WO2023084174A1 - Method, device and computer program product for configuring a distributed computing system - Google Patents

Abstract

The invention, in one embodiment, relates to a method for determining configurations of a distributed system of computing units for implementing a deep-learning algorithm, said determination implementing a recommendation based on a knowledge model, said method being implemented by a device comprising a processor that causes said device to implement the method, the method comprising: determining a deep-learning algorithm intended to be implemented in the distributed system; obtaining (S901) a knowledge domain including, for said algorithm, at least one observed configuration and a value of at least one performance indicator for said at least one observed configuration; determining (S902) a parametric model of the performance indicator or indicators on the basis of the knowledge domain; determining (S903) at least one configuration different from said at least one observed configuration and estimating the value of the performance indicator or indicators associated with said different configuration on the basis of said model in order to complete the knowledge domain; selecting (S904) at least one configuration among the configurations of the completed knowledge domain that satisfies at least one constraint relating to the at least one performance indicator; and generating a signal representative of said at least one selected configuration. Other embodiments relate to an implementation device and to a computer program product.

Description

METHOD, DEVICE AND PROGRAMMED PRODUCT

COMPUTER FOR EA CONFIGURING A DISTRIBUTED CAECUE SYSTEM

Technical field of the invention

The present invention relates to a method, device and computer program product for configuring a distributed computing system. The invention relates more particularly to the determination of one or more configurations for the implementation of an algorithm by the distributed system to be configured, the determination being based on a model enriched with knowledge. The algorithm is for example a deep learning algorithm.

Technical background

Computer recommender systems can be classified into four broad categories: recommenders based on collaborative filtering;

- recommenders based on content similarity;

- recommenders based on a knowledge model;

- hybrid recommenders combining the characteristics of several recommenders from the previous categories.

Deep learning algorithms are very time-, computer-resource- and energy-consuming. Having a specific recommendation on the distributed system configuration according to its needs and/or constraints makes it possible to limit these consumptions.

Deep learning algorithms are based on stochastic optimizations.

These recommenders are relevant if they manage to offer a certain exhaustiveness of the possible choices in order to best meet the constraints and needs. However, due to the previously mentioned stochastic optimization, as well as the long cost for database training resulting from real experiments and observations, obtaining the set of possible configurations is often not possible. feasible. Document [1] describes radiotherapy planning using a knowledge-based recommendation system.

Summary of the invention

An embodiment relates to a method for determining configurations of a distributed system of computing units for the implementation of a deep learning algorithm, said determination implementing a recommendation based on a knowledge model, said method being implemented by a device comprising a processor which causes said device to implement the method, the method comprising: determining a deep learning algorithm to be implemented in the distributed system; obtaining a knowledge domain comprising, for said algorithm, at least one observed configuration and a value of at least one performance indicator for said at least one observed configuration; the determination of a parametric model of the performance indicator(s) according to the knowledge domain; the selection of at least one configuration from among the configurations of the knowledge domain completed and meeting at least one constraint relating to the at least one performance indicator; generating a signal representative of said at least one selected configuration.

Thus, it is only necessary to obtain experimental data for a limited number of configurations - the knowledge domain can be completed by implementing the parametric model. It is in this area of knowledge thus supplemented - exhaustively or not - that one can then proceed to the filtering of the configurations corresponding to one or more constraints, for example constraints fixed by a user or predetermined, to select among the configurations meeting these constraints one or more best suited configurations.

The signal generated can be displayed, the information it contains can be stored or serve as a command to one or more computing unit servers. According to a particular embodiment, the selection is made by a decision algorithm according to a weighting of at least one performance indicator, the method further comprising the display of the configuration(s) selected by implementing said signal and receiving a command to identify a unique configuration among the selected configurations which will be applied to the distributed system.

According to a particular embodiment, the selection is performed by a decision algorithm which selects a unique configuration.

According to a particular embodiment, the method further comprises the reservation of calculation units according to the unique configuration.

According to a particular embodiment, the method further comprises the estimation of the variability of said at least one performance indicator for a different configuration.

