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+ from ctypes import c_void_p
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+
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+ from torch import Tensor
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+
5
+ # Defined in torch/csrc/inductor/aoti_runner/pybind.cpp
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+
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+ # Tensor to AtenTensorHandle
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+ def unsafe_alloc_void_ptrs_from_tensors(tensors: list[Tensor]) -> list[c_void_p]: ...
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+ def unsafe_alloc_void_ptr_from_tensor(tensor: Tensor) -> c_void_p: ...
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+
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+ # AtenTensorHandle to Tensor
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+ def alloc_tensors_by_stealing_from_void_ptrs(
13
+ handles: list[c_void_p],
14
+ ) -> list[Tensor]: ...
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+ def alloc_tensor_by_stealing_from_void_ptr(
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+ handle: c_void_p,
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+ ) -> Tensor: ...
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+
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+ class AOTIModelContainerRunnerCpu: ...
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+ class AOTIModelContainerRunnerCuda: ...
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+ class AOTIModelContainerRunnerXpu: ...
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+
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+ # Defined in torch/csrc/inductor/aoti_package/pybind.cpp
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+ class AOTIModelPackageLoader: ...
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+ from torch.types import _bool, _int
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+
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+ # Defined in torch/csrc/cpu/Module.cpp
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+
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+ def _is_avx2_supported() -> _bool: ...
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+ def _is_avx512_supported() -> _bool: ...
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+ def _is_avx512_vnni_supported() -> _bool: ...
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+ def _is_avx512_bf16_supported() -> _bool: ...
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+ def _is_amx_tile_supported() -> _bool: ...
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+ def _is_amx_fp16_supported() -> _bool: ...
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+ def _init_amx() -> _bool: ...
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+ def _L1d_cache_size() -> _int: ...
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+ def _L2_cache_size() -> _int: ...
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+ from enum import IntEnum
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+
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+ # Defined in torch/csrc/cuda/shared/cudnn.cpp
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+ is_cuda: bool
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+
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+ def getRuntimeVersion() -> tuple[int, int, int]: ...
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+ def getCompileVersion() -> tuple[int, int, int]: ...
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+ def getVersionInt() -> int: ...
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+
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+ class RNNMode(IntEnum):
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+ rnn_relu = ...
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+ rnn_tanh = ...
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+ lstm = ...
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+ gru = ...
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+ def getVersionInt() -> int: ...
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+ from typing import Any
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+
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+ import torch
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+
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+ # This module is defined in torch/csrc/distributed/autograd/init.cpp
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+
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+ class DistAutogradContext:
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+ def _context_id(self) -> int: ...
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+ def _recv_functions(self) -> dict[int, Any]: ...
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+ def _send_functions(self) -> dict[int, Any]: ...
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+ def _known_worker_ids(self) -> set[int]: ...
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+
13
+ def _new_context() -> DistAutogradContext: ...
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+ def _release_context(context_id: int) -> None: ...
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+ def _get_max_id() -> int: ...
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+ def _is_valid_context(worker_id: int) -> bool: ...
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+ def _retrieve_context(context_id: int) -> DistAutogradContext: ...
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+ def _current_context() -> DistAutogradContext: ...
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+ def _init(worker_id: int) -> None: ...
20
+ def _get_debug_info() -> dict[str, str]: ...
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+ def backward(
22
+ context_id: int,
23
+ roots: list[torch.Tensor],
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+ retain_graph: bool = False,
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+ ) -> None: ...
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+ def get_gradients(context_id: int) -> dict[torch.Tensor, torch.Tensor]: ...
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1
+ r"""
2
+ The ``distributions`` package contains parameterizable probability distributions
3
+ and sampling functions. This allows the construction of stochastic computation
4
+ graphs and stochastic gradient estimators for optimization. This package
5
+ generally follows the design of the `TensorFlow Distributions`_ package.
6
+
7
+ .. _`TensorFlow Distributions`:
8
+ https://arxiv.org/abs/1711.10604
9
+
10
+ It is not possible to directly backpropagate through random samples. However,
11
+ there are two main methods for creating surrogate functions that can be
12
+ backpropagated through. These are the score function estimator/likelihood ratio
13
+ estimator/REINFORCE and the pathwise derivative estimator. REINFORCE is commonly
14
+ seen as the basis for policy gradient methods in reinforcement learning, and the
15
+ pathwise derivative estimator is commonly seen in the reparameterization trick
16
+ in variational autoencoders. Whilst the score function only requires the value
17
+ of samples :math:`f(x)`, the pathwise derivative requires the derivative
18
+ :math:`f'(x)`. The next sections discuss these two in a reinforcement learning
19
+ example. For more details see
20
+ `Gradient Estimation Using Stochastic Computation Graphs`_ .
21
+
22
+ .. _`Gradient Estimation Using Stochastic Computation Graphs`:
23
+ https://arxiv.org/abs/1506.05254
24
+
25
+ Score function
26
+ ^^^^^^^^^^^^^^
27
+
28
+ When the probability density function is differentiable with respect to its
29
+ parameters, we only need :meth:`~torch.distributions.Distribution.sample` and
30
+ :meth:`~torch.distributions.Distribution.log_prob` to implement REINFORCE:
31
+
32
+ .. math::
33
+
34
+ \Delta\theta = \alpha r \frac{\partial\log p(a|\pi^\theta(s))}{\partial\theta}
35
+
36
+ where :math:`\theta` are the parameters, :math:`\alpha` is the learning rate,
37
+ :math:`r` is the reward and :math:`p(a|\pi^\theta(s))` is the probability of
38
+ taking action :math:`a` in state :math:`s` given policy :math:`\pi^\theta`.
