diff --git a/engine-proto/gram-test/Engine.jl b/engine-proto/gram-test/Engine.jl
index e8bda9c..2fb41e0 100644
--- a/engine-proto/gram-test/Engine.jl
+++ b/engine-proto/gram-test/Engine.jl
@@ -104,7 +104,7 @@ function realize_gram(
   
   # do gradient descent
   Δ_proj = proj_diff(gram, L'*Q*L)
-  loss = norm(Δ_proj)
+  loss = dot(Δ_proj, Δ_proj)
   for step in 1:max_descent_steps
     # stop if the loss is tolerably low
     if loss < tol
@@ -128,7 +128,7 @@ function realize_gram(
       history.stepsize[end] = stepsize
       L = L_last + stepsize * neg_grad
       Δ_proj = proj_diff(gram, L'*Q*L)
-      loss = norm(Δ_proj)
+      loss = dot(Δ_proj, Δ_proj)
       improvement = loss_last - loss
       if improvement >= target_improvement * stepsize * slope
         history.backoff_steps[end] = backoff_steps