# Source code for numpyro.contrib.control_flow.scan

```
# Copyright Contributors to the Pyro project.
# SPDX-License-Identifier: Apache-2.0
from collections import OrderedDict
from functools import partial
from jax import device_put, lax, random
import jax.numpy as jnp
from jax.tree_util import tree_flatten, tree_map, tree_unflatten
from numpyro import handlers
from numpyro.ops.pytree import PytreeTrace
from numpyro.primitives import _PYRO_STACK, Messenger, apply_stack
from numpyro.util import not_jax_tracer
def _subs_wrapper(subs_map, i, length, site):
if site["type"] != "sample":
return
value = None
if isinstance(subs_map, dict) and site["name"] in subs_map:
value = subs_map[site["name"]]
elif callable(subs_map):
rng_key = site["kwargs"].get("rng_key")
subs_map = (
handlers.seed(subs_map, rng_seed=rng_key)
if rng_key is not None
else subs_map
)
value = subs_map(site)
if value is not None:
value_ndim = jnp.ndim(value)
sample_shape = site["kwargs"]["sample_shape"]
fn_ndim = len(sample_shape + site["fn"].shape())
if value_ndim == fn_ndim:
# this branch happens when substitute_fn is init_strategy,
# where we apply init_strategy to each element in the scanned series
return value
elif value_ndim == fn_ndim + 1:
# this branch happens when we substitute a series of values
shape = jnp.shape(value)
if shape[0] == length:
return value[i]
elif shape[0] < length:
rng_key = site["kwargs"]["rng_key"]
assert rng_key is not None
# we use the substituted values if i < shape[0]
# and generate a new sample otherwise
return lax.cond(
i < shape[0],
(value, i),
lambda val: val[0][val[1]],
rng_key,
lambda val: site["fn"](rng_key=val, sample_shape=sample_shape),
)
else:
raise RuntimeError(
f"Substituted value for site {site['name']} "
"requires length less than or equal to scan length."
f" Expected length <= {length}, but got {shape[0]}."
)
else:
raise RuntimeError(
f"Something goes wrong. Expected ndim = {fn_ndim} or {fn_ndim+1},"
f" but got {value_ndim}. This might happen when you use nested scan,"
" which is currently not supported. Please report the issue to us!"
)
class _promote_fn_shapes(Messenger):
# a helper messenger to promote shapes of `fn`
# + msg: fn.batch_shape = (3,), value.shape = (2, 3) + fn.event_shape
# process_message(msg): promote fn so that fn.batch_shape = (1, 3).
def postprocess_message(self, msg):
if msg["type"] == "sample" and msg["value"] is not None:
fn, value = msg["fn"], msg["value"]
value_batch_ndims = jnp.ndim(value) - fn.event_dim
fn_batch_ndim = len(fn.batch_shape)
if fn_batch_ndim < value_batch_ndims:
prepend_shapes = (1,) * (value_batch_ndims - fn_batch_ndim)
msg["fn"] = tree_map(
lambda x: jnp.reshape(x, prepend_shapes + jnp.shape(x)), fn
)
def _promote_scanned_value_shapes(value, fn):
# a helper function to promote shapes of `value`
# + msg: fn.batch_shape = (T, 2, 3), value.shape = (T, 3,) + fn.event_shape
# process_message(msg): promote value so that value.shape = (T, 1, 3) + fn.event_shape
value_batch_ndims = jnp.ndim(value) - fn.event_dim
fn_batch_ndim = len(fn.batch_shape)
if fn_batch_ndim > value_batch_ndims:
prepend_shapes = (1,) * (fn_batch_ndim - value_batch_ndims)
return jnp.reshape(
value, jnp.shape(value)[:1] + prepend_shapes + jnp.shape(value)[1:]
)
else:
return value
def scan_enum(
f,
init,
xs,
length,
reverse,
rng_key=None,
substitute_stack=None,
history=1,
first_available_dim=None,
):
from numpyro.contrib.funsor import (
config_enumerate,
enum,
markov,
trace as packed_trace,
)
# amount number of steps to unroll
history = min(history, length)
unroll_steps = min(2 * history - 1, length)
if reverse:
x0 = tree_map(lambda x: x[-unroll_steps:][::-1], xs)
xs_ = tree_map(lambda x: x[:-unroll_steps], xs)
else:
x0 = tree_map(lambda x: x[:unroll_steps], xs)
xs_ = tree_map(lambda x: x[unroll_steps:], xs)
carry_shapes = []
def body_fn(wrapped_carry, x, prefix=None):
i, rng_key, carry = wrapped_carry
init = True if (not_jax_tracer(i) and i in range(unroll_steps)) else False
rng_key, subkey = random.split(rng_key) if rng_key is not None else (None, None)
# we need to tell unconstrained messenger in potential energy computation
# that only the item at time `i` is needed when transforming
fn = handlers.infer_config(f, config_fn=lambda msg: {"_scan_current_index": i})
seeded_fn = handlers.seed(fn, subkey) if subkey is not None else fn
for subs_type, subs_map in substitute_stack:
subs_fn = partial(_subs_wrapper, subs_map, i, length)
if subs_type == "condition":
seeded_fn = handlers.condition(seeded_fn, condition_fn=subs_fn)
elif subs_type == "substitute":
seeded_fn = handlers.substitute(seeded_fn, substitute_fn=subs_fn)
if init:
# handler the name to match the pattern of sakkar_bilmes product
with handlers.scope(
prefix="_PREV_" * (unroll_steps - i), divider="", hide_types=["plate"]
):
new_carry, y = config_enumerate(seeded_fn)(carry, x)
trace = {}
else:
# Like scan_wrapper, we collect the trace of scan's transition function
# `seeded_fn` here. To put time dimension to the correct position, we need to
# promote shapes to make `fn` and `value`
# at each site have the same batch dims (e.g. if `fn.batch_shape = (2, 3)`,
# and value's batch_shape is (3,), then we promote shape of
# value so that its batch shape is (1, 3)).
# Here we will promote `fn` shape first. `value` shape will be promoted after scanned.
# We don't promote `value` shape here because we need to store carry shape
# at this step. If we reshape the `value` here, output carry might get wrong shape.
with _promote_fn_shapes(), packed_trace() as trace:
new_carry, y = config_enumerate(seeded_fn)(carry, x)
# store shape of new_carry at a global variable
if len(carry_shapes) < (history + 1):
carry_shapes.append([jnp.shape(x) for x in tree_flatten(new_carry)[0]])
# make new_carry have the same shape as carry
# FIXME: is this rigorous?
new_carry = tree_map(
lambda a, b: jnp.reshape(a, jnp.shape(b)), new_carry, carry
)
return (i + 1, rng_key, new_carry), (PytreeTrace(trace), y)
with handlers.block(
hide_fn=lambda site: not site["name"].startswith("_PREV_")
), enum(first_available_dim=first_available_dim):
wrapped_carry = (0, rng_key, init)
y0s = []
# We run unroll_steps + 1 where the last step is used for rolling with `lax.scan`
for i in markov(range(unroll_steps + 1), history=history):
if i < unroll_steps:
wrapped_carry, (_, y0) = body_fn(
wrapped_carry, tree_map(lambda z: z[i], x0)
)
if i > 0:
# reshape y1, y2,... to have the same shape as y0
y0 = tree_map(
lambda z0, z: jnp.reshape(z, jnp.shape(z0)), y0s[0], y0
)
y0s.append(y0)
# shapes of the first `history - 1` steps are not useful to interpret the last carry
# shape so we don't need to record them here
if (i >= history - 1) and (len(carry_shapes) < history + 1):
carry_shapes.append(
jnp.shape(x) for x in tree_flatten(wrapped_carry[-1])[0]
)
else:
# this is the last rolling step
y0s = tree_map(lambda *z: jnp.stack(z, axis=0), *y0s)
# return early if length = unroll_steps
if length == unroll_steps:
return wrapped_carry, (PytreeTrace({}), y0s)
wrapped_carry = device_put(wrapped_carry)
wrapped_carry, (pytree_trace, ys) = lax.scan(
body_fn, wrapped_carry, xs_, length - unroll_steps, reverse
)
first_var = None
for name, site in pytree_trace.trace.items():
# currently, we only record sample or deterministic in the trace
# we don't need to adjust `dim_to_name` for deterministic site
if site["type"] not in ("sample",):
continue