According to a particular embodiment, said at least one performance indicator of a configuration comprises one or more of: the required training time of the system for the configuration considered; the relative precision of calculation; the power consumed by the system for the configuration considered.

According to a particular embodiment, the parametric models applied on the one hand to the inverse of the training time and on the other hand to the calculation precision are affine functions of a number of calculation units of the distributed system implemented in the configuration considered, and the determination of the parametric model includes the determination of the parameters of the affine function associated with each performance indicator.

According to a particular embodiment, the power consumed is an affine function of the square of the number of calculation units of the distributed system to be used in the configuration envisaged.

According to a particular embodiment, the decision algorithm classifies the filtered configurations according to a score depending on the performance indicator(s) and weighting coefficients of the latter.

According to a particular embodiment, the method further comprises obtaining at least one constraint on an intrinsic characteristic of hardware configuration, said constraint being taken into account within the framework of the filtering of the configurations.

According to a particular embodiment, said deep learning algorithm implements a convolutional neural network. According to a particular embodiment, the above method is applied in the context of image segmentation.

An exemplary embodiment relates to a device comprising a processor and a memory, said memory comprising instructions which, when they are executed by the processor, lead the device to implement the steps of one of the methods described.

A computer program product comprising instructions which, when the program is executed by a device comprising a processor, causes the device to perform the steps of one of the methods described.

Brief description of figures

Other characteristics and advantages of the invention will appear during the reading of the detailed description which will follow for the understanding of which reference will be made to the appended drawings in which:

- figure 1 is a diagram of a neural network that can be used for the implementation of a deep learning algorithm according to the state of the art;

- Figure 2 is a block diagram of a system in which a device according to one embodiment is implemented;

- Figure 3 is an algorigram of a recommender based on a knowledge model according to an example embodiment;

- Figure 4 is a graph representing the acceleration of the training time as a function of the number of calculation units;

- Figure 5 is an example of a graphical interface allowing a user to interact with the recommender according to an example embodiment;

- Figure 6 is an enlarged view of a first part of the user interface of Figure 5 offering a functionality for choosing constraints and weighting coefficients of these constraints;

FIG. 7 is an enlarged view of a second part of the user interface of FIG. 5 proposing a functionality for choosing parameters for displaying recommender configurations; - Figure 8 is an enlarged view of a third part of the user interface of Figure 5 and corresponding to a visualization of different configurations;

- Figure 9 is a flowchart of a method according to a non-limiting embodiment.

Detailed description of the invention

The following description uses medical imaging as an application example. However, the invention is not limited to this specific application and can be implemented in fields other than image analysis.

Figure 1 is an example of a neural network 10 architecture that can be used to implement a deep learning algorithm. The neural network in figure 1 is a very simple and well-known network intended to illustrate the basics of how such a network works within the framework of a deep learning algorithm - much more complex networks can be used and are therefore otherwise known to the person skilled in the art. The network of Figure 1 comprises an input layer 11, one or more so-called hidden layers 12 and an output layer 13. The different layers comprise neurons 14 and each layer is connected to the next layer - by these connections, each layer takes into account the output of the previous layer. The connections are weighted and the weighting weights define the influence of a neuron on another neuron, the latter receiving the sum of the weighted outputs of preceding neurons. This sum is processed by a so-called activation or propagation function which generates the output of the neuron. The input layer receives external data, for example images from medical imaging. The output layer provides the desired result, for example the recognition of an object in the image or even a segmented image. The learning of the network can for example be carried out by implementing a method of backpropagation of the gradient within the framework of a supervised training, on the basis of known input data generating a known result, the difference between the effective output generated by the network and the expected result making it possible to adapt the parameters of the network in a manner known per se, in particular by adjusting the weights to minimize errors. These weights will have been initialized randomly. FIG. 2 is a block diagram of a system comprising a device 200 for recommending configurations according to a non-limiting embodiment. The device 200 comprises a processor 201, a random access memory 202, a mass memory 203 (for example a ROM, a hard disk, a static memory, etc.), a communication interface 205 and an interface 206 for the connection of peripheral devices. The various elements of the device 200 are interconnected by means of an internal communication bus 204. The mass memory 203 notably stores software code 213 which implements the methods described when it is executed by the processor 201. The device is connected to a or several user interface devices 208, such as for example a keyboard, and/or a mouse. A display device 207 is also connected to the device 200. Although the figure shows a display device external to the device 200, it can also be integrated into the device 200. The device 200 communicates with a server 209 through a network of communication 210, for example the internet. The server 209 controls one or more banks 211 of calculation units 212. According to an exemplary embodiment, these calculation units are graphics processing units (also called 'Graphics Processing Units' or 'GPU's in English), but Other types of processing units can also be implemented. The device 200 can reserve computing capacities of the banks 211 with the server 209 for the needs of executing a deep learning algorithm. This reservation can for example be made on the basis of a configuration of the distributed calculation system, this configuration being able for example to be defined by a number of calculation units to be reserved. Although the server 209 is represented in FIG. 2 separately from the banks of calculation units 211, these two entities can be collocated. All communications can be wired or wireless.

