From a203f6bc1b37c6d10693a2011000d9fbfd87e56f Mon Sep 17 00:00:00 2001
From: Aaron Fenyes <aaron.fenyes@fareycircles.ooo>
Date: Thu, 18 Sep 2025 13:20:04 -0700
Subject: [PATCH] Keep optimizing until the total loss is stationary

---
 app-proto/src/engine.rs | 18 +++++++++++-------
 1 file changed, 11 insertions(+), 7 deletions(-)

diff --git a/app-proto/src/engine.rs b/app-proto/src/engine.rs
index 441d854..e51fcbc 100644
--- a/app-proto/src/engine.rs
+++ b/app-proto/src/engine.rs
@@ -413,7 +413,9 @@ pub fn realize_gram(
     let scale_adjustment = (gram.0.len() as f64).sqrt();
     let tol = scale_adjustment * scaled_tol;
     
-    // initialize the softness parameter
+    // set up constants and variables related to minimizing the soft loss
+    const GRAD_TOL: f64 = 1e-9;
+    let mut grad_size = f64::INFINITY;
     let mut softness = 1.0;
     
     // convert the frozen indices to stacked format
@@ -468,10 +470,13 @@ pub fn realize_gram(
             hess[(k, k)] = 1.0;
         }
         
-        // stop if the hard loss is tolerably low
+        // stop if the hard loss is tolerably low and the total loss is close to
+        // stationary. we use `neg_grad_stacked` to measure the size of the
+        // gradient because it's been projected onto the frozen subspace
         history.config.push(state.config.clone());
         history.scaled_loss.push(state.loss_hard / scale_adjustment);
-        if state.loss_hard < tol { break; }
+        grad_size = neg_grad_stacked.norm_squared();
+        if state.loss_hard < tol && grad_size < GRAD_TOL { break; }
         
         // compute the Newton step
         /* TO DO */
@@ -509,15 +514,14 @@ pub fn realize_gram(
         
         // if we're near a minimum of the total loss, but the hard loss still
         // isn't tolerably low, make the soft constraints softer
-        const GRAD_TOL: f64 = 1e-4;
+        const SOFTNESS_BACKOFF_THRESHOLD: f64 = 1e-6;
         const SOFTNESS_BACKOFF: f64 = 0.5;
-        if neg_grad.norm_squared() < GRAD_TOL {
-            // if we're close to a minimum, make the soft constraints softer
+        if state.loss_hard >= tol && grad_size < SOFTNESS_BACKOFF_THRESHOLD {
             softness *= SOFTNESS_BACKOFF;
             console_log!("Softness decreased to {softness}");
         }
     }
-    let result = if state.loss_hard < tol {
+    let result = if state.loss_hard < tol && grad_size < GRAD_TOL {
         // express the uniform basis in the standard basis
         const UNIFORM_DIM: usize = 4;
         let total_dim_unif = UNIFORM_DIM * assembly_dim;