Solveig Lelaurain
email: solveig.lelaurain@gmail.com

David Fonte

Jean-Christophe Giger

Séverin Guignard

& Grégory

Lo Monaco

Legitimizing intimate partner violence: The role of romantic love and the mediating effect of patriarchal ideologies

Keywords: domestic violence, romantic love, ambivalent sexism, violence legitimization, intimate partner violence "

Romantic love in heterosexual relationships is recognized as an important aspect to be considered in relation to the psychosocial mechanisms associated with the persistence of intimate partner violence and the help-seeking barriers faced by female victims. However, few studies have explored the processes underlying the relationship between this form of love and attitudes toward this kind of violence. To do this, the current study aims to analyse the relationship between the adherence to romantic love and the legitimization of intimate partner violence (i.e., perceived severity of violence, victim blame and exoneration of the perpetrator). It was also to test the mediating effect of patriarchal ideologies (i.e., ambivalent sexism and domestic violence myths) on this relationship. Two hundred and thirty-five French adults (51.1% women) were surveyed. The data were analysed with structural equation models in order to study the mediations between the variables considered. Consistent with our hypotheses, the results showed that the more the participants adhered to romantic love, the more they blamed the victim and exonerated the perpetrator. They also showed a positive relationship between romantic love, ambivalent sexism, and domestic violence myths. Finally, the results demonstrated that this positive relationship is mediatized by ambivalent sexism and domestic violence myths. The findings illustrate the need to deconstruct romantic love ideology and the psychosocial logics underlying the legitimization of intimate partner violence.

Introduction

Intimate partner violence (IPV) is a worldwide social problem affecting between 10 and 71 % of women in their lifetimes [START_REF] Garcia-Moreno | Prevalence of intimate partner violence: Findings from the WHO multi-country study on women's health and domestic violence[END_REF]. This phenomenon has been acknowledged as one of the leading causes of injuries for women [START_REF] Hague | Domestic violence: Action for change[END_REF]. However, this common violence remains rarely denounced and prosecuted (see [START_REF] Lelaurain | Intimate partner violence and helpseeking: A systematic review and social psychological tracks for future research[END_REF], for a review on help-seeking barriers). Thus, one of the most important scientific issues in this field concerns the understanding of the psychological and social mechanisms underlying the persistence of this violence and the help-seeking barriers faced by victims. Patriarchal ideologies defining sociosymbolic relationships between genders affect judgments toward survivors and contribute to the non-recognition or acceptance of IPV [START_REF] Baldry | Helping victims of intimate partner violence: The influence of group norms among lay people and the police[END_REF][START_REF] Lelaurain | Social Representations and Conditional Logics in Legitimization of Intimate Partner Violence[END_REF].

Beyond simply underlining these ideologies, Peterson Del Mar (1996, p. 174) proposes to "examine our most cherished values and most powerful cultural traits" that could contribute to the acceptance of IPV". Among these ideologies, romantic love seems to be one of the most widespread and socially accepted. For example, the above-mentioned French newspaper headlines illustrate the spontaneous relationship that people make between IPV and romantic love in the social field. However, romantic love has often been considered as a peripheral aspect of the IPV phenomenon in literature (Power, Koch, Kralick, & Jackson, 2006). Thus, our objective in the present study was to tackle the question of the effect of adherence to romantic love, ambivalent sexism, and domestic violence myths on IPV legitimization.

Romantic love and acceptance of IPV

Romantic love is a set of beliefs about the power of love and the perfection of romance including for example, idealization of the partner, mysticism, complete involvement and exclusiveness or jealousy (see [START_REF] Knox | Attitudes of college students toward love[END_REF]Sprecher & Metts, 1998). It also refers to the nature of love and more specifically the characteristics or criteria for an ideal relationship [START_REF] Bartell | Romanticism[END_REF] as to how it should develop, function, and be maintained.

Romantic love was established as a reference model for heterosexual love relationships in the

Western culture of the 19 th and 20 th centuries, valuing sexual and amorous exclusivity, predestination of the encounter and conjugal perpetuity [START_REF] Marquet | L'amour romantique à l'épreuve d'internet [Romantic love to the test of the internet[END_REF].