The aim of the recommender device 200 is to propose a distributed computing system configuration according to specifications given by a user. According to the present embodiment, these specifications, representative of the objectives expected by the user, are based on one or more characteristics of the configurations of the distributed computing system and/or on one or more performance criteria defined by a user. The performance criterion or criteria may comprise one or more of the training (or learning) time of the algorithm, the precision (or loss of precision) or even the electrical power consumed. An example of a user-defined combination of criteria could be a training time of less than three hours and a 95% accuracy. Not all criteria need to be defined. These criteria or their combinations are also called 'constraints' and the recommender device is then considered to be a constrained recommender in the sense that the criteria specified by the user constrain certain parts of the data domain. As such, constrained knowledge-based recommenders are also known as 'knowledge-based configurations'. The device will then have to determine a suitable configuration, in the form of a number of calculation units to be reserved and if necessary implement this configuration. According to one embodiment, the recommender device 200 determines a suitable configuration, which can then be implemented by the user via a device other than the device 200. According to the present example embodiment, the device 200 implements implements a recommender based on a constrained knowledge model.

FIG. 3 is an algorigram of a recommendation method according to an exemplary embodiment.

The recommendation method receives as input at least the following data:

A domain of knowledge 301

This domain includes configurations of the distributed system (as indicated for example in the form of number of calculation units) - as well as the performances associated with these configurations (in terms of training time of the implemented algorithm, the relative precision, of the power required or of the energy consumption) - determined experimentally for a given task, for example a medical image segmentation task.

- The 302 specifications given by the user

According to one embodiment, these specifications include minimum and/or maximum limits or specific values of the performance criteria. According to a variant embodiment, these criteria can also be predetermined, or be automatically derived from data available elsewhere such as, for example, the costs to be respected. The costs to be respected are for example established on the basis of cost functions according to performance criteria as above, or alternatively ecological and/or economic criteria. According to a variant embodiment, the recommendation method also receives as input decision criteria 303 used to schedule or even classify the configurations meeting the user's specifications. In the example of FIG. 3, these criteria are determined by an expert, but they can also be provided by the user or by another person.

The flowchart in Figure 3 has two main steps, steps A and B, each divided into sub-steps Ax and By:

A - The first of these steps, step A, concerns the enrichment of the initial knowledge domain 301. This step A comprises three sub-steps:

Al - A first sub-step (step Al) of parameterization of the knowledge domain. This step determines a parametric modeling of the performance criteria of the considered deep learning algorithm according to the number of calculation units.

A2 - A second substep (step A2) of estimating untested configurations implementing the parametric model and providing a set of configurations 305 in step B described below. This sub-step adds to the knowledge domain configurations that are not experienced (i.e. not part of the configurations of the initial knowledge domain) but potentially possible. The knowledge domain thus complemented is called the enriched knowledge domain.

According to a first non-limiting example, if all the experiments were carried out with an even number of calculation units, then this step will add the configurations for an odd number of calculation units.

According to another non-limiting example, there is for example a bank of sixteen calculation units. To measure the variability, four measurements are carried out by groups of calculation units. If we were to measure all the configurations, we should have 4*16 = 64 simulations. A limited number of configurations are tested, for example configurations with 1, 2, 4, 8 and 16 computing units - i.e. 4*5=20 configurations to be tested experimentally, i.e. less than a third of the total number of potential experiments . The reduction in the number of experiments is all the more significant as it may be necessary to conduct them for different types of computing units. A calculation unit type can be defined by a calculation power and/or the manufacturer of the calculation unit and/or the energy cost of the calculation unit. The configurations added to enrich the domain of knowledge include all the unexperienced configurations. According to a third more general non-limiting example, untested configurations are added which correspond to regular increments of calculation units between the minimum number of calculation units of the tested configurations and the maximum number of calculation units of the tested configurations .

According to a fourth, more general, non-limiting example, the untested configurations are added corresponding to any whole number of calculation units between the minimum number of calculation units of the tested configurations and the maximum number of calculation units of the tested configurations.

According to a fifth, more general, non-limiting example of embodiment, the number of calculation units taken into account to determine the added non-tested configurations may be greater than the number of calculation units of the tested configurations.

In all the cases, one adds only the configurations corresponding to numbers of units of calculation which do not appear in the experimented configurations.

Thanks to the parametric model, it will be possible to estimate the training time as well as the precision for numbers of calculation units of these added configurations.

A3 - A third sub-step (step A3) for estimating the variability of the performance criteria. With data relating to multiple experiments, it is possible to estimate a difference in the values of the performance criteria for each of the configurations, even if they have not been tested. Indeed, each parameter of the linear model is estimated with a confidence interval.

The data output from this step is also provided as input to step B.

B - The second step, step B, concerns the selection of the recommended configuration(s). Step B includes two sub-steps:

B1 - A first sub-step (step Bl) of filtering the configurations of the enriched knowledge domain according to the user's specifications and taking into account the variability of the performance criteria. According to a variant embodiment, the variability is predefined by a confidence interval.

B2—A second sub-step (step B2) which orders the configurations of the subset of configurations on the basis of one or more decision criteria 303 and determines the recommended configuration(s). These decision criteria make it possible, where appropriate, to favor certain performance criteria over others. According to an example of Non-limiting achievement, these decision criteria include weightings associated with the performance criteria.

According to a non-limiting exemplary embodiment, the scheduling algorithm is chosen from a family of algorithms called “Multi Criteria Decision Making” or “MCDM” in English. According to a particular embodiment, it is the simple additive weighting algorithm (“Simple Additive Weighting” or “SAW” in English) which is implemented. The SAW algorithm is for example described in [4],

The recommendation process in FIG. 3 outputs a recommended configuration 304 that meets the specifications given by the user. According to a variant embodiment, if several configurations meet the specifications, the most relevant of these recommendations is provided.

The recommendation can then be implemented. For example, device 200 may communicate the recommended configuration to the server for resource reservation. A step of validation by the user can optionally be provided, as well as an optional step of supplying additional information by the user (such as for example the chosen date, the source of the learning data on which the calculation units will have to access etc.).

According to a variant embodiment, the recommendation process provides a list comprising several recommended configurations classified according to the scheduling algorithm, the user then being able to choose the configuration that suits him.

In the following, a particular embodiment in the field of image segmentation will be described in detail. In this context, the following will be used as examples of deep learning algorithms: an algorithm implementing a fully convolutional network (also called 'Fully Convolutional Network' in English, or 'FCN'); and an algorithm called 'UN and', also implementing a convolutional neural network. The two algorithms used are known elsewhere and respectively described in [2] and [3]. They are particularly suitable for image segmentation. It should however be noted that these algorithms are given only by way of example and in a non-limiting manner to illustrate the embodiment examples. Other deep learning algorithms can be used. Both algorithms are convolutional neural networks. The FCN network is a succession of convolutional filters which decreases the size of the successive images at the input of these filters. The U-Net network has a first phase of compression like the FCN network, then a so-called "expansion" phase where the size of the images at the outputs of the convolutional filters increases, which gives a U-shape to the network and gives it its name. The Unet network, thanks to its two parts (compression/expansion), has good local and global properties for segmentation. The advantage of successive convolution filters is to have good invariance properties with respect to rotations and translations in the image. The Unet network has seven layers of convolutional filters, while the FCN has eight.

