# US 2021/0279526 A1 · Method of modelling for checking the results provided by an artificial neural network and other associated methods

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- Number: US 2021/0279526 A1
- Document ID: US20210279526A1
- Status: Published application
- Kind: A1
- Application number: 17/255,824
- Filed: 2019-06-28
- Published: 2021-09-09
- Earliest claimed: 2018-06-29
- Assignees: Dreamquark
- Applicants: Dreamquark
- Inventors: Benoît SCHMAUCH; Johan FERRET; Nicolas MERIC
- Web page: https://patentgrep.com/patent/US20210279526A1

## CPC

- G06N 3/08: Learning methods
- G06F 18/217: {Validation; Performance evaluation; Active pattern learning techniques}
- G06N 3/045: Combinations of networks
- G06N 3/0499: Feedforward networks
- G06N 3/09: Supervised learning
- G06N 5/045: Explanation of inference; Explainable artificial intelligence [XAI]; Interpretable artificial intelligence
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

A method of modelling for checking the results provided by an artificial neural network, includes generating an artificial neural network; training the artificial neural network on a training database; testing the artificial neural network on at least one test datum dependent on a plurality of variables vi; so as to obtain a result R per test datum, the result R being dependent on the variables vi; for each result R: approximating by a linear model a first function F1 dependent solely on the result R so as to obtain a second function F2, the first function F1 and the second function F2 being dependent on the variables vi; simplifying the second function F2 to obtain a third function F3 dependent on a smaller number of variables vi; applying to the third function F3 the inverse function of the first function F1 to obtain an operating model of the neural network.

## Claims

### Claim 1

Method of modelling for checking the results provided by an artificial neural network comprising the following steps implemented by a computer:
generating an artificial neural network;
training the artificial neural network on a training database;
testing the artificial neural network on at least one test datum dependent on a plurality of variables vi so as to obtain a result R per test datum, the result R being dependent on the variables vi;
for each result R:
approximating by a linear model a first function F1 dependent solely on the result R so as to obtain a second function F2, the first function F1 and the second function F2 being dependent on the variables vi;
simplifying the second function F2 to obtain a third function F3 dependent on a smaller number of variables vi;
applying to the third function F3 the inverse function of the first function F1 to obtain an operating model of the neural network.

### Claim 2 (depends on 1)

The method of modelling according to claim 1, wherein the second function F2 is expressed as the sum of a y-intercept point b and of the sum of the variables vi each multiplied by a slope
F
2
=
b
+
∑
i
⁢
a
i
⁢
v
i

### Claim 3 (depends on 1)

The method of modelling according to claim 1, wherein a first variable v1 correlated with a second variable v2 is expressed according to the second variable v2 as the sum of an uncorrelated variable ε1 and of a correlation coefficient C12 multiplied by the second variable v2:
v1=C12v2+ε1

### Claim 4 (depends on 2)

The method of modelling according to claim 2, wherein a first variable v1 correlated with a second variable v2 is expressed according to the second variable v2 as the sum of an uncorrelated variable ε1 and of a correlation coefficient C12 multiplied by the second variable v2:
v1=C12v2+ε1
and wherein the step of simplifying comprises the following sub-steps:
creating a variable vector Vv comprising the variables vi;
creating an empty synthetic variable vector Vvs;
creating an empty contribution coefficient vector Vc;
carrying out at least one time the following sub-steps:
for each variable vk of the variable vector Vv, expressing a contribution coefficient Wk according to the slope ak of said variable vk, of the slopes ai and of the correlation coefficients Cki of the variables vi of the variable vector Vv correlated with said variable vk;
comparing the absolute values of the contribution coefficients Wi and determining a reference variable vref that has the contribution coefficient Wref with the highest absolute value;
adding to the synthetic variable vector Vvs said reference variable vref;
adding to the contribution coefficient vector Vc the contribution coefficient Wref of said reference variable vref;
for each variable vk of the variable vector Vv different from the reference variable vref and correlated with the reference variable vref, expressing said correlated variable vk according to the reference variable vref and normalising the uncorrelated variable εk so as to obtain a new variable vk′;
emptying the variable vector Vv and fill the variable vector Vv with the new variables vi′;
expressing the variables contained in the synthetic variable vector Vvs according to the variables vi of the second function F2 so as to obtain remaining variables vrp;
expressing a remaining variable slope arp for each remaining variable vrp using the contribution coefficient vector Vc.

### Claim 5 (depends on 4)

The method of modelling according to claim 4, wherein the third function F3 is expressed as the sum of the y-intercept point b and of the sum of the remaining variables vrp each one multiplied by its remaining variable slope arp:
F
3
=
b
+
∑
p
⁢
a
⁢
r
p
⁢
v
⁢
r
p

### Claim 6 (depends on 1)

Method of checking the results provided by an artificial neural network comprising all the steps of the method of modelling according to claim 1 and an additional step of evaluating the training database using at least one operating model.

### Claim 7 (depends on 1)

Method of comparing the performances of a first artificial neural network and of a second artificial neural network, comprising:
applying the method of modelling according to claim 1 to the first artificial neural network so as to obtain at least one first operating model of the first artificial neural network;
applying the method of modelling according to claim 1 to the second artificial neural network so as to obtain at least one second operating model of the second artificial neural network;
comparing the performance of the first artificial neural network and of the second artificial neural network by comparing each first operating model of the first artificial neural network and each second operating model of the second artificial neural network that correspond to the same test datum.

### Claim 8 (depends on 1)

A computer adapted to implement the method of modelling according to claim 1.

### Claim 9 (depends on 1)

A computer program product comprising instructions that, when the program is executed by a computer, lead the latter to implement the steps of the method of modelling according to claim 1.

### Claim 10 (depends on 9)

A non-transitory recording medium that is readable by a computer, on which the computer program product is recorded according to claim 9.

### Claim 11 (depends on 1)

Method of analysing a decision making by an artificial neural network, the decision having been taken based on at least one test datum, the method comprising the steps of the method of modelling according to claim 1 followed by a step of generating an explanatory report of the decision making using the operating model of the artificial neural network that corresponds to the test datum.