ 1.02 0 0 1 62.067 398.435 Tm [(In)-369(contrast,)-400(each)-369(feature)-368(graph)-369(propag)5(ate)-369(features)-369(via)]TJ/F19 9.9626 Tf 1 0 0 1 51.952 389.026 Tm [(^)]TJ/F217 9.9626 Tf -1.84 -2.546 Td [(A)]TJ/F24 6.9738 Tf 8.662 3.615 Td [(F)]TJ/F217 9.9626 Tf 6.908 -3.615 Td [(x)]TJ/F24 6.9738 Tf 6.047 3.615 Td [(F)]TJ/F123 9.9626 Tf 1.02 0 0 1 78.637 386.48 Tm [(,)-270(which)-265(e)14(xplicitly)-265(model)-265(\223interaction\224)-265(between)-265(fea-)]TJ 1.02 0 0 1 50.112 374.524 Tm [(tures.)-312(In)-248(this)-248(sense,)-249(feature)-248(graph)-248(doesn')18(t)-248(lose)-248(information)]TJ 1.02 0 0 1 50.112 362.569 Tm [(of)-271(edges)-270(b)19(ut)-271(encode)-270(them)-271(into)-271(the)-271(feature)-270(adjacenc)14(y)64(.)-381(This)]TJ 1.02 0 0 1 50.112 350.614 Tm [(e)15(xplains)-297(its)-297(superiority)-297(o)14(v)15(er)-297(e)15(xisting)-297(graph)-297(models)-297(in)-297(re)15(g-)]TJ 1.02 0 0 1 50.112 338.659 Tm [(ular)-272(graph)-273(learning)-272(as)-273(sho)25(wn)-272(in)-273(Section)]TJ
1 0 0 rg 1 0 0 RG
[-272(5)]TJ
0 g 0 G
[(.)-386(T)78(ak)10(e)-272(a)-273(citation)]TJ 1.02 0 0 1 50.112 326.704 Tm [(graph)-331(as)-330(e)14(xample,)-352(a)-331(k)10(e)15(yw)10(ord)-331(in)-331(an)-330(article)-331(may)-331(in\003uence)]TJ 1.02 0 0 1 50.112 314.749 Tm [(another)-261(k)10(e)14(yw)10(ord)-261(in)-261(the)-261(article)-261(citing)-261(the)-261(former)54(.)-352(Ho)24(we)25(v)15(er)39(,)]TJ 1.02 0 0 1 50.112 302.793 Tm [(element-wise)-306(graph)-307(propag)5(ation)-307(lik)10(e)]TJ 1 0 0 1 203.531 302.793 Tm [(\()]TJ
1 0 0 rg 1 0 0 RG
[(2)]TJ
0 g 0 G
[(\))]TJ 1.02 0 0 1 218.262 302.793 Tm [(cannot)-307(e)15(xplicitly)]TJ 1.02 0 0 1 50.112 290.838 Tm [(model)-287(this)-287(relationship)-287([)]TJ
0 1 0 rg 0 1 0 RG
1 0 0 1 150.322 290.838 Tm [(20)]TJ
0 g 0 G
1.02 0 0 1 160.285 290.838 Tm [(,)]TJ
0 1 0 rg 0 1 0 RG
1 0 0 1 165.743 290.838 Tm [(22)]TJ
0 g 0 G
1.02 0 0 1 175.706 290.838 Tm [(,)]TJ
0 1 0 rg 0 1 0 RG
1 0 0 1 181.164 290.838 Tm [(41)]TJ
0 g 0 G
1.02 0 0 1 191.127 290.838 Tm [(,)]TJ
0 1 0 rg 0 1 0 RG
1 0 0 1 196.586 290.838 Tm [(57)]TJ
0 g 0 G
1.02 0 0 1 206.548 290.838 Tm [(].)-430(Although)-287(feature)]TJ 1.005 0 0 1 50.112 278.883 Tm [(graph)-248(is)-248(also)-248(suitable)-249(for)-248(re)15(gular)-248(graph)-248(learning,)-248(we)-249(mainly)]TJ 1 0 0 1 50.112 266.928 Tm [(focus)-250(our)-250(discussion)-250(on)-250(lifelong)-250(graph)-250(learning.)]TJ 1.02 0 0 1 62.067 252.724 Tm [(Feature)-402(graphs)-402(ha)20(v)14(e)-402(a)-402(lo)25(w)-402(computational)-402(comple)14(xi)1(ty)63(.)]TJ 1.014 0 0 1 50.112 240.769 Tm [(Concretely)64(,)-245(the)-246(comple)15(xity)-245(for)-246(calculating)-245(the)-246(feature)-245(adja-)]TJ 0.994 0 0 1 50.112 228.814 Tm [(cenc)15(y)-252(is)]TJ/F25 9.9626 Tf 1 0 0 1 84.645 228.814 Tm [(O)]TJ/F19 9.9626 Tf 8.208 