From 6baca8ca736d7e5b00cff704d7a9e2e0859aa660 Mon Sep 17 00:00:00 2001
From: tm91236 <205063739+tm91236@users.noreply.github.com>
Date: Mon, 7 Apr 2025 14:58:01 +0000
Subject: [PATCH 1/2] chore: dropped support for python 3.9

---
 .github/ISSUE_TEMPLATE/bug_report.yml       |    1 -
 .github/workflows/release.yml               |    1 -
 .github/workflows/unittests.yml             |    1 -
 .pre-commit-config.yaml                     |    2 +-
 .pylintrc                                   |    2 +-
 CHANGELOG.md                                |    1 +
 benchmark/blobs_benchmark.py                |    5 +-
 benchmark/david_benchmark.py                |    3 +-
 benchmark/mnist_benchmark.py                |    6 +-
 coreax/approximation.py                     |   46 +-
 coreax/benchmark_util.py                    |   24 +-
 coreax/coreset.py                           |   21 +-
 coreax/data.py                              |   74 +-
 coreax/kernels/base.py                      |  272 +-
 coreax/kernels/scalar_valued.py             |    8 +-
 coreax/kernels/util.py                      |    5 +-
 coreax/least_squares.py                     |    8 +-
 coreax/metrics.py                           |   12 +-
 coreax/score_matching.py                    |   28 +-
 coreax/solvers/base.py                      |    6 +-
 coreax/solvers/composite.py                 |   14 +-
 coreax/solvers/coresubset.py                |   68 +-
 coreax/solvers/recombination.py             |   14 +-
 coreax/util.py                              |   56 +-
 coreax/weights.py                           |   14 +-
 documentation/source/conf.py                |    8 +-
 examples/coreset_in_model_pipeline.py       |    3 +-
 examples/cubature_recombination.py          |    4 +-
 examples/david_map_reduce_weighted.py       |    3 +-
 examples/herding_approximate_gram_matrix.py |    3 +-
 examples/herding_basic.py                   |    3 +-
 examples/herding_basic_weighted.py          |    3 +-
 examples/herding_duo_composite_kernel.py    |    3 +-
 examples/herding_refine_weighted.py         |    3 +-
 examples/herding_stein_weighted.py          |    3 +-
 examples/herding_stein_weighted_ssm.py      |    3 +-
 examples/iterative_probabilistic_kh.py      |    3 +-
 examples/pounce.py                          |    3 +-
 examples/pounce_map_reduce.py               |    3 +-
 examples/pounce_map_reduce_ssm.py           |    3 +-
 pyproject.toml                              |    4 +-
 tests/coverage/compare.py                   |    3 +-
 tests/performance/compare.py                |    3 +-
 tests/performance/run.py                    |    2 +-
 tests/unit/test_coreset.py                  |   11 +-
 tests/unit/test_kernels.py                  |   16 +-
 tests/unit/test_least_squares.py            |    6 +-
 tests/unit/test_score_matching.py           |    3 +-
 tests/unit/test_solvers.py                  |   34 +-
 tests/unit/test_weights.py                  |    5 +-
 uv.lock                                     | 3253 ++++++-------------
 51 files changed, 1461 insertions(+), 2622 deletions(-)

diff --git a/.github/ISSUE_TEMPLATE/bug_report.yml b/.github/ISSUE_TEMPLATE/bug_report.yml
index a674fd16d..6cad0fc33 100644
--- a/.github/ISSUE_TEMPLATE/bug_report.yml
+++ b/.github/ISSUE_TEMPLATE/bug_report.yml
@@ -41,7 +41,6 @@ body:
       description: Which version or versions of Python are you seeing the problem on?
       multiple: true
       options:
-        - "3.9"
         - "3.10"
         - "3.11"
         - "3.12"
diff --git a/.github/workflows/release.yml b/.github/workflows/release.yml
index 47c4ccf63..58f0f1d6e 100644
--- a/.github/workflows/release.yml
+++ b/.github/workflows/release.yml
@@ -45,7 +45,6 @@ jobs:
       fail-fast: false
       matrix:
         python-version:
-          - "3.9"
           - "3.10"
           - "3.11"
           - "3.12"
diff --git a/.github/workflows/unittests.yml b/.github/workflows/unittests.yml
index 14ec2a6df..03fb3e08f 100644
--- a/.github/workflows/unittests.yml
+++ b/.github/workflows/unittests.yml
@@ -14,7 +14,6 @@ jobs:
       fail-fast: false
       matrix:
         python-version:
-          - "3.9"
           - "3.10"
           - "3.11"
           - "3.12"
diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 2ad666527..412b598c3 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -95,7 +95,7 @@ repos:
     rev: v0.13.0
     hooks:
       # Run the linter.
-      - id: ruff
+      - id: ruff-check
         args: [ --fix ]
         # Abort if ruff linter fails as there is some duplication of functionality with
         # the slow pylint hook
diff --git a/.pylintrc b/.pylintrc
index f106999b1..7dc24483d 100644
--- a/.pylintrc
+++ b/.pylintrc
@@ -96,7 +96,7 @@ persistent=yes
 
 # Minimum Python version to use for version dependent checks. Will default to
 # the version used to run pylint.
-py-version=3.9
+py-version=3.10
 
 # Discover python modules and packages in the file system subtree.
 recursive=no
diff --git a/CHANGELOG.md b/CHANGELOG.md
index 30998ce38..92f923730 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -22,6 +22,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 ### Removed
 
  - Internal `SilentTQDM` class has been removed; all user-facing functionality has been preserved.
+ - Dropped support for python 3.9 which is near end-of-life.
 
 ### Deprecated
 
diff --git a/benchmark/blobs_benchmark.py b/benchmark/blobs_benchmark.py
index b317c1965..a008b20b4 100644
--- a/benchmark/blobs_benchmark.py
+++ b/benchmark/blobs_benchmark.py
@@ -31,7 +31,6 @@
 import json
 import os
 import time
-from typing import Union
 
 import jax
 import jax.numpy as jnp
@@ -96,8 +95,8 @@ def setup_stein_kernel(
 
     # Define the score function as the gradient of log density given by the KDE
     def score_function(
-        x: Union[Shaped[Array, " n d"], Shaped[Array, ""], float, int],
-    ) -> Union[Shaped[Array, " n d"], Shaped[Array, " 1 1"]]:
+        x: Shaped[Array, " n d"] | Shaped[Array, ""] | float | int,
+    ) -> Shaped[Array, " n d"] | Shaped[Array, " 1 1"]:
         """
         Compute the score function (gradient of log density) for a single point.
 
diff --git a/benchmark/david_benchmark.py b/benchmark/david_benchmark.py
index 779736328..3b0477f65 100644
--- a/benchmark/david_benchmark.py
+++ b/benchmark/david_benchmark.py
@@ -38,7 +38,6 @@
 import math
 import time
 from pathlib import Path
-from typing import Optional
 
 import equinox as eqx
 import jax.numpy as jnp
@@ -60,7 +59,7 @@
 # (disable line too long and too many statements ruff)
 def benchmark_coreset_algorithms(
     in_path: Path = Path("../examples/data/david_orig.png"),
-    out_path: Optional[Path] = Path(
+    out_path: Path | None = Path(
         "../examples/benchmarking_images/david_benchmark_results.png"
     ),
     downsampling_factor: int = 1,
diff --git a/benchmark/mnist_benchmark.py b/benchmark/mnist_benchmark.py
index 4f12ca134..6fdb54cb6 100644
--- a/benchmark/mnist_benchmark.py
+++ b/benchmark/mnist_benchmark.py
@@ -40,7 +40,7 @@
 import json
 import os
 import time
-from typing import Any, NamedTuple, Optional, Union
+from typing import Any, NamedTuple
 
 import equinox as eqx
 import jax
@@ -143,7 +143,7 @@ def __call__(self, x: jnp.ndarray, training: bool = True) -> jnp.ndarray:
 class TrainState(train_state.TrainState):
     """Custom train state with batch statistics and dropout RNG."""
 
-    batch_stats: Optional[dict[str, jnp.ndarray]]
+    batch_stats: dict[str, jnp.ndarray] | None
     dropout_rng: KeyArrayLike
 
 
@@ -416,7 +416,7 @@ def prepare_datasets() -> tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray, jnp.ndarr
 def train_model(
     data_bundle: dict[str, jnp.ndarray],
     key: KeyArrayLike,
-    config: dict[str, Union[int, float]],
+    config: dict[str, int | float],
 ) -> dict[str, float]:
     """
     Train the model and return the results.
diff --git a/coreax/approximation.py b/coreax/approximation.py
index ee092e27f..b83482585 100644
--- a/coreax/approximation.py
+++ b/coreax/approximation.py
@@ -30,14 +30,14 @@
 
 from collections.abc import Callable
 from functools import partial
-from typing import TYPE_CHECKING, Any, Union
+from typing import TYPE_CHECKING, Any, Literal
 
 import jax
 import jax.numpy as jnp
 import jax.random as jr
 from jax import Array
 from jaxtyping import Shaped
-from typing_extensions import Literal, override
+from typing_extensions import override
 
 from coreax.data import Data, _atleast_2d_consistent
 from coreax.kernels import UniCompositeKernel
@@ -177,14 +177,12 @@ class MonteCarloApproximateKernel(RandomRegressionKernel):
 
     def gramian_row_mean(
         self,
-        x: Union[
-            Shaped[Array, " n d"],
-            Shaped[Array, " d"],
-            Shaped[Array, ""],
-            float,
-            int,
-            Data,
-        ],
+        x: Shaped[Array, " n d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int
+        | Data,
         **kwargs: Any,
     ) -> Shaped[Array, " n"]:
         r"""
@@ -232,14 +230,12 @@ class ANNchorApproximateKernel(RandomRegressionKernel):
 
     def gramian_row_mean(
         self,
-        x: Union[
-            Shaped[Array, " n d"],
-            Shaped[Array, " d"],
-            Shaped[Array, ""],
-            float,
-            int,
-            Data,
-        ],
+        x: Shaped[Array, " n d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int
+        | Data,
         **kwargs: Any,
     ) -> Shaped[Array, " n"]:
         r"""
@@ -305,14 +301,12 @@ class NystromApproximateKernel(RandomRegressionKernel):
 
     def gramian_row_mean(
         self,
-        x: Union[
-            Shaped[Array, " n d"],
-            Shaped[Array, " d"],
-            Shaped[Array, ""],
-            float,
-            int,
-            Data,
-        ],
+        x: Shaped[Array, " n d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int
+        | Data,
         **kwargs: Any,
     ) -> Shaped[Array, " n"]:
         r"""
diff --git a/coreax/benchmark_util.py b/coreax/benchmark_util.py
index 395e26f74..4668e6589 100644
--- a/coreax/benchmark_util.py
+++ b/coreax/benchmark_util.py
@@ -21,7 +21,7 @@
 """
 
 from collections.abc import Callable
-from typing import Optional, TypeVar, Union
+from typing import TypeVar
 
 import jax
 import jax.numpy as jnp
@@ -61,12 +61,12 @@ class IterativeKernelHerding(KernelHerding[_Data]):  # pylint: disable=too-many-
     """
 
     num_iterations: int = 1
-    t_schedule: Optional[Array] = None
+    t_schedule: Array | None = None
 
     def reduce(
         self,
         dataset: _Data,
-        solver_state: Optional[HerdingState] = None,
+        solver_state: HerdingState | None = None,
     ) -> tuple[Coresubset[_Data], HerdingState]:
         """
         Perform Kernel Herding reduction followed by additional refinement iterations.
@@ -118,7 +118,7 @@ def initialise_solvers(  # noqa: C901
     train_data_umap: Data,
     key: KeyArrayLike,
     cpp_oversampling_factor: int,
-    leaf_size: Optional[int] = None,
+    leaf_size: int | None = None,
 ) -> dict[str, Callable[[int], Solver]]:
     """
     Initialise and return a list of solvers for various coreset algorithms.
@@ -147,7 +147,7 @@ def initialise_solvers(  # noqa: C901
     kernel = SquaredExponentialKernel(length_scale=length_scale)
     sqrt_kernel = kernel.get_sqrt_kernel(16)
 
-    def _get_thinning_solver(_size: int) -> Union[KernelThinning, MapReduce]:
+    def _get_thinning_solver(_size: int) -> KernelThinning | MapReduce:
         """
         Set up kernel thinning solver.
 
@@ -169,7 +169,7 @@ def _get_thinning_solver(_size: int) -> Union[KernelThinning, MapReduce]:
             return thinning_solver
         return MapReduce(thinning_solver, leaf_size=leaf_size)
 
-    def _get_herding_solver(_size: int) -> Union[KernelHerding, MapReduce]:
+    def _get_herding_solver(_size: int) -> KernelHerding | MapReduce:
         """
         Set up kernel herding solver.
 
@@ -185,7 +185,7 @@ def _get_herding_solver(_size: int) -> Union[KernelHerding, MapReduce]:
             return herding_solver
         return MapReduce(herding_solver, leaf_size=leaf_size)
 
-    def _get_stein_solver(_size: int) -> Union[SteinThinning, MapReduce]:
+    def _get_stein_solver(_size: int) -> SteinThinning | MapReduce:
         """
         Set up Stein thinning solver.
 
@@ -200,8 +200,8 @@ def _get_stein_solver(_size: int) -> Union[SteinThinning, MapReduce]:
 
         # Define the score function as the gradient of log density given by the KDE
         def score_function(
-            x: Union[Shaped[Array, " n d"], Shaped[Array, ""], float, int],
-        ) -> Union[Shaped[Array, " n d"], Shaped[Array, " 1 1"]]:
+            x: Shaped[Array, " n d"] | Shaped[Array, ""] | float | int,
+        ) -> Shaped[Array, " n d"] | Shaped[Array, " 1 1"]:
             """
             Compute the score function (gradient of log density) for a single point.
 
@@ -264,7 +264,7 @@ def _get_compress_solver(_size: int) -> CompressPlusPlus:
 
     def _get_probabilistic_herding_solver(
         _size: int,
-    ) -> Union[IterativeKernelHerding, MapReduce]:
+    ) -> IterativeKernelHerding | MapReduce:
         """
         Set up KernelHerding with probabilistic selection.
 
@@ -289,7 +289,7 @@ def _get_probabilistic_herding_solver(
 
     def _get_iterative_herding_solver(
         _size: int,
-    ) -> Union[IterativeKernelHerding, MapReduce]:
+    ) -> IterativeKernelHerding | MapReduce:
         """
         Set up KernelHerding with probabilistic selection.
 
