Ryma Boumazouza
email: boumazouza@cril.univ-artois.fr

Fahima Cheikh-Alili

Bertrand Mazure
email: mazure@cril.univ-artois.fr

Karim Tabia
email: tabia@cril.univ-artois.fr

A Symbolic Approach for Counterfactual Explanations (Preprint version)

Keywords: eXplainable AI, MCS, Counterfactual Explanation

We propose a novel symbolic approach to provide counterfactual explanations for a classifier predictions. Contrary to most explanation approaches where the goal is to understand which and to what extent parts of the data helped to give a prediction, counterfactual explanations indicate which features must be changed in the data in order to change this classifier prediction. Our approach is symbolic in the sense that it is based on encoding the decision function of a classifier in an equivalent CNF formula. In this approach, counterfactual explanations are seen as the Minimal Correction Subsets (MCS), a well-known concept in knowledge base reparation. Hence, this approach takes advantage of the strengths of already existing and proven solutions for the generation of MCS. Our preliminary experimental studies on Bayesian classifiers show the potential of this approach on several datasets.

Introduction

Recently, a symbolic approach for explaining classifiers has been proposed in [START_REF] Shih | A symbolic approach to explaining bayesian network classifiers[END_REF]. This approach first compiles a classifier into an equivalent and tractable symbolic representation then enumerates some forms of explanations such as prime implicants. It has many nice features in terms of tractability, explanation enumeration and formal analysis of classifiers. This paper proposes a novel approach that is designed to equip such symbolic approaches [START_REF] Shih | A symbolic approach to explaining bayesian network classifiers[END_REF] with a module for counterfactual explainability. Intuitively, we view the process of computing counterfactual explanations as the one of computing Minimal Correction Subsets (MCS generation) where the knowledge base stands for the classifier and the data instance in hand. As we will show later, our symbolic approach for counterfactual generation has many nice features added to the fact of lying on well-known concepts and efficient existing techniques for MCS generation. The inputs to our approach are a classifier's decision function f compiled into an equivalent symbolic representation in the form of an Ordered Decision Diagram (ODD) and a data instance x. Our contribution is to model the problem of counterfactual generation as the one of MCS generation. We will show the properties of this encoding and highlight the links between MCS and counterfactual explanations. Our experiments show that using existing MCS generation tools, one can efficiently compute counterfactual explanations as far as a classifier can be compiled into an ODD which is the case of Bayesian network classifiers [START_REF] Shih | A symbolic approach to explaining bayesian network classifiers[END_REF], decision trees and some neural nets [START_REF] Shi | On tractable representations of binary neural networks[END_REF].

2 From a symbolic representation of a classifier to an equivalent CNF encoding

Our approach for counterfactual explanation proceeds in two steps : The first one is encoding a symbolic representation (given in the form of an ODD) into an equivalent CNF representation. The second step consists in computing MCSs meant as counterfactual explanations given the CNF representation of the classifier and any data instance. In this section, we describe the first step of our approach. Let us first formally recall some definitions used in the remainder of this paper. For the sake of simplicity, the presentation is limited to binary classifiers with binary features but the approach still applies to non binary classifiers as stressed in [START_REF] Shih | A symbolic approach to explaining bayesian network classifiers[END_REF]. A decision function describes the classifier's behavior independently from the way it is implemented.

Definition 3. (Ordered Decision Diagram ODD) An Ordered Decision Diagram (ODD) is a rooted, directed acyclic graph, defined over an ordered set of discrete variables, and encoding a decision function. Each node is labeled with a variable X i , i = 1, . . . , n and has an outgoing edge corresponding to each value x i of the variable X i , except for the sink nodes, which represent the terminal nodes.

An Ordered Binary Decision Diagram OBDD is an ODD where all the variables are binary. If there is an edge from a node labeled X i to a node labeled X j , then i<j (more on tractable representations such as ODDs can be found in [START_REF] Shih | Compiling bayesian network classifiers into decision graphs[END_REF]).

Example 1. Figure 1a shows a naive Bayes classifier for deciding whether a student will be admitted to a university (class variable: Admit (A)). The features of an applicant are: work-experience (WE), first-time-applicant (FA), entranceexam (E) and gpa (GPA). In Figure 1b, we provide the OBDD representing the classifier decision function f with the variable ordering (WE, FA, E, GPA).