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [(nF)]TJ/F18 6.9738 Tf 13.771 3.615 Td [(2)]TJ -1.384 -6.824 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(\))]TJ/F19 9.9626 Tf 3.612 3.209 Td [(\))]TJ/F123 9.9626 Tf 0.994 0 0 1 122.273 228.814 Tm [(,)-252(where)]TJ/F22 9.9626 Tf 1 0 0 1 153.926 228.814 Tm [(n)]TJ/F123 9.9626 Tf 0.994 0 0 1 162.397 228.814 Tm [(is)-252(the)-251(e)15(xpected)-252(number)-251(of)-252(node)]TJ 1.02 0 0 1 50.112 216.859 Tm [(neighbors)-323(in)-323(the)-323(continuum.)-538(Therefore,)-342(re)14(g)5(ardless)-323(of)-323(the)]TJ 0.98 0 0 1 50.112 204.903 Tm [(number)-219(of)-218(layers,)-226(which)-219(is)-219(a)-219(constant)-218(for)-219(speci\002c)-219(models,)-226(the)]TJ 0.98 0 0 1 50.112 192.948 Tm [(comple)15(xity)-204(of)-204(graph)-203(propag)5(ation)-204(for)-204(a)-204(feature)-204(broadcast)-204(layer)]TJ 1.02 0 0 1 50.112 180.993 Tm [(and)-302(a)-302(feature)-303(transform)-302(layer)-302(is)-302(of)]TJ/F25 9.9626 Tf 1 0 0 1 194.071 180.993 Tm [(O)]TJ/F19 9.9626 Tf 8.208 0 Td [(\()]TJ/F22 9.9626 Tf 3.875 0 Td [(F)]TJ/F18 6.9738 Tf 7.79 3.615 Td [(2)]TJ -1.384 -6.824 Td [(\()]TJ/F21 6.9738 Tf 3.114 0 Td [(l)]TJ/F18 6.9738 Tf 2.559 0 Td [(\))]TJ/F22 9.9626 Tf 3.612 3.209 Td [(C)]TJ/F18 6.9738 Tf 7.12 -1.799 Td [(\()]TJ/F21 6.9738 Tf 3.114 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(\))]TJ/F22 9.9626 Tf 3.611 1.799 Td [(C)]TJ/F18 6.9738 Tf 7.121 -1.799 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(+1\))]TJ/F19 9.9626 Tf 13.698 1.799 Td [(\))]TJ/F123 9.9626 Tf 1.02 0 0 1 271.688 180.993 Tm [(and)]TJ/F25 9.9626 Tf 1 0 0 1 50.112 166.935 Tm [(O)]TJ/F19 9.9626 Tf 8.208 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [(F)]TJ/F18 6.9738 Tf 6.407 -1.799 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(\))]TJ/F22 9.9626 Tf 3.612 1.799 Td [(F)]TJ/F18 6.9738 Tf 6.406 -1.799 Td [(\()]TJ/F21 6.9738 Tf 3.114 0 Td [(l)]TJ/F18 6.9738 Tf 2.559 0 Td [(+1\))]TJ/F22 9.9626 Tf 13.699 1.799 Td [(C)]TJ/F18 6.9738 Tf 7.833 3.615 Td [(2)]TJ -0.712 -6.824 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(\))]TJ/F19 9.9626 Tf 3.611 3.209 Td [(\))]TJ/F123 9.9626 Tf 1.017 0 0 1 123.944 166.935 Tm [(,)-245(respecti)24(v)15(ely)64(.)-304(If)-245(we)-245(tak)9(e)]TJ/F22 9.9626 Tf 1 0 0 1 225.28 166.935 Tm [(E)]TJ/F18 6.9738 Tf 7.355 -1.799 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(\))]TJ/F19 9.9626 Tf 6.379 1.799 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(F)]TJ/F18 6.9738 Tf 6.406 -1.799 Td [(\()]TJ/F21 6.9738 Tf 3.114 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(\))]TJ/F22 9.9626 Tf 3.611 1.799 Td [(C)]TJ/F18 6.9738 Tf 7.121 -1.799 Td [(\()]TJ/F21 6.9738 Tf 3.113 0 Td [(l)]TJ/F18 6.9738 Tf 2.56 0 Td [(\))]TJ/F123 9.9626 Tf 0.98 0 0 1 50.112 154.98 Tm [(as)-237(the)-237(number)-237(of)-237(elements)-237(of)-237(the)-238(f)1(eatures,)-241(the)-237(comple)15(xity)-237(for)]TJ 