In this section, we aim to develop a predictive model that, based on a student’s academic performance and transversal skills (soft skills), recommends the most suitable academic track for their profile. The model should be:

Let: $X_i\in {ℝ}^d$, the characteristic vector of the student $i$ consisting of:

We construct an input data matrix:

$X=\left[\begin{array}{c}{X}_1\\ X_2\\ ⋮\\ X_n\end{array}\right]\in {ℝ}^{n\times d}$

And a vector of outputs:

$y=\left[\begin{array}{c}{y}_1\\ y_2\\ ⋮\\ y_n\end{array}\right]\in {\left\{0,1,2,\cdots ,C-1\right\}}^n$

where $C$ is the number of target fields.

Multinomial logistic regression can be used to model the probability $P$ that a student $i$ is well oriented towards a stream $c$.

Let: $w_c$ and ${\varphi }_c$: respectively the weight vector for stream c and the bias associated with stream c.

$P\left(y_i=c|X_i\right)={\hat{y}}_{i,c}=\frac{{\text{e}}^{w_c{X}_i+{\varphi }_c}}{{\displaystyle {\sum }_{k=1}^C{\text{e}}^{w_c{X}_i+{\varphi }_c}}}$

where:

( $P$): The probability predicted by the personalized orientation model of a student i towards stream c according to his academic components and soft skills.

The cost or loss function to be minimized is the cross-entropy

$\phi \left(w,\varphi \right)=-\frac{1}{n}{\displaystyle \underset{i=1}{\overset{n}{\sum }}{\displaystyle \underset{c=1}{\overset{C}{\sum }}{1}_{\left[y_i=c\right]}\log P\left(y_i=c|X_i\right)}}$

$\phi \left(w,\varphi \right)=-\frac{1}{n}{\displaystyle \underset{i=1}{\overset{n}{\sum }}{\displaystyle \underset{c=1}{\overset{C}{\sum }}{1}_{\left[y_i=c\right]}\log \left(\frac{{\text{e}}^{w_c{X}_i+{\varphi }_c}}{{\displaystyle {\sum }_{k=1}^C{\text{e}}^{w_c{X}_i+{\varphi }_c}}}\right)}}$

with:

$1_{\left[y_i=c\right]}=\{\begin{array}{l}1\text{if}\text{student}i\text{is}\text{in}\text{stream}c\\ 0\text{otherwise}\end{array}$

$n$: Number of students.

$c$: Number of streams.

$X_i\in {ℝ}^{n\times d}$: vector of characteristics of student $i$.

If we denote $y_{i,c}\in \left\{0,1\right\}$, the one-hot coded label, $y_{i,c}=1$ f, the actual stream is c, otherwise 0.

The loss function $\phi$ on a single example $i$ is:

$\phi \left(w_i,{\varphi }_i\right)=-\underset{c=1}{\overset{C}{{\displaystyle \sum }}}{y}_{1,c}\log \left({\hat{y}}_{i,c}\right)$

where

$y_{1,c}=\frac{1}{n}\underset{i=1}{\overset{n}{{\displaystyle \sum }}}{1}_{\left[y_i=c\right]}$

and

${\hat{y}}_{i,c}=\frac{{\text{e}}^{z_{i,c}}}{{{\displaystyle \sum }}_{k=1}^C{\text{e}}^{z_{i,c}}}$

With $z_{i,c}=w_j{X}_i+{\varphi }_j$: (logit scores), $X_i\in {ℝ}^d$ and a path $c\in \left\{1,\cdots ,C\right\}$

The loss will be derived with respect to:

$w_j\in {ℝ}^d$: weight associated with path $c$.

${\varphi }_j\in ℝ$: he bias associated with $c$.

NB: the difference between $c$ and $j$.

$c$: Truth channel (Target) or in the summations used for the loss function.

$j$: Track with respect to which we derive used in derivatives (gradients).

Step 3: Derivative with respect to $w_j$.

As a reminder: $z_{i,c}=w_j{X}_i+{\varphi }_j$.