Here, the sinks correspond to the values of the class variable (A). Let us now focus on our target representation. A CNF (Clausal Normal Form) formula is a conjunction of clauses. A clause is a formula composed of a disjunction of literals. A literal is either a Boolean variable or its negation. A quantifier-free formula is built from atomic formulae using conjunction ∧, disjunction ∨, and negation ¬. An interpretation µ assigns values from {0, 1} to every Boolean variable. Let Σ be a CNF formula, µ satisfies Σ iff µ satisfies all clauses of Σ. There are several methods to encode a decision diagram as a CNF formula. For instance in [START_REF] Cabodi | Improving sat-based bounded model checking by means of bdd-based approximate traversals[END_REF], the authors proposed a method called "Single-Cut-Node" to store a BDD (Binary Decision Diagram) as a CNF where they model BDD nodes as multiplexers. A second method called "The No-Cut method" creates clauses starting from f corresponding to the "off-set" and a last method called "The Auxiliary-Variable-Cut" which combines the two other methods. For the sake of simplicity and clarity, we choose the simplest method which does not involve adding new variables during the encoding process since we want to restrict our explanations to the input variables of the classifier. We implement a simple way to encode the symbolic representation of a classifier as a CNF formula based on the "The No-Cut" method [START_REF] Cabodi | Improving sat-based bounded model checking by means of bdd-based approximate traversals[END_REF]. In our case, since we are dealing with binary Boolean functions (binary features and class variable), our tractable representation of the decision function f is an OBDD. We use along with this paper positive/true/1 and negative/false/0 interchangeably. Let us first define an "off-set" of a Boolean function and a CNF formula.

Definition 4. (Off-Set of a Boolean function) The Off-set of a Boolean function f , denoted as f 0 , is f 0 ={v ∈ n i=1 {0, 1} i |f (v) = 0} If f 0 ={0, 1} n , then f is unsatisfiable. Otherwise, f is satisfiable.
Intuitively, f 0 is the set of counter-models of f . This concept of "off-set" contains the counter-models we need to enumerate in order to construct our CNF's clauses. The OBDD is used to enumerate all the paths from the root to the 0-sink node (the off-set), where each element of f 0 corresponds to a path within it.

Definition 5. (CNF encoding of an OBDD) Let f be the decision function encoded by an ordered binary decision diagram OBDD f . Let also Offset(OBDD f ) be the off-set of OBDD f . We define the obtained CNF formula from OBDD f as Σ f =∧¬e i where e i ∈f 0 and i=1..|f 0 |.

Let α be the associated formula of f . The intuition is that ¬ α ≡ ∨ e i where e i ∈ f 0 . Then f comes down to negating ∨ e i allowing to obtain directly f in the form of a CNF. Following Definition 5, we have:

-Every variable of the feature space X= {X 1 ,...,X n } of the classifier will correspond to a Boolean variable in the CNF Σ f . -The class variable Y of the classifier is captured by the truth value of the CNF (Σ f ). -Modeling a prediction made by the classifier for a given data instance x comes down to the truth value of: (CNF Σ f ∧ Σ x ) where Σ x stands for the data instance x encoded as a CNF by a set of unit 1 clauses.

Our encoding guarantees the logical equivalence between the OBDD f and the obtained CNF Σ f . The following proposition formally states this result.

Proposition 1. Let f be a binary decision function and OBDD f its compiled representation. Let also Σ f be the CNF representation of the decision function f obtained following Definition 5. Then an interpretation µ is model of Σ f iff it is mapped to 1 by f . Proposition 1 states that Σ f is logically equivalent to the function f . i.e, they have the same truth value for each data instance x. Thus, we can assert the following result.

Lemma 1. Given a binary classifier, a data instance x and the predicted class

f (x) = y, (Σ f ∧ Σ x ) is SAT iff f (x)=1 .
We stress that both of the compilation of the classifier to a symbolic representation and the encoding into a CNF formula, is done only once in our approach and can be re-used to explain as many instances as wanted.

Generating Counterfactual Explanations

Intuitively, a counterfactual explanation for an instance of interest x and a classifier f is the minimum changes to x needed to alter the output of f . Let us now define formally the concept of counterfactual explanation. Definition 6. (Counterfactual Explanation) Let x be a complete data instance and f (x) its prediction by the decision function f . A counterfactual explanation x of x is such that:

