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254 lines
9.2 KiB
Python
254 lines
9.2 KiB
Python
# Copyright 2018 The JAX Authors.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# https://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""Utilities for pseudo-random number generation.
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The :mod:`jax.random` package provides a number of routines for deterministic
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generation of sequences of pseudorandom numbers.
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Basic usage
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-----------
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>>> seed = 1701
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>>> num_steps = 100
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>>> key = jax.random.key(seed)
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>>> for i in range(num_steps):
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... key, subkey = jax.random.split(key)
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... params = compiled_update(subkey, params, next(batches)) # doctest: +SKIP
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PRNG keys
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---------
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Unlike the *stateful* pseudorandom number generators (PRNGs) that users of NumPy and
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SciPy may be accustomed to, JAX random functions all require an explicit PRNG state to
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be passed as a first argument.
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The random state is described by a special array element type that we call a **key**,
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usually generated by the :py:func:`jax.random.key` function::
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>>> from jax import random
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>>> key = random.key(0)
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>>> key
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Array((), dtype=key<fry>) overlaying:
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[0 0]
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This key can then be used in any of JAX's random number generation routines::
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>>> random.uniform(key)
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Array(0.41845703, dtype=float32)
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Note that using a key does not modify it, so reusing the same key will lead to the same result::
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>>> random.uniform(key)
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Array(0.41845703, dtype=float32)
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If you need a new random number, you can use :meth:`jax.random.split` to generate new subkeys::
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>>> key, subkey = random.split(key)
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>>> random.uniform(subkey)
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Array(0.10536897, dtype=float32)
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.. note::
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Typed key arrays, with element types such as ``key<fry>`` above,
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were introduced in JAX v0.4.16. Before then, keys were
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conventionally represented in ``uint32`` arrays, whose final
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dimension represented the key's bit-level representation.
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Both forms of key array can still be created and used with the
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:mod:`jax.random` module. New-style typed key arrays are made with
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:py:func:`jax.random.key`. Legacy ``uint32`` key arrays are made
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with :py:func:`jax.random.PRNGKey`.
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To convert between the two, use :py:func:`jax.random.key_data` and
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:py:func:`jax.random.wrap_key_data`. The legacy key format may be
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needed when interfacing with systems outside of JAX (e.g. exporting
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arrays to a serializable format), or when passing keys to JAX-based
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libraries that assume the legacy format.
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Otherwise, typed keys are recommended. Caveats of legacy keys
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relative to typed ones include:
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* They have an extra trailing dimension.
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* They have a numeric dtype (``uint32``), allowing for operations
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that are typically not meant to be carried out over keys, such as
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integer arithmetic.
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* They do not carry information about the RNG implementation. When
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legacy keys are passed to :mod:`jax.random` functions, a global
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configuration setting determines the RNG implementation (see
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"Advanced RNG configuration" below).
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To learn more about this upgrade, and the design of key types, see
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`JEP 9263
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<https://jax.readthedocs.io/en/latest/jep/9263-typed-keys.html>`_.
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Advanced
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--------
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Design and background
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=====================
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**TLDR**: JAX PRNG = `Threefry counter PRNG <http://www.thesalmons.org/john/random123/papers/random123sc11.pdf>`_
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+ a functional array-oriented `splitting model <https://dl.acm.org/citation.cfm?id=2503784>`_
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See `docs/jep/263-prng.md <https://github.com/jax-ml/jax/blob/main/docs/jep/263-prng.md>`_
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for more details.
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To summarize, among other requirements, the JAX PRNG aims to:
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1. ensure reproducibility,
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2. parallelize well, both in terms of vectorization (generating array values)
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and multi-replica, multi-core computation. In particular it should not use
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sequencing constraints between random function calls.
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Advanced RNG configuration
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==========================
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JAX provides several PRNG implementations. A specific one can be
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selected with the optional ``impl`` keyword argument to
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``jax.random.key``. When no ``impl`` option is passed to the ``key``
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constructor, the implementation is determined by the global
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``jax_default_prng_impl`` configuration flag. The string names of
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available implementations are:
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- ``"threefry2x32"`` (**default**):
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A counter-based PRNG based on a variant of the Threefry hash function,
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as described in `this paper by Salmon et al., 2011
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<http://www.thesalmons.org/john/random123/papers/random123sc11.pdf>`_.
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- ``"rbg"`` and ``"unsafe_rbg"`` (**experimental**): PRNGs built atop
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`XLA's Random Bit Generator (RBG) algorithm
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<https://openxla.org/xla/operation_semantics#rngbitgenerator>`_.