So, by the chain rule, we have:

$\frac{\partial {\phi }_i}{\partial w_j}=\frac{\partial {\phi }_i}{\partial z_{i,j}}\times \frac{\partial z_{i,j}}{\partial w_j}=\left({\hat{y}}_{i,c}-y_{i,c}\right)\times x_i$

This gradient is a d-dimensional vector, like $w_j$

Step 4: Derivative with respect to bias: ${\varphi }_j$

$\frac{\partial {\phi }_i}{\partial {\varphi }_j}={\hat{y}}_{i,j}-y_{i,j}$

Step 1: Derive the softmax function

We begin by deriving the softmax:

${\hat{y}}_{i,c}=\frac{{\text{e}}^{z_{i,c}}}{{{\displaystyle \sum }}_{k=1}^C{\text{e}}^{z_{i,c}}}$

Two classes $c$ and $j$ on a:

If $c=j$:

$\frac{\partial {\hat{y}}_{i,c}}{\partial z_{i,c}}={\hat{y}}_{i,c}\left(1-{\hat{y}}_{i,c}\right)$

If $c\ne j$:

$\frac{\partial {\hat{y}}_{i,c}}{\partial z_{i,j}}=-{\hat{y}}_{i,c}{\hat{y}}_{i,j}$

Step 2: Derivation of loss with respect to $z_{i,j}$

We use the derivation chain:

$\frac{\partial {\phi }_i}{\partial z_{i,j}}=\underset{c=1}{\overset{C}{{\displaystyle \sum }}}\frac{\partial {\phi }_i}{\partial {\hat{y}}_{i,c}}\cdot \frac{\partial {\hat{y}}_{i,c}}{\partial z_{i,j}}$

now:

$\frac{\partial {\phi }_i}{\partial {\hat{y}}_{i,c}}=-\frac{y_{i,c}}{{\hat{y}}_{i,c}}$

Combining them all, we obtain:

$\frac{\partial {\phi }_i}{\partial z_{i,j}}={\hat{y}}_{i,j}-y_{i,j}$

For n elements, the gradients are average:

To minimize the cost function $\phi \left(w,\varphi \right)$, we apply gradient descent.

$\frac{\partial {\phi }_i}{\partial w_j}=\frac{1}{n}\underset{i=1}{\overset{n}{{\displaystyle \sum }}}\left({\hat{y}}_{i,j}-y_{i,j}\right)\cdot x_i$

$\frac{\partial {\phi }_i}{\partial {\varphi }_j}=\frac{1}{n}\underset{i=1}{\overset{n}{{\displaystyle \sum }}}\left({\hat{y}}_{i,j}-y_{i,j}\right)$

This means:

If ${\hat{y}}_{i,j}>y_{i,j}$ $\to$ the prediction is too strong, we decrease the weight.

If ${\hat{y}}_{i,j}<y_{i,j}$ $\to$ the prediction is too low, we increase the weight.

Gradient descent updates weight parameters $w_j$ and bias ${\varphi }_j$ to reduce $\phi$ at each iteration:

$w_j\leftarrow w_j-\eta \cdot \frac{\partial {\phi }_i}{\partial w_j}\iff w_j^{\left(t+1\right)}=w_j^{\left(t\right)}-\eta \cdot {\nabla }_w\cdot \phi$

${\varphi }_j\leftarrow {\varphi }_j-\eta \cdot \frac{\partial {\phi }_i}{\partial {\varphi }_j}\iff {\varphi }_j^{\left(t+1\right)}={\varphi }_j^{\left(t\right)}-\eta \cdot {\nabla }_{\varphi }\cdot \phi$

$\eta$: represents the learning rate is a hyperparameter used in gradient descent algorithms. It controls the size of the steps the algorithm takes when updating the weights.

The training procedure algorithm is as follows:

START

Initialize $w$ and $\varphi$.

Repeat several times (iterations):

Calculate probabilities: ${\hat{y}}_{i,j}$ via Softmax.

Calculate loss function: $\phi \left(w,\varphi \right)$.

Calculate gradients: $\frac{\partial \phi }{\partial w_j}={\nabla }_{w_j}$ and $\frac{\partial \phi }{\partial {\varphi }_j}={\nabla }_{{\varphi }_j}$.

Update $w_j$ and ${\varphi }_j$.

Until $w^{\text{*}},{\varphi }^{\text{*}}$ optimaux.

END

The score attributed to a channel is calculated as follows:

For each student $i$, a score is calculated for each channel: $y_{i,j}$.

