diff --git a/shimmer/modules/global_workspace.py b/shimmer/modules/global_workspace.py
index 7aec98ff..852bc1cc 100644
--- a/shimmer/modules/global_workspace.py
+++ b/shimmer/modules/global_workspace.py
@@ -684,6 +684,7 @@ def __init__(
         learn_logit_scale: bool = False,
         use_normalized_constrastive: bool = True,
         contrastive_loss: ContrastiveLossType | None = None,
+        precision_softmax_temp: float = 0.01,
     ) -> None:
         """
         Initializes a Global Workspace
@@ -712,6 +713,8 @@ def __init__(
             contrastive_loss (`ContrastiveLossType | None`): a contrastive loss
                 function used for alignment. `learn_logit_scale` will not affect custom
                 contrastive losses.
+            precision_softmax_temp (`float`): temperature to use in softmax of
+                precision
         """
         domain_mods = freeze_domain_modules(domain_mods)
 
@@ -722,6 +725,7 @@ def __init__(
             gw_decoders,
             sensitivity_selection,
             sensitivity_precision,
+            precision_softmax_temp,
         )
 
         selection_mod = FixedSharedSelection()
diff --git a/shimmer/modules/gw_module.py b/shimmer/modules/gw_module.py
index 9c1922eb..3dd1b600 100644
--- a/shimmer/modules/gw_module.py
+++ b/shimmer/modules/gw_module.py
@@ -338,6 +338,7 @@ def __init__(
         gw_decoders: Mapping[str, nn.Module],
         sensitivity_selection: float = 1,
         sensitivity_precision: float = 1,
+        precision_softmax_temp: float = 0.01,
     ) -> None:
         """
         Initializes the GWModuleBayesian.
@@ -353,6 +354,8 @@ def __init__(
                  GW representation to a unimodal latent representation.
             sensitivity_selection (`float`): sensivity coef $c'_1$
             sensitivity_precision (`float`): sensitivity coef $c'_2$
+            precision_softmax_temp (`float`): temperature to use in softmax of
+                precision
         """
         super().__init__(domain_modules, workspace_dim, gw_encoders, gw_decoders)
 
@@ -366,6 +369,7 @@ def __init__(
 
         self.sensitivity_selection = sensitivity_selection
         self.sensitivity_precision = sensitivity_precision
+        self.precision_softmax_temp = precision_softmax_temp
 
     def get_precision(self, domain: str, x: torch.Tensor) -> torch.Tensor:
         """
@@ -437,7 +441,9 @@ def fuse(
             domains.append(x[domain])
         combined_scores = compute_fusion_scores(
             torch.stack(scores).unsqueeze(-1),
-            torch.softmax(torch.stack(precisions), dim=0),
+            torch.softmax(
+                torch.tanh(torch.stack(precisions)) * self.precision_softmax_temp, dim=0
+            ),
             self.sensitivity_selection,
             self.sensitivity_precision,
         )
diff --git a/shimmer/modules/losses.py b/shimmer/modules/losses.py
index 7ba5dbf5..08273a93 100644
--- a/shimmer/modules/losses.py
+++ b/shimmer/modules/losses.py
@@ -312,12 +312,14 @@ def contrastive_loss_bayesian(
                 loss_name = f"contrastive_{domain1_name}_and_{domain2_name}"
                 z2 = gw_mod.encode({domain2_name: domain2})[domain2_name]
                 z2_precision = gw_mod.get_precision(domain2_name, domain2)
-                coef = torch.stack([z1_precision, z2_precision]).softmax(dim=0)
-                loss_output = contrastive_fn(
-                    z1 * coef[0] * coef[1], z2 * coef[0] * coef[1]
+                coef = torch.softmax(
+                    gw_mod.precision_softmax_temp
+                    * torch.stack([z1_precision, z2_precision]),
+                    dim=0,
                 )
+                norm = torch.sqrt(coef[0] * coef[1])
+                loss_output = contrastive_fn(z1 * norm, z2 * norm)
                 loss_output_no_norm = contrastive_fn(z1, z2)
-
                 losses[loss_name] = loss_output.loss
                 metrics.update(
                     {f"{loss_name}_{k}": v for k, v in loss_output.metrics.items()}