diff --git a/adaptive/learner/average_learner.py b/adaptive/learner/average_learner.py
index ef27a2ef4..2705eb04e 100644
--- a/adaptive/learner/average_learner.py
+++ b/adaptive/learner/average_learner.py
@@ -1,6 +1,8 @@
 from __future__ import annotations
 
 from math import sqrt
+from numbers import Integral as Int
+from numbers import Real
 from typing import Callable
 
 import cloudpickle
@@ -8,7 +10,7 @@
 
 from adaptive.learner.base_learner import BaseLearner
 from adaptive.notebook_integration import ensure_holoviews
-from adaptive.types import Float, Int, Real
+from adaptive.types import Float
 from adaptive.utils import (
     assign_defaults,
     cache_latest,
diff --git a/adaptive/learner/average_learner1D.py b/adaptive/learner/average_learner1D.py
index ef99e50a5..aa4be9d71 100644
--- a/adaptive/learner/average_learner1D.py
+++ b/adaptive/learner/average_learner1D.py
@@ -5,6 +5,8 @@
 from collections import defaultdict
 from copy import deepcopy
 from math import hypot
+from numbers import Integral as Int
+from numbers import Real
 from typing import Callable, DefaultDict, Iterable, List, Sequence, Tuple
 
 import numpy as np
@@ -14,7 +16,6 @@
 
 from adaptive.learner.learner1D import Learner1D, _get_intervals
 from adaptive.notebook_integration import ensure_holoviews
-from adaptive.types import Int, Real
 from adaptive.utils import assign_defaults, partial_function_from_dataframe
 
 try:
@@ -576,10 +577,10 @@ def tell_many_at_point(self, x: Real, seed_y_mapping: dict[int, Real]) -> None:
                     self._update_interpolated_loss_in_interval(*interval)
                 self._oldscale = deepcopy(self._scale)
 
-    def _get_data(self) -> dict[Real, Real]:
+    def _get_data(self) -> dict[Real, dict[Int, Real]]:
         return self._data_samples
 
-    def _set_data(self, data: dict[Real, Real]) -> None:
+    def _set_data(self, data: dict[Real, dict[Int, Real]]) -> None:
         if data:
             for x, samples in data.items():
                 self.tell_many_at_point(x, samples)
diff --git a/adaptive/learner/learner1D.py b/adaptive/learner/learner1D.py
index 3af731e29..9987da468 100644
--- a/adaptive/learner/learner1D.py
+++ b/adaptive/learner/learner1D.py
@@ -4,6 +4,8 @@
 import itertools
 import math
 from copy import copy, deepcopy
+from numbers import Integral as Int
+from numbers import Real
 from typing import Any, Callable, Dict, List, Sequence, Tuple, Union
 
 import cloudpickle
@@ -15,7 +17,7 @@
 from adaptive.learner.learnerND import volume
 from adaptive.learner.triangulation import simplex_volume_in_embedding
 from adaptive.notebook_integration import ensure_holoviews
-from adaptive.types import Float, Int, Real
+from adaptive.types import Float
 from adaptive.utils import (
     assign_defaults,
     cache_latest,
diff --git a/adaptive/learner/sequence_learner.py b/adaptive/learner/sequence_learner.py
index 959b233c9..557c7a588 100644
--- a/adaptive/learner/sequence_learner.py
+++ b/adaptive/learner/sequence_learner.py
@@ -1,13 +1,13 @@
 from __future__ import annotations
 
 from copy import copy
+from numbers import Integral as Int
 from typing import Any, Tuple
 
 import cloudpickle
 from sortedcontainers import SortedDict, SortedSet
 
 from adaptive.learner.base_learner import BaseLearner
-from adaptive.types import Int
 from adaptive.utils import assign_defaults, partial_function_from_dataframe
 
 try:
diff --git a/adaptive/types.py b/adaptive/types.py
index 67268f822..a49b332a6 100644
--- a/adaptive/types.py
+++ b/adaptive/types.py
@@ -1,3 +1,5 @@
+from numbers import Integral as Int
+from numbers import Real
 from typing import Union
 
 import numpy as np
@@ -9,6 +11,7 @@
     from typing_extensions import TypeAlias
 
 Float: TypeAlias = Union[float, np.float_]
-Int: TypeAlias = Union[int, np.int_]
-Real: TypeAlias = Union[Float, Int]
 Bool: TypeAlias = Union[bool, np.bool_]
+
+
+__all__ = ["Float", "Bool", "Int", "Real"]