JEP 9263: Typed keys & pluggable RNGs

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docs/jep/9263-typed-keys.md

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+# JEP 9263: Typed keys & pluggable RNGs
+
+*Jake VanderPlas, Roy Frostig*
+
+*August 2023*
+
+## Overview
+Going forward, RNG keys in JAX will be more type-safe and customizable.
+Rather than representing a single PRNG key by a length-2  `uint32` array,
+it will be represented as a scalar array with a special RNG dtype that
+satisfies `jnp.issubdtype(key.dtype, jax.dtypes.prng_key)`.
+
+For now, old-style RNG keys can still be created with
+{func}`jax.random.PRNGKey`:
+```python
+>>> key = jax.random.PRNGKey(0)
+>>> key
+Array([0, 0], dtype=uint32)
+>>> key.shape
+(2,)
+>>> key.dtype
+dtype('uint32')
+```
+Starting now, new-style RNG keys can be created with
+{func}`jax.random.key`:
+```
+>>> key = jax.random.key(0)
+>>> key
+Array((), dtype=key<fry>) overlaying:
+[0 0]
+>>> key.shape
+()
+>>> key.dtype
+key<fry>
+```
+This (scalar-shaped) array behaves the same as any other JAX array, except
+that its element type is a key (and associated metadata). We can make
+non-scalar key arrays as well, for example by applying {func}`jax.vmap` to
+{func}`jax.random.key`:
+```python
+>>> key_arr = jax.vmap(jax.random.key)(jnp.arange(4))
+>>> key_arr
+Array((4,), dtype=key<fry>) overlaying:
+[[0 0]
+ [0 1]
+ [0 2]
+ [0 3]]
+>>> key_arr.shape
+(4,)
+```
+Aside from switching to a new constructor, most PRNG-related code should
+continue to work as expected. You can continue to use keys in
+{mod}`jax.random` APIs as before; for example:
+```python
+# split
+new_key, subkey = jax.random.split(key)
+
+# random number generation
+data = jax.random.uniform(key, shape=(5,))
+```
+However, not all numerical operations work on key arrays. They now
+intentionally raise errors:
+```python
+>>> key = key + 1
+ValueError: dtype=key<fry> is not a valid dtype for JAX type promotion.
+```
+If for some reason you need to recover the underlying buffer
+(the old-style key), you can do so with {func}`jax.random.key_data`:
+```python
+>>> jax.random.key_data(key)
+Array([0, 0], dtype=uint32)
+```
+For old-style keys, {func}`~jax.random.key_data` is an identity operation.
+
+## What does this mean for users?
+For JAX users, this change does not require any code changes now, but we hope
+that you will find the upgrade worthwhile and switch to using typed keys. To
+try this out, replace uses of jax.random.PRNGKey() with jax.random.key(). This
+may introduce breakages in your code that fall into one of a few categories:
+
+- If your code performs unsafe/unsupported operations on keys (such as indexing,
+  arithmetic, transposition, etc; see Type Safety section below), this change
+  will catch it. You can update your code to avoid such unsupported operations,
+  or use {func}`jax.random.key_data` and {func}`jax.extend.random.wrap_key_data`
+  to manipulate raw key buffers in an unsafe way.
+- If your code includes explicit logic about `key.shape`, you may need to update
+  this logic to account for the fact that the trailing key buffer dimension is
+  no longer an explicit part of the shape.
+- If your code includes explicit logic about `key.dtype`, you will need to
+  upgrade it to use the new public APIs for reasoning about RNG dtypes, such as
+  `dtypes.issubdtype(dtype, dtypes.prng_key)`.
+- If you call a JAX-based library which does not yet handle typed PRNG keys, you
+  can use `raw_key = jax.random.key_data(key)` for now to recover the raw buffer,
+  but please keep a TODO to remove this once the downstream library supports
+  typed RNG keys.
+
+At some point in the future, we plan to deprecate {func}`jax.random.PRNGKey` and
+require the use of {func}`jax.random.key`.
+
+### JAX library authors
+If you maintain a JAX-based library, your users are also JAX users. Know that JAX
+will continue to support "raw" old-style keys in {mod}`jax.random` for now, so
+callers may expect them to remain accepted everywhere. If you prefer to require
+new-style typed keys in your library, then you may want to enforce them with a
+check along the following lines:
+```python
+from jax import dtypes
+
+def ensure_typed_key_array(key: Array) -> Array:
+  if dtypes.issubdtype(key.dtype, dtypes.prng_key):
+    return key
+  else:
+    raise TypeError("New-style typed JAX PRNG keys required")
+```
+
+## Motivation
+Two major motivating factors for this change are customizability and safety.
+
+### Customizing PRNG implementations
+JAX currently operates with a single, globally configured PRNG algorithm. A
+PRNG key is a vector of unsigned 32-bit integers, which jax.random APIs consume
+to produce pseudorandom streams. Any higher-rank uint32 array is interpreted as
+an array of such key buffers, where the trailing dimension represents keys.
