diff --git a/clrs/_src/algorithms/searching.py b/clrs/_src/algorithms/searching.py
index c998c655..b6916833 100644
--- a/clrs/_src/algorithms/searching.py
+++ b/clrs/_src/algorithms/searching.py
@@ -179,7 +179,8 @@ def partition(A, A_pos, p, r, target, probes):
               'i': probing.mask_one(A_pos[i + 1], A.shape[0]),
               'j': probing.mask_one(A_pos[j], A.shape[0]),
               'i_rank': (i + 1) * 1.0 / A.shape[0],
-              'target': target * 1.0 / A.shape[0]
+              'target': target * 1.0 / A.shape[0],
+              'pivot': probing.mask_one(A_pos[r], A.shape[0]),
           })
 
     tmp = A[i + 1]
@@ -199,8 +200,10 @@ def partition(A, A_pos, p, r, target, probes):
             'i': probing.mask_one(A_pos[i + 1], A.shape[0]),
             'j': probing.mask_one(A_pos[r], A.shape[0]),
             'i_rank': (i + 1 - p) * 1.0 / A.shape[0],
-            'target': target * 1.0 / A.shape[0]
-        })
+            'target': target * 1.0 / A.shape[0],
+            'pivot': probing.mask_one(A_pos[i + 1], A.shape[0]),
+        },
+        )
 
     return i + 1
 
diff --git a/clrs/_src/probing.py b/clrs/_src/probing.py
index d9e9ad4a..b1aaccbb 100644
--- a/clrs/_src/probing.py
+++ b/clrs/_src/probing.py
@@ -145,7 +145,7 @@ def finalize(probes: ProbesDict):
         else:
           # Only one instance of input/output exist. Remove leading axis.
           probes[stage][loc][name]['data'] = np.squeeze(
-              np.array(probes[stage][loc][name]['data']))
+              np.array(probes[stage][loc][name]['data']), axis=0)
 
 
 def split_stages(
diff --git a/clrs/_src/samplers.py b/clrs/_src/samplers.py
index 9cf32e27..f77b4ed1 100644
--- a/clrs/_src/samplers.py
+++ b/clrs/_src/samplers.py
@@ -72,6 +72,7 @@ def __init__(
       num_samples: int,
       *args,
       seed: Optional[int] = None,
+      track_max_steps: bool = True,
       **kwargs,
   ):
     """Initializes a `Sampler`.
@@ -85,6 +86,13 @@ def __init__(
         If -1, samples are generated on the fly with each call to `next`.
       *args: Algorithm args.
       seed: RNG seed.
+      track_max_steps: if True and sampling on the fly (`num_samples`==-1),
+        we keep track of the maximum unroll length so far to pad batched samples
+        to that length. This is desirable when batches are used in compiled
+        functions that need recompilation every time the batch size changes.
+        Also, we get an initial value for max_steps by generating 1000 samples,
+        which will slow down initialization. If uniform shape of the batches
+        is not a concern, set `track_max_steps` to False.
       **kwargs: Algorithm kwargs.
     """
 
@@ -95,19 +103,21 @@ def __init__(
     self._algorithm = algorithm
     self._args = args
     self._kwargs = kwargs
+    self._track_max_steps = track_max_steps
 
     if num_samples < 0:
       logging.warning('Sampling dataset on-the-fly, unlimited samples.')
-      # Just get an initial estimate of max hint length
-      self.max_steps = -1
-      for _ in range(1000):
-        data = self._sample_data(*args, **kwargs)
-        _, probes = algorithm(*data)
-        _, _, hint = probing.split_stages(probes, spec)
-        for dp in hint:
-          assert dp.data.shape[1] == 1  # batching axis
-          if dp.data.shape[0] > self.max_steps:
-            self.max_steps = dp.data.shape[0]
+      if track_max_steps:
+        # Get an initial estimate of max hint length
+        self.max_steps = -1
+        for _ in range(1000):
+          data = self._sample_data(*args, **kwargs)
+          _, probes = algorithm(*data)
+          _, _, hint = probing.split_stages(probes, spec)
+          for dp in hint:
+            assert dp.data.shape[1] == 1  # batching axis
+            if dp.data.shape[0] > self.max_steps:
+              self.max_steps = dp.data.shape[0]
     else:
       logging.info('Creating a dataset with %i samples.', num_samples)
       (self._inputs, self._outputs, self._hints,
@@ -148,10 +158,11 @@ def next(self, batch_size: Optional[int] = None) -> Feedback:
     """
     if batch_size:
       if self._num_samples < 0:  # generate on the fly
+        min_length = self.max_steps if self._track_max_steps else 0
         inputs, outputs, hints, lengths = self._make_batch(
-            batch_size, self._spec, self.max_steps,
+            batch_size, self._spec, min_length,
             self._algorithm, *self._args, **self._kwargs)
-        if hints[0].data.shape[0] > self.max_steps:
+        if self._track_max_steps and hints[0].data.shape[0] > self.max_steps:
           logging.warning('Increasing hint lengh from %i to %i',
                           self.max_steps, hints[0].data.shape[0])
           self.max_steps = hints[0].data.shape[0]
@@ -261,6 +272,7 @@ def build_sampler(
     num_samples: int,
     *args,
     seed: Optional[int] = None,
+    track_max_steps: bool = True,
     **kwargs,
 ) -> Tuple[Sampler, specs.Spec]:
   """Builds a sampler. See `Sampler` documentation."""
@@ -276,8 +288,15 @@ def build_sampler(
   if set(clean_kwargs) != set(kwargs):
     logging.warning('Ignoring kwargs %s when building sampler class %s',
                     set(kwargs).difference(clean_kwargs), sampler_class)
-  sampler = sampler_class(algorithm, spec, num_samples, seed=seed,
-                          *args, **clean_kwargs)
+  sampler = sampler_class(
+      algorithm,
+      spec,
+      num_samples,
+      seed=seed,
+      track_max_steps=track_max_steps,
+      *args,
+      **clean_kwargs,
+  )
   return sampler, spec
 
 
diff --git a/clrs/_src/specs.py b/clrs/_src/specs.py
index 5de850cb..c6efa0a8 100644
--- a/clrs/_src/specs.py
+++ b/clrs/_src/specs.py
@@ -161,7 +161,8 @@ class OutputClass:
         'i': (Stage.HINT, Location.NODE, Type.MASK_ONE),
         'j': (Stage.HINT, Location.NODE, Type.MASK_ONE),
         'i_rank': (Stage.HINT, Location.GRAPH, Type.SCALAR),
-        'target': (Stage.HINT, Location.GRAPH, Type.SCALAR)
+        'target': (Stage.HINT, Location.GRAPH, Type.SCALAR),
+        'pivot': (Stage.HINT, Location.NODE, Type.MASK_ONE),
     },
     'minimum': {
         'pos': (Stage.INPUT, Location.NODE, Type.SCALAR),