-x ⊆ x (x is a subset or a part of x) -f (x[x])= 1-f (x) ( prediction inversion) -There is no x ⊂ x such that f (x[x])=f (x[x]) (minimality)
In Definition 6, the term x[x] denotes the data instance x where variables included in x are reversed. In our setting, a counterfactual x is defined as a part of the data instance x such that x is minimal and x allows to flip the prediction f (x). The explanation comes as follow: an output y is returned because variables from the features space X had values (x 1 , x 2 ...). If instead, X had values (x 1 , x 2 , ...) while all other variables had remained constant, the output y would have been returned. Counterfactual explanations are expected to explain both the outcome of a prediction and how that would change if things had been different. In an "approved vs rejected" application like the common example of loan applications, a counterfactual explanation would answer the question What do I need to change in my application for the bank to approve my application ?. Our main idea is to model the counterfactual explanation task as a Partial Max-SAT problem. Recall that our CNF encoding of an OBDD representation of a classifier's decision function f ensures that a negative (resp. positive) prediction leads to an unsatisfiable (resp. satisfiable) CNF Boolean formula. Namely, f (x)=1 iff (Σ f ∧Σ x ) is satisfiable. In the case where f (x)=0, Σ f ∧ Σ x is unsatisfiable and it is possible to identify the subsets of Σ x allowing to restore the consistency of Σ f ∧Σ x (recall that Σ f is satisfiable unless the classifier f always predicts 0 regardless of the instance x). This is a well-known problem dealt with in many areas such as knowledge base reparation, consistency restoration, etc. We will see later how to provide explanations when the outcome is positive, namely f (x)=1, using the same mechanisms. It is important to note that our CNF is composed of two parts: Σ f and Σ x , where Σ f encodes the classifier and it is satisfiable and Σ x encode the data instances x and represented as a set of unit clauses.In the case of negative predictions, since Σ f ∧Σ x is unsatisfiable (inconsistent), we can compute a sort of reparation set that is composed of the subsets of data instance x that cause the unsatisfiability of Σ f ∧Σ x . This is known as the minimal correction subset (MCS). Definition 7. (MSS) A maximal satisfiable subset (in short, MSS) Φ of a CNF Σ is a subset (of clauses) Φ ⊆ Σ that is satisfiable and such that ∀ α ∈ Σ \ Φ, Φ ∪ {α} is unsatisfiable.

Definition 8. (MCS (Co-MSS))

A minimal correction subset (in short MCS, also called Co-MSS) Ψ of a CNF Σ is a set of formulas Ψ ⊆ Σ whose complement in Σ, i.e., Σ \ Ψ , is an MSS of Σ In our case, given a data instance x and a function f , and their respective CNFs Σ x and Σ f , an MCS Φ ensures the minimality property and tells what clauses to remove from Σ f ∧Σ x to restore its consistency. Note that although the number of MCSs can be exponential in the worst case, it remains low in many benchmarks.

Counterfactuals for negative predictions through MCSs

Our main idea for explaining a negative prediction for an instance x is to compute its MCSs. An MCS identifies the subset of clauses to be repaired to restore the satisfiability of the CNF formula. In order for an MCS to correspond to a counterfactual explanation, it should contain only the unit clauses belonging to Σ x indicating what features need to be removed or flipped such that the whole CNF (namely, Σ f ∧Σ x ) becomes again satisfiable. This leads to splitting the CNF into two subsets: hard constraints (those that could not be included in any MCS) and soft ones (those that could be relaxed, hence included in MCSs). The concepts of Partial Max-SAT, Hard and Soft constraints(clauses) are defined as follows:

Definition 9. (Partial Max-SAT) Given a Boolean CNF formula Σ in which some clauses are hard and some are soft, Partial Max-SAT is the problem of finding a truth assignment that satisfies all the hard constraints and the maximum number of soft ones.

In order to solve Partial Max-SAT, we will consider the general setting, where a formula is composed of two disjoint sets of clauses Σ = Σ H ∪ Σ S [START_REF] Biere | Handbook of satisfiability[END_REF], where Σ H denotes the hard clauses and Σ S denotes the soft ones. In our modeling for counterfactual generation, the set of hard clauses is Σ f while soft clauses is Σ x representing the data instance x to explain. The CNF encoding of the classifier Σ f as a set of hard clauses is presented in the previous section. The CNF encoding of the data instance Σ x as soft clauses is done as follows. Let Σ x be the soft Clauses, defined as follow:

-Each clause α ∈ Σ x is composed of exactly one literal (∀α ∈ Σ x , |α| = 1) -Each literal representing a Boolean variable of Σ x corresponds to a Boolean variable {X i ∈ X/i ∈ [1, n]} of the feature space of the decision function f .

Following our approach, an MCS for Σ f ∧Σ x comes down to a subset of soft clauses, namely a part of x that is enough to remove in order to restore the consistency, hence to flip the prediction f (x)=0. Proposition 2 states that each MCS computed for Σ f ∧Σ x represents a counterfactual explanation x ⊆ x for the prediction f (x)=0 and vice versa. Proposition 2. Let f be the decision function, OBDD f its compiled symbolic representation, x be a data instance predicted negatively (f (x) = 0) and

Σ f ∧Σ x an unsatisfiable CNF. Let CF (x, f ) be the set of counterfactuals of x wrt. f . Let MCS(Σ f,x ) the set of MCSs of Σ f ∧ Σ x . Then: ∀x ⊆ x, x ∈ CF f (x, f (x)) ⇐⇒ x ∈ M CS(Σ f,x ) (1)
The MCS enumeration is done over the soft clauses, which practically should reduce the time needed to enumerate all the MCS since we will have less clauses to consider. As for positively predicted instances, we can simply work on the negation of OBDD f representation of the decision function f namely, we will rely on the CNF Σ ¬f ∧Σ x to compute the counterfactuals in a similar way.

