Probabilistic inference in machine learning using a quantum oracle
Methods, systems, and apparatus, including computer programs encoded on computer storage media, for using a quantum oracle to make inference in complex machine learning models that is capable of solving artificial intelligent problems. Input to the quantum oracle is derived from the training data and the model parameters, which maps at least part of the interactions of interconnected units of the model to the interactions of qubits in the quantum oracle. The output of the quantum oracle is used to determine values used to compute loss function values or loss function gradient values or both during a training process.
1 . A method performed by a system of one or more computers for probabilistic inference in a model for use in machine learning, the model comprising interconnected units, the method comprising:
receiving data for training the model, the data comprising observed data for training and validating the model;
deriving input to a quantum information processor using the received data and a state of the model, wherein the input maps at least some interactions of different interconnected units of the model to interactions of qubits in the quantum information processor;
providing the input to the quantum information processor for learning part of the inference in the model; and
receiving, from the quantum information processor, data representing the learned inference.
2 . The method of claim 1 , wherein learning part of the inference in the model comprises learning values of variables in a hidden layer of the model.
3 . The method of claim 1 , further comprising computing a value of a loss function or a value of a gradient of the loss function using the data representing the learned inference for training or validating the model.
4 . The method of claim 3 , wherein the loss function is given by
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where T represents temperature, x represents variables corresponding to the observed data for use as input data during the training of the model, y represents variables corresponding to the observed data used as labels during the training of the model, s represents variables in a hidden layer of the model, p represents a probability distribution, and F represents a tempered log-partition function.
5 . The method of claim 3 , wherein computing a value of a gradient of the loss function comprises performing a contrastive divergence algorithm, wherein learning part of the inference in the model comprises computing values of variables in a hidden layer of the model as part of the contrastive divergence algorithm.
6 . The method of claim 1 , wherein the observed data comprises variables in visible layers of the model.
7 . A method performed by a quantum information processor, the method comprising:
receiving, as input, data for learning part of an inference in a model comprising interconnected units, wherein
the input is derived using i) data for training the model, the data comprising observed data for training and validating the model, and ii) a state of the model, and
the input maps at least some interactions of different interconnected units of the model to interactions of qubits in the quantum information processor;
processing the input to learn the part of the inference in the model; and
providing, as output, data representing the learned part of the inference.
8 . The method of claim 7 , wherein processing the input to learn part of the inference in the model comprises processing the input to learn values of variables in a hidden layer of the model.
9 . The method of claim 7 , wherein processing the input to learn part of the inference in the model comprises computing values of variables in a hidden layer of the model as part of a contrastive divergence algorithm.
10 . The method of claim 7 , wherein the observed data comprises variables in visible layers of the model.
11 . A system for probabilistic inference in a model for use in machine learning, the model comprising interconnected units, the system comprising one or more computers and one or more storage devices storing instructions that are operable, when executed by the one or more computers, to cause the one or more computers to perform operations comprising:
receiving data for training the model, the data comprising observed data for training and validating the model;
deriving input to a quantum information processor using the received data and a state of the model, wherein the input maps at least some interactions of different interconnected units of the model to interactions of qubits in the quantum information processor;
providing the input to the quantum information processor for learning part of the inference in the model; and
receiving, from the quantum information processor, data representing the learned inference.
12 . The system of claim 11 , wherein learning part of the inference in the model comprises learning values of variables in a hidden layer of the model.
13 . The system of claim 11 , wherein the operations further comprise computing a value of a loss function or a value of a gradient of the loss function using the data representing the learned inference for training or validating the model.
14 . The system of claim 13 , wherein the loss function is given by
L
T
=
-
log
p
~
(
x
^
,
y
^
)
=
-
F
T
(
log
p
(
x
^
,
s
,
y
^
)
)
+
log
∑
x
,
y
exp
(
F
T
(
log
p
(
x
,
s
,
y
)
)
)
where T represents temperature, x represents variables corresponding to the observed data for use as input data during the training of the model, y represents variables corresponding to the observed data used as labels during the training of the model, s represents variables in a hidden layer of the model, p represents a probability distribution, and F represents a tempered log-partition function.
15 . The system of claim 13 , wherein computing a value of a gradient of the loss function comprises performing a contrastive divergence algorithm, wherein learning part of the inference in the model comprises computing values of variables in a hidden layer of the model as part of the contrastive divergence algorithm.
16 . The system of claim 11 , wherein the observed data comprises variables in visible layers of the model.
17 . A quantum system, comprising a quantum information processor having hardware connections comprising couplers that connect qubits included in the quantum information processor, wherein the quantum system is configured to perform operations comprising:
receiving, as input, data for learning part of an inference in a model comprising interconnected units, wherein
the input is derived using i) data for training the model, the data comprising observed data for training and validating the model, and ii) a state of the model, and
the input maps at least some interactions of different interconnected units of the model to interactions of qubits in the quantum information processor;
processing the input to learn the part of the inference in the model; and
providing, as output, data representing the learned part of the inference.
18 . The system of claim 17 , wherein processing the input to learn part of the inference in the model comprises processing the input to learn values of variables in a hidden layer of the model.
19 . The system of claim 17 , wherein processing the input to learn part of the inference in the model comprises computing values of variables in a hidden layer of the model as part of a contrastive divergence algorithm.
20 . The system of claim 17 , wherein the observed data comprises variables in visible layers of the model.