Engine prototype #13

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Vectornaut wants to merge 117 commits from engine-proto into main
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@ -120,6 +120,7 @@ function realize_gram(
# find negative gradient of loss function
neg_grad = 4*Q*L*Δ_proj
slope = norm(neg_grad)
dir = neg_grad / slope
# store current position, loss, and slope
L_last = L
@ -135,7 +136,7 @@ function realize_gram(
empty!(history.last_line_loss)
for backoff_steps in 0:max_backoff_steps
history.stepsize[end] = stepsize
L = L_last + stepsize * neg_grad
L = L_last + stepsize * dir
Δ_proj = proj_diff(gram, L'*Q*L)
loss = dot(Δ_proj, Δ_proj)
improvement = loss_last - loss