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Local PRNG for amplifying seed entropy into seeds for base operations.
Writing sampling code which correctly sets the pseudo-random number generator (PRNG) seed is surprisingly difficult. This class serves as a helper for the TensorFlow Probability coding pattern designed to avoid common mistakes.
A common first-cut implementation of a sampler for the beta distribution is to compute the ratio of a gamma with itself plus another gamma. This code snippet tries to do that, but contains a surprisingly common error:
def broken_beta(shape, alpha, beta, seed): x = tf.random.gamma(shape, alpha, seed=seed) y = tf.random.gamma(shape, beta, seed=seed) return x / (x + y)
The mistake is that the two gamma draws are seeded with the same
seed. This causes them to always produce the same results, which,
in turn, leads this code snippet to always return
0.5. Because it
can happen across abstraction boundaries, this kind of error is
surprisingly easy to make when handling immutable seeds.
TensorFlow Probability adopts a code style designed to eliminate the above class of error, without exacerbating others. The goals of this code style are:
Support reproducibility of results (by encouraging seeding of all pseudo-random operations).
Avoid shared-write global state (by not relying on a global PRNG).
Prevent accidental seed reuse by TF Probability implementers. This goal is served with the local pseudo-random seed generator provided in this module.
Mitigate potential accidental seed reuse by TF Probability clients (with a salting scheme).
Prevent accidental resonances with downstream PRNGs (by hashing the output).
Implementing a high-performance PRNG for generating large amounts of entropy. That's the job of the underlying TensorFlow PRNG we are seeding.
Avoiding random seed collisions, aka "birthday attacks".
def random_beta(shape, alpha, beta, seed): # (a) seed = SeedStream(seed, salt="random_beta") # (b) x = tf.random.gamma(shape, alpha, seed=seed()) # (c) y = tf.random.gamma(shape, beta, seed=seed()) # (c) return x / (x + y)
The elements of this pattern are:
Accept an explicit seed (line a) as an argument in all public functions, and write the function to be deterministic (up to any numerical issues) for fixed seed.
- Rationale: This provides the client with the ability to reproduce results. Accepting an immutable seed rather than a mutable PRNG object reduces code coupling, permitting different sections to be reproducible independently.
Use that seed only to initialize a local
SeedStreaminstance (line b).
- Rationale: Avoids accidental seed reuse.
Supply the name of the function being implemented as a salt to the
SeedStreaminstance (line b). This serves to keep the salts unique; unique salts ensure that clients of TF Probability will see different functions always produce independent results even if called with the same seeds.
Seed each callee operation with the output of a unique call to the
SeedStreaminstance (lines c). This ensures reproducibility of results while preventing seed reuse across callee invocations.
SeedStream instances (with unique salts) is defensive
programming against a client accidentally committing a mistake
similar to our motivating example. Consider the following situation
that might arise without salting:
def tfp_foo(seed): seed = SeedStream(seed, salt="") foo_stuff = tf.random.normal(seed=seed()) ... def tfp_bar(seed): seed = SeedStream(seed, salt="") bar_stuff = tf.random.normal(seed=seed()) ... def client_baz(seed): foo = tfp_foo(seed=seed) bar = tfp_bar(seed=seed) ...
The client should have used different seeds as inputs to
bar. However, because they didn't, and because
both sample a Gaussian internally as their first action, the
bar_stuff will be the same, and the
bar will not be independent, leading to subtly
incorrect answers from the client's simulation. This kind of bug is
particularly insidious for the client, because it depends on a
Distributions implementation detail, namely the order in which
bar invoke the samplers they depend on. In particular, a
Bayesflow team member can introduce such a bug in previously
(accidentally) correct client code by performing an internal
refactoring that causes this operation order alignment.
A salting discipline eliminates this problem by making sure that the
seeds seen by
foo's callees will differ from those seen by
callees, even if
bar are invoked with the same input
__init__( seed, salt )
seed: Any Python object convertible to string, supplying the initial entropy. If
None, operations seeded with seeds drawn from this
SeedStreamwill follow TensorFlow semantics for not being seeded.
salt: Any Python object convertible to string, supplying auxiliary entropy. Must be unique across the Distributions and TensorFlow Probability code base. See class docstring for rationale.
Returns a fresh integer usable as a seed in downstream operations.
SeedStream was initialized with
None. This has the effect that downstream operations (both
SeedStreams and primitive TensorFlow ops) will behave as though
they were unseeded.
The returned integer is non-negative, and uniformly distributed in
the half-open interval
[0, 2**512). This is consistent with
TensorFlow, as TensorFlow operations internally use the residue of
the given seed modulo
2**31 - 1 (see
seed: A fresh integer usable as a seed in downstream operations, or