# add `time` dimension, the name will be '_time_{first variable in the trace}'
if first_var is None:
first_var = name
# we haven't promote shapes of values yet during `lax.scan`, so we do it here
site["value"] = _promote_scanned_value_shapes(site["value"], site["fn"])
# XXX: site['infer']['dim_to_name'] is not enough to determine leftmost dimension because
# we don't record 1-size dimensions in this field
time_dim = -min(
len(site["fn"].batch_shape), jnp.ndim(site["value"]) - site["fn"].event_dim
)
site["infer"]["dim_to_name"][time_dim] = "_time_{}".format(first_var)
# similar to carry, we need to reshape due to shape alternating in markov
ys = tree_map(
lambda z0, z: jnp.reshape(z, z.shape[:1] + jnp.shape(z0)[1:]), y0s, ys
)
# then join with y0s
ys = tree_map(lambda z0, z: jnp.concatenate([z0, z], axis=0), y0s, ys)
# we also need to reshape `carry` to match sequential behavior
i = (length + 1) % (history + 1)
t, rng_key, carry = wrapped_carry
carry_shape = carry_shapes[i]
flatten_carry, treedef = tree_flatten(carry)
flatten_carry = [
jnp.reshape(x, t1_shape) for x, t1_shape in zip(flatten_carry, carry_shape)
]
carry = tree_unflatten(treedef, flatten_carry)
wrapped_carry = (t, rng_key, carry)
return wrapped_carry, (pytree_trace, ys)
def scan_wrapper(
f,
init,
xs,
length,
reverse,
rng_key=None,
substitute_stack=[],
enum=False,
history=1,
first_available_dim=None,
):
if length is None:
length = tree_flatten(xs)[0][0].shape[0]
if enum and history > 0:
return scan_enum(
f,
init,
xs,
length,
reverse,
rng_key,
substitute_stack,
history,
first_available_dim,
)
def body_fn(wrapped_carry, x):
i, rng_key, carry = wrapped_carry
rng_key, subkey = random.split(rng_key) if rng_key is not None else (None, None)
with handlers.block():
# we need to tell unconstrained messenger in potential energy computation
# that only the item at time `i` is needed when transforming
fn = handlers.infer_config(
f, config_fn=lambda msg: {"_scan_current_index": i}
)
seeded_fn = handlers.seed(fn, subkey) if subkey is not None else fn
for subs_type, subs_map in substitute_stack:
subs_fn = partial(_subs_wrapper, subs_map, i, length)
if subs_type == "condition":
seeded_fn = handlers.condition(seeded_fn, condition_fn=subs_fn)
elif subs_type == "substitute":
seeded_fn = handlers.substitute(seeded_fn, substitute_fn=subs_fn)
with handlers.trace() as trace:
carry, y = seeded_fn(carry, x)
return (i + 1, rng_key, carry), (PytreeTrace(trace), y)
wrapped_carry = device_put((0, rng_key, init))
last_carry, (pytree_trace, ys) = lax.scan(
body_fn, wrapped_carry, xs, length=length, reverse=reverse
)
for name, site in pytree_trace.trace.items():
if site["type"] != "sample":
continue
# we haven't promote shapes of values yet during `lax.scan`, so we do it here
site["value"] = _promote_scanned_value_shapes(site["value"], site["fn"])
return last_carry, (pytree_trace, ys)
[docs]def scan(f, init, xs, length=None, reverse=False, history=1):
"""
This primitive scans a function over the leading array axes of
`xs` while carrying along state. See :func:`jax.lax.scan` for more
information.
**Usage**:
.. doctest::
>>> import numpy as np
>>> import numpyro
>>> import numpyro.distributions as dist
>>> from numpyro.contrib.control_flow import scan
>>>
>>> def gaussian_hmm(y=None, T=10):
... def transition(x_prev, y_curr):
... x_curr = numpyro.sample('x', dist.Normal(x_prev, 1))
... y_curr = numpyro.sample('y', dist.Normal(x_curr, 1), obs=y_curr)
... return x_curr, (x_curr, y_curr)
...
... x0 = numpyro.sample('x_0', dist.Normal(0, 1))
... _, (x, y) = scan(transition, x0, y, length=T)
... return (x, y)
>>>
>>> # here we do some quick tests
>>> with numpyro.handlers.seed(rng_seed=0):
... x, y = gaussian_hmm(np.arange(10.))
