diff --git a/include/suboptimal/autodiff/Variable.h b/include/suboptimal/autodiff/Variable.h
index 9b9369c..be17817 100644
--- a/include/suboptimal/autodiff/Variable.h
+++ b/include/suboptimal/autodiff/Variable.h
@@ -66,6 +66,11 @@ struct Variable {
    */
   static Variable Constant(double value);
 
+  /**
+   * Updates the stored expression graph of the variable
+   */
+  void updateGraph() const;
+
   /**
    * Updates the value of the variable, traversing the expression tree and updating all expressions and variables this
    * variable depends on
diff --git a/src/autodiff/Expression.cpp b/src/autodiff/Expression.cpp
index 7cedfe2..ef969cc 100644
--- a/src/autodiff/Expression.cpp
+++ b/src/autodiff/Expression.cpp
@@ -85,7 +85,10 @@ void Expression::updateValue() {
     // Expression represents either a constant or an independent variable, so no update is needed
     return;
   }
-  updateChildren();
+
+  if (children.empty() && (lhs != nullptr || rhs != nullptr)) {
+    updateChildren();
+  }
 
   for (const auto expr : std::ranges::reverse_view(children)) {
     if (expr->isUnary()) {
diff --git a/src/autodiff/Variable.cpp b/src/autodiff/Variable.cpp
index 95116c0..2210cd8 100644
--- a/src/autodiff/Variable.cpp
+++ b/src/autodiff/Variable.cpp
@@ -16,6 +16,10 @@ Variable Variable::Constant(double value) {
   return std::make_shared<Expression>(value);
 }
 
+void Variable::updateGraph() const {
+  expr->updateChildren();
+}
+
 void Variable::updateValue() const {
   expr->updateValue();
 }
diff --git a/src/autodiff/derivatives.cpp b/src/autodiff/derivatives.cpp
index c64b353..bbe00a3 100644
--- a/src/autodiff/derivatives.cpp
+++ b/src/autodiff/derivatives.cpp
@@ -10,6 +10,8 @@
 
 namespace suboptimal {
 Gradient::Gradient(const Variable& var, const Eigen::Ref<const VectorXv>& wrt) : var{var}, wrt{wrt}, value(wrt.size()) {
+  var.updateGraph();
+
   std::ranges::for_each(wrt, [](const Variable& v) { v.expr->adjoint = 0.0; });
   var.expr->updateAdjoints();
   for (int i = 0; i < wrt.size(); i++) {
@@ -39,8 +41,6 @@ VectorXv Gradient::getExpr() {
     }
   }
 
-  var.expr->updateChildren();
-
   // Initialize adjoint expressions
   std::ranges::for_each(var.expr->children,
                         [](Expression* expr) { expr->adjoint_expr = std::make_shared<Expression>(0.0); });