diff --git a/CHANGELOG.md b/CHANGELOG.md
index c21064e48..faa29afc5 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -17,6 +17,11 @@ changes that do not affect the user.
 - Refactored the underlying optimization problem that `UPGrad` and `DualProj` have to solve to
   project onto the dual cone. This may minimally affect the output of these aggregators.
 
+### Fixed
+- Removed arbitrary exception handling in `IMTLG` and `AlignedMTL` when the computation fails. In
+  practice, this fix should only affect some matrices with extremely large values, which should
+  not usually happen.
+
 ## [0.5.0] - 2025-02-01
 
 ### Added
diff --git a/src/torchjd/aggregation/aligned_mtl.py b/src/torchjd/aggregation/aligned_mtl.py
index c1423b65e..b1f5f8628 100644
--- a/src/torchjd/aggregation/aligned_mtl.py
+++ b/src/torchjd/aggregation/aligned_mtl.py
@@ -27,7 +27,6 @@
 
 import torch
 from torch import Tensor
-from torch.linalg import LinAlgError
 
 from ._pref_vector_utils import _pref_vector_to_str_suffix, _pref_vector_to_weighting
 from .bases import _WeightedAggregator, _Weighting
@@ -102,12 +101,7 @@ def forward(self, matrix: Tensor) -> Tensor:
     def _compute_balance_transformation(G: Tensor) -> Tensor:
         M = G.T @ G
 
-        try:
-            lambda_, V = torch.linalg.eigh(M, UPLO="U")  # More modern equivalent to torch.symeig
-        except LinAlgError:  # This can happen when the matrix has extremely large values
-            identity = torch.eye(len(M), dtype=M.dtype, device=M.device)
-            return identity
-
+        lambda_, V = torch.linalg.eigh(M, UPLO="U")  # More modern equivalent to torch.symeig
         tol = torch.max(lambda_) * len(M) * torch.finfo().eps
         rank = sum(lambda_ > tol)
 
diff --git a/src/torchjd/aggregation/imtl_g.py b/src/torchjd/aggregation/imtl_g.py
index 291edeb6a..f4fb82322 100644
--- a/src/torchjd/aggregation/imtl_g.py
+++ b/src/torchjd/aggregation/imtl_g.py
@@ -39,13 +39,9 @@ class _IMTLGWeighting(_Weighting):
 
     def forward(self, matrix: Tensor) -> Tensor:
         d = torch.linalg.norm(matrix, dim=1)
-
-        try:
-            v = torch.linalg.pinv(matrix @ matrix.T) @ d
-        except RuntimeError:  # This can happen when the matrix has extremely large values
-            v = torch.ones(matrix.shape[0], device=matrix.device, dtype=matrix.dtype)
-
+        v = torch.linalg.pinv(matrix @ matrix.T) @ d
         v_sum = v.sum()
+
         if v_sum.abs() < 1e-12:
             weights = torch.zeros_like(v)
         else: