Method and device for training a machine learning system
A computer-implemented method for training a machine learning system in which the machine learning system is configured to ascertain, based on at least a first input signal and a multiplicity of second input signals and second output signals corresponding to the second input signals, a first output signal corresponding to the first input signal, the first output signal characterizing a classification encumbered with an uncertainty and/or a regression encumbered with an uncertainty.
1 . A computer-implemented method for training a machine learning system, the machine learning system being configured to ascertain, based on at least a first input signal and a multiplicity of second input signals and second output signals corresponding to the second input signals, a first output signal that corresponds to the first input signal, the first output signal characterizing a classification encumbered with an uncertainty and/or a regression encumbered with the uncertainty, the method for training comprising the following steps:
ascertaining a multiplicity of training input signals, which are in context with one another, a corresponding training output signal being allocated to each training input signal;
dividing the multiplicity of training input signals and the corresponding training output signals into a multiplicity of second training input signals and corresponding second training output signals and into at least one first training input signal and a corresponding first training output signal;
ascertaining a context representation of the multiplicity of second training input signals and second training output signals;
ascertaining a predicted output signal for the at least one first training input signal using a decoder of the machine learning system and based on the ascertained context representation and the first training input signal;
ascertaining a loss value, which characterizes a difference between the predicted output signal and the first training output signal, the loss value being ascertained based on a loss function, and the loss function characterizes a probability density function or a logarithmized probability density function of a normal distribution;
ascertaining a gradient of a multiplicity of parameters of an encoder of the machine learning system and/or the decoder with regard to the loss value; and
varying the multiplicity of parameters based on the ascertained gradient.
2 . The method as recited in claim 1 , wherein the ascertaining of the first output signal using the machine learning system includes the following steps:
ascertaining a multiplicity of latent representations using the encoder of the machine learning system, each latent representation of the multiplicity of latent representations being ascertained based on at least a second input signal of the second input signals and a corresponding second output signal corresponding to the second input signal, the second input signal and the second output signal characterizing a context of the first input signal, and the latent representation including a first representation and a second representation, the first representation characterizing an expected value and the second representation characterizing a variance;
ascertaining a third representation based on the first representations of the latent representations of the multiplicity of latent representations, the third representation characterizing an accumulation of the first representations;
ascertaining a fourth representation based on the second representations of the latent representations of the multiplicity of latent representations, the fourth representation characterizing an accumulation of the second representations; and
ascertaining the first output signal using the decoder of the machine learning system, the decoder ascertaining the first output signal based on the third representation, the fourth representation, and the first input signal.
3 . The method as recited in claim 2 , wherein in the step of ascertaining the loss value, a first representation of the predicted output signal ascertained by the decoder is used as an expected value of the probability density function, and a second representation of the predicted output signal ascertained by the decoder is used as a variance or a covariance matrix of the probability density function.
4 . The method as recited in claim 2 , wherein the machine learning system is trained by a multiplicity of first training input signals and training output signals, and the loss value is ascertained according to the following formula
l
(
y
1
:
m
❘
x
1
:
m
,
μ
z
,
σ
z
2
)
=
-
∑
i
𝒩
(
y
i
❘
dec
(
x
i
,
μ
z
)
,
dec
(
x
i
,
σ
z
2
)
where x 1:m is the multiplicity of first training input signals, y 1:m are the training output signals allocated to the first training input signals, N is a probability density function of a normal distribution, dec(x i , μ z ) is a first representation of the predicted output signal ascertained using the decoder,
dec
(
x
i
,
σ
z
2
)
is a second representation of the predicted output signal ascertained using the decoder, the ascertained first representation being used as an expected value of the probability density function and the ascertained second representation being used as a variance or a covariance matrix of the probability density function.
5 . The method as recited in claim 2 , wherein in the step of ascertaining of the fourth representation
σ
z
2
,
the fourth representation
σ
z
2
is ascertained according to the following formula
σ
z
2
σ
z
2
σ
z
2
=
[
(
σ
0
2
)
⊖
+
∑
i
(
σ
i
2
)
⊖
]
⊖
σ
0
2
σ
z
2
σ
i
2
ii
⊖
where
σ
0
2
is an a priori assumption about the fourth representation
σ
z
2
,
σ
i
2
is a second representation ascertained by the encoder of a latent representation of the i th input signal and the i th output signal of the multiplicity of second input signals and second output signals, respectively, and ⊖ indicates an elementwise reciprocal value.
6 . The method as recited in claim 2 , wherein in the step of ascertaining the third representation μ z , the third representation μ z is ascertained according to the following formula
μ
z
μ
z
μ
z
=
μ
0
+
σ
z
2
⊙
∑
i
(
μ
i
-
μ
0
)
⊗
(
σ
i
2
)
μ
0
μ
z
μ
i
iiσ
z
2
σ
i
2
ii
⊙
⊗
where μ 0 is an a priori assumption about the third representation μ z , μ i is a first representation ascertained by the encoder of a latent representation of the i th input signal and the i th output signal of the multiplicity of second input signals and second output signals, respectively,
σ
z
2
is the third representation,
σ
i
2
is a second representations ascertained by the encoder of a latent representation of the i th input signal and the i th output signal of the multiplicity of second input signals and second output signals, respectively, ⊙ indicates an elementwise multiplication, and Ø indicates an elementwise division.