39
+
40
+ In practice we would sample an action from the output of a network, apply this
41
+ action in an environment, and then use ``log_prob`` to construct an equivalent
42
+ loss function. Note that we use a negative because optimizers use gradient
43
+ descent, whilst the rule above assumes gradient ascent. With a categorical
44
+ policy, the code for implementing REINFORCE would be as follows::
45
+
46
+ probs = policy_network(state)
47
+ # Note that this is equivalent to what used to be called multinomial
48
+ m = Categorical(probs)
49
+ action = m.sample()
50
+ next_state, reward = env.step(action)
51
+ loss = -m.log_prob(action) * reward
52
+ loss.backward()
53
+
54
+ Pathwise derivative
55
+ ^^^^^^^^^^^^^^^^^^^
56
+
57
+ The other way to implement these stochastic/policy gradients would be to use the
58
+ reparameterization trick from the
59
+ :meth:`~torch.distributions.Distribution.rsample` method, where the
60
+ parameterized random variable can be constructed via a parameterized
61
+ deterministic function of a parameter-free random variable. The reparameterized
62
+ sample therefore becomes differentiable. The code for implementing the pathwise
63
+ derivative would be as follows::
64
+
65
+ params = policy_network(state)
66
+ m = Normal(*params)
67
+ # Any distribution with .has_rsample == True could work based on the application
68
+ action = m.rsample()
69
+ next_state, reward = env.step(action) # Assuming that reward is differentiable
70
+ loss = -reward
71
+ loss.backward()
72
+ """
73
+
74
+ from . import transforms
75
+ from .bernoulli import Bernoulli
76
+ from .beta import Beta
77
+ from .binomial import Binomial
78
+ from .categorical import Categorical
79
+ from .cauchy import Cauchy
80
+ from .chi2 import Chi2
81
+ from .constraint_registry import biject_to, transform_to
82
+ from .continuous_bernoulli import ContinuousBernoulli
83
+ from .dirichlet import Dirichlet
84
+ from .distribution import Distribution
85
+ from .exp_family import ExponentialFamily
86
+ from .exponential import Exponential
87
+ from .fishersnedecor import FisherSnedecor
88
+ from .gamma import Gamma
89
+ from .geometric import Geometric
90
+ from .gumbel import Gumbel
91
+ from .half_cauchy import HalfCauchy
92
+ from .half_normal import HalfNormal
93
+ from .independent import Independent
94
+ from .inverse_gamma import InverseGamma
95
+ from .kl import _add_kl_info, kl_divergence, register_kl
96
+ from .kumaraswamy import Kumaraswamy
97
+ from .laplace import Laplace
98
+ from .lkj_cholesky import LKJCholesky
99
+ from .log_normal import LogNormal
100
+ from .logistic_normal import LogisticNormal
101
+ from .lowrank_multivariate_normal import LowRankMultivariateNormal
102
+ from .mixture_same_family import MixtureSameFamily
103
+ from .multinomial import Multinomial
104
+ from .multivariate_normal import MultivariateNormal
105
+ from .negative_binomial import NegativeBinomial
106
+ from .normal import Normal
107
+ from .one_hot_categorical import OneHotCategorical, OneHotCategoricalStraightThrough
108
+ from .pareto import Pareto
109
+ from .poisson import Poisson
110
+ from .relaxed_bernoulli import RelaxedBernoulli
111
+ from .relaxed_categorical import RelaxedOneHotCategorical
112
+ from .studentT import StudentT
113
+ from .transformed_distribution import TransformedDistribution
114
+ from .transforms import * # noqa: F403
115
+ from .uniform import Uniform
116
+ from .von_mises import VonMises
117
+ from .weibull import Weibull
118
+ from .wishart import Wishart
119
+
120
+
121
+ _add_kl_info()
122
+ del _add_kl_info
123
+
124
+ __all__ = [
125
+ "Bernoulli",
126
+ "Beta",
127
+ "Binomial",
128
+ "Categorical",
129
+ "Cauchy",
130
+ "Chi2",
131
+ "ContinuousBernoulli",
132
+ "Dirichlet",
133
+ "Distribution",
134
+ "Exponential",
135
+ "ExponentialFamily",
136
+ "FisherSnedecor",
137
+ "Gamma",
138
+ "Geometric",
139
+ "Gumbel",
140
+ "HalfCauchy",
141
+ "HalfNormal",
142
+ "Independent",
143
+ "InverseGamma",
144
+ "Kumaraswamy",
145
+ "LKJCholesky",
146
+ "Laplace",
147
+ "LogNormal",
148
+ "LogisticNormal",
149
+ "LowRankMultivariateNormal",
150
+ "MixtureSameFamily",
151
+ "Multinomial",
152
+ "MultivariateNormal",
153
+ "NegativeBinomial",
154
+ "Normal",
155
+ "OneHotCategorical",
156
+ "OneHotCategoricalStraightThrough",
157
+ "Pareto",
158
+ "RelaxedBernoulli",
159
+ "RelaxedOneHotCategorical",
160
+ "StudentT",
161
+ "Poisson",
162
+ "Uniform",
163
+ "VonMises",
164
+ "Weibull",
165
+ "Wishart",
166
+ "TransformedDistribution",
167
+ "biject_to",
168
+ "kl_divergence",
169
+ "register_kl",
170
+ "transform_to",
171
+ ]
172
+ __all__.extend(transforms.__all__)
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