Experiments

This section provides our experiments to evaluate our approach of generating counterfactual explanations. Given a data instance of interest x and the decision function f , we encode both f and x as a CNF formula and model counterfactuals generation as a Partial maximum satisfiability problem formed by conjoining Σ f and Σ x . We start by considering typical binary classification problems and focus on Binary Naive Bayes Classifiers (BNC). To test our approach, we compiled synthetic naive Bayes classifiers to OBDDs using the approach proposed in [START_REF] Shih | Compiling bayesian network classifiers into decision graphs[END_REF], then we encode these OBDDs into CNF formulas before getting into the generation of the MCSs. We mention that for each network size, we used an average of 4 to 10 networks to run our experiments. The decision threshold used for the compilation of the synthetic BNCs is .5. expected, we notice a large increase in the OBDD size as the number of features of the classifier grows up. Moreover, it seems that the OBDD size also strongly depends on the classifier's parameters in addition to the number of features.

Compiling Bayes classifiers into OBDDs

Dumping OBDDs as CNF formulas

Next step will be to encode the obtained OBDD into CNF Boolean formulas, simply denoted CNF(f ). The latter has the same variables as the classifier. We aim in the following to compare the size of both OBDDs and CNFs of classifiers with different sizes. As observed experimentally in Table 2, the time and size (number of clauses) of the generated CNF are strongly correlated to the size of its OBDD. While the compilation time scales linearly with the number of nodes of the OBDD, the size of the CNF can be much smaller, depending on the classifier's parameters (threshold of the used BNC and variable order used for OBDD). We remind that this encoding is done only once for a given classifier and, then, can subsequently be used for explaining any number of instances.

MCSs generation

Once we got the CNF (Σ f ∧ Σ x ), we can get to the generation of MCSs. In our experiments, we use the boosting algorithm for the MCSs generation proposed in [START_REF] Grégoire | Boosting mcses enumeration[END_REF] and implemented in EnumELSRMRCache1 : a tool for MCSs enumeration.

Recall that our input is a CNF composed of hard clauses (encoding the classifier) and soft ones (encoding the data instance to explain). The data instances were randomly generated. The aim here is to compare the number of counterfactual explanations with the size of OBDD and CNF representations. Table 2 summarizes the results of the average number of counterfactual explanations generated given a data instance and a classifier. The experiments are carried out on classifiers, OBDDs and CNFs with different sizes. As expected, the number of explanations increases with the CNF size in general, but remains strongly related to: (1) the classifier and OBDD parameters (variable ordering), and (2) to the data instance itself. As shown in Table 2, the average run-time does not seem to depend on the number of MCSs generated but more on the number of features of the classifier, which is expected since the time-consuming part of generating the MCSs is related to the size of the representations in terms of number of clauses and their size. To sum up the results, it can be said that as long as we can get a symbolic tractable representation of a classifier, our approach can provide counterfactual explanations. The number of different MCSs of the CNF Boolean formulas remains low in our case since our approach computes the MCSs over the soft clauses only, which experimentally significantly reduces the time of MCSs enumeration. Finally, the obtained results suggest that the number of counterfactuals is probably very small compared with other types of explanations computed for symbolic representations (e.g. prime-implicant, minimum cardinality, etc,.), but this remains to be confirmed on benchmarks with different properties.

Concluding remarks

The approach proposed in this paper allows to equip the symbolic approach proposed in [START_REF] Shih | Compiling bayesian network classifiers into decision graphs[END_REF] with a module for counterfactual explanations. Our approach is simple and takes advantage of well-defined concepts and proven tools for MCSs. Moreover, our approach is specifically designed to provide actionable explanations. The main issue currently is that it requires a compilation step to get the symbolic representation of a classifier (compilers already exist for Bayesian networks [START_REF] Shih | Compiling bayesian network classifiers into decision graphs[END_REF], decision trees and some neural nets [START_REF] Shi | On tractable representations of binary neural networks[END_REF]). Another problem that need to be treated is the scaling of the compilation algorithm for classifiers with a large number of features.

Definition 1 .

 1 (Binary Classifier) A Binary Classifier is defined by two sets of variables: A feature space X= {X 1 ,...,X n } where |X| = n, and a binary class variable denoted Y . Both the features and the class variable take values in {0,1}. Definition 2. (Decision Function of A Classifier) A decision function of a classifier (X, Y ) is a function f : X → Y mapping each instantiation x of X to y=f (x).

