diff --git a/src/heretic/model.py b/src/heretic/model.py
index 6419550..933bc7a 100644
--- a/src/heretic/model.py
+++ b/src/heretic/model.py
@@ -192,7 +192,7 @@ class Model:
                 projector = torch.outer(
                     layer_refusal_direction,
                     layer_refusal_direction,
-                )
+                ).to(self.model.dtype)
 
                 for matrix in matrices:
                     # In-place subtraction is safe as we're not using Autograd.
@@ -265,7 +265,7 @@ class Model:
         hidden_states = outputs.hidden_states[0]
 
         # The returned tensor has shape (prompt, layer, component).
-        return torch.stack(
+        residuals = torch.stack(
             # layer_hidden_states has shape (prompt, position, component),
             # so this extracts the hidden states at the end of each prompt,
             # and stacks them up over the layers.
@@ -273,6 +273,10 @@ class Model:
             dim=1,
         )
 
+        # Upcast the data type to avoid precision (bfloat16) or range (float16)
+        # problems during calculations involving residual vectors.
+        return residuals.to(torch.float32)
+
     def get_residuals_batched(self, prompts: list[str]) -> torch.Tensor:
         residuals = []