feat: add GAT method

gnn.go

@@ -14,22 +14,20 @@ const (
 	Sample  int     = 10000
 	Batch   int     = 5
 	Dropout float64 = 0.5
-	RateWo  float64 = 0.1
-	RateWi  float64 = 0.1
-	RateB   float64 = 0.1
+	Rate    float64 = 0.1
 )
 
 type (
 	Parameter struct {
-		Wo, Wi, B, A Matrix
+		W, B, A Matrix
 	}
 
 	Layer struct {
-		d       int
-		f       func(Matrix) Matrix
-		p       Parameter
-		D       Vector
-		O, I, E Matrix
+		d    int
+		f    func(Matrix) Matrix
+		p    Parameter
+		D    Vector
+		A, E Matrix
 	}
 )
 
@@ -65,24 +63,35 @@ func GetEmbedding(G Graph, u, k int, l []Layer, train bool) Matrix {
 		}
 		return l[k].E
 	}
-	l[k-1].O, l[k-1].I, l[k].E = MakeMatrix(1, l[k-1].d), MakeMatrix(1, l[k-1].d), MakeMatrix(1, l[k].d)
-	Do, Di := 0, 0
-	for v, w := range G.A[u] {
-		if w == 1 {
-			l[k-1].O.Add(GetEmbedding(G, v, k-1, l, train))
-			Do++
-		} else {
-			l[k-1].I.Add(GetEmbedding(G, v, k-1, l, train))
-			Di++
-		}
-	}
-	if Do > 0 {
-		l[k].E.Add(l[k-1].O.Divide(float64(Do)).Multiply(l[k].p.Wo))
-	}
-	if Di > 0 {
-		l[k].E.Add(l[k-1].I.Divide(float64(Di)).Multiply(l[k].p.Wi))
+	l[k-1].A, l[k].E = MakeMatrix(1, l[k-1].d), MakeMatrix(1, l[k].d)
+	// GCN
+	// deg := 0
+	// for v := range G.A[u] {
+	// 	l[k-1].A.Add(GetEmbedding(G, v, k-1, l, train))
+	// 	deg++
+	// }
+	// l[k].E.Add(GetEmbedding(G, u, k-1, l, train).Multiply(l[k].p.B))
+	// if deg > 0 {
+	// 	l[k].E.Add(l[k-1].A.Divide(float64(deg)).Multiply(l[k].p.W))
+	// }
+	// GAT
+	A := MakeMatrix(0, l[k-1].d)
+	for v := range G.A[u] {
+		A = append(A, GetEmbedding(G, v, k-1, l, train)[0])
 	}
 	l[k].E.Add(GetEmbedding(G, u, k-1, l, train).Multiply(l[k].p.B))
+	if A.N() > 0 {
+		C := MakeMatrix(1, A.N())
+		Me := l[k-1].E[0].Modulus()
+		for i := 0; i < A.N(); i++ {
+			Ma := A[i].Modulus()
+			if Me != 0 && Ma != 0 {
+				C[0][i] = l[k-1].E[0].Dot(A[i]) / Me / Ma
+			}
+		}
+		l[k-1].A.Add(Softmax(C).Multiply(A))
+		l[k].E.Add(l[k-1].A.Multiply(l[k].p.W))
+	}
 	if train && l[k].D != nil {
 		l[k].E.Dropout(l[k].D)
 	}
@@ -108,25 +117,25 @@ func StartRefine(wg *sync.WaitGroup, A, B Matrix, c float64) {
 }
 