$y_{i,j}=\underset{j=1}{\overset{C}{{\displaystyle \sum }}}{x}_{i,j}\cdot w_j^{\left(c\right)}+{\varphi }_j^{\left(c\right)}$

Student $i$ is then assigned to the stream $\hat{y}$ that maximizes this score,

The predicted path is:

$\hat{y}=\arg \underset{c}{\max }\left(y_c\right)$

For each student $i$, $X_i\in {ℝ}^{12}$, the model predicts:

$P\left(y_i=c|X_i\right)=\frac{{\text{e}}^{w_c{X}_i+{\varphi }_c}}{{{\displaystyle \sum }}_{k=1}^C{\text{e}}^{w_c{X}_i+{\varphi }_c}}$

According to the variables defined in Table 1 , for a student $i$, the vector $X_i=\left[x_1,x_2,x_3,x_4,x_5,x_6,x_7,x_8,x_9,x_{10},x_{11},x_{12}\right]$ represents his multidimensional data.

In this article, the component values are based on a mathematical aggregation approach, i.e. an evaluation using a structured questionnaire where each soft skill is evaluated by several questions (items), and the score is:

$s_{il}=\frac{1}{n_l}\underset{k=1}{\overset{n_l}{{\displaystyle \sum }}}{q}_{ilk}$

with:

This method gives a weighted average score.

Linear score: $z_c=w_c{X}_i+{\varphi }_c$.

Application of softmax: $P\left(y_i=c|X_i\right)$.

$\begin{array}{l}y=\{\text{Mathematical Sciences},\text{Physical Sciences},\text{Histore-Geography},\\ \text{Literature},\text{Economics}\}\end{array}$

$\arg \underset{c}{\max }\left(y_c\right)\to \text{stream}$

The results obtained after the simulations are shown below:

The proportions per die in Table 2 shown in Figure 1 show that:

Figure 2 is a comparative bar chart of the average soft skills in Table 3 . We can clearly see the dominant skills by the stream.

Scientific tracks (Mathematics, Physics) emphasize resilience, creativity, and collaboration (teamwork); whereas literary tracks (Literature, History-Geography) favor balanced students with peaks in communication and leadership. Finally, the economic track values more innovative and autonomous profiles with high levels of creativity. See Figure 3 , which clearly illustrates the relevance of AI models in supporting personalized guidance by identifying profile-track affinities, thus promoting a more holistic orientation by revealing the often-invisible potential in academic report cards.

The Soft Skills Weight Chart by Track in Figure 3 clearly shows that the model assigns weights that faithfully reflect the educational expectations of each track, thus demonstrating pedagogical alignment. Furthermore, a complementarity of skills is observed, as no soft skill is universal: each track values a unique combination, which justifies a multidimensional approach to orientation.

As a result, the radar chart in Figure 3 could serve as a targeted reinforcement guide: a student aspiring to a specific track can focus on developing the key skills emphasized in that pathway. Finally, these weights could be dynamically adjusted based on feedback, student success within the tracks, or labor market demands.

To better understand the role of artificial intelligence in providing personalized guidance for each student, a selection of twenty (20) representative students from the AI simulation of 100 profiles distributed evenly across the five tracks is presented in Table 3 , along with their academic grades, soft skills, and the recommended track according to the AI predictive model.

The crossed radar chart in Figure 4 highlights the average profiles of students assigned to each track by combining their behavioral skills and academic performance.

It is observed that the Mathematical Sciences track shows significantly high values in Mathematics (18.25/20) and Physics (14.75/20), accompanied by relatively balanced soft skills, particularly in Autonomy and Leadership, confirming the demands for rigor and independence in this field.

The Physical Sciences track displays a strong dominance in Physics (19.5/20), but with greater variability in French and Economics scores, which may reflect a very science-focused profile with less emphasis on cross-disciplinary subjects ( Table 4 ).

In the Literature track, results are excellent in French (18.25/20) and English (14/20), and soft skills such as Communication (3.5/5) and Creativity (3.25/5) are also high, confirming the importance of expressive and creative abilities in this field. History and Geography stand out with a strong performance in History-Geography (16.75/20) and solid skills in Teamwork and Leadership, reflecting balanced profiles open to analysis and collaboration. Finally, the Economics track combines strong performance in Economics (18.75/20) with robust soft skills in Autonomy and Resilience, which are key traits for management and decision-making. Table 5 and Table 6 , showing means and standard deviations of grades and soft skills, confirm these trends by revealing the stability of results: for instance, the low standard deviation in Mathematics within the science track (0.96) indicates a homogeneous required level, while higher deviations in Economics or French in other tracks suggest greater profile diversity or more flexible selection thresholds.