@@ -314,7 +314,7 @@ def _get_iterative_herding_solver(
 
     def _get_cubic_iterative_herding_solver(
         _size: int,
-    ) -> Union[IterativeKernelHerding, MapReduce]:
+    ) -> IterativeKernelHerding | MapReduce:
         """
         Set up KernelHerding with probabilistic selection.
 
diff --git a/coreax/coreset.py b/coreax/coreset.py
index 1d22f809a..b63fa583c 100644
--- a/coreax/coreset.py
+++ b/coreax/coreset.py
@@ -20,7 +20,6 @@
     Final,
     Generic,
     TypeVar,
-    Union,
     overload,
 )
 
@@ -131,14 +130,14 @@ def __init__(self, nodes: Data, pre_coreset_data: _TOriginalData_co) -> None:
     @classmethod
     @overload
     def build(
-        cls, nodes: Union[Data, Array], pre_coreset_data: Array
+        cls, nodes: Data | Array, pre_coreset_data: Array
     ) -> "PseudoCoreset[Data]": ...
 
     @classmethod
     @overload
     def build(
         cls,
-        nodes: Union[Data, Array],
+        nodes: Data | Array,
         pre_coreset_data: tuple[Array, Array],
     ) -> "PseudoCoreset[SupervisedData]": ...
 
@@ -146,15 +145,15 @@ def build(
     @overload
     def build(
         cls,
-        nodes: Union[Data, Array],
+        nodes: Data | Array,
         pre_coreset_data: _TOriginalData,
     ) -> "PseudoCoreset[_TOriginalData]": ...
 
     @classmethod
     def build(
         cls,
-        nodes: Union[Data, Array],
-        pre_coreset_data: Union[_TOriginalData, Array, tuple[Array, Array]],
+        nodes: Data | Array,
+        pre_coreset_data: _TOriginalData | Array | tuple[Array, Array],
     ) -> "PseudoCoreset[Data]\
         | PseudoCoreset[SupervisedData]\
         | PseudoCoreset[_TOriginalData]\
@@ -253,14 +252,14 @@ def __init__(self, indices: Data, pre_coreset_data: _TOriginalData_co) -> None:
     @classmethod
     @overload
     def build(
-        cls, indices: Union[Data, Array], pre_coreset_data: Array
+        cls, indices: Data | Array, pre_coreset_data: Array
     ) -> "Coresubset[Data]": ...
 
     @classmethod
     @overload
     def build(
         cls,
-        indices: Union[Data, Array],
+        indices: Data | Array,
         pre_coreset_data: tuple[Array, Array],
     ) -> "Coresubset[SupervisedData]": ...
 
@@ -268,15 +267,15 @@ def build(
     @overload
     def build(
         cls,
-        indices: Union[Data, Array],
+        indices: Data | Array,
         pre_coreset_data: _TOriginalData,
     ) -> "Coresubset[_TOriginalData]": ...
 
     @classmethod
     def build(
         cls,
-        indices: Union[Data, Array],
-        pre_coreset_data: Union[_TOriginalData, Array, tuple[Array, Array]],
+        indices: Data | Array,
+        pre_coreset_data: _TOriginalData | Array | tuple[Array, Array],
     ) -> "Coresubset[Data] | Coresubset[SupervisedData] | Coresubset[_TOriginalData]":
         """
         Construct a Coresubset from Data or raw Arrays.
diff --git a/coreax/data.py b/coreax/data.py
index e7215a180..e18c725cf 100644
--- a/coreax/data.py
+++ b/coreax/data.py
@@ -15,7 +15,7 @@
 """Data-structures for representing weighted and/or supervised data."""
 
 from collections.abc import Sequence
-from typing import Optional, Union, overload
+from typing import Union, overload
 
 import equinox as eqx
 import jax.numpy as jnp
@@ -27,13 +27,13 @@
 
 @overload
 def _atleast_2d_consistent(
-    arrays: Union[Shaped[Array, ""], float, int],
+    arrays: Shaped[Array, ""] | float | int,
 ) -> Shaped[Array, " 1 1"]: ...
 
 
 @overload
 def _atleast_2d_consistent(
-    arrays: Sequence[Union[Shaped[Array, ""], float, int]],
+    arrays: Sequence[Shaped[Array, ""] | float | int],
 ) -> list[Shaped[Array, " 1 1"]]: ...
 
 
@@ -52,43 +52,37 @@ def _atleast_2d_consistent(  # pyright:ignore[reportOverlappingOverload]
 @overload
 def _atleast_2d_consistent(  # pyright:ignore[reportOverlappingOverload]
     arrays: Sequence[
-        Union[
-            Shaped[Array, " _n _d _*p"],
-            Shaped[Array, " _n"],
-            Shaped[Array, ""],
-            float,
-            int,
-        ]
+        Shaped[Array, " _n _d _*p"]
+        | Shaped[Array, " _n"]
+        | Shaped[Array, ""]
+        | float
+        | int
     ],
 ) -> list[
-    Union[Shaped[Array, " _n _d _*p"], Shaped[Array, " _n 1"], Shaped[Array, " 1 1"]]
+    Shaped[Array, " _n _d _*p"] | Shaped[Array, " _n 1"] | Shaped[Array, " 1 1"]
 ]: ...
 
 
 @jit
 def _atleast_2d_consistent(  # pyright:ignore[reportOverlappingOverload]
-    *arrays: Union[
-        Shaped[Array, " n d *p"],
-        Shaped[Array, " n"],
-        Shaped[Array, ""],
-        float,
-        int,
-        Sequence[
-            Union[
-                Shaped[Array, " _n _d _*p"],
-                Shaped[Array, " _n"],
-                Shaped[Array, ""],
-                float,
-                int,
-            ]
-        ],
+    *arrays: Shaped[Array, " n d *p"]
+    | Shaped[Array, " n"]
+    | Shaped[Array, ""]
+    | float
+    | int
+    | Sequence[
+        Shaped[Array, " _n _d _*p"]
+        | Shaped[Array, " _n"]
+        | Shaped[Array, ""]
+        | float
+        | int
     ],
-) -> Union[
-    Shaped[Array, " n d *p"],
-    Shaped[Array, " n 1"],
-    Shaped[Array, " 1 1"],
-    list[Union[Shaped[Array, " _n _d _*p"], Shaped[Array, " _n"], Shaped[Array, ""]]],
-]:
+) -> (
+    Shaped[Array, " n d *p"]
+    | Shaped[Array, " n 1"]
+    | Shaped[Array, " 1 1"]
+    | list[Shaped[Array, " _n _d _*p"] | Shaped[Array, " _n"] | Shaped[Array, ""]]
+):
     r"""
     Given an array or sequence of arrays ensure they are at least 2-dimensional.
 
@@ -149,14 +143,12 @@ class Data(eqx.Module):
     """
 
     data: Shaped[Array, " n d"] = eqx.field(converter=_atleast_2d_consistent)
-    weights: Union[Shaped[Array, " n"], Shaped[Array, ""], int, float]
+    weights: Shaped[Array, " n"] | Shaped[Array, ""] | int | float
 
     def __init__(
         self,
         data: Shaped[Array, " n d"],
-        weights: Optional[
-            Union[Shaped[Array, " n"], Shaped[Array, ""], int, float]
-        ] = None,
+        weights: Shaped[Array, " n"] | Shaped[Array, ""] | int | float | None = None,
     ):
         """Initialise `Data` class, handle non-Array weight attribute."""
         self.data = _atleast_2d_consistent(data)
@@ -179,7 +171,7 @@ def __jax_array__(  # pyright:ignore[reportOverlappingOverload]
 
     def __jax_array__(
         self: Union["Data", "SupervisedData"],
-    ) -> Union[Shaped[Array, " n d"], Shaped[Array, " n d+p"]]:
+    ) -> Shaped[Array, " n d"] | Shaped[Array, " n d+p"]:
         """
         Return value of `jnp.asarray(Data(...))` and `jnp.asarray(SupervisedData(...))`.
 
@@ -251,9 +243,7 @@ def __init__(
         self,
         data: Shaped[Array, " n d"],
         supervision: Shaped[Array, " n p"],
-        weights: Optional[
-            Union[Shaped[Array, " n"], Shaped[Array, ""], int, float]
-        ] = None,
+        weights: Shaped[Array, " n"] | Shaped[Array, ""] | int | float | None = None,
     ):
         """Initialise SupervisedData class."""
         self.supervision = supervision
@@ -267,13 +257,13 @@ def __check_init__(self):
             )
 
 
-def as_data(x: Union[Shaped[Array, " n d"], Data]) -> Data:
+def as_data(x: Shaped[Array, " n d"] | Data) -> Data:
     """Cast ``x`` to a `Data` instance."""
     return x if isinstance(x, Data) else Data(x)
 
 
 def as_supervised_data(
-    xy: Union[tuple[Shaped[Array, " n d"], Shaped[Array, " n p"]], SupervisedData],
+    xy: tuple[Shaped[Array, " n d"], Shaped[Array, " n p"]] | SupervisedData,
 ) -> SupervisedData:
     """Cast ``xy`` to a `SupervisedData` instance."""
     return xy if isinstance(xy, SupervisedData) else SupervisedData(*xy)
diff --git a/coreax/kernels/base.py b/coreax/kernels/base.py
index aaf102875..efdae61ed 100644
--- a/coreax/kernels/base.py
+++ b/coreax/kernels/base.py
@@ -50,7 +50,7 @@
 """
 
 from abc import abstractmethod
-from typing import Any, Literal, Optional, Union, overload
+from typing import Any, Literal, Union, overload
 
 import equinox as eqx
 import jax
@@ -126,19 +126,23 @@ def compute(
     @overload
     def compute(  # pyright: ignore[reportOverlappingOverload]
         self,
-        x: Union[Shaped[Array, " d"], Shaped[Array, ""], float, int],
-        y: Union[Shaped[Array, " d"], Shaped[Array, ""], float, int],
+        x: Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
+        y: Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
     ) -> Shaped[Array, " 1 1"]: ...
 
     def compute(
         self,
-        x: Union[
-            Shaped[Array, " n d"], Shaped[Array, " d"], Shaped[Array, ""], float, int
-        ],
-        y: Union[
-            Shaped[Array, " m d"], Shaped[Array, " d"], Shaped[Array, ""], float, int
-        ],
-    ) -> Union[Shaped[Array, " n m"], Shaped[Array, "1 1"]]:
+        x: Shaped[Array, " n d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int,
+        y: Shaped[Array, " m d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int,
+    ) -> Shaped[Array, " n m"] | Shaped[Array, "1 1"]:
         r"""
         Evaluate the kernel on input data ``x`` and ``y``.
 
@@ -160,8 +164,8 @@ def compute(
     @abstractmethod
     def compute_elementwise(
         self,
-        x: Union[Shaped[Array, " d"], Shaped[Array, ""], float, int],
-        y: Union[Shaped[Array, " d"], Shaped[Array, ""], float, int],
+        x: Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
+        y: Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
     ) -> Shaped[Array, ""]:
         r"""
         Evaluate the kernel on individual input vectors ``x`` and ``y``, not-vectorised.
@@ -187,21 +191,23 @@ def grad_x(  # pyright: ignore[reportOverlappingOverload]
     @overload
     def grad_x(
         self,
-        x: Union[Shaped[Array, ""], float, int],
-        y: Union[Shaped[Array, ""], float, int],
+        x: Shaped[Array, ""] | float | int,
+        y: Shaped[Array, ""] | float | int,
     ) -> Shaped[Array, " 1 1 1"]: ...
 
     def grad_x(
         self,
-        x: Union[
-            Shaped[Array, " n d"], Shaped[Array, " d"], Shaped[Array, ""], float, int
-        ],
-        y: Union[
-            Shaped[Array, " m d"], Shaped[Array, " d"], Shaped[Array, ""], float, int
-        ],
-    ) -> Union[
-        Shaped[Array, " n m d"], Shaped[Array, " 1 1 d"], Shaped[Array, "1 1 1"]
-    ]:
+        x: Shaped[Array, " n d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int,
+        y: Shaped[Array, " m d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int,
+    ) -> Shaped[Array, " n m d"] | Shaped[Array, " 1 1 d"] | Shaped[Array, "1 1 1"]:
         r"""
         Evaluate the gradient (Jacobian) of the kernel function w.r.t. ``x``.
 
@@ -230,21 +236,23 @@ def grad_y(  # pyright: ignore[reportOverlappingOverload]
     @overload
     def grad_y(
         self,
-        x: Union[Shaped[Array, ""], float, int],
-        y: Union[Shaped[Array, ""], float, int],
+        x: Shaped[Array, ""] | float | int,
+        y: Shaped[Array, ""] | float | int,
     ) -> Shaped[Array, " 1 1 1"]: ...
 
     def grad_y(
         self,
-        x: Union[
-            Shaped[Array, " n d"], Shaped[Array, " d"], Shaped[Array, ""], float, int
-        ],
-        y: Union[
-            Shaped[Array, " m d"], Shaped[Array, " d"], Shaped[Array, ""], float, int
-        ],
-    ) -> Union[
-        Shaped[Array, " n m d"], Shaped[Array, " 1 1 d"], Shaped[Array, "1 1 1"]
-    ]:
+        x: Shaped[Array, " n d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int,
+        y: Shaped[Array, " m d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int,
+    ) -> Shaped[Array, " n m d"] | Shaped[Array, " 1 1 d"] | Shaped[Array, "1 1 1"]:
         r"""
         Evaluate the gradient (Jacobian) of the kernel function w.r.t. ``y``.
 
@@ -268,15 +276,15 @@ def grad_x_elementwise(
     @overload
     def grad_x_elementwise(
         self,
-        x: Union[Shaped[Array, ""], float, int],
-        y: Union[Shaped[Array, ""], float, int],
+        x: Shaped[Array, ""] | float | int,
+        y: Shaped[Array, ""] | float | int,
     ) -> Shaped[Array, ""]: ...
 
     def grad_x_elementwise(
         self,
-        x: Union[Shaped[Array, " d"], Shaped[Array, ""], float, int],
-        y: Union[Shaped[Array, " d"], Shaped[Array, ""], float, int],
-    ) -> Union[Shaped[Array, " d"], Shaped[Array, ""]]:
+        x: Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
+        y: Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
+    ) -> Shaped[Array, " d"] | Shaped[Array, ""]:
         r"""
         Evaluate the element-wise gradient of the kernel function w.r.t. ``x``.
 
@@ -301,15 +309,15 @@ def grad_y_elementwise(
     @overload
     def grad_y_elementwise(
         self,
-        x: Union[Shaped[Array, ""], float, int],
-        y: Union[Shaped[Array, ""], float, int],
+        x: Shaped[Array, ""] | float | int,
+        y: Shaped[Array, ""] | float | int,
     ) -> Shaped[Array, ""]: ...
 
     def grad_y_elementwise(
         self,
-        x: Union[Shaped[Array, " d"], Shaped[Array, ""], float, int],
-        y: Union[Shaped[Array, " d"], Shaped[Array, ""], float, int],
-    ) -> Union[Shaped[Array, " d"], Shaped[Array, ""]]:
+        x: Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
+        y: Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
+    ) -> Shaped[Array, " d"] | Shaped[Array, ""]:
         r"""
         Evaluate the element-wise gradient of the kernel function w.r.t. ``y``.
 