In the context of this example, the two algorithms above are applied to the segmentation of medical images. For the purposes of the example, learning is performed on the basis of two sets of data:

- A first set of data concerns the segmentation of brain tumours. This first dataset will be labeled 'BRATS' (see reference [5]) in the rest of the description. It includes 750 magnetic resonance images (MRI) from 19 different medical institutions: a first group of 484 images is used for training and a second group of 266 images is used to test the model resulting from the training. Each image is accompanied by a manual reference annotation locating the tumour. This dataset can be obtained at the links indicated in reference [5],

- A second set of data concerns the segmentation of a cardiac chamber, called the left atrium. The dataset will be labeled 'Atrium' (see reference [6]) in the rest of the description). It includes thirty three-dimensional cardiac MRI images, including twenty for learning and ten for the test phase. This dataset can be obtained at the link indicated in reference [6], In both games, the annotations consist of colored masks overlaying the images and identifying the segmented part.

According to step Al, a parametric model of the performance criteria is established. According to the present embodiment, this model comprises three equations, one for each performance criterion.

The first equation corresponds to the relationship between the inverse of the training time and the number of calculation units. It is proposed to model this relationship in the form of a linear equation, the linearity can be shown statistically:

Equation (1): (1/Training time) = A * number of calculation units + B where A and B are two coefficients to be estimated.

Figure 4 is a graph that shows the acceleration of learning as a function of the number of calculation units for each of the two algorithms and the two sets of data mentioned above. The acceleration on the ordinate is given by the learning time for one computation unit divided by the learning time for N computation units. In the example of Figure 4, the number of iterations or ‘epochs’ of the optimization algorithm is fixed beforehand and constant.

The second equation models accuracy as a function of the number of compute units:

Equation (2): Precision = C * number of calculation units + D where C and D are two coefficients to be estimated.

Regarding the second equation, the inventors assumed an increase in the loss of precision when increasing the number of calculation units. The parameters of learning algorithms are obtained after complex optimizations based on stochastic (ie random) algorithms. A first consequence is that the optima obtained are multiple and with plateaus. Moreover, they are very dependent on the datasets used. By parallelizing the optimization, we divide the data set according to the number of calculation units. In this non-limiting example where the data of training are sets of images, each calculation unit for example supports several images of a set. Each result will be in this tray all the less precise as the set of data will be divided. Because the results of each compute unit are merged into the model, the merged model will not be more accurate.

Moreover, each cost function f(W,D) depends on the weights W to be estimated as well as the data D. By dividing the dataset over each computational unit, the cost function implemented by each computational unit will be therefore different, and its local optimum will be too. Compared to figure 1, the weights W are attached to the links between the layers 14, while the data D is represented by the block 11.

The sum of the results of the optimizations on each calculation unit will therefore be a priori an approximation that is all the greater as the number of calculation units increases.

The third equation models the power consumed:

Equation (3): Power = PUE * Training time * (Pcpu + Pram + Nbr GPUs * Pgpu) / 1000 where 'PUE' is the Effective Power Used (taken equal to 1.58), 'Pcpu' is the power related to server CPU usage, 'Pram' is the power related to the server's memory usage, and 'Pgpu' is the power related to each compute unit of the server. Each of these powers is dependent on the material used.

Equation (3) comes from the article referenced in [7],

The values of the different powers can be obtained from the manufacturers of the different components. By way of example, power values for specific equipment are shown in Table 1:

Une fois les coefficients et paramètres de puissance du modèle paramétrique estimés, respectivement déterminés, on estime les performances moyennes (temps d’entraînement, précision et puissance) pour un nombre d’unités de calcul allant de 0 à N. Pour chaque estimation, on précisera les écarts types. [Table 1]

Once the coefficients and power parameters of the parametric model have been estimated, respectively determined, the average performances are estimated (training time, precision and power) for a number of calculation units ranging from 0 to N. For each estimate, specify the standard deviations.

