diff --git a/.jules/bolt.md b/.jules/bolt.md
new file mode 100644
index 0000000..f394bdc
--- /dev/null
+++ b/.jules/bolt.md
@@ -0,0 +1,3 @@
+## 2025-05-21 - [Vectorized Distance Numerical Precision]
+**Learning:** Using the expansion formula ||a-b||^2 = ||a||^2 + ||b||^2 - 2ab for vectorized distance calculation provides significant speedup but can introduce small floating-point discrepancies (negative values) due to subtractive cancellation.
+**Action:** Always use np.maximum(dists_sq, 0) when using this formula to ensure distances are non-negative.
diff --git a/face_engine/models/basic_estimator.py b/face_engine/models/basic_estimator.py
index fbbf2b9..3344cf0 100644
--- a/face_engine/models/basic_estimator.py
+++ b/face_engine/models/basic_estimator.py
@@ -20,21 +20,43 @@ def __init__(self):
         self.class_names = None
 
     def fit(self, embeddings, class_names, **kwargs):
-        self.embeddings = embeddings
+        self.embeddings = np.asarray(embeddings)
         self.class_names = class_names
+        # Pre-calculate squared norms of fitted embeddings for faster distance computation
+        self.norms_sq = np.sum(np.square(self.embeddings), axis=1)
 
     def predict(self, embeddings):
         if self.class_names is None:
             raise TrainError("Model is not fitted yet!")
 
-        scores = []
-        class_names = []
-        for embedding in embeddings:
-            distances = np.linalg.norm(self.embeddings - embedding, axis=1)
-            index = np.argmin(distances)
-            score = np.exp(-0.5 * distances[index] ** 2)
-            scores.append(score)
-            class_names.append(self.class_names[index])
+        # Ensure embeddings is a numpy array
+        embeddings = np.asarray(embeddings)
+
+        # Vectorized distance calculation using the expansion formula:
+        # ||a - b||^2 = ||a||^2 + ||b||^2 - 2 * a . b
+        # This is significantly faster than looping and using np.linalg.norm.
+
+        # Get pre-calculated squared norms of fitted embeddings
+        # Use getattr for backward compatibility with models fitted in older versions
+        norms_sq_fitted = getattr(self, "norms_sq", None)
+        if norms_sq_fitted is None:
+            norms_sq_fitted = np.sum(np.square(self.embeddings), axis=1)
+
+        norms_sq_input = np.sum(np.square(embeddings), axis=1)
+        dot_product = np.dot(embeddings, self.embeddings.T)
+
+        # dists_sq shape: (n_input, n_fitted)
+        dists_sq = norms_sq_input[:, np.newaxis] + norms_sq_fitted - 2 * dot_product
+
+        # Clip to 0 to avoid tiny negative values due to floating point precision
+        dists_sq = np.maximum(dists_sq, 0)
+
+        indices = np.argmin(dists_sq, axis=1)
+        min_dists_sq = dists_sq[np.arange(len(embeddings)), indices]
+
+        scores = np.exp(-0.5 * min_dists_sq).tolist()
+        class_names = [self.class_names[i] for i in indices]
+
         return scores, class_names
 
     def save(self, dirname):