@@ -334,19 +342,23 @@ def divergence_x_grad_y(
     @overload
     def divergence_x_grad_y(
         self,
-        x: Union[Shaped[Array, " d"], Shaped[Array, ""], float, int],
-        y: Union[Shaped[Array, " d"], Shaped[Array, ""], float, int],
+        x: Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
+        y: Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
     ) -> Shaped[Array, " 1 1"]: ...
 
     def divergence_x_grad_y(
         self,
-        x: Union[
-            Shaped[Array, " n d"], Shaped[Array, " d"], Shaped[Array, ""], float, int
-        ],
-        y: Union[
-            Shaped[Array, " m d"], Shaped[Array, " d"], Shaped[Array, ""], float, int
-        ],
-    ) -> Union[Shaped[Array, " n m"], Shaped[Array, " 1 1"]]:
+        x: Shaped[Array, " n d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int,
+        y: Shaped[Array, " m d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int,
+    ) -> Shaped[Array, " n m"] | Shaped[Array, " 1 1"]:
         r"""
         Evaluate the divergence operator w.r.t. ``x`` of Jacobian w.r.t. ``y``.
 
@@ -364,8 +376,8 @@ def divergence_x_grad_y(
 
     def divergence_x_grad_y_elementwise(
         self,
-        x: Union[Shaped[Array, " d"], Shaped[Array, ""], float, int],
-        y: Union[Shaped[Array, " d"], Shaped[Array, ""], float, int],
+        x: Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
+        y: Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
     ) -> Shaped[Array, ""]:
         r"""
         Evaluate the element-wise divergence w.r.t. ``x`` of Jacobian w.r.t. ``y``.
@@ -386,17 +398,15 @@ def divergence_x_grad_y_elementwise(
 
     def gramian_row_mean(
         self,
-        x: Union[
-            Shaped[Array, " n d"],
-            Shaped[Array, " d"],
-            Shaped[Array, ""],
-            float,
-            int,
-            Data,
-        ],
+        x: Shaped[Array, " n d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int
+        | Data,
         *,
-        block_size: Union[int, None, tuple[Optional[int], Optional[int]]] = None,
-        unroll: Union[int, bool, tuple[Union[int, bool], Union[int, bool]]] = 1,
+        block_size: int | None | tuple[int | None, int | None] = None,
+        unroll: int | bool | tuple[int | bool, int | bool] = 1,
     ) -> Shaped[Array, " n"]:
         r"""
         Compute the (blocked) row-mean of the kernel's Gramian matrix.
@@ -414,101 +424,85 @@ def gramian_row_mean(
     @overload
     def compute_mean(
         self,
-        x: Union[
-            Shaped[Array, " n d"],
-            Shaped[Array, " d"],
-            Shaped[Array, ""],
-            float,
-            int,
-            Data,
-        ],
-        y: Union[
-            Shaped[Array, " m d"],
-            Shaped[Array, " d"],
-            Shaped[Array, ""],
-            float,
-            int,
-            Data,
-        ],
+        x: Shaped[Array, " n d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int
+        | Data,
+        y: Shaped[Array, " m d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int
+        | Data,
         axis: Literal[0] = 0,
         *,
-        block_size: Union[int, None, tuple[Optional[int], Optional[int]]] = None,
-        unroll: Union[int, bool, tuple[Union[int, bool], Union[int, bool]]] = 1,
+        block_size: int | None | tuple[int | None, int | None] = None,
+        unroll: int | bool | tuple[int | bool, int | bool] = 1,
     ) -> Shaped[Array, " #m"]: ...
 
     @overload
     def compute_mean(
         self,
-        x: Union[
-            Shaped[Array, " n d"],
-            Shaped[Array, " d"],
-            Shaped[Array, ""],
-            float,
-            int,
-            Data,
-        ],
-        y: Union[
-            Shaped[Array, " m d"],
-            Shaped[Array, " d"],
-            Shaped[Array, ""],
-            float,
-            int,
-            Data,
-        ],
+        x: Shaped[Array, " n d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int
+        | Data,
+        y: Shaped[Array, " m d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int
+        | Data,
         axis: Literal[1] = 1,
         *,
-        block_size: Union[int, None, tuple[Optional[int], Optional[int]]] = None,
-        unroll: Union[int, bool, tuple[Union[int, bool], Union[int, bool]]] = 1,
+        block_size: int | None | tuple[int | None, int | None] = None,
+        unroll: int | bool | tuple[int | bool, int | bool] = 1,
     ) -> Shaped[Array, " #n"]: ...
 
     @overload
     def compute_mean(
         self,
-        x: Union[
-            Shaped[Array, " n d"],
-            Shaped[Array, " d"],
-            Shaped[Array, ""],
-            float,
-            int,
-            Data,
-        ],
-        y: Union[
-            Shaped[Array, " m d"],
-            Shaped[Array, " d"],
-            Shaped[Array, ""],
-            float,
-            int,
-            Data,
-        ],
+        x: Shaped[Array, " n d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int
+        | Data,
+        y: Shaped[Array, " m d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int
+        | Data,
         axis: None = None,
         *,
-        block_size: Union[int, None, tuple[Optional[int], Optional[int]]] = None,
-        unroll: Union[int, bool, tuple[Union[int, bool], Union[int, bool]]] = 1,
+        block_size: int | None | tuple[int | None, int | None] = None,
+        unroll: int | bool | tuple[int | bool, int | bool] = 1,
     ) -> Shaped[Array, ""]: ...
 
     def compute_mean(
         self,
-        x: Union[
-            Shaped[Array, " n d"],
-            Shaped[Array, " d"],
-            Shaped[Array, ""],
-            float,
-            int,
-            Data,
-        ],
-        y: Union[
-            Shaped[Array, " m d"],
-            Shaped[Array, " d"],
-            Shaped[Array, ""],
-            float,
-            int,
-            Data,
-        ],
-        axis: Optional[int] = None,
+        x: Shaped[Array, " n d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int
+        | Data,
+        y: Shaped[Array, " m d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int
+        | Data,
+        axis: int | None = None,
         *,
-        block_size: Union[int, None, tuple[Optional[int], Optional[int]]] = None,
-        unroll: Union[int, bool, tuple[Union[int, bool], Union[int, bool]]] = 1,
-    ) -> Union[Shaped[Array, " n"], Shaped[Array, " m"], Shaped[Array, ""]]:
+        block_size: int | None | tuple[int | None, int | None] = None,
+        unroll: int | bool | tuple[int | bool, int | bool] = 1,
+    ) -> Shaped[Array, " n"] | Shaped[Array, " m"] | Shaped[Array, ""]:
         r"""
         Compute the (blocked) mean of the matrix :math:`K_{ij} = k(x_i, y_j)`.
 
diff --git a/coreax/kernels/scalar_valued.py b/coreax/kernels/scalar_valued.py
index 3aac9a4c4..622282cd8 100644
--- a/coreax/kernels/scalar_valued.py
+++ b/coreax/kernels/scalar_valued.py
@@ -14,7 +14,7 @@
 
 """Scalar-valued kernel functions."""
 
-from typing import Callable, Union
+from collections.abc import Callable
 
 import equinox as eqx
 import jax.numpy as jnp
@@ -481,7 +481,7 @@ def __check_init__(self):
     def _compute_summation_term(
         self,
         body: float,
-        iteration: Union[Shaped[Array, " *number_of_iterations"], int],
+        iteration: Shaped[Array, " *number_of_iterations"] | int,
     ) -> Shaped[Array, ""]:
         r"""
         Compute the summation term of the Matérn kernel for a given iteration.
@@ -775,8 +775,8 @@ class SteinKernel(UniCompositeKernel):
     """
 
     score_function: Callable[
-        [Union[Shaped[Array, " n d"], Shaped[Array, ""], float, int]],
-        Union[Shaped[Array, " n d"], Shaped[Array, " 1 1"]],
+        [Shaped[Array, " n d"] | Shaped[Array, ""] | float | int],
+        Shaped[Array, " n d"] | Shaped[Array, " 1 1"],
     ]
 
     @override
diff --git a/coreax/kernels/util.py b/coreax/kernels/util.py
index 0d76e52ae..33725fba3 100644
--- a/coreax/kernels/util.py
+++ b/coreax/kernels/util.py
@@ -15,7 +15,6 @@
 """Utility functions for the kernels subpackage."""
 
 from math import ceil
-from typing import Union
 
 import equinox as eqx
 import jax.numpy as jnp
@@ -28,7 +27,7 @@
 
 
 def _block_data_convert(
-    x: Union[Data, Shaped[Array, " n d"]], block_size: Union[int, None]
+    x: Data | Shaped[Array, " n d"], block_size: int | None
 ) -> tuple[Data, int]:
     """Convert 'x' into padded and weight normalized blocks of size 'block_size'."""
     x = as_data(x).normalize(preserve_zeros=True)
@@ -49,7 +48,7 @@ def _reshape(x: Array) -> Array:
 
 
 def median_heuristic(
-    x: Union[Shaped[Array, " n d"], Shaped[Array, " n"], Shaped[Array, ""], float, int],
+    x: Shaped[Array, " n d"] | Shaped[Array, " n"] | Shaped[Array, ""] | float | int,
 ) -> Shaped[Array, ""]:
     """
     Compute the median heuristic for setting kernel bandwidth.
diff --git a/coreax/least_squares.py b/coreax/least_squares.py
index 0aa335d27..ea4ce8fd0 100644
--- a/coreax/least_squares.py
+++ b/coreax/least_squares.py
@@ -53,7 +53,7 @@
 
 from abc import abstractmethod
 from collections.abc import Sequence
-from typing import Any, Optional, Union, cast
+from typing import Any, cast
 
 import equinox as eqx
 import jax
@@ -103,7 +103,7 @@ def solve_stack(
         regularisation_parameter: float,
         targets: Shaped[Array, " l n m"],
         identity: Shaped[Array, " n n"],
-        in_axes: Union[int, None, Sequence[Any]] = (0, None, 0, None),
+        in_axes: int | None | Sequence[Any] = (0, None, 0, None),
     ) -> Shaped[Array, " l n n"]:
         r"""
         Compute least-squares solutions to stack of regularised linear matrix equations.
@@ -144,7 +144,7 @@ class MinimalEuclideanNormSolver(RegularisedLeastSquaresSolver):
         of the ``array``. An alternate value of -1 will use machine precision.
     """
 
-    rcond: Optional[float] = None
+    rcond: float | None = None
 
     @override
     def solve(
@@ -268,7 +268,7 @@ class RandomisedEigendecompositionSolver(RegularisedLeastSquaresSolver):
     random_key: KeyArrayLike
     oversampling_parameter: int = 25
     power_iterations: int = 1
-    rcond: Optional[float] = None
+    rcond: float | None = None
 
     def __check_init__(self):
         """Validate inputs."""
diff --git a/coreax/metrics.py b/coreax/metrics.py
index d1512e145..790f3cdd1 100644
--- a/coreax/metrics.py
+++ b/coreax/metrics.py
@@ -24,7 +24,7 @@
 
 from abc import abstractmethod
 from itertools import product
-from typing import Any, Generic, Optional, TypeVar, Union
+from typing import Any, Generic, TypeVar
 
 import equinox as eqx
 import jax.numpy as jnp
@@ -91,8 +91,8 @@ def compute(
         reference_data: Data,
         comparison_data: Data,
         *,
-        block_size: Union[int, None, tuple[Union[int, None], Union[int, None]]] = None,
-        unroll: Union[int, bool, tuple[Union[int, bool], Union[int, bool]]] = 1,
+        block_size: int | None | tuple[int | None, int | None] = None,
+        unroll: int | bool | tuple[int | bool, int | bool] = 1,
         **kwargs: Any,
     ) -> Shaped[Array, ""]:
         r"""
@@ -195,7 +195,7 @@ class KSD(Metric[Data]):
     """
 
     kernel: coreax.kernels.ScalarValuedKernel
-    score_matching: Optional[ScoreMatching] = None
+    score_matching: ScoreMatching | None = None
     precision_threshold: float = 1e-12
 
     def compute(
@@ -205,8 +205,8 @@ def compute(
         *,
         laplace_correct: bool = False,
         regularise: bool = False,
-        block_size: Optional[int] = None,
-        unroll: Union[int, bool, tuple[Union[int, bool], Union[int, bool]]] = 1,
+        block_size: int | None = None,
+        unroll: int | bool | tuple[int | bool, int | bool] = 1,
         **kwargs: Any,
     ) -> Shaped[Array, ""]:
         r"""
diff --git a/coreax/score_matching.py b/coreax/score_matching.py
index 34bc29905..2f0897814 100644
--- a/coreax/score_matching.py
+++ b/coreax/score_matching.py
@@ -34,7 +34,7 @@
 from abc import abstractmethod
 from collections.abc import Callable, Sequence
 from functools import partial
-from typing import Union, overload
+from typing import overload
 
 import equinox as eqx
 import numpy as np
@@ -77,9 +77,9 @@ class ScoreMatching(eqx.Module):
     @abstractmethod
     @overload
     def match(
-        self, x: Union[Shaped[Array, " 1 1"], Shaped[Array, ""], float, int]
+        self, x: Shaped[Array, " 1 1"] | Shaped[Array, ""] | float | int
     ) -> Callable[
-        [Union[Shaped[Array, " 1 1"], Shaped[Array, ""], float, int]],
+        [Shaped[Array, " 1 1"] | Shaped[Array, ""] | float | int],
         Shaped[Array, " 1 1"],
     ]: ...
 
@@ -91,14 +91,14 @@ def match(  # pyright: ignore[reportOverlappingOverload]
 
     @abstractmethod
     def match(
-        self, x: Union[Shaped[Array, " n d"], Shaped[Array, ""], float, int]
-    ) -> Union[
-        Callable[[Shaped[Array, " n d"]], Shaped[Array, " n d"]],
-        Callable[
-            [Union[Shaped[Array, " 1 1"], Shaped[Array, ""], float, int]],
+        self, x: Shaped[Array, " n d"] | Shaped[Array, ""] | float | int
+    ) -> (
+        Callable[[Shaped[Array, " n d"]], Shaped[Array, " n d"]]
+        | Callable[
+            [Shaped[Array, " 1 1"] | Shaped[Array, ""] | float | int],
             Shaped[Array, " 1 1"],
-        ],
-    ]:
+        ]
+    ):
         r"""
         Match some model score function to dataset :math:`X\in\mathbb{R}^{n \times d}`.
 