In the context of this example, the estimation of the coefficients of the first two equations is carried out using a least squares regression. Of course, other methods can be used to make this estimate. In what follows, we check the validity of the hypothesis of linear equations for equations (1) and (2), with respect to the two different data sets chosen, by testing whether the coefficients obtained (at least A and C ) are not harmed.

For equation (1):

[Table 2]

[Table 3]

We can notice that the model is valid for the two algorithms and the two sets of data. It should be noted that for the UNET model, the coefficient B is equal to zero (zero being included in the confidence interval). There is therefore a linear relationship between the inverse of the training time and the number of calculation units.

For equation (2):

[Table 4]

[Table 5]

For the two algorithms and the two data sets, the coefficients C and D are statistically different from 0.

As a result, the accuracy of each algorithm for each dataset can be modeled by a linear equation.

It can be observed that for equation (1), the coefficients A and B are very close for the same algorithm. For equation (2), different coefficients D can be observed but coefficients C, namely the slopes, similar for the algorithms and the two sets of data. This coefficient C can be seen as the relative loss of precision as a function of the number of calculation units. The variable D can be seen as the intrinsic precision of each dataset, and more or less depending on the complexity of the dataset. In the following, a statistical test validation of the hypothesis that the performance of a specific algorithm on one dataset can be transposed to another dataset is described. The principles of such a statistical validation are described in [8], with a view to introducing a vocabulary used later, if we consider a linear model of type Y= aX + b, where Y is the precision or the time of training and X is the number of calculation units, the variable 'a' is representative of the concept of dynamics according to the number of calculation units and the variable 'b' is representative of the bias.

For equation (1):

We consider the following equation:

Equation (4): (1 / Training time) = Kl + K2 * number of calculation units + K3 * Z + K4 * number of calculation units * Z where (Kl, K2, K3, K4) are of the variables to be estimated and Z is the variable making it possible to indicate to which data set the value of the training time belongs (one of the pairs (Kl, K3) and (K2, K4) being quoted at 0, the other to 1). More precisely, if Z =0, we find equation (1) for a couple. If Z=l, we have:

Equation (5): (1 / Training time) = (K1+K3) + (K2+K4) * number of calculation units

If K3 and K4 are statistically equal to 0, then we can consider that each algorithm has the same properties on the two sets of data.

[Tableau 7]

[Table 6]

[Table 7]

We observe that K3 and K4 are different from 0 for the two algorithms. The consequence is that we can predict the training time for the same algorithm (UNET or FCN) for different datasets.

For equation (2):

We consider the following equation:

Equation (6): Precision = Kl + K2 * number of calculation units + K3 * Z + K4 * number of calculation units * Z where (Kl , K2, K3, K4) are variables to be estimated and Z is the variable making it possible to consider to which data set the value of the training time belongs (one of the pairs (K1, K3) and (K2, K4) being quoted at 0, the other at 1). More precisely, if Z =0, we find equation (2) for a couple. If Z=l, we have:

Equation (7): Precision = (K1+K3) + (K2+K4) * Number of number of calculation units

If K3 and K4 are equal to 0 statistically, then we can consider that each algorithm has the same properties on the two sets of data.

[Table 8]

[Table 9]

We observe in particular that the dynamics of loss of precision between two data sets is similar for the UNET algorithm (because statistically K4 = 0), but that this model is not valid between the two data sets for the FCN algorithm (because K4 is different from 0). For the two algorithms, the bias is different for the two datasets.

Note that the K4 value obtained for the FCN algorithm is very small (-0.1242). For 18 calculation units, there is therefore an additional relative loss of precision of 18*- 0.1242= 2.23. However, this value can be considered negligible.

It should be noted that from a certain number N of calculation units, the advantage of the time saving resulting from the sharing of the calculation is counterbalanced by the additional communication time between the devices. Moreover, the loss in precision can be all the more important as the quantity of data seen by each calculation unit is small.

