# 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 lax, random, tree_flatten, tree_map, tree_multimap, tree_unflatten
import jax.numpy as jnp
from jax.tree_util import register_pytree_node_class
from numpyro import handlers
from numpyro.primitives import _PYRO_STACK, Messenger, apply_stack
from numpyro.util import not_jax_tracer
@register_pytree_node_class
class PytreeTrace:
def __init__(self, trace):
self.trace = trace
def tree_flatten(self):
trace, aux_trace = {}, {}
for name, site in self.trace.items():
if site['type'] in ['sample', 'deterministic']:
trace[name], aux_trace[name] = {}, {'_control_flow_done': True}
for key in site:
if key in ['fn', 'args', 'value', 'intermediates']:
trace[name][key] = site[key]
# scanned sites have stop field because we trace them inside a block handler
elif key != 'stop':
aux_trace[name][key] = site[key]
return (trace,), aux_trace
@classmethod
def tree_unflatten(cls, aux_data, children):
trace, = children
for name, site in trace.items():
site.update(aux_data[name])
return cls(trace)
def _subs_wrapper(subs_map, i, length, site):
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_shapes(Messenger):
# a helper messenger to promote shapes of `fn` and `value`
# + msg: fn.batch_shape = (2, 3), value.shape = (3,) + fn.event_shape
# process_message(msg): promote value so that value.shape = (1, 3) + fn.event_shape
# + 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 process_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)
prepend_shapes = (1,) * abs(fn_batch_ndim - value_batch_ndims)
if fn_batch_ndim > value_batch_ndims:
msg["value"] = jnp.reshape(value, prepend_shapes + jnp.shape(value))
elif fn_batch_ndim < value_batch_ndims:
msg["fn"] = tree_map(lambda x: jnp.reshape(x, prepend_shapes + jnp.shape(x)), fn)
def scan_enum(f, init, xs, length, reverse, rng_key=None, substitute_stack=None):
from numpyro.contrib.funsor import enum, config_enumerate, markov, trace as packed_trace
# XXX: This implementation only works for history size=1 but can be
# extended to history size > 1 by running `f` `history_size` times
# for initialization. However, `sequential_sum_product` does not
# support history size > 1, so we skip supporting it here.
# Note that `funsor.sum_product.sarkka_bilmes_product` does support history > 1.
if reverse:
x0 = tree_map(lambda x: x[-1], xs)
xs_ = tree_map(lambda x: x[:-1], xs)
else:
x0 = tree_map(lambda x: x[0], xs)
xs_ = tree_map(lambda x: x[1:], xs)
carry_shape_at_t1 = None
def body_fn(wrapped_carry, x, prefix=None):
i, rng_key, carry = wrapped_carry
init = True if (not_jax_tracer(i) and i == 0) else False
rng_key, subkey = random.split(rng_key) if rng_key is not None else (None, None)
seeded_fn = handlers.seed(f, subkey) if subkey is not None else f
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:
with handlers.scope(prefix="_init"):
new_carry, y = seeded_fn(carry, x)
trace = {}
else:
with handlers.block(), packed_trace() as trace, promote_shapes(), enum(), markov():
# 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)).
new_carry, y = config_enumerate(seeded_fn)(carry, x)
# store shape of new_carry at a global variable
nonlocal carry_shape_at_t1
carry_shape_at_t1 = [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_multimap(lambda a, b: jnp.reshape(a, jnp.shape(b)),
new_carry, carry)
return (i + jnp.array(1), rng_key, new_carry), (PytreeTrace(trace), y)
with markov():
wrapped_carry = (0, rng_key, init)
wrapped_carry, (_, y0) = body_fn(wrapped_carry, x0)
if length == 1:
ys = tree_map(lambda x: jnp.expand_dims(x, 0), y0)
return wrapped_carry, (PytreeTrace({}), ys)
wrapped_carry, (pytree_trace, ys) = lax.scan(body_fn, wrapped_carry, xs_, length - 1, reverse)
first_var = None
for name, site in pytree_trace.trace.items():
# add `time` dimension, the name will be '_time_{first variable in the trace}'
if first_var is None:
first_var = name
leftmost_dim = min(site['infer']['dim_to_name'])
site['infer']['dim_to_name'][leftmost_dim - 1] = '_time_{}'.format(first_var)
# similar to carry, we need to reshape due to shape alternating in markov
ys = tree_multimap(lambda z0, z: jnp.reshape(z, z.shape[:1] + jnp.shape(z0)), y0, ys)
# we also need to reshape `carry` to match sequential behavior
if length % 2 == 0:
t, rng_key, carry = wrapped_carry
flatten_carry, treedef = tree_flatten(carry)
flatten_carry = [jnp.reshape(x, t1_shape)
for x, t1_shape in zip(flatten_carry, carry_shape_at_t1)]
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):
if length is None:
length = tree_flatten(xs)[0][0].shape[0]
if enum:
return scan_enum(f, init, xs, length, reverse, rng_key, substitute_stack)
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():
seeded_fn = handlers.seed(f, subkey) if subkey is not None else f
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)
return lax.scan(body_fn, (jnp.array(0), rng_key, init), xs, length=length, reverse=reverse)
[docs]def scan(f, init, xs, length=None, reverse=False):
"""
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))`.
Currently, only the equivalence to
:class:`~numpyro.contrib.funsor.enum_messenger.markov(history_size=1)`
is supported. A :class:`~numpyro.handlers.trace` of `scan` with discrete latent
variables will contain the following sites:
+ init sites: those sites belong to the first trace of `f`. Each of
them will have name prefixed with `_init/`.
+ 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
: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)
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': []},
'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():
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():
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
```