@@ -562,7 +562,7 @@ def match(self, x):
 
         @overload
         def score_function(
-            x_: Union[Shaped[Array, " 1 1"], Shaped[Array, ""], float, int],
+            x_: Shaped[Array, " 1 1"] | Shaped[Array, ""] | float | int,
         ) -> Shaped[Array, " 1 1"]: ...
 
         @overload
@@ -571,8 +571,8 @@ def score_function(  # pyright: ignore[reportOverlappingOverload]
         ) -> Shaped[Array, " n d"]: ...
 
         def score_function(
-            x_: Union[Shaped[Array, " n d"], Shaped[Array, ""], float, int],
-        ) -> Union[Shaped[Array, " n d"], Shaped[Array, " 1 1"]]:
+            x_: Shaped[Array, " n d"] | Shaped[Array, ""] | float | int,
+        ) -> Shaped[Array, " n d"] | Shaped[Array, " 1 1"]:
             r"""
             Compute the score function using a kernel density estimation.
 
@@ -613,7 +613,7 @@ def score_function(
 def convert_stein_kernel(
     x: Shaped[Array, " n d"],
     kernel: ScalarValuedKernel,
-    score_matching: Union[ScoreMatching, None],
+    score_matching: ScoreMatching | None,
 ) -> SteinKernel:
     r"""
     Convert the kernel to a :class:`~coreax.kernels.SteinKernel`.
diff --git a/coreax/solvers/base.py b/coreax/solvers/base.py
index ff9b41310..d2b756630 100644
--- a/coreax/solvers/base.py
+++ b/coreax/solvers/base.py
@@ -15,7 +15,7 @@
 """Abstract base classes for constructing different types of coreset solvers."""
 
 from abc import abstractmethod
-from typing import Generic, Optional, TypeVar
+from typing import Generic, TypeVar
 
 import equinox as eqx
 
@@ -38,7 +38,7 @@ class Solver(eqx.Module, Generic[_Coreset, _Data, _State]):
 
     @abstractmethod
     def reduce(
-        self, dataset: _Data, solver_state: Optional[_State] = None
+        self, dataset: _Data, solver_state: _State | None = None
     ) -> tuple[_Coreset, _State]:
         r"""
         Reduce ``dataset`` to a coreset - solve the coreset problem.
@@ -82,7 +82,7 @@ class RefinementSolver(CoresubsetSolver[_Data, _State], Generic[_Data, _State]):
 
     @abstractmethod
     def refine(
-        self, coresubset: Coresubset[_Data], solver_state: Optional[_State] = None
+        self, coresubset: Coresubset[_Data], solver_state: _State | None = None
     ) -> tuple[Coresubset[_Data], _State]:
         """
         Refine a coresubset - swap/update coresubset indices.
diff --git a/coreax/solvers/composite.py b/coreax/solvers/composite.py
index 7bed3e955..82c8d38d0 100644
--- a/coreax/solvers/composite.py
+++ b/coreax/solvers/composite.py
@@ -16,7 +16,7 @@
 
 import math
 import warnings
-from typing import Generic, Optional, TypeVar, Union, overload
+from typing import Generic, TypeAlias, TypeVar, overload
 
 import equinox as eqx
 import jax
@@ -26,14 +26,14 @@
 from jax import Array
 from jaxtyping import Integer
 from sklearn.neighbors import BallTree, KDTree
-from typing_extensions import TypeAlias, override
+from typing_extensions import override
 
 from coreax.coreset import AbstractCoreset, Coresubset
 from coreax.data import Data, SupervisedData
 from coreax.solvers.base import ExplicitSizeSolver, PaddingInvariantSolver, Solver
 from coreax.util import tree_zero_pad_leading_axis
 
-BinaryTree: TypeAlias = Union[KDTree, BallTree]
+BinaryTree: TypeAlias = KDTree | BallTree
 _Data = TypeVar("_Data", Data, SupervisedData)
 _Coreset = TypeVar("_Coreset", bound=AbstractCoreset)
 _State = TypeVar("_State")
@@ -125,7 +125,7 @@ def __check_init__(self):
 
     @override
     def reduce(  # noqa: C901
-        self, dataset: _Data, solver_state: Optional[_State] = None
+        self, dataset: _Data, solver_state: _State | None = None
     ) -> tuple[_Coreset, _State]:
         # There is no obvious way to use state information here.
         del solver_state
@@ -141,15 +141,15 @@ def _reduce_coreset(
         ) -> tuple[_Coreset, _State, None]: ...
 
         def _reduce_coreset(
-            data: _Data, _indices: Optional[_Indices] = None
-        ) -> tuple[_Coreset, _State, Optional[_Indices]]:
+            data: _Data, _indices: _Indices | None = None
+        ) -> tuple[_Coreset, _State, _Indices | None]:
             if len(data) <= self.leaf_size:
                 coreset, state = self.base_solver.reduce(data)
                 if _indices is not None and isinstance(coreset, Coresubset):
                     _indices = _indices[coreset.indices.data]
                 return coreset, state, _indices
 
-            def wrapper(partition: _Data) -> tuple[_Data, Optional[Array]]:
+            def wrapper(partition: _Data) -> tuple[_Data, Array | None]:
                 """
                 Apply the `reduce` method of the base solver on a partition.
 
diff --git a/coreax/solvers/coresubset.py b/coreax/solvers/coresubset.py
index 80c240476..c125b6bcd 100644
--- a/coreax/solvers/coresubset.py
+++ b/coreax/solvers/coresubset.py
@@ -16,7 +16,7 @@
 
 import math
 from collections.abc import Callable
-from typing import Literal, Optional, TypeVar, Union, overload
+from typing import Literal, TypeVar, overload
 from warnings import warn
 
 import equinox as eqx
@@ -129,8 +129,8 @@ def _greedy_kernel_selection(
     output_size: int,
     kernel: ScalarValuedKernel,
     unique: bool,
-    block_size: Optional[Union[int, tuple[Optional[int], Optional[int]]]],
-    unroll: Union[int, bool, tuple[Union[int, bool], Union[int, bool]]],
+    block_size: int | tuple[int | None, int | None] | None,
+    unroll: int | bool | tuple[int | bool, int | bool],
 ) -> Coresubset[_Data]:
     """
     Iterative-greedy coresubset point selection loop.
@@ -282,17 +282,17 @@ class KernelHerding(
 
     kernel: ScalarValuedKernel
     unique: bool = True
-    block_size: Optional[Union[int, tuple[Optional[int], Optional[int]]]] = None
-    unroll: Union[int, bool, tuple[Union[int, bool], Union[int, bool]]] = 1
+    block_size: int | tuple[int | None, int | None] | None = None
+    unroll: int | bool | tuple[int | bool, int | bool] = 1
     probabilistic: bool = False
-    temperature: Union[float, Scalar] = eqx.field(default=1.0)
+    temperature: float | Scalar = eqx.field(default=1.0)
     random_key: KeyArrayLike = eqx.field(default_factory=lambda: jax.random.key(0))
 
     @override
     def reduce(
         self,
         dataset: _Data,
-        solver_state: Optional[HerdingState] = None,
+        solver_state: HerdingState | None = None,
     ) -> tuple[Coresubset[_Data], HerdingState]:
         initial_coresubset = _initial_coresubset(0, self.coreset_size, dataset)
         return self.refine(initial_coresubset, solver_state)
@@ -300,7 +300,7 @@ def reduce(
     def refine(
         self,
         coresubset: Coresubset[_Data],
-        solver_state: Optional[HerdingState] = None,
+        solver_state: HerdingState | None = None,
     ) -> tuple[Coresubset[_Data], HerdingState]:
         """
         Refine a coresubset with 'Kernel Herding'.
@@ -365,9 +365,9 @@ def selection_function(
     def reduce_iterative(
         self,
         dataset: _Data,
-        solver_state: Optional[HerdingState] = None,
+        solver_state: HerdingState | None = None,
         num_iterations: int = 1,
-        t_schedule: Optional[Shaped[Array, " {num_iterations}"]] = None,
+        t_schedule: Shaped[Array, " {num_iterations}"] | None = None,
     ) -> tuple[Coresubset[_Data], HerdingState]:
         """
         Reduce a dataset to a coreset by refining iteratively.
@@ -464,13 +464,13 @@ class SteinThinning(
     """
 
     kernel: ScalarValuedKernel
-    score_matching: Optional[ScoreMatching] = None
+    score_matching: ScoreMatching | None = None
     unique: bool = True
     regularise: bool = True
-    regulariser_lambda: Optional[float] = None
-    block_size: Optional[Union[int, tuple[Optional[int], Optional[int]]]] = None
-    unroll: Union[int, bool, tuple[Union[int, bool], Union[int, bool]]] = 1
-    kde_bw_method: Optional[Union[str, int, Callable]] = None
+    regulariser_lambda: float | None = None
+    block_size: int | tuple[int | None, int | None] | None = None
+    unroll: int | bool | tuple[int | bool, int | bool] = 1
+    kde_bw_method: str | int | Callable | None = None
 
     @override
     def reduce(
@@ -582,7 +582,7 @@ class RPCholesky(CoresubsetSolver[_Data, RPCholeskyState], ExplicitSizeSolver):
     unique: bool = True
 
     def reduce(
-        self, dataset: _Data, solver_state: Optional[RPCholeskyState] = None
+        self, dataset: _Data, solver_state: RPCholeskyState | None = None
     ) -> tuple[Coresubset[_Data], RPCholeskyState]:
         """
         Reduce 'dataset' to a :class:`~coreax.coreset.Coresubset` with 'RPCholesky'.
@@ -701,8 +701,8 @@ def _setup_batch_solver(  # pragma: no cover # pyright: ignore reportOverlapping
     coreset_size: int,
     coresubset: Coresubset,
     num_data_pairs: int,
-    candidate_batch_size: Optional[int],
-    loss_batch_size: Optional[int],
+    candidate_batch_size: int | None,
+    loss_batch_size: int | None,
     random_key: KeyArrayLike,
     setup_identity: Literal[True] = True,
     setup_loss_batch_indices: Literal[True] = True,
@@ -716,8 +716,8 @@ def _setup_batch_solver(  # pragma: no cover
     coreset_size: int,
     coresubset: Coresubset,
     num_data_pairs: int,
-    candidate_batch_size: Optional[int],
-    loss_batch_size: Optional[int],
+    candidate_batch_size: int | None,
+    loss_batch_size: int | None,
     random_key: KeyArrayLike,
     setup_identity: Literal[False] = False,
     setup_loss_batch_indices: Literal[False] = False,
@@ -731,8 +731,8 @@ def _setup_batch_solver(  # pragma: no cover
     coreset_size: int,
     coresubset: Coresubset,
     num_data_pairs: int,
-    candidate_batch_size: Optional[int],
-    loss_batch_size: Optional[int],
+    candidate_batch_size: int | None,
+    loss_batch_size: int | None,
     random_key: KeyArrayLike,
     setup_identity: Literal[True] = True,
     setup_loss_batch_indices: Literal[False] = False,
@@ -746,8 +746,8 @@ def _setup_batch_solver(  # pragma: no cover
     coreset_size: int,
     coresubset: Coresubset,
     num_data_pairs: int,
-    candidate_batch_size: Optional[int],
-    loss_batch_size: Optional[int],
+    candidate_batch_size: int | None,
+    loss_batch_size: int | None,
     random_key: KeyArrayLike,
     setup_identity: Literal[False] = False,
     setup_loss_batch_indices: Literal[True] = True,
@@ -758,17 +758,17 @@ def _setup_batch_solver(
     coreset_size: int,
     coresubset: Coresubset,
     num_data_pairs: int,
-    candidate_batch_size: Optional[int],
-    loss_batch_size: Optional[int],
+    candidate_batch_size: int | None,
+    loss_batch_size: int | None,
     random_key: KeyArrayLike,
     setup_identity: bool = False,
     setup_loss_batch_indices: bool = True,
 ) -> tuple[
     Shaped[Array, " n"],
     Shaped[Array, " n p"],
-    Optional[Shaped[Array, " n p"]],
+    Shaped[Array, " n p"] | None,
     Shaped[Array, " p n"],
-    Optional[Shaped[Array, " n n"]],
+    Shaped[Array, " n n"] | None,
 ]:
     """
     Set up the matrices required to initialise a batched solver.
@@ -1177,15 +1177,15 @@ class GreedyKernelPoints(
     feature_kernel: ScalarValuedKernel
     regularisation_parameter: float = 1e-6
     unique: bool = True
-    candidate_batch_size: Optional[int] = None
-    loss_batch_size: Optional[int] = None
-    least_squares_solver: Optional[RegularisedLeastSquaresSolver] = None
+    candidate_batch_size: int | None = None
+    loss_batch_size: int | None = None
+    least_squares_solver: RegularisedLeastSquaresSolver | None = None
 
     @override
     def reduce(
         self,
         dataset: SupervisedData,
-        solver_state: Optional[GreedyKernelPointsState] = None,
+        solver_state: GreedyKernelPointsState | None = None,
     ) -> tuple[Coresubset[SupervisedData], GreedyKernelPointsState]:
         initial_coresubset = _initial_coresubset(-1, self.coreset_size, dataset)
         return self.refine(initial_coresubset, solver_state)
@@ -1193,7 +1193,7 @@ def reduce(
     def refine(  # noqa: PLR0915
         self,
         coresubset: Coresubset[SupervisedData],
-        solver_state: Optional[GreedyKernelPointsState] = None,
+        solver_state: GreedyKernelPointsState | None = None,
     ) -> tuple[Coresubset[SupervisedData], GreedyKernelPointsState]:
         """
         Refine a coresubset with :class:`GreedyKernelPointsState`.
@@ -1387,7 +1387,7 @@ def reduce(
 
     def kt_half_recursive(
         self,
-        current_coreset: Union[_Data, Coresubset[_Data]],
+        current_coreset: _Data | Coresubset[_Data],
         m: int,
         original_dataset: _Data,
     ) -> list[Coresubset[_Data]]:
diff --git a/coreax/solvers/recombination.py b/coreax/solvers/recombination.py
index bf7d0212d..a89579d1c 100644
--- a/coreax/solvers/recombination.py
+++ b/coreax/solvers/recombination.py
@@ -87,7 +87,7 @@
 
 import math
 from collections.abc import Callable
-from typing import Generic, Literal, NamedTuple, Optional, TypeVar, Union
+from typing import Generic, Literal, NamedTuple, TypeVar
 
 import jax
 import jax.numpy as jnp
@@ -126,7 +126,7 @@ class RecombinationSolver(CoresubsetSolver[_Data, _State], Generic[_Data, _State
         compatible as the coreset size :math:`m^\prime` is unknown at compile time.
     """
 
