§ Vp«f‚&ãó—dZddlmZmZmZmZmZmZmZm Z m Z m Z m Z m Z mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/ddiZ0ddl1Z1e1j2rnddl3m4Z5e5e6e0¦«Z7[5[1dS)uqUtilities for pseudo-random number generation. The :mod:`jax.random` package provides a number of routines for deterministic generation of sequences of pseudorandom numbers. Basic usage ----------- >>> seed = 1701 >>> num_steps = 100 >>> key = jax.random.key(seed) >>> for i in range(num_steps): ... key, subkey = jax.random.split(key) ... params = compiled_update(subkey, params, next(batches)) # doctest: +SKIP PRNG keys --------- Unlike the *stateful* pseudorandom number generators (PRNGs) that users of NumPy and SciPy may be accustomed to, JAX random functions all require an explicit PRNG state to be passed as a first argument. The random state is described by a special array element type that we call a **key**, usually generated by the :py:func:`jax.random.key` function:: >>> from jax import random >>> key = random.key(0) >>> key Array((), dtype=key) overlaying: [0 0] This key can then be used in any of JAX's random number generation routines:: >>> random.uniform(key) Array(0.41845703, dtype=float32) Note that using a key does not modify it, so reusing the same key will lead to the same result:: >>> random.uniform(key) Array(0.41845703, dtype=float32) If you need a new random number, you can use :meth:`jax.random.split` to generate new subkeys:: >>> key, subkey = random.split(key) >>> random.uniform(subkey) Array(0.10536897, dtype=float32) .. note:: Typed key arrays, with element types such as ``key`` above, were introduced in JAX v0.4.16. Before then, keys were conventionally represented in ``uint32`` arrays, whose final dimension represented the key's bit-level representation. Both forms of key array can still be created and used with the :mod:`jax.random` module. New-style typed key arrays are made with :py:func:`jax.random.key`. Legacy ``uint32`` key arrays are made with :py:func:`jax.random.PRNGKey`. To convert between the two, use :py:func:`jax.random.key_data` and :py:func:`jax.random.wrap_key_data`. The legacy key format may be needed when interfacing with systems outside of JAX (e.g. exporting arrays to a serializable format), or when passing keys to JAX-based libraries that assume the legacy format. Otherwise, typed keys are recommended. Caveats of legacy keys relative to typed ones include: * They have an extra trailing dimension. * They have a numeric dtype (``uint32``), allowing for operations that are typically not meant to be carried out over keys, such as integer arithmetic. * They do not carry information about the RNG implementation. When legacy keys are passed to :mod:`jax.random` functions, a global configuration setting determines the RNG implementation (see "Advanced RNG configuration" below). To learn more about this upgrade, and the design of key types, see `JEP 9263 `_. Advanced -------- Design and background ===================== **TLDR**: JAX PRNG = `Threefry counter PRNG `_ + a functional array-oriented `splitting model `_ See `docs/jep/263-prng.md `_ for more details. To summarize, among other requirements, the JAX PRNG aims to: 1. ensure reproducibility, 2. parallelize well, both in terms of vectorization (generating array values) and multi-replica, multi-core computation. In particular it should not use sequencing constraints between random function calls. Advanced RNG configuration ========================== JAX provides several PRNG implementations. A specific one can be selected with the optional ``impl`` keyword argument to ``jax.random.key``. When no ``impl`` option is passed to the ``key`` constructor, the implementation is determined by the global ``jax_default_prng_impl`` configuration flag. The string names of available implementations are: - ``"threefry2x32"`` (**default**): A counter-based