Fig. 1 :

 1 Fig. 1: A Naive Bayes network classifier and its corresponding OBDD.

Table 1

 1 summarizes the compilation experiments we ran on BNCs with different sizes. For each category of classifiers having the same number of features, we compute the average size of their corresponding OBDD (number of nodes). As

	Nb Features 5	10	16	20	22	25
	OBDDsize 9	42	370	1020 2546 8626

Table 1 :

 1 Average size of the OBDD representations.

Table 2 :

 2 Average size of OBDD/CNF, runtime (ms), and number of the counterfactual explanations (MCSs).

available at http://www.cril.univ-artois.fr/enumcs/


1

Where are we in the Recognition of Young Adult Carers in France?

Abstract

Young adult carers (YACs) are people aged 18-25 years who provide care to a relative who is ill or has a disability. France begins to come to the YAC issue. YAC students were mentioned for the first time in a national policy document in 2018. By interviewing 110 students, this review showed that more than 80% of them did not know what a YAC was. If students are not aware of this status, they cannot self-identify as carers and seek support. During policy development, it is therefore important to support YACs by raising awareness.

What is a Young Adult Carer?

Individuals who provide regular, nonprofessional assistance with activities of daily living or support to a relative who has an illness, disability, or loss of autonomy due to age, are called carers [START_REF] Blanc | Les aidants familiaux[END_REF]. Carers are often adults, but can also be children, adolescents, or young adults, in which case they are referred to as young carers. The term young adult carers (YACs) is used to define the 18-25 years age group [START_REF] Levine | Young adult caregivers: A first look at an unstudied population[END_REF]. YACs are therefore young people "who provide or intend to provide care, assistance or support to another family member on an unpaid basis. The person receiving care is often a parent but can be a sibling, grandparent, partner, own child or other relative who is disabled, has some chronic illness, mental health problem or other condition (including substance misuse) connected with a need for care, support or supervision" (Becker & Becker, 2008a, p. 6).

Only few studies investigated YAC prevalence. Among the youth, prevalence is reported to be 18.10% in the United States [START_REF] Grenard | Impact of caregiving during emerging adulthood on frequent mental distress, smoking, and drinking behaviors: United States, 2015-2017[END_REF], 6% in Australia (Australian Bureau of Statistics, 2016), and 9.80% in New Zealand [START_REF] Mcdonald | An exploratory study of young carers and their families in New Zealand[END_REF]. There are no prevalence studies among youth in Europe while Becker and Becker (2008a) estimated that 5.30% of 16-24 years old are carers in the United Kingdom. Regarding specifically the student population, only one study investigated it in Norway and put it at 5.50% [START_REF] Haugland | The burden of care: A national survey on the prevalence, demographic characteristics and health problems among young adult carers attending higher education in Norway[END_REF]. Among French students, an initial estimate put it at 19% [START_REF] Dorard | Are there young carers in France? Results from the ADOCARE and CAMPUS-CARE studies among high school and college students[END_REF].

YACs are acknowledged to be an understudied population [START_REF] Levine | Young adult caregivers: A first look at an unstudied population[END_REF] who need to be specifically targeted [START_REF] Day | Young adult carers: A literature review informing the re-conceptualisation of young adult caregiving in Australia[END_REF].

Taking on a caregiving role in young adulthood has been associated with poorer physical and mental health, as well as reduced education, employment, and future life opportunities (Becker & Sempik, 2019;[START_REF] Kettell | Young adult carers in higher education: The motivations, barriers and challenges involved -a UK study[END_REF]. [START_REF] Kent | Time to recognize and support emerging adult caregivers in public health[END_REF] recently argued that it is time to recognize and support YACs, highlighting the need to examine current policies, cultural narratives, and norms surrounding family caregiving.

Awareness and Policies Worldwide: The French Situation

In a cross-national study and in line with Leu andBecker's (2017) classification, Leu et al. (2022) ranked countries according to their awareness and policy responses to young carers. They identified seven levels of awareness: (1) incorporated/sustainable (i.e., extensive awareness with sustained and sustainable policies, legal rights, and services); (2) advanced (i.e., widespread awareness with specific legal rights, but policy responses still fragmented and not sustained); (3) intermediate (i.e., some awareness with some dedicated services, mostly local but a few nationwide, with partial legal rights); (4) preliminary (i.e., little awareness with few, if any, dedicated services at national or local levels, and no legal rights);

(5) emerging (i.e., growing awareness but with no specific services); (6) awakening (i.e., embryonic awareness with the idea of vulnerable children); and (7) no response (i.e., nonawareness). These different levels of awareness reflect a wide range of policies and legislation, from protection and support with a clear definition of young carers to a total lack of recognition [START_REF] Leu | Cross-national analysis of legislation, policy and service frameworks for adolescent young carers in Europe[END_REF]. Nevertheless, no country has yet reached the incorporated/sustainable level. The top levels implies that young carers are precisely defined in legislation and benefit from clear legal rights such as financial grants or right to respite. It also implies that they benefit from specific service frameworks within all academic institution and local health services through national programs and practice models [START_REF] Leu | The 2021 cross-national and comparative classification of in-country awareness and policy responses to 'young carers[END_REF]. Above all, the top levels of awareness could not be reached until responses and law built are not based on reliable research evidence and clear legal rights [START_REF] Joseph | Young Carers Research, Practice and Policy: An Overview and Critical Perspective on Possible Future Directions[END_REF].