-    test_functions: Optional[Callable[[Array], Real[Array, " m-1"]]] = None
+    test_functions: Callable[[Array], Real[Array, " m-1"]] | None = None
     mode: Literal["implicit-explicit", "implicit", "explicit"] = "implicit-explicit"
 
     def __check_init__(self):
@@ -175,7 +175,7 @@ class CaratheodoryRecombination(RecombinationSolver[Data, None]):
         rcond is :data:`None`, it defaults to `floating point eps * max(n, d)`
     """
 
-    rcond: Optional[float] = None
+    rcond: float | None = None
 
     @override
     def reduce(
@@ -277,7 +277,7 @@ def _eliminate(state: _EliminationState) -> _EliminationState:
 
 def _push_forward(
     nodes: Shaped[Array, " n"],
-    test_functions: Optional[Callable[[Array], Real[Array, " m-1"]]],
+    test_functions: Callable[[Array], Real[Array, " m-1"]] | None,
     augment: bool = True,
 ) -> Shaped[Array, "n m"]:
     r"""
@@ -355,7 +355,7 @@ def _co_linearize(
 # pylint: enable=line-too-long
 def _resolve_null_basis(
     nodes: Shaped[Array, "n m"],
-    rcond: Union[float, None] = None,
+    rcond: float | None = None,
 ) -> tuple[Shaped[Array, "n n"], Integer[Array, ""]]:
     r"""
     Resolve the largest left null space basis, and its rank, for passed the node matrix.
@@ -386,7 +386,7 @@ def _resolve_null_basis(
 # Credit: https://github.com/patrick-kidger/lineax/blob/9b923c8df6556551fedc7adeea7979b5c7b3ffb0/lineax/_misc.py#L34  # noqa: E501
 # pylint: enable=line-too-long
 def _resolve_rcond(
-    shape: tuple[int, ...], dtype: DTypeLike, rcond: Optional[float] = None
+    shape: tuple[int, ...], dtype: DTypeLike, rcond: float | None = None
 ) -> Float[Array, ""]:
     """
     Resolve the relative condition number (rcond).
@@ -497,7 +497,7 @@ class TreeRecombination(RecombinationSolver[Data, None]):
         performing recombination, is equal to `n_nodes / tree_reduction_factor`;
     """
 
-    rcond: Union[float, None] = None
+    rcond: float | None = None
     tree_reduction_factor: int = 2
 
     @override
diff --git a/coreax/util.py b/coreax/util.py
index bc65905fd..9b6fd0623 100644
--- a/coreax/util.py
+++ b/coreax/util.py
@@ -30,8 +30,7 @@ class factories and checks for numerical precision.
 from typing import (
     Any,
     NamedTuple,
-    Optional,
-    Union,
+    TypeAlias,
 )
 
 import equinox as eqx
@@ -40,7 +39,6 @@ class factories and checks for numerical precision.
 import jax.tree_util as jtu
 from jax import Array, block_until_ready, jit, vmap
 from jaxtyping import Shaped
-from typing_extensions import TypeAlias
 
 _logger = logging.getLogger(__name__)
 logging.basicConfig(level=logging.INFO, stream=sys.stdout)
@@ -71,13 +69,13 @@ class JITCompilableFunction(NamedTuple):
 
     fn: Callable
     fn_args: tuple = ()
-    fn_kwargs: Optional[dict[str, Any]] = None
-    jit_kwargs: Optional[dict[str, Any]] = None
-    name: Optional[str] = None
+    fn_kwargs: dict[str, Any] | None = None
+    jit_kwargs: dict[str, Any] | None = None
+    name: str | None = None
 
     def without_name(
         self,
-    ) -> tuple[Callable, tuple, Optional[dict[str, Any]], Optional[dict[str, Any]]]:
+    ) -> tuple[Callable, tuple, dict[str, Any] | None, dict[str, Any] | None]:
         """Return the tuple (fn, fn_args, fn_kwargs, jit_kwargs)."""
         return self.fn, self.fn_args, self.fn_kwargs, self.jit_kwargs
 
@@ -136,7 +134,7 @@ def _pad(x: Shaped[Array, " n"]) -> Shaped[Array, " n + pad_width"]:
 
 
 def apply_negative_precision_threshold(
-    x: Union[Shaped[Array, ""], float, int], precision_threshold: float = 1e-8
+    x: Shaped[Array, ""] | float | int, precision_threshold: float = 1e-8
 ) -> Shaped[Array, ""]:
     """
     Round a number to 0.0 if it is negative but within precision_threshold of 0.0.
@@ -152,19 +150,15 @@ def apply_negative_precision_threshold(
 def pairwise(
     fn: Callable[
         [
-            Union[Shaped[Array, " d"], Shaped[Array, ""], float, int],
-            Union[Shaped[Array, " d"], Shaped[Array, ""], float, int],
+            Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
+            Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
         ],
         Shaped[Array, " *d"],
     ],
 ) -> Callable[
     [
-        Union[
-            Shaped[Array, " n d"], Shaped[Array, " d"], Shaped[Array, ""], float, int
-        ],
-        Union[
-            Shaped[Array, " m d"], Shaped[Array, " d"], Shaped[Array, ""], float, int
-        ],
+        Shaped[Array, " n d"] | Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
+        Shaped[Array, " m d"] | Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
     ],
     Shaped[Array, " n m *d"],
 ]:
@@ -178,12 +172,16 @@ def pairwise(
 
     @wraps(fn)
     def pairwise_fn(
-        x: Union[
-            Shaped[Array, " n d"], Shaped[Array, " d"], Shaped[Array, ""], float, int
-        ],
-        y: Union[
-            Shaped[Array, " m d"], Shaped[Array, " d"], Shaped[Array, ""], float, int
-        ],
+        x: Shaped[Array, " n d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int,
+        y: Shaped[Array, " m d"]
+        | Shaped[Array, " d"]
+        | Shaped[Array, ""]
+        | float
+        | int,
     ) -> Shaped[Array, " n m *d"]:
         x = jnp.atleast_2d(x)
         y = jnp.atleast_2d(y)
@@ -198,8 +196,8 @@ def pairwise_fn(
 
 @jit
 def squared_distance(
-    x: Union[Shaped[Array, " d"], Shaped[Array, ""], float, int],
-    y: Union[Shaped[Array, " d"], Shaped[Array, ""], float, int],
+    x: Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
+    y: Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
 ) -> Shaped[Array, ""]:
     """
     Calculate the squared distance between two vectors.
@@ -216,8 +214,8 @@ def squared_distance(
 
 @jit
 def difference(
-    x: Union[Shaped[Array, " d"], Shaped[Array, ""], float, int],
-    y: Union[Shaped[Array, " d"], Shaped[Array, ""], float, int],
+    x: Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
+    y: Shaped[Array, " d"] | Shaped[Array, ""] | float | int,
 ) -> Shaped[Array, ""]:
     """
     Calculate vector difference for a pair of vectors.
@@ -262,8 +260,8 @@ def sample_batch_indices(
 def jit_test(
     fn: Callable,
     fn_args: tuple = (),
-    fn_kwargs: Optional[dict] = None,
-    jit_kwargs: Optional[dict] = None,
+    fn_kwargs: dict | None = None,
+    jit_kwargs: dict | None = None,
 ) -> tuple[float, float]:
     """
     Measure execution times of two runs of a JIT-compilable function.
@@ -342,7 +340,7 @@ def speed_comparison_test(
     function_setups: Sequence[JITCompilableFunction],
     num_runs: int = 10,
     log_results: bool = False,
-    normalisation: Optional[tuple[float, float]] = None,
+    normalisation: tuple[float, float] | None = None,
 ) -> tuple[list[tuple[Array, Array]], dict[str, Array]]:
     """
     Compare compilation time and runtime of a list of JIT-able functions.
diff --git a/coreax/weights.py b/coreax/weights.py
index 1862c7fba..bedb71246 100644
--- a/coreax/weights.py
+++ b/coreax/weights.py
@@ -32,7 +32,7 @@
 """
 
 from abc import abstractmethod
-from typing import Generic, TypeVar, Union
+from typing import Generic, TypeVar
 
 import equinox as eqx
 import jax.numpy as jnp
@@ -113,8 +113,8 @@ def _prepare_kernel_system(
     coreset: Data,
     epsilon: float = 1e-10,
     *,
-    block_size: Union[int, None, tuple[Union[int, None], Union[int, None]]] = None,
-    unroll: Union[int, bool, tuple[Union[int, bool], Union[int, bool]]] = 1,
+    block_size: int | None | tuple[int | None, int | None] = None,
+    unroll: int | bool | tuple[int | bool, int | bool] = 1,
 ) -> tuple[Array, Array]:
     r"""
     Return the row mean of :math`k(coreset, dataset)` and the coreset Gramian.
@@ -217,8 +217,8 @@ def solve(
         coreset: _Data,
         epsilon: float = 1e-10,
         *,
-        block_size: Union[int, None, tuple[Union[int, None], Union[int, None]]] = None,
-        unroll: Union[int, bool, tuple[Union[int, bool], Union[int, bool]]] = 1,
+        block_size: int | None | tuple[int | None, int | None] = None,
+        unroll: int | bool | tuple[int | bool, int | bool] = 1,
         **solver_kwargs,
     ) -> Shaped[Array, " m"]:
         r"""
@@ -285,8 +285,8 @@ def solve(
         coreset: _Data,
         epsilon: float = 1e-10,
         *,
-        block_size: Union[int, None, tuple[Union[int, None], Union[int, None]]] = None,
-        unroll: Union[int, bool, tuple[Union[int, bool], Union[int, bool]]] = 1,
+        block_size: int | None | tuple[int | None, int | None] = None,
+        unroll: int | bool | tuple[int | bool, int | bool] = 1,
         **solver_kwargs,
     ) -> Shaped[Array, " m"]:
         r"""
diff --git a/documentation/source/conf.py b/documentation/source/conf.py
index b4edece72..6dba454d9 100644
--- a/documentation/source/conf.py
+++ b/documentation/source/conf.py
@@ -23,7 +23,7 @@
 import sys
 from pathlib import Path
 from types import ModuleType
-from typing import Any, Optional, TypeVar, Union
+from typing import Any, TypeVar
 from unittest import mock
 
 import sphinx.config
@@ -226,9 +226,7 @@
 }
 
 
-def typehints_formatter(
-    annotation: Any, config: sphinx.config.Config
-) -> Union[str, None]:
+def typehints_formatter(annotation: Any, config: sphinx.config.Config) -> str | None:
     """
     Properly replace custom type aliases.
 
@@ -301,7 +299,7 @@ def typehints_formatter(
 def create_custom_inv_file(
     module: ModuleType,
     custom_refs: dict[str, dict[str, str]],
-    file_name: Optional[str] = None,
+    file_name: str | None = None,
 ) -> None:
     """
     Create an objects.inv file containing custom routes.
diff --git a/examples/coreset_in_model_pipeline.py b/examples/coreset_in_model_pipeline.py
index 9b7da32c4..6d0ec9631 100644
--- a/examples/coreset_in_model_pipeline.py
+++ b/examples/coreset_in_model_pipeline.py
@@ -22,7 +22,6 @@
 
 from pathlib import Path
 from time import time
-from typing import Optional
 
 import equinox as eqx
 import jax.numpy as jnp
@@ -45,7 +44,7 @@
 # pylint: disable=too-many-statements
 # pylint: disable=duplicate-code
 def main(
-    out_path: Optional[Path] = None,
+    out_path: Path | None = None,
 ) -> tuple[tuple[float, float], tuple[float, float], tuple[float, float]]:
     """
     Run machine learning pipeline example.
diff --git a/examples/cubature_recombination.py b/examples/cubature_recombination.py
index c9e60223c..f4f6ac8da 100644
--- a/examples/cubature_recombination.py
+++ b/examples/cubature_recombination.py
@@ -23,8 +23,8 @@
 
 import functools as ft
 import itertools
-from collections.abc import Iterable
-from typing import Callable, Literal
+from collections.abc import Callable, Iterable
+from typing import Literal
 
 import jax
 import jax.numpy as jnp
diff --git a/examples/david_map_reduce_weighted.py b/examples/david_map_reduce_weighted.py
index 307a22586..935a31058 100644
--- a/examples/david_map_reduce_weighted.py
+++ b/examples/david_map_reduce_weighted.py
@@ -37,7 +37,6 @@
 """
 
 from pathlib import Path
-from typing import Optional
 
 import cv2
 import equinox as eqx
@@ -98,7 +97,7 @@ def downsample_opencv(image_path: str, downsampling_factor: int) -> np.ndarray:
 
 def main(
     in_path: Path = Path("../examples/data/david_orig.png"),
-    out_path: Optional[Path] = None,
+    out_path: Path | None = None,
     downsampling_factor: int = 1,
 ) -> tuple[float, float]:
     """
diff --git a/examples/herding_approximate_gram_matrix.py b/examples/herding_approximate_gram_matrix.py
index 0e85cce20..a1b326bd1 100644
--- a/examples/herding_approximate_gram_matrix.py
+++ b/examples/herding_approximate_gram_matrix.py
@@ -25,7 +25,6 @@
 """
 
 from pathlib import Path
-from typing import Optional
 
 import equinox as eqx
 import jax.numpy as jnp
@@ -48,7 +47,7 @@
 # pylint warnings raised that go against this approach
 # pylint: disable=duplicate-code
 # pylint: disable=too-many-locals
-def main(out_path: Optional[Path] = None) -> tuple[float, float]:
+def main(out_path: Path | None = None) -> tuple[float, float]:
     """
     Run the tabular data herding example with an approximate kernel Gramian row-mean.
 
diff --git a/examples/herding_basic.py b/examples/herding_basic.py
index e36cfeb90..92e254d93 100644
--- a/examples/herding_basic.py
+++ b/examples/herding_basic.py
@@ -24,7 +24,6 @@
 """
 
 from pathlib import Path
-from typing import Optional
 
 import equinox as eqx
 import jax.numpy as jnp
@@ -50,7 +49,7 @@
 # pylint: disable=too-many-locals
 # pylint: disable=too-many-statements
 # pylint: disable=duplicate-code
-def main(out_path: Optional[Path] = None) -> tuple[float, float, float, float]:
+def main(out_path: Path | None = None) -> tuple[float, float, float, float]:
     """
     Run the basic herding on tabular data example.
 
diff --git a/examples/herding_basic_weighted.py b/examples/herding_basic_weighted.py
index bf019da92..d59d7d81e 100644
--- a/examples/herding_basic_weighted.py
+++ b/examples/herding_basic_weighted.py
@@ -24,7 +24,6 @@
 """
 
 from pathlib import Path
-from typing import Optional
 
 import equinox as eqx
 import jax.numpy as jnp
@@ -50,7 +49,7 @@
 # pylint warnings raised that go against this approach
 # pylint: disable=too-many-locals
 # pylint: disable=duplicate-code
-def main(out_path: Optional[Path] = None) -> tuple[float, float, float, float]:
+def main(out_path: Path | None = None) -> tuple[float, float, float, float]:
     """
     Run the basic herding on tabular data example.
 