PRNG based on a variant of the Threefry hash function, as described in `this paper by Salmon et al., 2011 `_. - ``"rbg"`` and ``"unsafe_rbg"`` (**experimental**): PRNGs built atop `XLA's Random Bit Generator (RBG) algorithm `_. - ``"rbg"`` uses XLA RBG for random number generation, whereas for key derivation (as in ``jax.random.split`` and ``jax.random.fold_in``) it uses the same method as ``"threefry2x32"``. - ``"unsafe_rbg"`` uses XLA RBG for both generation as well as key derivation. Random numbers generated by these experimental schemes have not been subject to empirical randomness testing (e.g. BigCrush). Key derivation in ``"unsafe_rbg"`` has also not been empirically tested. The name emphasizes "unsafe" because key derivation quality and generation quality are not well understood. Additionally, both ``"rbg"`` and ``"unsafe_rbg"`` behave unusually under ``jax.vmap``. When vmapping a random function over a batch of keys, its output values can differ from its true map over the same keys. Instead, under ``vmap``, the entire batch of output random numbers is generated from only the first key in the input key batch. For example, if ``keys`` is a vector of 8 keys, then ``jax.vmap(jax.random.normal)(keys)`` equals ``jax.random.normal(keys[0], shape=(8,))``. This peculiarity reflects a workaround to XLA RBG's limited batching support. Reasons to use an alternative to the default RNG include that: 1. It may be slow to compile for TPUs. 2. It is relatively slower to execute on TPUs. **Automatic partitioning:** In order for ``jax.jit`` to efficiently auto-partition functions that generate sharded random number arrays (or key arrays), all PRNG implementations require extra flags: - For ``"threefry2x32"``, and ``"rbg"`` key derivation, set ``jax_threefry_partitionable=True``. - For ``"unsafe_rbg"``, and ``"rbg"`` random generation", set the XLA flag ``--xla_tpu_spmd_rng_bit_generator_unsafe=1``. The XLA flag can be set using an the ``XLA_FLAGS`` environment variable, e.g. as ``XLA_FLAGS=--xla_tpu_spmd_rng_bit_generator_unsafe=1``. For more about ``jax_threefry_partitionable``, see https://jax.readthedocs.io/en/latest/notebooks/Distributed_arrays_and_automatic_parallelization.html#generating-random-numbers **Summary:** .. table:: :widths: auto ================================= ======== ========= === ========== ===== ============ Property Threefry Threefry* rbg unsafe_rbg rbg** unsafe_rbg** ================================= ======== ========= === ========== ===== ============ Fastest on TPU ✅ ✅ ✅ ✅ efficiently shardable (w/ pjit) ✅ ✅ ✅ identical across shardings ✅ ✅ ✅ ✅ identical across CPU/GPU/TPU ✅ ✅ exact ``jax.vmap`` over keys ✅ ✅ ================================= ======== ========= === ========== ===== ============ (*): with ``jax_threefry_partitionable=1`` set (**): with ``XLA_FLAGS=--xla_tpu_spmd_rng_bit_generator_unsafe=1`` set é).ÚPRNGKeyÚballÚ bernoulliÚbinomialÚbetaÚbitsÚ categoricalÚcauchyÚ chisquareÚchoiceÚcloneÚ dirichletÚdouble_sided_maxwellÚ exponentialÚfÚfold_inÚgammaÚgeneralized_normalÚ geometricÚgumbelÚkeyÚkey_dataÚkey_implÚlaplaceÚlogisticÚloggammaÚ lognormalÚmaxwellÚmultivariate_normalÚnormalÚ orthogonalÚparetoÚ permutationÚpoissonÚ rademacherÚrandintÚrandom_gamma_pÚrayleighÚsplitÚtÚ triangularÚtruncated_normalÚuniformÚwaldÚ weibull_minÚ wrap_key_dataÚshuffle)zSjax.random.shuffle is deprecated. Use jax.random.permutation with independent=True.NN)Údeprecation_getattr)8Ú__doc__Újax._src.randomrrrrrrr r r r r rrrrrrrrrrrrrrrrrrr r!r"r#r$r%r&r'r(r)r*r+r,r-r.r/r0Ú _deprecationsÚtypingÚ TYPE_CHECKINGÚjax._src.deprecationsr2Ú_deprecation_getattrÚ__name__Ú __getattr__©óúJ/var/www/html/nettyfy-visnx/env/lib/python3.11/site-packages/jax/random.pyúr?sKððzðzð~/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ð/ðfðð€ ð€ € € Ø ÔðØàOÐOÐOÐOÐOÐOØ$Ð$ X¨}Ñ=Ô=€+ØØ €F€Fr=