>>> assert x.shape == (10,) and y.shape == (10,)
>>> assert np.all(y == np.arange(10))
>>>
>>> with numpyro.handlers.seed(rng_seed=0): # generative
... x, y = gaussian_hmm()
>>> assert x.shape == (10,) and y.shape == (10,)
.. warning:: This is an experimental utility function that allows users to use
JAX control flow with NumPyro's effect handlers. Currently, `sample` and
`deterministic` sites within the scan body `f` are supported. If you notice
that any effect handlers or distributions are unsupported, please file an issue.
.. note:: It is ambiguous to align `scan` dimension inside a `plate` context.
So the following pattern won't be supported
.. code-block:: python
with numpyro.plate('N', 10):
last, ys = scan(f, init, xs)
All `plate` statements should be put inside `f`. For example, the corresponding
working code is
.. code-block:: python
def g(*args, **kwargs):
with numpyro.plate('N', 10):
return f(*arg, **kwargs)
last, ys = scan(g, init, xs)
.. note:: Nested scan is currently not supported.
.. note:: We can scan over discrete latent variables in `f`. The joint density is
evaluated using parallel-scan (reference [1]) over time dimension, which
reduces parallel complexity to `O(log(length))`.
A :class:`~numpyro.handlers.trace` of `scan` with discrete latent
variables will contain the following sites:
+ init sites: those sites belong to the first `history` traces of `f`.
Sites at the `i`-th trace will have name prefixed with
`'_PREV_' * (2 * history - 1 - i)`.
+ scanned sites: those sites collect the values of the remaining scan
loop over `f`. An addition time dimension `_time_foo` will be
added to those sites, where `foo` is the name of the first site
appeared in `f`.
Not all transition functions `f` are supported. All of the restrictions from
Pyro's enumeration tutorial [2] still apply here. In addition, there should
not have any site outside of `scan` depend on the first output of `scan`
(the last carry value).
**References**
1. *Temporal Parallelization of Bayesian Smoothers*,
Simo Sarkka, Angel F. Garcia-Fernandez
(https://arxiv.org/abs/1905.13002)
2. *Inference with Discrete Latent Variables*
(http://pyro.ai/examples/enumeration.html#Dependencies-among-plates)
:param callable f: a function to be scanned.
:param init: the initial carrying state
:param xs: the values over which we scan along the leading axis. This can
be any JAX pytree (e.g. list/dict of arrays).
:param length: optional value specifying the length of `xs`
but can be used when `xs` is an empty pytree (e.g. None)
:param bool reverse: optional boolean specifying whether to run the scan iteration
forward (the default) or in reverse
:param int history: The number of previous contexts visible from the current context.
Defaults to 1. If zero, this is similar to :class:`numpyro.plate`.
:return: output of scan, quoted from :func:`jax.lax.scan` docs:
"pair of type (c, [b]) where the first element represents the final loop
carry value and the second element represents the stacked outputs of the
second output of f when scanned over the leading axis of the inputs".
"""
# if there are no active Messengers, we just run and return it as expected:
if not _PYRO_STACK:
(length, rng_key, carry), (pytree_trace, ys) = scan_wrapper(
f, init, xs, length=length, reverse=reverse
)
return carry, ys
else:
# Otherwise, we initialize a message...
initial_msg = {
"type": "control_flow",
"fn": scan_wrapper,
"args": (f, init, xs, length, reverse),
"kwargs": {"rng_key": None, "substitute_stack": [], "history": history},
"value": None,
}
# ...and use apply_stack to send it to the Messengers
msg = apply_stack(initial_msg)
(length, rng_key, carry), (pytree_trace, ys) = msg["value"]
if not msg["kwargs"].get("enum", False):
for msg in pytree_trace.trace.values():
if msg["type"] == "plate":
continue
apply_stack(msg)
else:
from numpyro.contrib.funsor import to_funsor
from numpyro.contrib.funsor.enum_messenger import LocalNamedMessenger
for msg in pytree_trace.trace.values():
if msg["type"] == "plate":
continue
with LocalNamedMessenger():
dim_to_name = msg["infer"].get("dim_to_name")
to_funsor(
msg["value"],
dim_to_name=OrderedDict(
[(k, dim_to_name[k]) for k in sorted(dim_to_name)]
),
)
apply_stack(msg)
return carry, ys
```