7 . The method as recited in claim 2 , wherein the encoder includes a neural network which is configured to ascertain the first representations and the second representations of the latent representations based on the multiplicity of second input signals and second output signals.
8 . The method as recited in claim 2 , wherein the encoder includes a first neural network which is configured to ascertain the first representations of the latent representations based on the multiplicity of second input signals and second output signals, and the encoder includes a second neural network which is configured to ascertain the second representations of the latent representations based on the multiplicity of second input signals and second output signals.
9 . The method as recited in claim 2 , wherein the decoder includes a neural network which is configured to ascertain the first output signal based on the third representation, the fourth representation, and the first input signal.
10 . The method as recited in claim 2 , wherein the decoder includes a first neural network which is configured to ascertain the first representation of the first output signal based on the third representation and the first input signal, and the decoder includes a second neural network which is configured to ascertain the second representation of the first output signal based on the fourth representation and the first input signal.
11 . A computer-implemented method for operating a machine learning system, comprising the following steps:
training the machine learning system, the machine learning system being configured to ascertain, based on at least a first input signal and a multiplicity of second input signals and second output signals corresponding to the second input signals, a first output signal that corresponds to the first input signal, the first output signal characterizing a classification encumbered with an uncertainty and/or a regression encumbered with the uncertainty, the training including:
ascertaining a multiplicity of training input signals, which are in context with one another, a corresponding training output signal being allocated to each training input signal,
dividing the multiplicity of training input signals and the corresponding training output signals into a multiplicity of second training input signals and corresponding second training output signals and into at least one first training input signal and a corresponding first training output signal,
ascertaining a context representation of the multiplicity of second training input signals and second training output signals,
ascertaining a predicted output signal for the at least one first training input signal using a decoder of the machine learning system and based on the ascertained context representation and the first training input signal,
ascertaining a loss value, which characterizes a difference between the predicted output signal and the first training output signal, the loss value being ascertained based on a loss function, and the loss function characterizes a probability density function or a logarithmized probability density function of a normal distribution,
ascertaining a gradient of a multiplicity of parameters of an encoder of the machine learning system and/or the decoder with regard to the loss value, and
varying the multiplicity of parameters based on the ascertained gradient; and
ascertaining the first output signal for the first input signal using the trained machine learning system.
12 . The method as recited in claim 11 , wherein based on the ascertained first output signal, a device is operated accordingly.
13 . A training device for training a machine learning system, the machine learning system being configured to ascertain, based on at least a first input signal and a multiplicity of second input signals and second output signals corresponding to the second input signals, a first output signal that corresponds to the first input signal, the first output signal characterizing a classification encumbered with an uncertainty and/or a regression encumbered with the uncertainty, the training device configured to:
ascertain a multiplicity of training input signals, which are in context with one another, a corresponding training output signal being allocated to each training input signal;
divide the multiplicity of training input signals and the corresponding training output signals into a multiplicity of second training input signals and corresponding second training output signals and into at least one first training input signal and a corresponding first training output signal;
ascertain a context representation of the multiplicity of second training input signals and second training output signals;
ascertain a predicted output signal for the at least one first training input signal using a decoder of the machine learning system and based on the ascertained context representation and the first training input signal;
ascertain a loss value, which characterizes a difference between the predicted output signal and the first training output signal, the loss value being ascertained based on a loss function, and the loss function characterizes a probability density function or a logarithmized probability density function of a normal distribution;
ascertain a gradient of a multiplicity of parameters of an encoder of the machine learning system and/or the decoder with regard to the loss value; and
vary the multiplicity of parameters based on the ascertained gradient.
14 . A non-transitory machine-readable memory medium on which is stored a computer program for training a machine learning system, the machine learning system being configured to ascertain, based on at least a first input signal and a multiplicity of second input signals and second output signals corresponding to the second input signals, a first output signal that corresponds to the first input signal, the first output signal characterizing a classification encumbered with an uncertainty and/or a regression encumbered with the uncertainty, the computer program, when executed by a processor, causing the processor to perform the following steps:
ascertaining a multiplicity of training input signals, which are in context with one another, a corresponding training output signal being allocated to each training input signal;
dividing the multiplicity of training input signals and the corresponding training output signals into a multiplicity of second training input signals and corresponding second training output signals and into at least one first training input signal and a corresponding first training output signal;
ascertaining a context representation of the multiplicity of second training input signals and second training output signals;
ascertaining a predicted output signal for the at least one first training input signal using a decoder of the machine learning system and based on the ascertained context representation and the first training input signal;
ascertaining a loss value, which characterizes a difference between the predicted output signal and the first training output signal, the loss value being ascertained based on a loss function, and the loss function characterizes a probability density function or a logarithmized probability density function of a normal distribution;
ascertaining a gradient of a multiplicity of parameters of an encoder of the machine learning system and/or the decoder with regard to the loss value; and
varying the multiplicity of parameters based on the ascertained gradient.
15 . The method as recited in claim 1 , wherein the first output signal characterizes a position of an object in an image and a variance in connection with the position.
16 . The computer-implemented method as recited in claim 11 , wherein the first output signal characterizes a position of an object in an image and a variance in connection with the position.
17 . The training device as recited in claim 13 , wherein the first output signal characterizes a position of an object in an image and a variance in connection with the position.
18 . The non-transitory machine-readable memory medium as recited in claim 14 , wherein the first output signal characterizes a position of an object in an image and a variance in connection with the position.