Young carers, and more precisely YACs, more often than not go unrecognized and fall into a gap between adult and children's services [START_REF] Becker | Service needs and delivery following the onset of caring amongst children and young adults: Evidenced based review[END_REF][START_REF] Leu | Cross-national analysis of legislation, policy and service frameworks for adolescent young carers in Europe[END_REF].

In the United Kingdom, classified as an advanced country, specific legislation to protect and support young carers are well developed. Nevertheless, there is no national services policy which results in unequal offers across the country [START_REF] Leu | The 2021 cross-national and comparative classification of in-country awareness and policy responses to 'young carers[END_REF] and only few services are specifically designed for YAC as carers aged 18-25 (Becker & Becker, 2008a). Regarding intermediate countries such as Australia, or emerging countries like the United States, there is no support service infrastructure [START_REF] Day | Young adult carers: A literature review informing the re-conceptualisation of young adult caregiving in Australia[END_REF][START_REF] Hamilton | Bounded agency in young carers' lifecourse-stage domains and transitions[END_REF][START_REF] Kent | Time to recognize and support emerging adult caregivers in public health[END_REF].

France is an emerging country with growing public and specialist awareness of young carers, as is also the case of countries such as Ireland, the United States, and Finland [START_REF] Leu | The 2021 cross-national and comparative classification of in-country awareness and policy responses to 'young carers[END_REF]. Since 2016, an NGO called the National Association for Young Carers (Jeune AiDants Ensemble; JADE) has been working to increase awareness and offer respite for young carers. Initially active at a local level, JADE is currently extending its presence across the country. In parallel, other NGOs have been developing specific responses to young carers' needs, such as the creation of support groups or hotlines [START_REF] Thual | État des lieux des dispositifs -Premières observations[END_REF]. Currently, no public

Investigating French Students' Awareness of YAC Issues

Compared to other European countries, the pursuit of studies in higher education is a strong societal expectation in France (van de Velde, 2088; [START_REF] Minni | Emploi et chômage des 15-29 ans en 2015. Un jeune sur dix au chômage[END_REF]. Under this "diploma tyranny" (van de Velde, 2008), in 2016, only 8.8% of 18-24 years had no diploma and was not in education or training program (Institut national de la jeunesse et de l'éducation populaire, 2019). This is partly explained by the difficulty of finding a job without a higher education degree [START_REF] Minni | Emploi et chômage des 15-29 ans en 2015. Un jeune sur dix au chômage[END_REF]. The pursuit of studies is facilitated by particularly low university fees and national grants. In this specific context, it is then expected that YACs could be students.

As part of the CAMPUS-CARE project 1 on the effect of caregiving on the health and wellbeing of a sample of young adult students, we conducted interviews with 110 French students (Mage = 21.25 years, SD = 2.00; 75% female). Of these, 86% were enrolled on a BA course, and 14% on an MA course (58.41% studying literature, art and human sciences; 19.80% studying law and economics; 4.95% studying science and technology; 3.96% in medicine school; information missing for 9 participants). These programs are representative of the French university context and are mostly composed of females [START_REF] Abdouni | Repères & références statistiques sur l'enseignements, la formation et la recherche[END_REF].

All participants were recruited at university, and all gave their informed consent to participate in an interview. The latter consisted of a maximum of four algorithm-based questions. The first question was "Do you know what a YAC is?" If participants answered "yes", they were then asked to provide a definition. If they answered "no", they were asked a second question: "Do you know what a carer is?" If they answered "yes", they were then asked to give a definition, as in the first question. Interviews were independently realized by four female researchers, were recorded and then transcribed for analysis. The responses were not crosschecked, but they were first analyzed by one person who proposed a coding which was discussed with two senior researchers for validation and final analysis Results demonstrate that only 17.27% of the 110 participants were able to give a correct definition of a YAC, by giving all the following elements: providing assistance, supporting an ill/disabled family member or friend; helping in a weekly or regular basis; and being unpaid to do that; χ 2 (N = 110, df = 1) = 41.13; p < .001. In other words, 82.73% of participants were not able to provide a precise definition. These participants could be divided into different subcategories, according to their degree of knowledge: (1) those who truly did not know (75.52%); (2) those who had a partial understanding but whose definitions lacked precision (4.39%); and (3) those who thought that they knew but who gave incorrect definitions (20%). Among the participants in the first subcategory, 94.23% did not know how to define the term carer. Among those in the third subcategory, results revealed a variety of definitions, such as being a volunteer for a charity, mentoring university students, or being altruists. Overall, results demonstrated that the overwhelming majority of our sample did not know about YACs.