Moreover, the fact that the models are robust for the different datasets which are of different sizes and number of images can be explained by the data augmentation phase practiced very generally in deep learning analyses. Even if the datasets are heterogeneous, they are standardized in number and size for the same algorithm. Finally the hyper parameters (the parameters intrinsic to each algorithm like the speed of convergence of the optimization algorithm, the number of images analyzed in each iteration, etc.. ..) are fixed for a specific algorithm.

The parametric model of a deep learning algorithm can therefore be transposed to different types of data.

FIG. 5 represents a non-limiting example of a graphic interface 500 that can be implemented to interact with the recommender device 200. This graphic interface can be an interface accessible remotely with respect to the device, for example via a computer browser. It can be used both to acquire the different data and the user's choices and to present the recommendation(s) obtained and thus makes it possible to manage the filtering of the configurations as well as the decision algorithm.

The interface has four parts:

1 - A first part makes it possible to indicate the constraints imposed on the performance criteria (which corresponds to the data 302 of figure 3) as well as to adjust the weights associated with each criterion (which corresponds to the data 303 of figure 3 ).

In the example of figure 5, this part is positioned in the left column (area

501). Figure 6 illustrates this part in detail.

2 - A second part is used to select the parameters managing the visualization of the recommended configurations. This visualization allows the user in particular to refine the configuration of the recommendation device.

In the example of Figure 5, this part is positioned in the right column (area

502). Figure 7 illustrates this part in detail.

3 - A third part makes it possible to visualize one or more performance criteria as well as the associated variability, and this for several configurations. The configurations taken into account in this part can cover a wide spectrum and are given for information only. Figure 8 illustrates this part in detail.

In the example of figure 5, this part is positioned in the lower central part (zone

503).

4 - A fourth part displays the result of the recommendation, namely a configuration or several configurations indicated according to a schedule. In the example of FIG. 5, this part is positioned in the lower central part (zone 504).

The example illustrated by Figures 5 to 8 can be placed as before in the context of medical imaging. The servers with their calculation units are available for a limited time, for example only at night because they are used for another application during the day. A maximum learning time of 12 hours is set. The loss of precision is left free. These two choices are made in the left column (501) of the interface. Apart from the constraint on time, it is not desired to favor precision over time or vice versa. An identical weight of '5' out of '10' is assigned to each of these two criteria.

We then obtain a recommended configuration of seven calculation units, to be used for a training time of 9h48 with a variability of 1h05, which is well below the fixed maximum time of 12 hours.

Zone 504 can then present the result as follows, in the form of several ordered configurations

[Table 10]

It should be noted that the three configurations offer a learning time of less than 12 hours.

Figure 8 shows area 503 of the interface for this example - the precision is given there for 19 values of the number of calculation units, with an indication of the range of variability around the average precision.

In a second example, no constraint is imposed on the time, but a constraint is imposed on the accuracy of the model. Indeed, in the context of CE marking, it is necessary to have an accuracy greater than 75% of Dice score. Precision will therefore be favored over the other criteria: a weight of 10 is assigned to precision while only a weight of 5 is assigned to time. This results in a recommended configuration of four calculation units to be used for an accuracy of 77.23% ± 0.57, which is well above the value desired in the context of CE marking. The first choice of configuration can then appear in the following form in the interface:

[Table 11]

Figure 9 is a flowchart of a non-limiting example embodiment.

According to a step S901, a knowledge domain comprising at least one observed configuration and a value of at least one performance indicator is obtained.

According to a step S902, a parametric model is determined on the basis of the knowledge model. According to a step S903, it is determined, with a view to completing the knowledge domain, at least one configuration different from the configuration(s) of the knowledge domain, and from the value of the at least one performance criterion on the basis of the parametric model . According to a step S904, a selection is made of at least one configuration from among the configurations of the knowledge domain completed and meeting at least one constraint relating to the at least one performance indicator.

This selection can be made by a decision algorithm. According to a particular mode, the decision algorithm will choose a single configuration, which gives good performance or optimal performance. For example, the decision algorithm can apply a cost function taking into account one or more performance indicators and optionally weighting coefficients of the indicator(s). According to another particular mode, a selection of a single configuration is made by a user who can in this be assisted by a decision algorithm which orders one or more configurations on the basis of a function indicative of the performance of each configuration.