0.982 0 0 1 50.112 143.024 Tm [(calculating)-255(each)-255(sample)-254(is)-255(roughly)-255(of)]TJ/F25 9.9626 Tf 1 0 0 1 198.748 143.024 Tm [(O)]TJ/F19 9.9626 Tf 8.208 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [(E)]TJ/F18 6.9738 Tf 7.929 3.616 Td [(2)]TJ/F19 9.9626 Tf 6.685 -3.616 Td [(+)]TJ/F22 9.9626 Tf 9.964 0 Td [(nF)]TJ/F18 6.9738 Tf 13.77 3.616 Td [(2)]TJ/F19 9.9626 Tf 4.47 -3.616 Td [(\))]TJ/F123 9.9626 Tf 0.982 0 0 1 257.522 143.024 Tm [(,)-255(where)]TJ 1.02 0 0 1 49.753 131.069 Tm [(we)-275(lea)20(v)15(e)-275(out)-275(the)-275(layer)-275(inde)15(x)-275(for)-274(simplicity)63(.)-393(Note)-274(that)-275(the)15(y)]TJ 0.999 0 0 1 50.112 119.114 Tm [(do)-251(not)-251(depend)-251(on)-252(the)-251(task)-251(number)40(,)-251(thus)-251(feature)-251(graphs)-251(ha)20(v)15(e)]TJ 1 0 0 1 50.112 107.159 Tm [(constant)-250(comple)15(xity)-250(with)-250(the)-250(increased)-250(learning)-250(tasks.)]TJ 1.02 0 0 1 62.067 92.955 Tm [(FGN)-249(is)-249(appli)1(cable)-249(e)24(v)15(en)-249(when)-249(the)-248(number)-249(of)-249(features)]TJ/F22 9.9626 Tf 1 0 0 1 278.572 92.955 Tm [(F)]TJ/F123 9.9626 Tf 1.016 0 0 1 50.112 81 Tm [(is)-246(v)14(ery)-246(lar)18(ge.)-306(In)-246(this)-246(case,)-247(we)-246(often)-246(use)-247(a)-246(feature)-246(transform)]TJ
0 g 0 G
0 g 0 G
1.02 0 0 1 308.862 710.037 Tm [(layer)]TJ 1 0 0 1 332.313 710.037 Tm [(\()]TJ
1 0 0 rg 1 0 0 RG
[(8)]TJ
0 g 0 G
[(\))]TJ 1.02 0 0 1 347.068 710.037 Tm [(as)-309(a)-309(feature)-308(e)14(xtractor)-308(to)-309(project)-309(the)-309(ra)15(w)-309(features)]TJ 1.001 0 0 1 308.862 698.082 Tm [(onto)-251(a)-250(lo)25(wer)-251(dimension.)-313(In)-250(the)-251(e)15(xperiments)-251(we)-250(reduced)-251(the)]TJ 1.02 0 0 1 308.862 686.127 Tm [(dimension)-326(of)-327(Cora)-326([)]TJ
0 1 0 rg 0 1 0 RG
1 0 0 1 392.76 686.127 Tm [(37)]TJ
0 g 0 G
1.02 0 0 1 402.723 686.127 Tm [(])-326(from)]TJ/F22 9.9626 Tf 1 0 0 1 432.496 686.127 Tm [(F)]TJ/F18 6.9738 Tf 6.406 -1.799 Td [(\(1\))]TJ/F19 9.9626 Tf 14.994 1.799 Td [(=)-431(1433)]TJ/F123 9.9626 Tf 1.02 0 0 1 489.185 686.127 Tm [(to)]TJ/F22 9.9626 Tf 1 0 0 1 500.407 686.127 Tm [(F)]TJ/F18 6.9738 Tf 6.407 -1.799 Td [(\(2\))]TJ/F19 9.9626 Tf 14.994 1.799 Td [(=)-431(10)]TJ/F123 9.9626 Tf 1.02 0 0 1 543.817 686.127 Tm [(,)]TJ 1 0 0 1 308.503 674.172 Tm [(which)-250(is)-250(also)-250(adopted)-250(by)-250(GCN,)-250(GA)111(T)74(,)-250(APPNP)111(,)-250(SA)40(GE,)-250(etc.)]TJ/F120 11.9552 Tf 0.359 -24.08 Td [(5.)-250(Experiments)]TJ/F120 9.9626 Tf 1.005 0 0 1 308.862 631.107 Tm [(Implementation)-249(Details)]TJ/F123 9.9626 Tf 1.005 0 0 1 414.248 631.107 Tm [(W)80(e)-250(perform)-249(comprehensi)24(v)15(e)-249(tests)]TJ 0.98 0 0 1 308.862 619.152 Tm [(on)-201(popular)-201(graph)-202(datas)1(ets)-202(including)-201(citation)-201(graph)-201(Cora,)-212(Cite-)]TJ 1.02 0 0 1 308.862 607.197 Tm [(seer)39(,)-268(Pubmed)-264([)]TJ