A Relevant Illustration: French Students are not Aware of YACs

Despite the French Government's action plan, our results were a relevant illustration that more than 80% of the students interviewed did not know what a YAC was. This lack of awareness and recognition of the carer status is partly related to the fact that, until recently, young people were not thought to play a role in informal caregiving [START_REF] Leu | Study protocol: Young carers and young adult carers in Switzerland[END_REF].

Moreover, young adults who take on a caregiving role may regard it as a family duty or a normal responsibility [START_REF] Struckmeyer | Emerging adulthood caregivers: Examining the unique experiences in this understudied population[END_REF], such that if the recipient of their care is a family member, they will define themselves solely according to their family relationship (e.g., child, grandchild, sibling; [START_REF] Lewis | Who am I?: An exploration of identity of young adult carers in the United Kingdom and United States[END_REF]. Even though they were given a definition of a carer at the beginning of interview, participants did not identify themselves as YACs [START_REF] Struckmeyer | Emerging adulthood caregivers: Examining the unique experiences in this understudied population[END_REF]. Identifying and assessing YACs is therefore a major challenge [START_REF] Kettell | Young adult carers in higher education: The motivations, barriers and challenges involved -a UK study[END_REF][START_REF] Kent | Time to recognize and support emerging adult caregivers in public health[END_REF].

In the light of the present findings, the second measure in the French carers action plan, which is YAC students' flexibility in their pace of study, may well go unnoticed. If students are not aware of the issues surrounding YACs, they cannot identify themselves as carers and subsequently ask for support. The measure concerning students should therefore be coupled with a public awareness campaign. For example, there could be a themed day in the academic community that would be open to students and education professionals, with interventions from carers' and students' associations, researchers, and healthcare or social professionals with expert knowledge of the issue. In September 2021, the University of Aix-Marseille staged such an event. It was organized by the faculty of law, and focused on YAC rights. More interventions of this kind should be held: they should be extended to cover all YAC needs, and driven by the French Government so that they reach all French students.

Awareness Amongst Professionals

Due to the hidden nature of the caring role [START_REF] Leu | Caring in mind? Professionals' awareness of young carers and young adult carers in Switzerland[END_REF], providing support to an illness/disabled relative could be seen as a familial obligation or a normal responsibility [START_REF] Lewis | Who am I?: An exploration of identity of young adult carers in the United Kingdom and United States[END_REF][START_REF] Struckmeyer | Emerging adulthood caregivers: Examining the unique experiences in this understudied population[END_REF]. Most YACs do not regard themselves as carers until a health or social care professional defines them as such (Becker & Becker, 2008a;[START_REF] Lewis | Who am I?: An exploration of identity of young adult carers in the United Kingdom and United States[END_REF]. Therefore, if professionals are not aware of YAC issues, most YACs will remain hidden. This constitutes a societal issue [START_REF] Smyth | So that's how I found out I was a young carer and that I actually had been a carer most of my life'. Identifying and supporting hidden young carers[END_REF], and to overcome this issue, education, health and social care professionals must be capable of identifying YACs at an early stage. In a recent study in Switzerland, a country considered to be at the preliminary level, with little awareness and recognition [START_REF] Leu | The 2021 cross-national and comparative classification of in-country awareness and policy responses to 'young carers[END_REF], fewer than 50% of professionals were found to be familiar with the term [START_REF] Leu | Caring in mind? Professionals' awareness of young carers and young adult carers in Switzerland[END_REF]. In France, recent research revealed that more than 80% of education professionals were unfamiliar with the young carers issue, even though almost all of them stated that they had already met one, after being given a broad definition [START_REF] Justin | What do French school staff know about young carers? A qualitative study about their perceptions[END_REF]. This finding for education professionals from primary, secondary and high school highlights all the work that still needs to be done. Raising awareness among education professionals is a first step that should be extended to professionals in higher education, to ensure that YAC students can also be identified.

Furthermore, as recommended by [START_REF] Leu | Cross-national analysis of legislation, policy and service frameworks for adolescent young carers in Europe[END_REF], health and social care professionals working with the relative who has an illness or disability should also be involved, as they are more likely to ask about the family situation and the possible presence of young carers.

Raising awareness by providing information through different support mechanisms (websites, brochures, newsletters, and checklists) could be useful [START_REF] Leu | Caring in mind? Professionals' awareness of young carers and young adult carers in Switzerland[END_REF], but the question is whether this is enough.