 func Train(G Graph) []Layer {
-	p1 := Parameter{MakeRandomMatrix(Input, Hidden), MakeRandomMatrix(Input, Hidden), MakeRandomMatrix(Input, Hidden), MakeRandomMatrix(Input*2, 1)}
-	p2 := Parameter{MakeRandomMatrix(Hidden, Output), MakeRandomMatrix(Hidden, Output), MakeRandomMatrix(Hidden, Output), MakeRandomMatrix(Hidden*2, 1)}
-	l := []Layer{{d: Input}, {d: Hidden, f: ReLU, p: p1}, {d: Output, f: Softmax, p: p2}}
+	p0 := Parameter{A: MakeRandomMatrix(Input*2, 1)}
+	p1 := Parameter{W: MakeRandomMatrix(Input, Hidden), B: MakeRandomMatrix(Input, Hidden), A: MakeRandomMatrix(Hidden*2, 1)}
+	p2 := Parameter{W: MakeRandomMatrix(Hidden, Output), B: MakeRandomMatrix(Hidden, Output)}
+	l := []Layer{{d: Input, p: p0}, {d: Hidden, f: ReLU, p: p1}, {d: Output, f: Softmax, p: p2}}
 	for i := 0; i < Sample; i++ {
 		if i%100 == 0 {
 			fmt.Println("sampling", i)
 		}
 		var wg sync.WaitGroup
 		l[0].D, l[1].D = MakeDropoutVector(Input), MakeDropoutVector(Hidden)
-		DWo2, DWi2, DB2 := MakeMatrix(Hidden, Output), MakeMatrix(Hidden, Output), MakeMatrix(Hidden, Output)
-		DWo1, DWi1, DB1 := MakeMatrix(Input, Hidden), MakeMatrix(Input, Hidden), MakeMatrix(Input, Hidden)
+		DW2, DB2 := MakeMatrix(Hidden, Output), MakeMatrix(Hidden, Output)
+		DW1, DB1 := MakeMatrix(Input, Hidden), MakeMatrix(Input, Hidden)
 		for j := 0; j < Batch; j++ {
 			u := nodeId[rand.Intn(len(nodeId))]
 			GetEmbedding(G, u, 2, l, true)
-			// GCN
-			delta := MakeMatrix(1, Output).Sub(l[2].E)
-			delta[0][G.L[u]] += 1
-			StartCalc(&wg, DWo2, l[1].O, delta)
-			StartCalc(&wg, DWi2, l[1].I, delta)
+			delta := MakeMatrix(1, Output)
+			delta[0][G.L[u]] = 1
+			delta.Sub(l[2].E).Divide(float64(Batch))
+			StartCalc(&wg, DW2, l[1].A, delta)
 			StartCalc(&wg, DB2, l[1].E, delta)
 			delta = delta.Multiply(l[2].p.B.Transpose())
 			for k := 0; k < Hidden; k++ {
@@ -134,18 +143,14 @@ func Train(G Graph) []Layer {
 					delta[0][k] = 0
 				}
 			}
-			StartCalc(&wg, DWo1, l[0].O, delta)
-			StartCalc(&wg, DWi1, l[0].I, delta)
+			StartCalc(&wg, DW1, l[0].A, delta)
 			StartCalc(&wg, DB1, l[0].E, delta)
-			// GAT
 			wg.Wait()
 		}
-		StartRefine(&wg, l[2].p.Wo, DWo2, float64(Batch)/RateWo)
-		StartRefine(&wg, l[2].p.Wi, DWi2, float64(Batch)/RateWi)
-		StartRefine(&wg, l[2].p.B, DB2, float64(Batch)/RateB)
-		StartRefine(&wg, l[1].p.Wo, DWo1, float64(Batch)/RateWo)
-		StartRefine(&wg, l[1].p.Wi, DWi1, float64(Batch)/RateWi)
-		StartRefine(&wg, l[1].p.B, DB1, float64(Batch)/RateB)
+		StartRefine(&wg, l[2].p.W, DW2, 1/Rate)
+		StartRefine(&wg, l[2].p.B, DB2, 1/Rate)
+		StartRefine(&wg, l[1].p.W, DW1, 1/Rate)
+		StartRefine(&wg, l[1].p.B, DB1, 1/Rate)
 		wg.Wait()
 	}
 	return l

test.out

@@ -126,2713 +126,2713 @@ sampling 9600
 sampling 9700
 sampling 9800
 sampling 9900
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+124 / 124 , 1664 / 2584
+100 , 64

vector.go

@@ -1,6 +1,9 @@
 package main
 
-import "math/rand"
+import (
+	"math"
+	"math/rand"
+)
 
 type Vector []float64
 
@@ -28,16 +31,31 @@ func MakeDropoutVector(n int) Vector {
 	return V
 }
 
-func (V Vector) N() int {
-	return len(V)
+func (A Vector) N() int {
+	return len(A)
 }
 
-func (V Vector) Max() (int, float64) {
-	id, max := 0, V[0]
-	for i := 1; i < V.N(); i++ {
-		if V[i] > max {
-			id, max = i, V[i]
+func (A Vector) Max() (int, float64) {
+	id, max := 0, A[0]
+	for i := 1; i < A.N(); i++ {
+		if A[i] > max {
+			id, max = i, A[i]
 		}
 	}
 	return id, max
 }
+
+func (A Vector) Dot(B Vector) float64 {
+	if A.N() != B.N() {
+		panic("Incompatible Dimensions")
+	}
+	sum := 0.
+	for i := 0; i < A.N(); i++ {
+		sum += A[i] * B[i]
+	}
+	return sum
+}
+
+func (A Vector) Modulus() float64 {
+	return math.Sqrt(A.Dot(A))
+}