0 1 0 rg 0 1 0 RG
1 0 0 1 369.47 607.197 Tm [(37)]TJ
0 g 0 G
1.02 0 0 1 379.432 607.197 Tm [(],)-269(and)-264(ogbn-arXi)25(v)-264([)]TJ
0 1 0 rg 0 1 0 RG
1 0 0 1 458.104 607.197 Tm [(28)]TJ
0 g 0 G
1.02 0 0 1 468.067 607.197 Tm [(].)-360(F)14(or)-263(each)-264(dataset,)]TJ 1.02 0 0 1 308.503 595.241 Tm [(we)-263(construct)-264(tw)10(o)-264(dif)25(ferent)-263(continua:)-341(data-incremental)-263(and)]TJ 1.02 0 0 1 308.862 583.286 Tm [(class-incremental.)-590(In)-341(da)1(ta-incremental)-341(tasks,)-364(all)-341(samples)]TJ 0.994 0 0 1 308.862 571.331 Tm [(are)-251(streamed)-252(randomly)65(,)-251(while)-251(in)-252(class-incremental)-251(tasks,)-252(all)]TJ 1.02 0 0 1 308.862 559.376 Tm [(samples)-330(from)-331(one)-330(class)-330(are)-331(streamed)-330(before)-330(switching)-331(to)]TJ 1.004 0 0 1 308.862 547.421 Tm [(the)-249(ne)15(xt)-250(class.)-310(In)-249(both)-250(tasks,)-249(each)-250(node)-249(is)-249(only)-250(presented)-249(to)]TJ 1.012 0 0 1 308.862 535.466 Tm [(the)-247(model)-247(once,)]TJ/F130 9.9626 Tf 1.012 0 0 1 375.408 535.466 Tm [(i.e)]TJ/F123 9.9626 Tf 1.012 0 0 1 385.207 535.466 Tm [(.,)-247(a)-247(sample)-246(cannot)-247(be)-247(used)-247(to)-246(update)-247(the)]TJ 1.001 0 0 1 308.862 523.51 Tm [(model)-248(parameters)-249(a)1(g)4(ai)1(n)-249(once)-248(dropped.)-309(F)15(or)-249(this)-248(e)15(xperiment,)]TJ 0.981 0 0 1 308.503 511.555 Tm [(we)-255(implement)-255(a)-255(tw)10(o-layer)-255(feature)-255(graph)-255(netw)11(ork)-255(in)-255(PyT)81(orch)]TJ 1.02 0 0 1 308.862 499.6 Tm [([)]TJ
0 1 0 rg 0 1 0 RG
1 0 0 1 312.246 499.6 Tm [(30)]TJ
0 g 0 G
1.02 0 0 1 322.208 499.6 Tm [(])-245(and)-245(adopt)-245(the)-245(SGD)-244([)]TJ
0 1 0 rg 0 1 0 RG
1 0 0 1 411.413 499.6 Tm [(19)]TJ
0 g 0 G
1.02 0 0 1 421.376 499.6 Tm [(])-245(optimizer)54(.)-304(See)-245(further)-245(detail)1(s)]TJ 1.014 0 0 1 308.862 487.645 Tm [(in)-246(Appendix)]TJ
1 0 0 rg 1 0 0 RG
[-247(A)]TJ
0 g 0 G
[(.)-246(W)78(e)-246(choose)-246(the)-247(most)-246(popular)-247(graph)-246(models)]TJ 1.02 0 0 1 308.862 475.69 Tm [(including)-318(GCN)-317([)]TJ
0 1 0 rg 0 1 0 RG
1 0 0 1 378.547 475.69 Tm [(20)]TJ
0 g 0 G
1.02 0 0 1 388.509 475.69 Tm [(],)-336(GA)109(T)-318([)]TJ
0 1 0 rg 0 1 0 RG
1 0 0 1 424.237 475.69 Tm [(41)]TJ
0 g 0 G
1.02 0 0 1 434.199 475.69 Tm [(],)-336(SA)39(GE)-317([)]TJ
0 1 0 rg 0 1 0 RG
1 0 0 1 476.284 475.69 Tm [(13)]TJ
0 g 0 G
1.02 0 0 1 486.247 475.69 Tm [(],)-336(and)-318(APPNP)]TJ 1.017 0 0 1 308.862 463.735 Tm [([)]TJ
0 1 0 rg 0 1 0 RG
1 0 0 1 312.236 463.735 Tm [(22)]TJ
0 g 0 G
1.017 0 0 1 322.198 463.735 Tm [(])-246(as)-247(our)-246(baseline.)-307(Comparison)-246(with)-246(other)-247(methods)-246(such)]TJ 1.002 0 0 1 308.862 451.779 Tm [(as)-249(SAINT)-250([)]TJ
0 1 0 rg 0 1 0 RG
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