Implications for Policy and Practice

In France, like in other emerging countries, much remains to be done at the public policy level. Our present finding showed that more than 80% of young adult students interviewed are not aware of YACs issue. This result could be compared to the one of [START_REF] Justin | What do French school staff know about young carers? A qualitative study about their perceptions[END_REF] who came to the same conclusion among French education professionals. The current French Government's measures for young are a first step that should be acknowledged, but they will not be sufficient if they are not coupled with awareness-raising campaigns.

The first measure about education professionals' awareness should concern all professionals who come into contact with young carers. Taking the example of more advanced countries, specific training, like in Switzerland and the United Kingdom, or information campaigns using media, like in Sweden (i.e., intermediate country), could be imagined raising professionals' awareness and young carers' recognition. To improve identification, the carers' alert thermometer for young carers, which could be used by all professionals and allows identifying young carers and screen the support needed, should be democratized [START_REF] Kettell | Development of the Carers' Alert Thermometer for Young Carers (CAT-YC) to identify and screen the support needs of young carers: a mixed method consensus study[END_REF]. Nevertheless, professionals' involvement implies a heightened understanding of the issues as well as a need to know how effectively support and help young carers [START_REF] Leu | Cross-national analysis of legislation, policy and service frameworks for adolescent young carers in Europe[END_REF]. To go further, in the Netherlands (i.e., preliminary country), an NGO has developed some guidelines for professionals through a toolkit on how to support children of parents with mental health problems [START_REF] Leu | The 2021 cross-national and comparative classification of in-country awareness and policy responses to 'young carers[END_REF]. NGOs should be considered as a key building block of policy development toward professionals.

Concerning the second measure on YAC students, we assume that much more could be done. Regarding literature, [START_REF] Kettell | Young adult carers in higher education: The motivations, barriers and challenges involved -a UK study[END_REF] suggested several ways to improve YAC students support at university. For example, a "carers' passport", like a card or a booklet, that would signify to all university staff that a student is also a carer. It could also be to clearly identify one member of the university staff as a resource to discuss YACs' needs and difficulties or to establish YACs student associations or societies to develop a sense of belonging and peer support. Furthermore, in time of the COVID-19 pandemic, YAC students appear more vulnerable than non-carers [START_REF] Landi | Young adult carers during the pandemic: The effects of parent illness and other ill family members on COVID-19 related and general mental health outcomes[END_REF] which suggests that COVID-19 support solutions should have a specific attention on YACs. The implementation of devoted support services at universities is underpinned by awareness campaigns for students and university professionals. Above all, in a more general perspective, it could be imagined, like in the United Kingdom, an annual young carers festival where young carers and government policy makers exchange to improve young carers' support at the national level [START_REF] Leu | A cross-national and comparative classification of in-country awareness and policy responses to 'young carers[END_REF].

Conclusion

Emerging countries (e.g., France) with regard to the issues of young carers should follow the example set by more advanced countries, by giving carers specific legal rights, dedicated services and interventions, and providing guidance for professionals [START_REF] Leu | The 2021 cross-national and comparative classification of in-country awareness and policy responses to 'young carers[END_REF]. Researchers should work with NGOs and the media on how to raise awareness and develop new policies. The transfer of research findings to society through policy is the precursor of change [START_REF] Leu | A cross-national and comparative classification of in-country awareness and policy responses to 'young carers[END_REF]. New policies should factor in the need to raise awareness among professionals as well as the general population, in order to support YACs.

Awareness is strength.

  services specifically target YACs. The COVID-19 pandemic drew attention to young adult students' needs, and several support solutions were put in place (e.g., Charbonnier et al., 2021), but YAC students remained invisible. Within the scientific community, specialist awareness has increased, with new research projects focusing on young carers and the YAC issue. These projects span several disciplines. For example, in psychology, the University Paris Cité is the lead partner in funded projects focusing on the education, health and wellbeing of young carers and YACs, as well as the awareness of health professionals. In law, funded projects hosted by the University of Aix-Marseille are examining carers' legal rights, with a focus on YAC students. Research so far has led to the development of training programs for carers, aimed specifically at young carers and YACs in several French universities. At the legislative level, the Carers' Act passed in 2008 concerned all carers without distinction. More recently, a carers action plan ("Agir pour les aidants") launched in October 2019 identified young carers as a distinct social group for the first time in a national policy document. Two of the measures concern young carers: the first is designed to enhance the awareness of education professionals, and the second one gives YAC students greater flexibility in their pace of study. This strategy assumes that education professionals and young adult students are actually aware of YAC issues, for how can young adult students benefit from it if they do not know what a YAC is? This raises the question of how aware French students are of YAC issues.

The CAMPUS-CARE project is led by researchers from the University Paris Cité, is funded by Klesia and had been approved by a French ethical research committee (CERES, N°

2019-62; and CNIL, N° 20200828_Campuscare). For more information, see: https://jaid.recherche.parisdescartes.fr/campus-care/