diff --git a/.jules/bolt.md b/.jules/bolt.md
new file mode 100644
index 0000000..80130e2
--- /dev/null
+++ b/.jules/bolt.md
@@ -0,0 +1,3 @@
+## 2025-05-15 - [Numerical Precision in Vectorized Distance Calculation]
+**Learning:** Using the expansion formula ||a-b||^2 = ||a||^2 + ||b||^2 - 2ab for vectorized Euclidean distance is much faster but can produce small negative values due to floating-point precision limits.
+**Action:** Always use np.maximum(dists_sq, 0) when calculating squared distances with this formula to ensure numerical stability.
diff --git a/face_engine/models/basic_estimator.py b/face_engine/models/basic_estimator.py
index fbbf2b9..2e46490 100644
--- a/face_engine/models/basic_estimator.py
+++ b/face_engine/models/basic_estimator.py
@@ -20,21 +20,40 @@ 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 for faster distance calculation in predict
+        self.norms_sq = np.sum(self.embeddings**2, 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])
+        embeddings = np.asarray(embeddings)
+        if len(embeddings) == 0:
+            return [], []
+
+        # Using expansion formula: ||a-b||^2 = ||a||^2 + ||b||^2 - 2ab
+        # to calculate squared Euclidean distances in a vectorized way.
+        input_norms_sq = np.sum(embeddings**2, axis=1, keepdims=True)
+
+        # Handle cases where model might have been loaded without pre-calculated norms
+        fitted_norms_sq = getattr(self, "norms_sq", None)
+        if fitted_norms_sq is None:
+            fitted_norms_sq = np.sum(self.embeddings**2, axis=1)
+
+        # Vectorized squared distance calculation: (M, 1) + (N,) - 2 * (M, N) -> (M, N)
+        dists_sq = input_norms_sq + fitted_norms_sq - 2 * np.dot(embeddings, self.embeddings.T)
+
+        # Ensure numerical stability (prevent 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):