diff --git a/users/zeyer/experiments/exp2024_04_23_baselines/ctc.py b/users/zeyer/experiments/exp2024_04_23_baselines/ctc.py
index afca16694..86af14ded 100644
--- a/users/zeyer/experiments/exp2024_04_23_baselines/ctc.py
+++ b/users/zeyer/experiments/exp2024_04_23_baselines/ctc.py
@@ -2170,6 +2170,13 @@ def __init__(
             # - static_prior is supposed to be static, also with non_critical_for_restore=True.
             _grad_prior_dim = self.target_dim if self.log_prob_normed_grad_exclude_blank else self.wb_target_dim
             self.grad_prior = rf.Parameter([_grad_prior_dim], auxiliary=True, initial=1.0 / _grad_prior_dim.dimension)
+            if self.prior_running_mean_per_layer:
+                for i in enc_aux_logits:
+                    setattr(
+                        self,
+                        f"grad_prior_{i}",
+                        rf.Parameter([_grad_prior_dim], auxiliary=True, initial=1.0 / _grad_prior_dim.dimension),
+                    )
 
         self.feature_batch_norm = None
         if config.bool("feature_batch_norm", False):
@@ -2311,7 +2318,7 @@ def log_probs_wb_from_logits(self, logits: Tensor, *, aux_layer: Optional[int] =
                 logits, axis=self.wb_target_dim, out_dims=[self.target_dim, dummy_blank_feat_dim]
             )
             log_probs_wo_blank = rf.log_softmax(logits_wo_blank, axis=self.target_dim)
-            log_probs_wo_blank = self._maybe_apply_on_log_probs(log_probs_wo_blank)
+            log_probs_wo_blank = self._maybe_apply_on_log_probs(log_probs_wo_blank, aux_layer=aux_layer)
             if self.blank_logit_shift:
                 logits_blank += self.blank_logit_shift
             log_probs_blank = rf.log_sigmoid(logits_blank)
@@ -2338,7 +2345,7 @@ def _update_running_stats():
 
             rf.cond(rf.get_run_ctx().train_flag, _update_running_stats, lambda: None)
 
-        log_probs = self._maybe_apply_on_log_probs(log_probs)
+        log_probs = self._maybe_apply_on_log_probs(log_probs, aux_layer=aux_layer)
         if self.ctc_am_scale == 1 and self.ctc_prior_scale == 0:  # fast path
             return log_probs
         log_probs_am = log_probs
@@ -2387,16 +2394,17 @@ def _update_running_stats():
             log_probs -= log_prob_prior * self.ctc_prior_scale
         return log_probs
 
-    def _maybe_apply_on_log_probs(self, log_probs: Tensor) -> Tensor:
+    def _maybe_apply_on_log_probs(self, log_probs: Tensor, *, aux_layer: Optional[int] = None) -> Tensor:
         """
         :param log_probs: either with blank or without blank
+        :param aux_layer:
         :return: log probs, maybe some smoothing applied (all on gradients so far, not on log probs itself)
         """
         assert log_probs.feature_dim in (self.wb_target_dim, self.target_dim)
         if not self.out_blank_separated:
             assert log_probs.feature_dim == self.wb_target_dim
 
-        log_probs = self._maybe_apply_log_probs_normed_grad(log_probs)
+        log_probs = self._maybe_apply_log_probs_normed_grad(log_probs, aux_layer=aux_layer)
 
         if self.ctc_label_smoothing_exclude_blank:
             if self.out_blank_separated:
@@ -2412,7 +2420,7 @@ def _maybe_apply_on_log_probs(self, log_probs: Tensor) -> Tensor:
 
         return log_probs
 
-    def _maybe_apply_log_probs_normed_grad(self, log_probs: Tensor) -> Tensor:
+    def _maybe_apply_log_probs_normed_grad(self, log_probs: Tensor, *, aux_layer: Optional[int] = None) -> Tensor:
         if not self.log_prob_normed_grad_opts:
             return log_probs
 
@@ -2440,7 +2448,10 @@ def _maybe_apply_log_probs_normed_grad(self, log_probs: Tensor) -> Tensor:
         assert "prior_running_mean" not in opts  # will be set by us here, and only when needed
         if opts.get("prior_running_mean_momentum") is not None:
             assert self.grad_prior is not None
-            opts["prior_running_mean"] = self.grad_prior.raw_tensor
+            grad_prior = self.grad_prior
+            if self.prior_running_mean_per_layer and aux_layer is not None:
+                grad_prior = getattr(self, f"grad_prior_{aux_layer}")
+            opts["prior_running_mean"] = grad_prior.raw_tensor
 
         assert log_probs.batch_dim_axis is not None and log_probs.feature_dim_axis is not None
         log_probs_ = log_probs.copy_template()
diff --git a/users/zeyer/experiments/exp2024_04_23_baselines/ctc_claix2023.py b/users/zeyer/experiments/exp2024_04_23_baselines/ctc_claix2023.py
index db2150d74..04f40c60f 100644
--- a/users/zeyer/experiments/exp2024_04_23_baselines/ctc_claix2023.py
+++ b/users/zeyer/experiments/exp2024_04_23_baselines/ctc_claix2023.py
@@ -676,6 +676,19 @@ def py():
                 },
             }
         },
+        "-lpNormedGradC05_11P07NExpL1_3": {
+            "prior_running_mean_per_layer": True,
+            "log_prob_normed_grad": {
+                "prior_running_mean_momentum": 0.001,
+                "func": {
+                    "clamp_min": 0.5,
+                    "clamp_max": 1.1,
+                    "scale_type": "inv_num_labels",
+                    "prior_exp": 0.7,
+                    "prior_renorm": True,
+                },
+            },
+        },
     }.items():
         ctc_train_exp(
             f"n12-spm10k-auxAED-b150k{name}",