diff --git a/microgopt.go b/microgopt.go
index 5431c4c..ef471ad 100644
--- a/microgopt.go
+++ b/microgopt.go
@@ -284,22 +284,19 @@ func gpt(tokenId int, posId int, keys [][][]*value, values [][][]*value) []*valu
 type value struct {
 	data       float64
 	grad       float64 // implicitly 0 to start
-	children   []*value
-	localGrads []*value
-}
-
-// this lets us build a set-like map with our Values.
-// If the slices were removed from the struct, that would make this method irrelevant.
-func (v *value) toKey() string {
-	k := fmt.Sprintf("%+v", v)
-	return k
+	lChild     *value
+	rChild     *value
+	lLocalGrad *value
+	rLocalGrad *value
 }
 
 func (v *value) Add(other *value) *value {
 	return &value{
 		data:       v.data + other.data,
-		children:   []*value{v, other},
-		localGrads: []*value{{data: 1.0}, {data: 1.0}},
+		lChild:     v,
+		rChild:     other,
+		lLocalGrad: &value{data: 1.0},
+		rLocalGrad: &value{data: 1.0},
 	}
 }
 
@@ -314,22 +311,20 @@ func (v *value) Div(other *value) *value {
 func (v *value) Mul(other *value) *value {
 	// note the swap here: children are stored as v, other but grads are other, v
 	return &value{
-		data:     v.data * other.data,
-		children: []*value{v, other},
-		localGrads: []*value{
-			{data: other.data},
-			{data: v.data},
-		},
+		data:       v.data * other.data,
+		rChild:     v,
+		lChild:     other,
+		rLocalGrad: &value{data: other.data},
+		lLocalGrad: &value{data: v.data},
 	}
 }
 
 func (v *value) Pow(other *value) *value {
 	return &value{
-		data:     math.Pow(v.data, other.data),
-		children: []*value{v},
-		localGrads: []*value{
-			other.Mul(&value{data: math.Pow(v.data, other.Sub(&value{data: 1}).data)}),
-		}}
+		data:       math.Pow(v.data, other.data),
+		rChild:     v,
+		rLocalGrad: other.Mul(&value{data: math.Pow(v.data, other.Sub(&value{data: 1}).data)}),
+	}
 }
 
 func (v *value) Neg() *value {
@@ -338,45 +333,41 @@ func (v *value) Neg() *value {
 
 func (v *value) Log() *value {
 	return &value{
-		data:     math.Log(v.data),
-		children: []*value{v},
-		localGrads: []*value{
-			(&value{data: 1}).Div(v),
-		},
+		data:       math.Log(v.data),
+		rChild:     v,
+		rLocalGrad: (&value{data: 1}).Div(v),
 	}
 }
 
 func (v *value) Exp() *value {
 	return &value{
-		data:     math.Exp(v.data),
-		children: []*value{v},
-		localGrads: []*value{
-			{data: math.Exp(v.data)},
-		},
+		data:       math.Exp(v.data),
+		rChild:     v,
+		rLocalGrad: &value{data: math.Exp(v.data)},
 	}
 }
 
 func (v *value) Relu() *value {
 	return &value{
-		data:     max(v.data, 0),
-		children: []*value{v},
-		localGrads: []*value{
-			{data: btof(v.data > 0)},
-		},
+		data:       max(v.data, 0),
+		rChild:     v,
+		rLocalGrad: &value{data: btof(v.data > 0)},
 	}
 }
 
 func (v *value) Backward() {
 	topo := []*value{}
-	visited := map[string]struct{}{}
+	visited := map[*value]struct{}{}
 
 	var buildTopo func(v *value)
 	buildTopo = func(v *value) {
-		k := v.toKey()
-		if _, ok := visited[k]; !ok {
-			visited[k] = struct{}{}
-			for _, child := range v.children {
-				buildTopo(child)
+		if _, ok := visited[v]; !ok {
+			visited[v] = struct{}{}
+			if v.rChild != nil {
+				buildTopo(v.rChild)
+			}
+			if v.lChild != nil {
+				buildTopo(v.lChild)
 			}
 			topo = append(topo, v)
 		}
@@ -384,8 +375,11 @@ func (v *value) Backward() {
 	buildTopo(v)
 	v.grad = 1.0
 	for _, v := range slices.Backward(topo) {
-		for i := range v.children {
-			v.children[i].grad += v.localGrads[i].data * v.grad
+		if v.rChild != nil {
+			v.rChild.grad += v.rLocalGrad.data * v.grad
+		}
+		if v.lChild != nil {
+			v.lChild.grad += v.lLocalGrad.data * v.grad
 		}
 	}
 }