+
+The drawbacks of this design became clearer as we introduced alternative PRNG
+implementations, which must be selected by setting a global or local
+configuration flag. Different PRNG implementations have different size key
+buffers, and different algorithms for generating random bits. Determining this
+behavior with a global flag is error-prone, especially when there is more than
+one key implementation in use process-wide.
+
+Our new approach is to carry the implementation as part of the PRNG key type,
+i.e. with the element type of the key array. Using the new key API, here is an
+example of generating pseudorandom values under the default threefry2x32
+implementation (which is implemented in pure Python and compiled with JAX), and
+under the non-default rbg implementation (which corresponds to a single XLA
+random-bit generation operation):
+```python
+>>> key = jax.random.key(0, impl='threefry2x32')  # this is the default impl
+>>> key
+Array((), dtype=key<fry>) overlaying:
+[0 0]
+>>> jax.random.uniform(key, shape=(3,))
+Array([0.9653214 , 0.31468165, 0.63302994], dtype=float32)
+
+>>> key = jax.random.key(0, impl='rbg')
+>>> key
+Array((), dtype=key<rbg>) overlaying:
+[0 0 0 0]
+>>> jax.random.uniform(key, shape=(3,))
+Array([0.39904642, 0.8805201 , 0.73571277], dtype=float32)
+```
+
+### Safe PRNG key use
+PRNG keys are really only meant to support a few operations in principle,
+namely key derivation (e.g. splitting) and random number generation. The PRNG
+is designed to generate independent pseudorandom numbers, provided keys are
+properly split and that every key is consumed once.
+
+Code that manipulates or consumes key data in other ways often indicates an
+accidental bug, and representing key arrays as raw uint32 buffers has allowed
+for easy misuse along these lines. Here are a few example misuses that we've
+encountered in the wild:
+
+#### Key buffer indexing
+Access to the underlying integer buffers makes it easy to try and derive keys
+in non-standard ways, sometimes with unexpectedly bad consequences:
+
+```{code-block} python
+:class: red-background
+# Incorrect
+key = random.PRNGKey(999)
+new_key = random.PRNGKey(key[1])  # identical to the original key!
+```
+```{code-block} python
+:class: green-background
+# Correct
+key = random.PRNGKey(999)
+key, new_key = random.split(key)
+```
+If this key were a new-style typed key made with `random.key(999)`, indexing
+into the key buffer would error instead.
+
+#### Key arithmetic
+
+Key arithmetic is a similarly treacherous way to derive keys from other keys.
+Deriving keys in a way that avoids {func}`jax.random.split` or
+{func}`jax.random.fold_in` by manipulating key data directly produces a batch
+of keys that—depending on the PRNG implementation—might then generate
+correlated random numbers within the batch:
+```{code-block} python
+:class: red-background
+# Incorrect
+key = random.PRNGKey(0)
+batched_keys = key + jnp.arange(10, dtype=key.dtype)[:, None]
+```
+```{code-block} python
+:class: green-background
+# Correct
+key = random.PRNGKey(0)
+batched_keys = random.split(key, 10)
+```
+New-style typed keys created with `random.key(0)` address this by disallowing
+arithmetic operations on keys.
+
+#### Inadvertent transposing of key buffers
+
+With "raw" old-style key arrays, it's easy to accidentally swap batch (leading)
+dimensions and key buffer (trailing) dimensions. Again this possibly results in
+keys that produce correlated pseudorandomness. A pattern that we've seen over
+time boils down to this:
+```{code-block} python
+:class: red-background
+# Incorrect
+keys = random.split(random.PRNGKey(0))
+data = jax.vmap(random.uniform, axis=1)(keys)
+```
+```{code-block} python
+:class: green-background
+# Correct
+keys = random.split(random.PRNGKey(0))
+data = jax.vmap(random.uniform, axis=0)(keys)
+```
+The bug here is subtle. By mapping over `axis=1`, this code makes new keys by
+combining a single element from each key buffer in the batch. The resulting
+keys are different from one another, but are effectively "derived" in a
+non-standard way. Again, the PRNG is not designed or tested to produce
+independent random streams from such a key batch.
+
+New-style typed keys created with `random.key(0)` address this by hiding the
+buffer representation of individual keys, instead treating keys as opaque
+elements of a key array. Key arrays have no trailing "buffer" dimension to
+index, transpose, or map over.
+
+#### Key reuse
+Unlike state-based PRNG APIs like {mod}`numpy.random`, JAX's functional PRNG
+does not implicitly update a key when it has been used.
+```{code-block} python
+:class: red-background
+# Incorrect
+key = random.PRNGKey(0)
+x = random.uniform(key, (100,))
+y = random.uniform(key, (100,))  # Identical values!
+```
+```{code-block} python
+:class: green-background
+# Correct
+key = random.PRNGKey(0)
+key1, key2 = random.split(random.key(0))
+x = random.uniform(key1, (100,))
+y = random.uniform(key2, (100,))
+```
+We're actively working on tools to detect and prevent unintended key reuse.
+This is still work in progress, but it relies on typed key arrays. Upgrading
+to typed keys now sets us up to introduce these safety features as we build
+them out.