diff --git a/examples/herding_duo_composite_kernel.py b/examples/herding_duo_composite_kernel.py
index b8ae6f319..4c8af57a5 100644
--- a/examples/herding_duo_composite_kernel.py
+++ b/examples/herding_duo_composite_kernel.py
@@ -25,7 +25,6 @@
 """
 
 from pathlib import Path
-from typing import Optional
 
 import equinox as eqx
 import jax.numpy as jnp
@@ -49,7 +48,7 @@
 # pylint warnings raised that go against this approach
 # pylint: disable=too-many-locals
 # pylint: disable=duplicate-code
-def main(out_path: Optional[Path] = None) -> tuple[float, float]:
+def main(out_path: Path | None = None) -> tuple[float, float]:
     """
     Run the basic herding on tabular data example.
 
diff --git a/examples/herding_refine_weighted.py b/examples/herding_refine_weighted.py
index c9cc7b312..1bfb447a9 100644
--- a/examples/herding_refine_weighted.py
+++ b/examples/herding_refine_weighted.py
@@ -27,7 +27,6 @@
 """
 
 from pathlib import Path
-from typing import Optional
 
 import equinox as eqx
 import jax.numpy as jnp
@@ -53,7 +52,7 @@
 # pylint warnings raised that go against this approach
 # pylint: disable=too-many-locals
 # pylint: disable=duplicate-code
-def main(out_path: Optional[Path] = None) -> tuple[float, float, float, float]:
+def main(out_path: Path | None = None) -> tuple[float, float, float, float]:
     """
     Run the kernel herding on tabular data with a refine post-processing step.
 
diff --git a/examples/herding_stein_weighted.py b/examples/herding_stein_weighted.py
index 779802b58..521f479dc 100644
--- a/examples/herding_stein_weighted.py
+++ b/examples/herding_stein_weighted.py
@@ -30,7 +30,6 @@
 """
 
 from pathlib import Path
-from typing import Optional
 
 import equinox as eqx
 import jax.numpy as jnp
@@ -56,7 +55,7 @@
 # pylint warnings raised that go against this approach
 # pylint: disable=too-many-locals
 # pylint: disable=duplicate-code
-def main(out_path: Optional[Path] = None) -> tuple[float, float]:
+def main(out_path: Path | None = None) -> tuple[float, float]:
     """
     Run the tabular herding example using weighted herding.
 
diff --git a/examples/herding_stein_weighted_ssm.py b/examples/herding_stein_weighted_ssm.py
index 34a4ff8e8..84c74affa 100644
--- a/examples/herding_stein_weighted_ssm.py
+++ b/examples/herding_stein_weighted_ssm.py
@@ -32,7 +32,6 @@
 """
 
 from pathlib import Path
-from typing import Optional
 
 import equinox as eqx
 import jax.numpy as jnp
@@ -58,7 +57,7 @@
 # pylint warnings raised that go against this approach
 # pylint: disable=too-many-locals
 # pylint: disable=duplicate-code
-def main(out_path: Optional[Path] = None) -> tuple[float, float]:
+def main(out_path: Path | None = None) -> tuple[float, float]:
     """
     Run the tabular herding example using weighted herding and sliced score matching.
 
diff --git a/examples/iterative_probabilistic_kh.py b/examples/iterative_probabilistic_kh.py
index e6244ef6e..38f926973 100644
--- a/examples/iterative_probabilistic_kh.py
+++ b/examples/iterative_probabilistic_kh.py
@@ -28,7 +28,6 @@
 """
 
 import time
-from typing import Optional
 
 import jax
 import jax.numpy as jnp
@@ -99,7 +98,7 @@ def iterative_refine_experiment(
     data: Data,
     coreset_size: int,
     n_iter: int,
-    t_schedule: Optional[Shaped[Array, " {n_iter}"]] = None,
+    t_schedule: Shaped[Array, " {n_iter}"] | None = None,
     seed: int = 0,
 ) -> tuple[Array, Coresubset]:
     """
diff --git a/examples/pounce.py b/examples/pounce.py
index ed5c6eb66..04431c8f1 100644
--- a/examples/pounce.py
+++ b/examples/pounce.py
@@ -30,7 +30,6 @@
 """
 
 from pathlib import Path
-from typing import Optional
 
 import equinox as eqx
 import imageio
@@ -54,7 +53,7 @@
 # pylint: disable=duplicate-code
 def main(
     in_path: Path = Path("../examples/data/pounce/pounce.gif"),
-    out_path: Optional[Path] = None,
+    out_path: Path | None = None,
 ) -> tuple[float, float]:
     """
     Run the 'pounce' example for video sampling with Stein kernel herding.
diff --git a/examples/pounce_map_reduce.py b/examples/pounce_map_reduce.py
index dac83bc31..650d8dd8b 100644
--- a/examples/pounce_map_reduce.py
+++ b/examples/pounce_map_reduce.py
@@ -34,7 +34,6 @@
 """
 
 from pathlib import Path
-from typing import Optional
 
 import equinox as eqx
 import imageio
@@ -58,7 +57,7 @@
 # pylint: disable=duplicate-code
 def main(
     in_path: Path = Path("../examples/data/pounce/pounce.gif"),
-    out_path: Optional[Path] = None,
+    out_path: Path | None = None,
 ) -> tuple[float, float]:
     """
     Run the 'pounce' example for video sampling with Stein kernel herding.
diff --git a/examples/pounce_map_reduce_ssm.py b/examples/pounce_map_reduce_ssm.py
index fa79b7985..9f33c9d0c 100644
--- a/examples/pounce_map_reduce_ssm.py
+++ b/examples/pounce_map_reduce_ssm.py
@@ -31,7 +31,6 @@
 """
 
 from pathlib import Path
-from typing import Optional
 
 import equinox as eqx
 import imageio
@@ -55,7 +54,7 @@
 # pylint: disable=duplicate-code
 def main(
     in_path: Path = Path("../examples/data/pounce/pounce.gif"),
-    out_path: Optional[Path] = None,
+    out_path: Path | None = None,
 ) -> tuple[float, float]:
     """
     Run the 'pounce' example for video sampling with score matching.
diff --git a/pyproject.toml b/pyproject.toml
index 4c3761570..5ee58f06f 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -7,14 +7,13 @@ name = "coreax"
 dynamic = ["version"]
 description = "Jax coreset algorithms."
 readme = "README.md"
-requires-python = ">=3.9"
+requires-python = ">=3.10"
 keywords = [
     "coreset",
 ]
 classifiers = [
     "Development Status :: 5 - Production/Stable",
     "Programming Language :: Python",
-    "Programming Language :: Python :: 3.9",
     "Programming Language :: Python :: 3.10",
     "Programming Language :: Python :: 3.11",
     "Programming Language :: Python :: 3.12",
@@ -101,7 +100,6 @@ environments = [
     "python_version=='3.12.*'",
     "python_version=='3.11.*'",
     "python_version=='3.10.*'",
-    "python_version=='3.9.*'",
 ]
 
 [project.urls]
diff --git a/tests/coverage/compare.py b/tests/coverage/compare.py
index b651778fc..ef04a40ba 100644
--- a/tests/coverage/compare.py
+++ b/tests/coverage/compare.py
@@ -20,7 +20,6 @@
 import re
 import sys
 from pathlib import Path
-from typing import Optional
 
 # A good amount of this code is duplicated in the performance comparison script, but we
 # ignore this so that both scripts can be standalone.
@@ -58,7 +57,7 @@ def parse_args() -> tuple[float, Path]:
     return float(args.coverage_total), Path(args.reference_directory)
 
 
-def date_from_filename(path: Path) -> Optional[tuple[datetime.datetime, str]]:
+def date_from_filename(path: Path) -> tuple[datetime.datetime, str] | None:
     """
     Extract the date from a coverage data file name.
 
diff --git a/tests/performance/compare.py b/tests/performance/compare.py
index a09482e7e..537fe08eb 100644
--- a/tests/performance/compare.py
+++ b/tests/performance/compare.py
@@ -19,7 +19,6 @@
 import json
 import re
 from pathlib import Path
-from typing import Optional
 
 from scipy.stats import ttest_ind_from_stats
 from typing_extensions import TypedDict
@@ -94,7 +93,7 @@ def parse_args() -> tuple[Path, Path, str, Path]:
     )
 
 
-def date_from_filename(path: Path) -> Optional[tuple[datetime.datetime, str]]:
+def date_from_filename(path: Path) -> tuple[datetime.datetime, str] | None:
     """
     Extract the date from a performance data file name.
 
diff --git a/tests/performance/run.py b/tests/performance/run.py
index 2dc254e54..1114a6c09 100644
--- a/tests/performance/run.py
+++ b/tests/performance/run.py
@@ -65,7 +65,7 @@
                     "execution_std": times[1][1].item(),
                     "num_runs": NUM_RUNS,
                 }
-                for setup, times in zip(function_setups, results)
+                for setup, times in zip(function_setups, results, strict=False)
             },
         }
         with open(args.output_file, "w", encoding="utf8") as f:
diff --git a/tests/unit/test_coreset.py b/tests/unit/test_coreset.py
index 3d15ef3cd..72848d016 100644
--- a/tests/unit/test_coreset.py
+++ b/tests/unit/test_coreset.py
@@ -16,7 +16,6 @@
 
 import warnings
 from dataclasses import dataclass
-from typing import Union
 from unittest.mock import MagicMock, Mock
 
 import equinox as eqx
@@ -49,10 +48,10 @@
 class CoresetTestSetup:
     """Dataclass holding parameters for Coreset tests."""
 
-    coreset_type: Union[type[Coresubset], type[PseudoCoreset]]
+    coreset_type: type[Coresubset] | type[PseudoCoreset]
     coreset_input: Data
     materialised_points: Data
-    pre_coreset_data: Union[Data, SupervisedData]
+    pre_coreset_data: Data | SupervisedData
 
 
 @pytest.mark.parametrize(
@@ -202,7 +201,7 @@ class TestCoresetErrors:
 
     @pytest.mark.parametrize("coreset_type", [Coresubset, PseudoCoreset])
     def test_coreset_too_large(
-        self, coreset_type: Union[type[Coresubset], type[PseudoCoreset]]
+        self, coreset_type: type[Coresubset] | type[PseudoCoreset]
     ):
         """Test we get an appropriate error if the coreset is too large."""
         indices_or_nodes = jnp.arange(10, dtype=jnp.int32)
@@ -215,7 +214,7 @@ def test_coreset_too_large(
 
     @pytest.mark.parametrize("coreset_type", [Coresubset, PseudoCoreset])
     def test_invalid_pre_coreset_data_type(
-        self, coreset_type: Union[type[Coresubset], type[PseudoCoreset]]
+        self, coreset_type: type[Coresubset] | type[PseudoCoreset]
     ):
         """Test we get an appropriate error if pre_coreset_data is the wrong type."""
         indices_or_nodes = jnp.arange(10, dtype=jnp.int32)
@@ -226,7 +225,7 @@ def test_invalid_pre_coreset_data_type(
 
     @pytest.mark.parametrize("coreset_type", [Coresubset, PseudoCoreset])
     def test_invalid_indices_or_points_type(
-        self, coreset_type: Union[type[Coresubset], type[PseudoCoreset]]
+        self, coreset_type: type[Coresubset] | type[PseudoCoreset]
     ):
         """Test we get an appropriate error if the indices/points are the wrong type."""
         pre_coreset_data = jnp.arange(10, dtype=jnp.int32)
diff --git a/tests/unit/test_kernels.py b/tests/unit/test_kernels.py
index bf9b5f43c..d82da4774 100644
--- a/tests/unit/test_kernels.py
+++ b/tests/unit/test_kernels.py
@@ -21,7 +21,7 @@
 
 from abc import ABC, abstractmethod
 from collections.abc import Callable
-from typing import Generic, Literal, NamedTuple, TypeVar, Union
+from typing import Generic, Literal, NamedTuple, TypeVar
 from unittest.mock import MagicMock
 
 import equinox as eqx
@@ -113,8 +113,8 @@ def test_compute_mean(
         self,
         jit_variant: Callable[[Callable], Callable],
         kernel: _ScalarValuedKernel,
-        block_size: Union[int, None, tuple[Union[int, None], Union[int, None]]],
-        axis: Union[int, None],
+        block_size: int | None | tuple[int | None, int | None],
+        axis: int | None,
     ) -> None:
         """
         Test the `compute_mean` methods.
@@ -234,19 +234,19 @@ def test_gradients(
     @abstractmethod
     def expected_grad_x(
         self, x: Array, y: Array, kernel: _ScalarValuedKernel
-    ) -> Union[Array, np.ndarray]:
+    ) -> Array | np.ndarray:
         """Compute expected gradient of the kernel w.r.t ``x``."""
 
     @abstractmethod
     def expected_grad_y(
         self, x: Array, y: Array, kernel: _ScalarValuedKernel
-    ) -> Union[Array, np.ndarray]:
+    ) -> Array | np.ndarray:
         """Compute expected gradient of the kernel w.r.t ``y``."""
 
     @abstractmethod
     def expected_divergence_x_grad_y(
         self, x: Array, y: Array, kernel: _ScalarValuedKernel
-    ) -> Union[Array, np.ndarray]:
+    ) -> Array | np.ndarray:
         """Compute expected divergence of the kernel w.r.t ``x`` gradient ``y``."""
 
