diff --git a/egs/librispeech/ASR/pruned_transducer_stateless7/scaling.py b/egs/librispeech/ASR/pruned_transducer_stateless7/scaling.py
index 208d15735..842233ef3 100644
--- a/egs/librispeech/ASR/pruned_transducer_stateless7/scaling.py
+++ b/egs/librispeech/ASR/pruned_transducer_stateless7/scaling.py
@@ -230,6 +230,41 @@ def random_cast_to_half(x: Tensor,
     return torch.where(is_too_small, random_val, x).to(torch.float16)
 
 
+
+class CutoffEstimator:
+    """
+    Estimates cutoffs of an arbitrary numerical quantity such that a specified
+    proportion of items will be above the cutoff on average.
+      p is the proportion of items that should be above the cutoff.
+
+    """
+    def __init__(self, p: float):
+        self.p = p
+        # total count of items
+        self.count = 0
+        # total count of items that were above the cutoff
+        self.count_above = 0
+        # initial cutoff value
+        self.cutoff = 0
+
+
+    def __call__(self, x: float) -> bool:
+        """
+        Returns true if x is above the cutoff.
+        """
+        ans = (x > self.cutoff)
+        self.count += 1
+        if ans:
+            self.count_above += 1
+        cur_p = self.count_above / self.count
+        print(f"cur_p = {cur_p}, cutoff = {self.cutoff}")
+        delta_p = cur_p - self.p
+        if (delta_p > 0) == ans:
+            q = abs(delta_p)
+            self.cutoff = x * q + self.cutoff * (1-q)
+        return ans
+
+
 class CachingEvalFunction(torch.autograd.Function):
     # @custom_fwd and @custom_bwd related to automatic mixed precision (amp) an ensure
     # that the backward path runs with the same autocast context as the forward pass.
@@ -605,6 +640,9 @@ class ActivationBalancer(torch.nn.Module):
         if prob is None:
             prob = ScheduledFloat((0.0, 0.4), (8000.0, 0.1), default=0.4)
         self.prob = prob
+        # 10% of the time we will return and do nothing because memory usage
+        # is too high.
+        self.mem_cutoff = CutoffEstimator(0.1)
 
         # actually self.num_channels is no longer needed except for an assertion.
         self.num_channels = num_channels
@@ -618,11 +656,9 @@ class ActivationBalancer(torch.nn.Module):
         self.scale_gain_factor = scale_gain_factor
 
 
-
-
-
     def forward(self, x: Tensor) -> Tensor:
-        if torch.jit.is_scripting() or not x.requires_grad:
+        if (torch.jit.is_scripting() or not x.requires_grad or
+            (x.is_cuda and self.mem_cutoff(torch.cuda.memory_allocated()))):
             return _no_op(x)
 
         prob = float(self.prob)
@@ -776,7 +812,7 @@ class Whiten(nn.Module):
             num_groups: int,
             whitening_limit: FloatLike,
             prob: Union[float, Tuple[float,float]],
-            grad_scale: float):
+            grad_scale: FloatLike):
         """
         Args:
           num_groups: the number of groups to divide the channel dim into before
@@ -801,6 +837,12 @@ class Whiten(nn.Module):
         assert grad_scale >= 0
         self.num_groups = num_groups
         self.whitening_limit = whitening_limit
+        self.grad_scale = grad_scale
+
+        # 10% of the time we will return and do nothing because memory usage
+        # is too high.
+        self.mem_cutoff = CutoffEstimator(0.1)
+
         if isinstance(prob, float):
             assert 0 < prob <= 1
             self.prob = prob
@@ -809,7 +851,6 @@ class Whiten(nn.Module):
             assert 0 < self.min_prob < self.max_prob <= 1
             self.prob = self.max_prob
         self.name = None # will be set in training loop
-        self.grad_scale = grad_scale
 
     def forward(self,
                 x: Tensor) -> Tensor:
@@ -829,7 +870,9 @@ class Whiten(nn.Module):
         you use the returned value, or the graph will be freed
         and nothing will happen in backprop.
         """
-        if not x.requires_grad or random.random() > self.prob or self.grad_scale == 0:
+        grad_scale = float(self.grad_scale)
+        if (not x.requires_grad or random.random() > self.prob or grad_scale == 0
+            or (x.is_cuda and self.mem_cutoff(torch.cuda.memory_allocated()))):
             return _no_op(x)
         else:
             whitening_limit = float(self.whitening_limit)
@@ -845,7 +888,7 @@ class Whiten(nn.Module):
             return WhiteningPenaltyFunction.apply(x,
                                                   self.num_groups,
                                                   whitening_limit,
-                                                  self.grad_scale,
+                                                  grad_scale,
                                                   self.name)