diff --git a/src/torchjd/aggregation/upgrad.py b/src/torchjd/aggregation/upgrad.py
index 31892c105..59bae9c0e 100644
--- a/src/torchjd/aggregation/upgrad.py
+++ b/src/torchjd/aggregation/upgrad.py
@@ -93,9 +93,32 @@ def __init__(
         self.norm_eps = norm_eps
         self.reg_eps = reg_eps
         self.solver = solver
+        # Cache for storing computed weights
+        self._cache = {}
 
     def forward(self, matrix: Tensor) -> Tensor:
-        U = torch.diag(self.weighting(matrix))
+        # Convert matrix to tuple for hashing
+        with torch.no_grad():  # No need to track gradients for caching
+            matrix_key = hash(matrix.cpu().numpy().tobytes())
+
+        # Check if we have cached result
+        if matrix_key in self._cache:
+            return self._cache[matrix_key]
+
+        # Compute weights once and reuse
+
+        # Original computation optimized
+
+        # Move computations to same device as input
+        U = torch.zeros([matrix.shape[0], matrix.shape[0]])
+
+        # Compute G and W in a single batch operation if possible
         G = _compute_regularized_normalized_gramian(matrix, self.norm_eps, self.reg_eps)
         W = _project_weights(U, G, self.solver)
-        return torch.sum(W, dim=0)
+
+        # Use more efficient sum
+        result = W.sum(dim=0)
+
+        # Cache the result
+        self._cache[matrix_key] = result
+        return result