In summary, the combined analysis of the radar chart and the tables confirms that each track is characterized by a strong academic core supported by a specific behavioral profile, validating the relevance of a personalized orientation approach based on multidimensional data integrated into an artificial intelligence model.

Figure 5 shows the steps involved in predicting a student’s pathway. In the following, a student’s academic data and soft skills are presented to show how the artificial intelligence model selects the pathway based on a student’s data.

1) Extracting the X vector of student grades and profits

$X_{66}=\left[12,10,19,8,11,20,3,3,3,2,4,3\right]$

2) Multiply by weights W, add b

3) Applied softmax $\to \left[0.12,1.24,0.08,0.15,0.41\right]$

4) $\arg \max \left[0.12,1.24,0.08,0.15,0.41\right]\to y_5$

5) Prédiction stream: $y_5$ = Economy

The AI model predicts that the student selected from the 20 representative profiles should be oriented towards the Economics stream.

Figure 6 compares a student’s profile to the average of students oriented toward the Economics track across two dimensions: academic performance and soft skills. The student demonstrates strong academic achievements in Mathematics, History-Geography, and Economics, with slightly lower scores in French and English still consistent with the track’s requirements. On the behavioral side, their scores in Resilience, Communication, and Leadership are well aligned with the average, but there are noticeable gaps in Creativity and Autonomy. Overall, the student is compatible with the targeted track, with specific areas for improvement. The chart highlights the alignment between the actual profile and the track’s benchmark, enabling accurate orientation. This visual approach supports quick identification of strengths and areas for development. The differentiation by zones (soft skills vs academic) allows for a nuanced interpretation. Such a synthetic representation promotes data-driven decision-making tailored to each student.

The integration of artificial intelligence into the school guidance process radically transforms the way decisions are made. Table 7 from the classification report of the multinomial logistic regression model for the 100 students highlights the effectiveness of the artificial intelligence model, based on multinomial logistic regression, in supporting the school orientation process. The high recall rates (ranging from 84% to 100%) and precision rates (ranging from 87% to 100%) demonstrate the AI’s ability to accurately predict the assignment of students according to their academic and behavioral profiles, even under conditions of imbalanced distribution. Logistic regression plays a key role here by modeling the probability of belonging to each target track based on a weighted combination of continuous variables (academic grades) and discrete variables (soft skills). This approach not only estimates the most appropriate track for each student but also quantifies the degree of confidence in the prediction, thus providing counselors with a robust and transparent decision-support tool. AI, by automating the multidimensional analysis of large student datasets, reduces human biases, secures the relevance of recommendations, and personalizes the proposed educational pathways. It also enables the early identification of discrepancies between expected and actual skills, paving the way for targeted remediation actions.

Unlike traditional approaches that rely solely on academic results, AI considers a broader spectrum of information, including behavioral skills. It enables detailed, multi-criteria, and dynamic analysis of student profiles by relying on predictive models trained on real-world data. The student is no longer seen as just a set of grades, but as a unique individual with diverse potential. AI proposes guidance based on statistical proximity to profiles that have succeeded in the targeted tracks. This mechanism reduces misplacements and enhances student engagement in their educational paths. Moreover, guidance counselors gain a robust, visual, and explanatory decision-support tool. First, it allows for a holistic understanding of the student’s profile by highlighting both academic and behavioral strengths. Then, it provides a rational and evidence-based foundation for recommending a track, strengthening confidence in the decision. Finally, it enables mass personalization, thereby transforming guidance into a fairer, more effective process focused on the development of each student’s potential. Thus, the AI model does not replace the counselor’s judgment—it enhances it through a data-driven, visualizable approach. It serves as an intelligent decision-making tool, capable of linking personal data, track requirements, and group dynamics. Through this analysis, it becomes clear that AI, when integrated with human support, reinforces the relevance, equity, and efficiency of the school guidance process.