+
+## Design of typed PRNG keys
+Typed PRNG keys are implemented as an instance of extended dtypes within JAX,
+of which the new PRNG dtypes are a sub-dtype.
+
+### Extended dtypes
+From the user perspective, an extended dtype dt has the following user-visible
+properties:
+
+- `jax.dtypes.issubdtype(dt, jax.dtypes.extended)` returns `True`: this is the
+  public API that should be used to detect whether a dtype is an extended dtype.
+- It has a class-level attribute `dt.type`, which returns a typeclass in the
+  hierarchy of `numpy.generic`. This is analogous to how `np.dtype('int32').type`
+  returns `numpy.int32`, which is not a dtype but rather a scalar type, and a
+  subclass of `numpy.generic`.
+- Unlike numpy scalar types, we do not allow instantiation of `dt.type` scalar
+  objects: this is in accordance with JAX's decision to represent scalar values
+  as zero-dimensional arrays.
+
+From a non-public implementation perspective, an extended dtype has the
+following properties:
+
+- Its type is a subclass of the private base class `jax._src.dtypes.ExtendedDtype`,
+  the non-public base class used for extended dtypes. An instance of
+  `ExtendedDtype` is analogous to an instance of `np.dtype`, like
+  `np.dtype('int32')`.
+- It has a private `_rules` attribute which allows the dtype to define how it
+  behaves under particular operations. For example,
+  `jax.lax.full(shape, fill_value, dtype)` will delegate to
+  `dtype._rules.full(shape, fill_value, dtype)` when `dtype` is an extended dtype.
+
+Why introduce extended dtypes in generality, beyond PRNGs? We reuse this same
+extended dtype mechanism elsewhere internally. For example, the
+`jax._src.core.bint` object, a bounded integer type used for experimental work
+on dynamic shapes, is another extended dtype. In recent JAX versions it satisfies
+the properties above (See [jax/_src/core.py#L1789-L1802](https://github.com/google/jax/blob/jax-v0.4.14/jax/_src/core.py#L1789-L1802)).
+
+### PRNG dtypes
+PRNG dtypes are defined as a particular case of extended dtypes. Specifically,
+this change introduces a new public scalar type class jax.dtypes.prng_key,
+which has the following property:
+```python
+>>> jax.dtypes.issubdtype(jax.dtypes.prng_key, jax.dtypes.extended)
+True
+```
+PRNG key arrays then have a dtype with the following properties:
+```python
+>>> key = jax.random.key(0)
+>>> jax.dtypes.issubdtype(key.dtype, jax.dtypes.extended)
+True
+>>> jax.dtypes.issubdtype(key.dtype, jax.dtypes.prng_key)
+True
+```
+And in addition to `key.dtype._rules` as outlined for extended dtypes in
+general, PRNG dtypes define `key.dtype.impl`, which contains the metadata
+that defines the PRNG implementation. The PRNG implementation is currently
+defined by the non-public `jax._src.prng.PRNGImpl` class. For now, `PRNGImpl`
+isn't meant to be a public API, but we might revisit this soon to allow for
+fully custom PRNG implementations.
+
+## Progress
+Following is a non-comprehensive list of key Pull Requests implementing the
+above design. The main tracking issue is {jax-issue}`9263`.
+
+- Implement pluggable PRNG via `PRNGImpl`: {jax-issue}`#6899` 
+- Implement `PRNGKeyArray`, without dtype: {jax-issue}`#11952`
+- Add a “custom element” dtype property to `PRNGKeyArray` with `_rules`
+  attribute: {jax-issue}`#12167`
+- Rename “custom element type” to “opaque dtype”: {jax-issue}`#12170`
+- Refactor `bint` to use the opaque dtype infrastructure: {jax-issue}`#12707`
+- Add `jax.random.key` to create typed keys directly: {jax-issue}`#16086`
+- Add `impl` argument to `key` and `PRNGKey`: {jax-issue}`#16589`
+- Rename “opaque dtype” to  “extended dtype” & define `jax.dtypes.extended`:
+  {jax-issue}`#16824`
+- Introduce `jax.dtypes.prng_key` and unify PRNG dtype with Extended dtype:
+  {jax-issue}`#16781`
+- Add a `jax_legacy_prng_key` flag to support warning or erroring when using
+  legacy (raw) PRNG keys: {jax-issue}`#17225`

docs/jep/index.rst

@@ -41,6 +41,7 @@ Then create a pull request that adds a file named
   2026: Custom JVP/VJP rules for JAX-transformable functions <2026-custom-derivatives>
   4008: Custom VJP and `nondiff_argnums` update <4008-custom-vjp-update>
   4410: Omnistaging <4410-omnistaging>
+  9263: Typed keys & pluggable RNGs <9263-typed-keys>
   9407: Design of Type Promotion Semantics for JAX <9407-type-promotion>
   9419: Jax and Jaxlib versioning <9419-jax-versioning>
   10657: Sequencing side-effects in JAX <10657-sequencing-effects>