diff --git a/learned_optimization/learned_optimizers/nn_adam.py b/learned_optimization/learned_optimizers/nn_adam.py
index d374d08..0e62762 100644
--- a/learned_optimization/learned_optimizers/nn_adam.py
+++ b/learned_optimization/learned_optimizers/nn_adam.py
@@ -82,7 +82,7 @@ class NNAdamState:
   """
   params: Any
   state: Any
-  iteration: int
+  iteration: jax.Array
   rolling_features: MeanAndMeanSquareAccumulator
   per_layer_lr: Any
   per_layer_beta1: Any
diff --git a/learned_optimization/optimizers/optax_opts.py b/learned_optimization/optimizers/optax_opts.py
index e8c1edd..8df1a53 100644
--- a/learned_optimization/optimizers/optax_opts.py
+++ b/learned_optimization/optimizers/optax_opts.py
@@ -384,11 +384,13 @@ def __init__(self,
 
   # SM3 doesn't support scalars, so we have to reshape the params and grads.
 
-  def init(self,
-           params: Any,
-           model_state: Optional[Any] = None,
-           num_steps: Optional[int] = None,
-           key: chex.PRNGKey = None) -> SM3OptState:
+  def init(
+      self,
+      params: Any,
+      model_state: Optional[Any] = None,
+      num_steps: Optional[int] = None,
+      key: Optional[chex.PRNGKey] = None,
+  ) -> SM3OptState:
     should_reshape = jax.tree_util.tree_map(lambda x: len(x.shape) == 0, params)  # pylint: disable=g-explicit-length-test
     params = jax.tree_util.tree_map(_expand_scalar, params, should_reshape)
     out = super().init(params, model_state, num_steps, key)
diff --git a/learned_optimization/outer_train.py b/learned_optimization/outer_train.py
index 119f402..31b79d1 100644
--- a/learned_optimization/outer_train.py
+++ b/learned_optimization/outer_train.py
@@ -207,7 +207,7 @@ def metrics_and_info_from_gradients(
     gathered_grads: Sequence[GradientsFromWorker],
     steps: Sequence[int],
     current_step: int,
-) -> Tuple[Mapping[str, float], Sequence[int], int]:
+) -> Tuple[Mapping[str, float], Sequence[Union[int, jax.Array]], int]:
   """Perform one outer-iteration on a batch of gradients from workers.
 
   Args:
@@ -222,17 +222,17 @@ def metrics_and_info_from_gradients(
     applied_inner_steps: number if inner steps performed this outer step.
   """
 
-  worker_ids = jnp.asarray([t.worker_id for t in gathered_grads])
-  inner_steps = onp.asarray([t.total_inner_steps for t in gathered_grads])
+  worker_ids = [t.worker_id for t in gathered_grads]
+  inner_steps = [t.total_inner_steps for t in gathered_grads]
 
-  applied_inner_steps = onp.sum(inner_steps)
+  applied_inner_steps = int(onp.sum(inner_steps))
   metrics = {}
   metrics["unique_worker"] = float(len(onp.unique(worker_ids)))
 
-  avg_stale = current_step - onp.mean(steps)
+  avg_stale = current_step - float(onp.mean(steps))
   metrics["avg_staleness"] = avg_stale
 
-  max_stale = current_step - onp.min(steps)
+  max_stale = current_step - float(onp.min(steps))
   metrics["max_staleness"] = max_stale
 
   return metrics, worker_ids, applied_inner_steps
diff --git a/learned_optimization/outer_trainers/full_es.py b/learned_optimization/outer_trainers/full_es.py
index bd0b64d..dcb111b 100644
--- a/learned_optimization/outer_trainers/full_es.py
+++ b/learned_optimization/outer_trainers/full_es.py
@@ -249,7 +249,7 @@ def last_recompute_antithetic_es(
     recompute_samples: int,
     clip_loss_diff: Optional[float] = None,
     sign_delta_loss_scalar: Optional[float] = None,
-) -> Tuple[float, MetaParams]:
+) -> Tuple[jax.Array, MetaParams]:
   """Compute an ES gradient estimate by recomputing the loss on both unrolls.
 
   Args:
diff --git a/learned_optimization/outer_trainers/truncated_es.py b/learned_optimization/outer_trainers/truncated_es.py
index 8154472..5015cea 100644
--- a/learned_optimization/outer_trainers/truncated_es.py
+++ b/learned_optimization/outer_trainers/truncated_es.py
@@ -46,7 +46,9 @@ def compute_es_grad(
     vec_pos: MetaParams,
     std: float,
     sign_delta_loss_scalar: Optional[float] = None,
-) -> Tuple[float, MetaParams, truncated_step_mod.TruncatedUnrollOut, float]:
+) -> Tuple[
+    jax.Array, MetaParams, truncated_step_mod.TruncatedUnrollOut, jax.Array
+]:
   """Compute the ES gradient estimate from the outputs of many unrolls.
 
   Args:
diff --git a/learned_optimization/outer_trainers/truncated_pes.py b/learned_optimization/outer_trainers/truncated_pes.py
index 1572ce9..2c3c052 100644
--- a/learned_optimization/outer_trainers/truncated_pes.py
+++ b/learned_optimization/outer_trainers/truncated_pes.py
@@ -53,8 +53,13 @@ def compute_pes_grad(
     vec_pos: MetaParams,
     std: float,
     sign_delta_loss_scalar: Optional[float] = None,
-) -> Tuple[float, MetaParams, MetaParams, truncated_step_mod.TruncatedUnrollOut,
-           float]:
+) -> Tuple[
+    jax.Array,
+    MetaParams,
+    MetaParams,
+    truncated_step_mod.TruncatedUnrollOut,
+    jax.Array,
+]:
   """Compute the PES gradient estimate from the outputs of many unrolls.
 
   Args:
diff --git a/learned_optimization/research/hysteresis/truncated_pes_no_hyst_same_data.py b/learned_optimization/research/hysteresis/truncated_pes_no_hyst_same_data.py
index bee573b..cec8514 100644
--- a/learned_optimization/research/hysteresis/truncated_pes_no_hyst_same_data.py
+++ b/learned_optimization/research/hysteresis/truncated_pes_no_hyst_same_data.py
@@ -130,6 +130,7 @@ def compute_gradient_estimate(
     rng = hk.PRNGSequence(key)
 
     # train on the circular buffer's data.
+    assert isinstance(self.circular_buffer, circular_buffer.CircularBuffer)
     reordered_data, unused_mask = self.circular_buffer.stack_reorder(
         buffer_state)