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- ``"rbg"`` uses XLA RBG for random number generation, whereas for
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key derivation (as in ``jax.random.split`` and
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``jax.random.fold_in``) it uses the same method as
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``"threefry2x32"``.
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- ``"unsafe_rbg"`` uses XLA RBG for both generation as well as key
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derivation.
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Random numbers generated by these experimental schemes have not
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been subject to empirical randomness testing (e.g. BigCrush).
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Key derivation in ``"unsafe_rbg"`` has also not been empirically
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tested. The name emphasizes "unsafe" because key derivation
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quality and generation quality are not well understood.
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Additionally, both ``"rbg"`` and ``"unsafe_rbg"`` behave unusually
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under ``jax.vmap``. When vmapping a random function over a batch
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of keys, its output values can differ from its true map over the
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same keys. Instead, under ``vmap``, the entire batch of output
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random numbers is generated from only the first key in the input
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key batch. For example, if ``keys`` is a vector of 8 keys, then
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``jax.vmap(jax.random.normal)(keys)`` equals
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``jax.random.normal(keys[0], shape=(8,))``. This peculiarity
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reflects a workaround to XLA RBG's limited batching support.
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Reasons to use an alternative to the default RNG include that:
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1. It may be slow to compile for TPUs.
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2. It is relatively slower to execute on TPUs.
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**Automatic partitioning:**
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In order for ``jax.jit`` to efficiently auto-partition functions that
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generate sharded random number arrays (or key arrays), all PRNG
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implementations require extra flags:
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- For ``"threefry2x32"``, and ``"rbg"`` key derivation, set
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``jax_threefry_partitionable=True``.
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- For ``"unsafe_rbg"``, and ``"rbg"`` random generation", set the XLA
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flag ``--xla_tpu_spmd_rng_bit_generator_unsafe=1``.
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The XLA flag can be set using an the ``XLA_FLAGS`` environment
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variable, e.g. as
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``XLA_FLAGS=--xla_tpu_spmd_rng_bit_generator_unsafe=1``.
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For more about ``jax_threefry_partitionable``, see
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https://jax.readthedocs.io/en/latest/notebooks/Distributed_arrays_and_automatic_parallelization.html#generating-random-numbers
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**Summary:**
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.. table::
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:widths: auto
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================================= ======== ========= === ========== ===== ============
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Property Threefry Threefry* rbg unsafe_rbg rbg** unsafe_rbg**
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================================= ======== ========= === ========== ===== ============
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Fastest on TPU ✅ ✅ ✅ ✅
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efficiently shardable (w/ pjit) ✅ ✅ ✅
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identical across shardings ✅ ✅ ✅ ✅
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identical across CPU/GPU/TPU ✅ ✅
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exact ``jax.vmap`` over keys ✅ ✅
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================================= ======== ========= === ========== ===== ============
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(*): with ``jax_threefry_partitionable=1`` set
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(**): with ``XLA_FLAGS=--xla_tpu_spmd_rng_bit_generator_unsafe=1`` set
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"""
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# Note: import <name> as <name> is required for names to be exported.
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# See PEP 484 & https://github.com/jax-ml/jax/issues/7570
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from jax._src.random import (
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PRNGKey as PRNGKey,
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ball as ball,
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bernoulli as bernoulli,
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binomial as binomial,
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beta as beta,
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bits as bits,
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categorical as categorical,
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cauchy as cauchy,
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chisquare as chisquare,
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choice as choice,
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clone as clone,
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dirichlet as dirichlet,
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double_sided_maxwell as double_sided_maxwell,
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exponential as exponential,
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f as f,
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fold_in as fold_in,
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gamma as gamma,
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generalized_normal as generalized_normal,
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geometric as geometric,
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gumbel as gumbel,
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key as key,
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key_data as key_data,
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key_impl as key_impl,
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laplace as laplace,
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logistic as logistic,
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loggamma as loggamma,
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lognormal as lognormal,
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maxwell as maxwell,
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multivariate_normal as multivariate_normal,
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normal as normal,
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orthogonal as orthogonal,
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pareto as pareto,
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permutation as permutation,
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poisson as poisson,
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rademacher as rademacher,
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randint as randint,
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random_gamma_p as random_gamma_p,
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rayleigh as rayleigh,
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split as split,
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t as t,
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triangular as triangular,
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truncated_normal as truncated_normal,
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uniform as uniform,
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wald as wald,
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weibull_min as weibull_min,
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wrap_key_data as wrap_key_data,
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)
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