diff --git a/CHANGELOG.md b/CHANGELOG.md
index 69116c24..e25a2a70 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -8,6 +8,13 @@ changelog does not include internal changes that do not affect the user.
 
 ## [Unreleased]
 
+### Fixed
+
+- Fixed `ExcessMTL` and `ExcessMTLWeighting` producing `nan` weights for the rest of the run when a
+  task had a zero gradient at the call that sets its baseline excess risk. The exponentiated
+  gradient update is now computed in log space, so a very large excess risk saturates the weights
+  instead of overflowing.
+
 ## [0.17.1] - 2026-09-23
 
 ### Fixed
diff --git a/src/torchjd/aggregation/_excess_mtl.py b/src/torchjd/aggregation/_excess_mtl.py
index ff8062fd..40b8a807 100644
--- a/src/torchjd/aggregation/_excess_mtl.py
+++ b/src/torchjd/aggregation/_excess_mtl.py
@@ -120,10 +120,11 @@ def forward(self, matrix: Matrix, /) -> Tensor:
         else:
             w = w / (self._initial_w + 1e-7)  # Scale processing (Section 3.2)
 
-        # Exponentiated gradient weight update (Equation 9)
+        # Exponentiated gradient weight update (Equation 9), done in log space so that a very
+        # large excess risk (e.g. a task whose baseline excess risk was zero) saturates the
+        # weights instead of overflowing to inf and turning them into nan for good.
         weights = cast(Tensor, self._weights)
-        weights = weights * torch.exp(w * self._robust_step_size)
-        weights = weights / weights.sum()
+        weights = torch.softmax(torch.log(weights) + w * self._robust_step_size, dim=0)
         self._weights = weights
         return weights
 
diff --git a/tests/unit/aggregation/test_excess_mtl.py b/tests/unit/aggregation/test_excess_mtl.py
index 04367062..c46c5a3f 100644
--- a/tests/unit/aggregation/test_excess_mtl.py
+++ b/tests/unit/aggregation/test_excess_mtl.py
@@ -1,3 +1,5 @@
+from typing import cast
+
 import torch
 from pytest import mark, raises
 from torch import Tensor
@@ -233,3 +235,44 @@ def test_excess_mtl_reset_delegates() -> None:
     agg(J)
     agg.reset()
     assert_close(first, agg(J))
+
+
+def test_zero_baseline_excess_risk_keeps_weights_finite() -> None:
+    """A task with a zero gradient at the baseline call must not poison the weights with nan."""
+    weighting = ExcessMTLWeighting()
+    first = randn_(2, 5)
+    first[1] = 0.0
+    weighting(first)
+
+    weights = weighting(randn_(2, 5))
+
+    assert torch.isfinite(weights).all()
+    assert_close(weights.sum(), tensor_(1.0))
+    assert weights[1] > weights[0]
+
+
+def test_all_zero_matrix_at_baseline_keeps_weights_finite() -> None:
+    weighting = ExcessMTLWeighting()
+    weighting(torch.zeros(3, 4))
+
+    weights = weighting(randn_(3, 4))
+
+    assert torch.isfinite(weights).all()
+    assert_close(weights.sum(), tensor_(1.0))
+
+
+def test_log_space_update_matches_direct_formula() -> None:
+    """On well-behaved inputs the update is the same as weights * exp(eta * w), normalized."""
+    weighting = ExcessMTLWeighting(robust_step_size=0.5)
+    weighting(randn_(3, 6))
+    before = cast(Tensor, weighting._weights).clone()
+    matrix = randn_(3, 6)
+
+    weights = weighting(matrix)
+
+    sq_grad_sum = cast(Tensor, weighting._sq_grad_sum)
+    w = (matrix**2 / torch.sqrt(sq_grad_sum + 1e-7)).sum(dim=1)
+    w = w / (cast(Tensor, weighting._initial_w) + 1e-7)
+    expected = before * torch.exp(0.5 * w)
+    expected = expected / expected.sum()
+    assert_close(weights, expected)