 
@@ -1069,8 +1069,8 @@ def test_compute_mean(
         self,
         jit_variant: Callable[[Callable], Callable],
         kernel: PoissonKernel,
-        block_size: Union[int, None, tuple[Union[int, None], Union[int, None]]],
-        axis: Union[int, None],
+        block_size: int | None | tuple[int | None, int | None],
+        axis: int | None,
     ) -> None:
         """
         Test the `compute_mean` methods with data from the domain.
diff --git a/tests/unit/test_least_squares.py b/tests/unit/test_least_squares.py
index 05cb7a454..987e9be51 100644
--- a/tests/unit/test_least_squares.py
+++ b/tests/unit/test_least_squares.py
@@ -25,7 +25,7 @@
     AbstractContextManager,
     nullcontext as does_not_raise,
 )
-from typing import Generic, NamedTuple, TypeVar, Union
+from typing import Generic, NamedTuple, TypeVar
 
 import jax.numpy as jnp
 import jax.random as jr
@@ -148,7 +148,7 @@ def test_approximator_inputs(
         self,
         array: Array,
         identity: Array,
-        rcond: Union[int, float, None],
+        rcond: int | float | None,
         context: AbstractContextManager,
     ) -> None:
         """Test `MinimalEuclideanNormSolver` handles inputs as expected."""
@@ -223,7 +223,7 @@ def test_approximator_inputs(
         self,
         array: Array,
         identity: Array,
-        rcond: Union[int, float, None],
+        rcond: int | float | None,
         context: AbstractContextManager,
     ) -> None:
         """Test `RandomisedEigendecompositionApproximator` handles invalid inputs."""
diff --git a/tests/unit/test_score_matching.py b/tests/unit/test_score_matching.py
index 4d2865a79..f5beac418 100644
--- a/tests/unit/test_score_matching.py
+++ b/tests/unit/test_score_matching.py
@@ -22,7 +22,6 @@
 
 import unittest
 from collections.abc import Callable
-from typing import Union
 from unittest.mock import MagicMock
 
 import equinox as eqx
@@ -1109,7 +1108,7 @@ class TestConvertSteinKernel:
     )
     def test_convert_stein_kernel(
         self,
-        score_matching: Union[None, MagicMock, KernelDensityMatching],
+        score_matching: None | MagicMock | KernelDensityMatching,
         kernel: ScalarValuedKernel,
     ) -> None:
         """Check handling of Stein kernels and standard kernels is consistent."""
diff --git a/tests/unit/test_solvers.py b/tests/unit/test_solvers.py
index 951bbc086..85aac7240 100644
--- a/tests/unit/test_solvers.py
+++ b/tests/unit/test_solvers.py
@@ -28,9 +28,7 @@
     Generic,
     Literal,
     NamedTuple,
-    Optional,
     TypeVar,
-    Union,
     cast,
 )
 from unittest.mock import MagicMock, patch
@@ -91,30 +89,30 @@
 _RefinementSolver = TypeVar("_RefinementSolver", bound=RefinementSolver)
 
 if TYPE_CHECKING:
-    # In Python 3.9-3.10, this raises
+    # In Python 3.10, this raises
     # `TypeError: Multiple inheritance with NamedTuple is not supported`.
     # Thus, we have to do the actual full typing here, and a non-generic one
     # below to be used at runtime.
     class _ReduceProblem(NamedTuple, Generic[_Data, _Solver]):
         dataset: _Data
         solver: _Solver
-        expected_coreset: Optional[AbstractCoreset] = None
+        expected_coreset: AbstractCoreset | None = None
 
     class _RefineProblem(NamedTuple, Generic[_RefinementSolver]):
         initial_coresubset: Coresubset
         solver: _RefinementSolver
-        expected_coresubset: Optional[Coresubset] = None
+        expected_coresubset: Coresubset | None = None
 else:
     # This is the implementation that's used at runtime.
     class _ReduceProblem(NamedTuple):
         dataset: _Data
         solver: _Solver
-        expected_coreset: Optional[AbstractCoreset] = None
+        expected_coreset: AbstractCoreset | None = None
 
     class _RefineProblem(NamedTuple):
         initial_coresubset: Coresubset
         solver: _RefinementSolver
-        expected_coresubset: Optional[Coresubset] = None
+        expected_coresubset: Coresubset | None = None
 
 
 class SolverTest:
@@ -151,7 +149,7 @@ def reduce_problem(
         return _ReduceProblem(Data(dataset), solver, expected_coreset)
 
     def check_solution_invariants(
-        self, coreset: AbstractCoreset, problem: Union[_RefineProblem, _ReduceProblem]
+        self, coreset: AbstractCoreset, problem: _RefineProblem | _ReduceProblem
     ) -> None:
         """
         Check that a coreset obeys certain expected invariant properties.
@@ -796,7 +794,7 @@ def test_functions_impl(x):
 
     @override
     def check_solution_invariants(
-        self, coreset: AbstractCoreset, problem: Union[_RefineProblem, _ReduceProblem]
+        self, coreset: AbstractCoreset, problem: _RefineProblem | _ReduceProblem
     ) -> None:
         r"""
         Check that a coreset obeys certain expected invariant properties.
@@ -1006,7 +1004,7 @@ class ExplicitSizeSolverTest(SolverTest):
 
     @override
     def check_solution_invariants(
-        self, coreset: AbstractCoreset, problem: Union[_RefineProblem, _ReduceProblem]
+        self, coreset: AbstractCoreset, problem: _RefineProblem | _ReduceProblem
     ) -> None:
         super().check_solution_invariants(coreset, problem)
         solver = problem.solver
@@ -1026,7 +1024,7 @@ def check_solution_invariants(
     def test_check_init(
         self,
         solver_factory: jtu.Partial,
-        coreset_size: Union[int, float, str],
+        coreset_size: int | float | str,
         context: AbstractContextManager,
     ) -> None:
         """
@@ -1073,7 +1071,7 @@ def solver_factory(self, request: pytest.FixtureRequest) -> jtu.Partial:
     def reduce_problem(
         self,
         request: pytest.FixtureRequest,
-        solver_factory: Union[type[Solver], jtu.Partial],
+        solver_factory: type[Solver] | jtu.Partial,
     ) -> _ReduceProblem:
         if request.param == "random":
             dataset = jr.uniform(self.random_key, self.shape)
@@ -1707,7 +1705,7 @@ class TestRandomSample(ExplicitSizeSolverTest):
 
     @override
     def check_solution_invariants(
-        self, coreset: AbstractCoreset, problem: Union[_RefineProblem, _ReduceProblem]
+        self, coreset: AbstractCoreset, problem: _RefineProblem | _ReduceProblem
     ) -> None:
         super().check_solution_invariants(coreset, problem)
         solver = cast(RandomSample, problem.solver)
@@ -1730,7 +1728,7 @@ class TestRPCholesky(ExplicitSizeSolverTest):
 
     @override
     def check_solution_invariants(
-        self, coreset: AbstractCoreset, problem: Union[_RefineProblem, _ReduceProblem]
+        self, coreset: AbstractCoreset, problem: _RefineProblem | _ReduceProblem
     ) -> None:
         """Check functionality of 'unique' in addition to the default checks."""
         super().check_solution_invariants(coreset, problem)
@@ -2044,7 +2042,7 @@ def solver_factory(self, request: pytest.FixtureRequest) -> jtu.Partial:
         ],
     )
     def test_regulariser_lambda(
-        self, test_lambda: Optional[Union[float, int]], reduce_problem: _ReduceProblem
+        self, test_lambda: float | int | None, reduce_problem: _ReduceProblem
     ) -> None:
         """Basic checks for the regularisation parameter, lambda."""
         dataset, base_solver, _ = reduce_problem
@@ -2411,7 +2409,7 @@ def solver_factory(self, request) -> jtu.Partial:
     def reduce_problem(
         self,
         request: pytest.FixtureRequest,
-        solver_factory: Union[type[Solver], jtu.Partial],
+        solver_factory: type[Solver] | jtu.Partial,
     ) -> _ReduceProblem:
         if request.param == "random":
             data_key, supervision_key = jr.split(self.random_key)
@@ -2427,7 +2425,7 @@ def reduce_problem(
 
     @override
     def check_solution_invariants(
-        self, coreset: AbstractCoreset, problem: Union[_RefineProblem, _ReduceProblem]
+        self, coreset: AbstractCoreset, problem: _RefineProblem | _ReduceProblem
     ) -> None:
         """Check functionality of 'unique' in addition to the default checks."""
         super().check_solution_invariants(coreset, problem)
@@ -2796,7 +2794,7 @@ def __init__(self, _data: np.ndarray, **kwargs):
                 del kwargs
                 self.data = _data
 
-            def get_arrays(self) -> tuple[Union[np.ndarray, None], ...]:
+            def get_arrays(self) -> tuple[np.ndarray | None, ...]:
                 """Mock sklearn.neighbours.BinaryTree.get_arrays method."""
                 return None, np.arange(len(self.data)), None, None
 
diff --git a/tests/unit/test_weights.py b/tests/unit/test_weights.py
index b166d64e1..949810c2c 100644
--- a/tests/unit/test_weights.py
+++ b/tests/unit/test_weights.py
@@ -21,7 +21,8 @@
 
 import cmath
 from abc import ABC, abstractmethod
-from typing import Callable, Generic, NamedTuple, Optional, TypeVar
+from collections.abc import Callable
+from typing import Generic, NamedTuple, TypeVar
 
 import jax.numpy as jnp
 import jax.random as jr
@@ -48,7 +49,7 @@
 class _Problem(NamedTuple):
     coreset: AbstractCoreset
     optimiser: WeightsOptimiser
-    target_metric: Optional[Metric]
+    target_metric: Metric | None
 
 
 class BaseWeightsOptimiserTest(ABC, Generic[_Data]):
diff --git a/uv.lock b/uv.lock
index 7bb454c0f..337c6bbcb 100644
--- a/uv.lock
+++ b/uv.lock
@@ -1,6 +1,6 @@
 version = 1
-revision = 3
-requires-python = ">=3.9"
+revision = 2
+requires-python = ">=3.10"
 resolution-markers = [
     "python_full_version >= '3.14' and sys_platform == 'darwin'",
     "python_full_version == '3.13.*' and sys_platform == 'darwin'",
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-    { name = "numpy", version = "2.2.6", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.10'" },
+    { name = "numba" },
+    { name = "numpy" },
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-    { name = "scipy", version = "1.16.1", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
+    { name = "scikit-learn" },
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+    { name = "scipy", version = "1.16.2", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
     { name = "tqdm" },
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 dependencies = [
     { name = "distlib" },
     { name = "filelock" },
     { name = "platformdirs" },
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 [[package]]

From d13132cb4250be307bbdc9812a2fd924883d837d Mon Sep 17 00:00:00 2001
From: tm91236 <205063739+tm91236@users.noreply.github.com>
Date: Wed, 1 Oct 2025 09:33:30 +0000
Subject: [PATCH 2/2] fix: minor type hint errors missed by autofix.

---
 coreax/data.py                    |    4 +-
 coreax/kernels/base.py            |   16 +-
 tests/performance/compare.py      |    2 +-
 tests/unit/test_score_matching.py |    2 +-
 uv.lock                           | 1468 +++++++++++++++++------------
 5 files changed, 871 insertions(+), 621 deletions(-)

diff --git a/coreax/data.py b/coreax/data.py
index e18c725cf..c8943fba8 100644
--- a/coreax/data.py
+++ b/coreax/data.py
@@ -15,7 +15,7 @@
 """Data-structures for representing weighted and/or supervised data."""
 
 from collections.abc import Sequence
-from typing import Union, overload
+from typing import overload
 
 import equinox as eqx
 import jax.numpy as jnp
@@ -170,7 +170,7 @@ def __jax_array__(  # pyright:ignore[reportOverlappingOverload]
     ) -> Shaped[Array, " n d+p"]: ...
 
     def __jax_array__(
-        self: Union["Data", "SupervisedData"],
+        self: "Data | SupervisedData",
     ) -> Shaped[Array, " n d"] | Shaped[Array, " n d+p"]:
         """
         Return value of `jnp.asarray(Data(...))` and `jnp.asarray(SupervisedData(...))`.
diff --git a/coreax/kernels/base.py b/coreax/kernels/base.py
index efdae61ed..9bd3c7ef8 100644
--- a/coreax/kernels/base.py
+++ b/coreax/kernels/base.py
@@ -50,7 +50,7 @@
 """
 
 from abc import abstractmethod
-from typing import Any, Literal, Union, overload
+from typing import Any, Literal, overload
 
 import equinox as eqx
 import jax
@@ -68,9 +68,7 @@
 class ScalarValuedKernel(eqx.Module):  # noqa: PLR0904
     """Abstract base class for scalar-valued kernels."""
 
-    def __add__(
-        self, addition: Union["ScalarValuedKernel", int, float]
-    ) -> "AdditiveKernel":
+    def __add__(self, addition: "ScalarValuedKernel | int | float") -> "AdditiveKernel":
         """Overload `+` operator."""
         if isinstance(addition, (int, float)):
             return AdditiveKernel(self, _Constant(addition))
@@ -82,14 +80,12 @@ def __add__(
         )
 
     def __radd__(
-        self, addition: Union["ScalarValuedKernel", int, float]
+        self, addition: "ScalarValuedKernel | int | float"
     ) -> "AdditiveKernel":
         """Overload right `+` operator, order is mathematically irrelevant."""
         return self.__add__(addition)
 
-    def __mul__(
-        self, product: Union["ScalarValuedKernel", int, float]
-    ) -> "ProductKernel":
+    def __mul__(self, product: "ScalarValuedKernel | int | float") -> "ProductKernel":
         """Overload `*` operator."""
         if isinstance(product, (int, float)):
             return ProductKernel(self, _Constant(product))
@@ -100,9 +96,7 @@ def __mul__(
             + "an integer or a float"
         )
 
-    def __rmul__(
-        self, product: Union["ScalarValuedKernel", int, float]
-    ) -> "ProductKernel":
+    def __rmul__(self, product: "ScalarValuedKernel | int | float") -> "ProductKernel":
         """Overload right `*` operator, order is mathematically irrelevant."""
         return self.__mul__(product)
 
diff --git a/tests/performance/compare.py b/tests/performance/compare.py
index 537fe08eb..452d8adf5 100644
--- a/tests/performance/compare.py
+++ b/tests/performance/compare.py
@@ -19,9 +19,9 @@
 import json
 import re
 from pathlib import Path
+from typing import TypedDict
 
 from scipy.stats import ttest_ind_from_stats
-from typing_extensions import TypedDict
 
 from coreax.util import format_time
 
diff --git a/tests/unit/test_score_matching.py b/tests/unit/test_score_matching.py
index f5beac418..0aa7e8811 100644
--- a/tests/unit/test_score_matching.py
+++ b/tests/unit/test_score_matching.py
@@ -1108,7 +1108,7 @@ class TestConvertSteinKernel:
     )
     def test_convert_stein_kernel(
         self,
-        score_matching: None | MagicMock | KernelDensityMatching,
+        score_matching: MagicMock | KernelDensityMatching | None,
         kernel: ScalarValuedKernel,
     ) -> None:
         """Check handling of Stein kernels and standard kernels is consistent."""
diff --git a/uv.lock b/uv.lock
index 337c6bbcb..79430f7a2 100644
--- a/uv.lock
+++ b/uv.lock
@@ -1,5 +1,5 @@
 version = 1
-revision = 2
+revision = 3
 requires-python = ">=3.10"
 resolution-markers = [
     "python_full_version >= '3.14' and sys_platform == 'darwin'",
@@ -8,9 +8,15 @@ resolution-markers = [
     "python_full_version == '3.13.*' and platform_machine == 'aarch64' and sys_platform == 'linux'",
     "(python_full_version >= '3.14' and platform_machine != 'aarch64' and sys_platform == 'linux') or (python_full_version >= '3.14' and sys_platform != 'darwin' and sys_platform != 'linux')",
     "(python_full_version == '3.13.*' and platform_machine != 'aarch64' and sys_platform == 'linux') or (python_full_version == '3.13.*' and sys_platform != 'darwin' and sys_platform != 'linux')",
-    "python_full_version == '3.12.*'",
-    "python_full_version == '3.11.*'",
-    "python_full_version < '3.11'",
+    "python_full_version == '3.12.*' and sys_platform == 'darwin'",
+    "python_full_version == '3.12.*' and platform_machine == 'aarch64' and sys_platform == 'linux'",
+    "(python_full_version == '3.12.*' and platform_machine != 'aarch64' and sys_platform == 'linux') or (python_full_version == '3.12.*' and sys_platform != 'darwin' and sys_platform != 'linux')",
+    "python_full_version == '3.11.*' and sys_platform == 'darwin'",
+    "python_full_version == '3.11.*' and platform_machine == 'aarch64' and sys_platform == 'linux'",
+    "(python_full_version == '3.11.*' and platform_machine != 'aarch64' and sys_platform == 'linux') or (python_full_version == '3.11.*' and sys_platform != 'darwin' and sys_platform != 'linux')",
+    "python_full_version < '3.11' and sys_platform == 'darwin'",
+    "python_full_version < '3.11' and platform_machine == 'aarch64' and sys_platform == 'linux'",
+    "(python_full_version < '3.11' and platform_machine != 'aarch64' and sys_platform == 'linux') or (python_full_version < '3.11' and sys_platform != 'darwin' and sys_platform != 'linux')",
 ]
 supported-markers = [
     "python_full_version >= '3.13'",
@@ -60,7 +66,7 @@ wheels = [
 