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Access links for MRI image data: http://medicaldecathlon.com/ and https://decathlon.grand-challenge.org/

[6] Tobon-Gomez C, Geers AJ, Peters J, Weese J, Pinto K, Karim R, et al. Benchmark for algorithms segmenting the left atrium from 3D CT and MRI datasets. IEEE transactions on medical imaging 2015;34(7): 1460-1473.

Access link for MRI image data: https://www.cardiacatlas.org/challenges/left-atrium-segmentation-challenge/

[7] Strubell, E., et al. “Energy and policy considerations for deep learning in NLP”. arXiv preprint arXiv: 1906.02243. (2019)).

[8] Andrade 2014, J.M., and M. G. Estévez-Pérez, “Statistical comparison of the slopes of two regression lines: A tutorial.” Analytica chimica acta 838 (2014): 1 - 12[9] Ge, Yaorong, and Q. Jackie Wu. "Knowledge-based planning for intensity-modulated radiation therapy: A review of data-driven approaches." Medical physics 46.6 (2019): 2760-2775.

Claims

24 CLAIMS 1. Method for determining configurations of a distributed system of computing units for the implementation of a deep learning algorithm, said determination implementing a recommendation based on a knowledge model, said method being implemented by a device comprising a processor which causes said device to implement the method, the method comprising: determining a deep learning algorithm to be implemented in the distributed system; obtaining (S901) a knowledge domain comprising, for said algorithm, at least one observed configuration and a value of at least one performance indicator for said at least one observed configuration; determining (S902) a parametric model of the performance indicator(s) based on the knowledge domain; the determination (S903) of at least one configuration different from said at least one observed configuration and an estimation of the value of the performance indicator(s) associated with said different configuration, on the basis of said model, with the aim of completing the domain of knowledge ; the selection (S904) of at least one configuration from among the configurations of the knowledge domain completed and meeting at least one constraint relating to the at least one performance indicator; generating a signal representative of said at least one selected configuration. 2. Method according to claim 1, in which the selection is carried out by a decision algorithm according to a weighting of at least one performance indicator, the method further comprising the display of the configuration(s) selected by implementing said signal and receiving a command to identify a unique configuration among the selected configurations which will be applied to the distributed system. 3. Method according to claim 1, in which the selection is carried out by a decision algorithm which selects a single configuration. 4. Method according to one of claims 2 or 3, further comprising the reservation of calculation units according to the unique configuration. Method according to one of the preceding claims, further comprising estimating the variability of said at least one performance indicator for a different configuration. Method according to one of the preceding claims, in which the said at least one performance indicator of a configuration comprises one or more of: the required training time of the system for the configuration considered; the relative precision of calculation; the power consumed by the system for the configuration considered. Method according to claim 6, in which the parametric models applied on the one hand to the inverse of the training time and on the other hand to the calculation precision are affine functions of a number of calculation units of the system distributed implemented in the configuration considered, and the determination of the parametric model includes the determination of the parameters of the affine function associated with each performance indicator. Method according to claim 6, in which the power consumed is an affine function of the square of the number of calculation units of the distributed system to be used in the configuration envisaged. Method according to one of the preceding claims, in which the decision algorithm classifies the filtered configurations according to a score depending on the performance indicator(s) and weighting coefficients of the latter. Method according to one of the preceding claims further comprising obtaining at least one constraint on an intrinsic characteristic of hardware configuration, said constraint being taken into account within the framework of the filtering of the configurations. Method according to one of the preceding claims, in which the deep learning algorithm implements a convolutional neural network. Method according to one of the preceding claims, the method being applied in the context of image segmentation. Device (200) comprising a processor (201) and a memory (203), said memory comprising instructions which, when they are executed by the processor, lead the device to implement the steps of the method according to one of the claims 1 to 12. Computer program product (213) comprising instructions which, when the program is executed by a device (200) comprising a processor (201), causes the device to implement the steps of the method according to one of claims 1 to 12.