diff --git a/.jules/bolt.md b/.jules/bolt.md
new file mode 100644
index 0000000..516b516
--- /dev/null
+++ b/.jules/bolt.md
@@ -0,0 +1,3 @@
+## 2025-05-15 - Vectorizing Euclidean Distance with Expansion Formula
+**Learning:** Using the expansion formula $||a-b||^2 = ||a||^2 + ||b||^2 - 2ab$ for vectorized distance calculation provides a significant speedup (~7x-17x) compared to per-query loops. However, it can introduce small negative values due to floating-point precision errors (subtractive cancellation), which must be handled with `np.maximum(dists_sq, 0)`.
+**Action:** Always use `np.maximum(dists_sq, 0)` when using the expansion formula and allow for small `rtol`/`atol` in tests.
diff --git a/face_engine/models/basic_estimator.py b/face_engine/models/basic_estimator.py
index fbbf2b9..e4aad75 100644
--- a/face_engine/models/basic_estimator.py
+++ b/face_engine/models/basic_estimator.py
@@ -18,23 +18,39 @@ class BasicEstimator(Estimator, name="basic"):
     def __init__(self):
         self.embeddings = None
         self.class_names = None
+        self.fitted_norms_sq = 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 calculation
+        self.fitted_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 embeddings.size == 0:
+            return [], []
+
+        # Vectorized Euclidean distance using the expansion: ||a-b||^2 = ||a||^2 + ||b||^2 - 2ab
+        # A: self.embeddings (N x D), B: embeddings (M x D)
+        # Resulting distances matrix: (M x N)
+        query_norms_sq = np.sum(embeddings**2, axis=1)
+        dot_product = np.dot(embeddings, self.embeddings.T)
+
+        # dists_sq = query_norms_sq[:, None] + fitted_norms_sq[None, :] - 2 * dot_product
+        dists_sq = query_norms_sq[:, np.newaxis] + self.fitted_norms_sq - 2 * dot_product
+        # Handle potential 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(indices)), 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):
@@ -46,3 +62,7 @@ def load(self, dirname):
         name = "%s.estimator.%s" % (self.name, "p")
         with open(os.path.join(dirname, name), "rb") as file:
             self.__dict__.update(pickle.load(file))
+
+        # Re-calculate fitted_norms_sq for backward compatibility
+        if self.embeddings is not None and self.fitted_norms_sq is None:
+            self.fitted_norms_sq = np.sum(self.embeddings**2, axis=1)