 [[package]]
 name = "anyio"
-version = "4.10.0"
+version = "4.11.0"
 source = { registry = "https://pypi.org/simple" }
 dependencies = [
     { name = "exceptiongroup", marker = "python_full_version < '3.11'" },
@@ -68,9 +74,9 @@ dependencies = [
     { name = "sniffio" },
     { name = "typing-extensions", marker = "python_full_version < '3.13'" },
 ]
-sdist = { url = "https://files.pythonhosted.org/packages/f1/b4/636b3b65173d3ce9a38ef5f0522789614e590dab6a8d505340a4efe4c567/anyio-4.10.0.tar.gz", hash = "sha256:3f3fae35c96039744587aa5b8371e7e8e603c0702999535961dd336026973ba6", size = 213252, upload-time = "2025-08-04T08:54:26.451Z" }
+sdist = { url = "https://files.pythonhosted.org/packages/c6/78/7d432127c41b50bccba979505f272c16cbcadcc33645d5fa3a738110ae75/anyio-4.11.0.tar.gz", hash = "sha256:82a8d0b81e318cc5ce71a5f1f8b5c4e63619620b63141ef8c995fa0db95a57c4", size = 219094, upload-time = "2025-09-23T09:19:12.58Z" }
 wheels = [
-    { url = "https://files.pythonhosted.org/packages/6f/12/e5e0282d673bb9746bacfb6e2dba8719989d3660cdb2ea79aee9a9651afb/anyio-4.10.0-py3-none-any.whl", hash = "sha256:60e474ac86736bbfd6f210f7a61218939c318f43f9972497381f1c5e930ed3d1", size = 107213, upload-time = "2025-08-04T08:54:24.882Z" },
+    { url = "https://files.pythonhosted.org/packages/15/b3/9b1a8074496371342ec1e796a96f99c82c945a339cd81a8e73de28b4cf9e/anyio-4.11.0-py3-none-any.whl", hash = "sha256:0287e96f4d26d4149305414d4e3bc32f0dcd0862365a4bddea19d7a1ec38c4fc", size = 109097, upload-time = "2025-09-23T09:19:10.601Z" },
 ]
 
 [[package]]
@@ -246,15 +252,15 @@ wheels = [
 
 [[package]]
 name = "beautifulsoup4"
-version = "4.13.5"
+version = "4.14.2"
 source = { registry = "https://pypi.org/simple" }
 dependencies = [
     { name = "soupsieve" },
     { name = "typing-extensions" },
 ]
-sdist = { url = "https://files.pythonhosted.org/packages/85/2e/3e5079847e653b1f6dc647aa24549d68c6addb4c595cc0d902d1b19308ad/beautifulsoup4-4.13.5.tar.gz", hash = "sha256:5e70131382930e7c3de33450a2f54a63d5e4b19386eab43a5b34d594268f3695", size = 622954, upload-time = "2025-08-24T14:06:13.168Z" }
+sdist = { url = "https://files.pythonhosted.org/packages/77/e9/df2358efd7659577435e2177bfa69cba6c33216681af51a707193dec162a/beautifulsoup4-4.14.2.tar.gz", hash = "sha256:2a98ab9f944a11acee9cc848508ec28d9228abfd522ef0fad6a02a72e0ded69e", size = 625822, upload-time = "2025-09-29T10:05:42.613Z" }
 wheels = [
-    { url = "https://files.pythonhosted.org/packages/04/eb/f4151e0c7377a6e08a38108609ba5cede57986802757848688aeedd1b9e8/beautifulsoup4-4.13.5-py3-none-any.whl", hash = "sha256:642085eaa22233aceadff9c69651bc51e8bf3f874fb6d7104ece2beb24b47c4a", size = 105113, upload-time = "2025-08-24T14:06:14.884Z" },
+    { url = "https://files.pythonhosted.org/packages/94/fe/3aed5d0be4d404d12d36ab97e2f1791424d9ca39c2f754a6285d59a3b01d/beautifulsoup4-4.14.2-py3-none-any.whl", hash = "sha256:5ef6fa3a8cbece8488d66985560f97ed091e22bbc4e9c2338508a9d5de6d4515", size = 106392, upload-time = "2025-09-29T10:05:43.771Z" },
 ]
 
 [[package]]
@@ -279,7 +285,7 @@ name = "build"
 version = "1.3.0"
 source = { registry = "https://pypi.org/simple" }
 dependencies = [
-    { name = "colorama", marker = "(python_full_version < '3.13' and os_name == 'nt' and sys_platform == 'darwin') or (python_full_version < '3.13' and os_name == 'nt' and sys_platform == 'linux') or (os_name == 'nt' and platform_machine != 'aarch64' and sys_platform == 'linux') or (os_name == 'nt' and sys_platform != 'darwin' and sys_platform != 'linux')" },
+    { name = "colorama", marker = "(os_name == 'nt' and platform_machine != 'aarch64' and sys_platform == 'linux') or (os_name == 'nt' and sys_platform != 'darwin' and sys_platform != 'linux')" },
     { name = "importlib-metadata", marker = "python_full_version < '3.10.2'" },
     { name = "packaging" },
     { name = "pyproject-hooks" },
@@ -477,13 +483,15 @@ name = "chex"
 version = "0.1.90"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
-    "python_full_version < '3.11'",
+    "python_full_version < '3.11' and sys_platform == 'darwin'",
+    "python_full_version < '3.11' and platform_machine == 'aarch64' and sys_platform == 'linux'",
+    "(python_full_version < '3.11' and platform_machine != 'aarch64' and sys_platform == 'linux') or (python_full_version < '3.11' and sys_platform != 'darwin' and sys_platform != 'linux')",
 ]
 dependencies = [
     { name = "absl-py", marker = "python_full_version < '3.11'" },
     { name = "jax", version = "0.6.2", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version < '3.11'" },
     { name = "jaxlib", version = "0.6.2", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version < '3.11'" },
-    { name = "numpy", marker = "python_full_version < '3.11'" },
+    { name = "numpy", version = "2.2.6", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version < '3.11'" },
     { name = "toolz", marker = "python_full_version < '3.11'" },
     { name = "typing-extensions", marker = "python_full_version < '3.11'" },
 ]
@@ -503,14 +511,18 @@ resolution-markers = [
     "python_full_version == '3.13.*' and platform_machine == 'aarch64' and sys_platform == 'linux'",
     "(python_full_version >= '3.14' and platform_machine != 'aarch64' and sys_platform == 'linux') or (python_full_version >= '3.14' and sys_platform != 'darwin' and sys_platform != 'linux')",
     "(python_full_version == '3.13.*' and platform_machine != 'aarch64' and sys_platform == 'linux') or (python_full_version == '3.13.*' and sys_platform != 'darwin' and sys_platform != 'linux')",
-    "python_full_version == '3.12.*'",
-    "python_full_version == '3.11.*'",
+    "python_full_version == '3.12.*' and sys_platform == 'darwin'",
+    "python_full_version == '3.12.*' and platform_machine == 'aarch64' and sys_platform == 'linux'",
+    "(python_full_version == '3.12.*' and platform_machine != 'aarch64' and sys_platform == 'linux') or (python_full_version == '3.12.*' and sys_platform != 'darwin' and sys_platform != 'linux')",
+    "python_full_version == '3.11.*' and sys_platform == 'darwin'",
+    "python_full_version == '3.11.*' and platform_machine == 'aarch64' and sys_platform == 'linux'",
+    "(python_full_version == '3.11.*' and platform_machine != 'aarch64' and sys_platform == 'linux') or (python_full_version == '3.11.*' and sys_platform != 'darwin' and sys_platform != 'linux')",
 ]
 dependencies = [
     { name = "absl-py", marker = "python_full_version >= '3.11'" },
-    { name = "jax", version = "0.7.1", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
-    { name = "jaxlib", version = "0.7.1", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
-    { name = "numpy", marker = "python_full_version >= '3.11'" },
+    { name = "jax", version = "0.7.2", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
+    { name = "jaxlib", version = "0.7.2", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
+    { name = "numpy", version = "2.3.3", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
     { name = "toolz", marker = "python_full_version >= '3.11'" },
     { name = "typing-extensions", marker = "python_full_version >= '3.11'" },
 ]
@@ -542,10 +554,12 @@ name = "contourpy"
 version = "1.3.2"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
-    "python_full_version < '3.11'",
+    "python_full_version < '3.11' and sys_platform == 'darwin'",
+    "python_full_version < '3.11' and platform_machine == 'aarch64' and sys_platform == 'linux'",
+    "(python_full_version < '3.11' and platform_machine != 'aarch64' and sys_platform == 'linux') or (python_full_version < '3.11' and sys_platform != 'darwin' and sys_platform != 'linux')",
 ]
 dependencies = [
-    { name = "numpy", marker = "python_full_version < '3.11'" },
+    { name = "numpy", version = "2.2.6", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version < '3.11'" },
 ]
 sdist = { url = "https://files.pythonhosted.org/packages/66/54/eb9bfc647b19f2009dd5c7f5ec51c4e6ca831725f1aea7a993034f483147/contourpy-1.3.2.tar.gz", hash = "sha256:b6945942715a034c671b7fc54f9588126b0b8bf23db2696e3ca8328f3ff0ab54", size = 13466130, upload-time = "2025-04-15T17:47:53.79Z" }
 wheels = [
@@ -618,11 +632,15 @@ resolution-markers = [
     "python_full_version == '3.13.*' and platform_machine == 'aarch64' and sys_platform == 'linux'",
     "(python_full_version >= '3.14' and platform_machine != 'aarch64' and sys_platform == 'linux') or (python_full_version >= '3.14' and sys_platform != 'darwin' and sys_platform != 'linux')",
     "(python_full_version == '3.13.*' and platform_machine != 'aarch64' and sys_platform == 'linux') or (python_full_version == '3.13.*' and sys_platform != 'darwin' and sys_platform != 'linux')",
-    "python_full_version == '3.12.*'",
-    "python_full_version == '3.11.*'",
+    "python_full_version == '3.12.*' and sys_platform == 'darwin'",
+    "python_full_version == '3.12.*' and platform_machine == 'aarch64' and sys_platform == 'linux'",
+    "(python_full_version == '3.12.*' and platform_machine != 'aarch64' and sys_platform == 'linux') or (python_full_version == '3.12.*' and sys_platform != 'darwin' and sys_platform != 'linux')",
+    "python_full_version == '3.11.*' and sys_platform == 'darwin'",
+    "python_full_version == '3.11.*' and platform_machine == 'aarch64' and sys_platform == 'linux'",
+    "(python_full_version == '3.11.*' and platform_machine != 'aarch64' and sys_platform == 'linux') or (python_full_version == '3.11.*' and sys_platform != 'darwin' and sys_platform != 'linux')",
 ]
 dependencies = [
-    { name = "numpy", marker = "python_full_version >= '3.11'" },
+    { name = "numpy", version = "2.3.3", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
 ]
 sdist = { url = "https://files.pythonhosted.org/packages/58/01/1253e6698a07380cd31a736d248a3f2a50a7c88779a1813da27503cadc2a/contourpy-1.3.3.tar.gz", hash = "sha256:083e12155b210502d0bca491432bb04d56dc3432f95a979b429f2848c3dbe880", size = 13466174, upload-time = "2025-07-26T12:03:12.549Z" }
 wheels = [
@@ -705,9 +723,9 @@ source = { editable = "." }
 dependencies = [
     { name = "equinox" },
     { name = "flax", version = "0.10.7", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version < '3.11'" },
-    { name = "flax", version = "0.11.2", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
+    { name = "flax", version = "0.12.0", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
     { name = "jax", version = "0.6.2", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version < '3.11'" },
-    { name = "jax", version = "0.7.1", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
+    { name = "jax", version = "0.7.2", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
     { name = "jaxopt" },
     { name = "jaxtyping" },
     { name = "optax" },
@@ -721,7 +739,8 @@ benchmark = [
     { name = "imageio" },
     { name = "llvmlite" },
     { name = "matplotlib" },
-    { name = "numpy" },
+    { name = "numpy", version = "2.2.6", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version < '3.11'" },
+    { name = "numpy", version = "2.3.3", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
     { name = "opencv-python-headless" },
     { name = "torch" },
     { name = "torchvision" },
@@ -740,7 +759,8 @@ doc = [
 example = [
     { name = "imageio" },
     { name = "matplotlib" },
-    { name = "numpy" },
+    { name = "numpy", version = "2.2.6", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version < '3.11'" },
+    { name = "numpy", version = "2.3.3", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
     { name = "opencv-python-headless" },
 ]
 test = [
@@ -748,7 +768,8 @@ test = [
     { name = "imageio" },
     { name = "llvmlite" },
     { name = "matplotlib" },
-    { name = "numpy" },
+    { name = "numpy", version = "2.2.6", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version < '3.11'" },
+    { name = "numpy", version = "2.3.3", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
     { name = "opencv-python-headless" },
     { name = "pytest" },
     { name = "pytest-cov" },
@@ -821,87 +842,101 @@ dev = [
 
 [[package]]
 name = "coverage"
-version = "7.10.6"
-source = { registry = "https://pypi.org/simple" }
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