Nowadays, the postmodern love relationship is not only built on the basis of romantic love, but also incorporates representations based on the independence and autonomy of individuals [START_REF] Chaumier | La déliaison amoureuse. De la fusion romantique au désir d'indépendance[END_REF]. We thus find several representations of love which coexist, and which are not the object of the same social valorization depending on the socio-cultural context [START_REF] Apostolidis | Une approche psychosociale de l'amour : logiques normatives et representations [A psychosocial approach to love: Normative logics and representations[END_REF]. As we can see in cultural productions for youth, romantic love remains one of the most socially valued representations of love [START_REF] Bonomi | Double crap!" Abuse and harmed identity in Fifty Shades of Grey[END_REF][START_REF] Borgia | Twilight: The glamorization of abuse, codependency, and white privilege[END_REF][START_REF] Hefner | From love at first sight to soul mate: The influence of romantic ideals in popular films on young people's beliefs about relationships[END_REF]. For instance, a study showed that almost 80% of Disney animated classics, at the time of the study, portrayed a couple that fell in love at first sight, got married, and "lived happily ever after" [START_REF] Tanner | Images of couples and families in Disney feature-length animated films[END_REF]. These love themed media products can generate idealistic expectations and practices of romantic love [START_REF] Segrin | Does television viewing cultivate unrealistic expectations about marriage[END_REF]. Such romantic narratives shape experiences, actions and understandings of love and relationships, and in turn men and women learn what is love through them [START_REF] Jackson | Love and romance as objects of feminist knowledge[END_REF].

Several studies have demonstrated the role of adherence to romantic love in the legitimization of IPV. For instance, the narratives of love and passion are very strong in the news media in framing intimate partner homicide, to the detriment of the structural and social dimensions underlying it [START_REF] Gius | I loved her so much, but I killed her" Romantic love as a representational frame for intimate partner femicide in three Italian newspapers[END_REF][START_REF] Deshong | Intimate partner violence in the Caribbean: State, activist and media responses[END_REF]. In particular, these authors highlighted that "the frame of 'romantic love' is used in order to legitimate and justify violence against women" (p.68). Indeed, men who are violent and murderous towards their wives are often described as being under the influence of uncontrollable emotions, such as having "too much pain" or being "too much in love", but rarely as aggressors [START_REF] Gius | I loved her so much, but I killed her" Romantic love as a representational frame for intimate partner femicide in three Italian newspapers[END_REF][START_REF] Romito | Un silence de mortes. La violence masculine occultée [A silence of dead[END_REF]. Thus, adhesion to romantic love can help to make IPV socially acceptable in perceiving violence as a male form of amorous expression, a signs of intimacy or affection rather than as something problematic [START_REF] Bonomi | Double crap!" Abuse and harmed identity in Fifty Shades of Grey[END_REF][START_REF] Bonomi | Fiction or not? Fifty Shades is associated with health risks in adolescent and young adult females[END_REF][START_REF] Lelaurain | Social Representations and Conditional Logics in Legitimization of Intimate Partner Violence[END_REF]. However, romantic love is not only a veil that diminishes the recognition of violence within a couple. It is also one of the main barriers to the victims leaving the violent partner [START_REF] Fanslow | Help-seeking behaviors and reasons for help seeking reported by a representative sample of women victims of intimate partner violence in New Zealand[END_REF][START_REF] Jaspard | Au nom de l'amour : les violences dans le couple. Résultats d'une enquête statistique nationale [In the name of love: Intimate partners violence. Results from a national statistical survey[END_REF][START_REF] Lelaurain | Intimate partner violence and helpseeking: A systematic review and social psychological tracks for future research[END_REF]. Love is also a "weapon" for IPV because male dominance often depends on the partner's emotional dependence [START_REF] Jaspard | Au nom de l'amour : les violences dans le couple. Résultats d'une enquête statistique nationale [In the name of love: Intimate partners violence. Results from a national statistical survey[END_REF].

The role of ambivalent sexism and domestic violence myths

According to feminist perspectives, the social valorisation of romantic love also helps to maintain gender inequalities through the naturalization of a culture of male dominance (see [START_REF] Monckton-Smith | Murder, gender and the media[END_REF]. Indeed, within many Western cultures, romantic heterosexual love is often used to maintain traditional gender relationships and to justify the order of women's subordination to men [START_REF] Chung | Violence, control, romance and gender equality: Young women and heterosexual relationships[END_REF][START_REF] Singh | Women want love, man wives: The discourse of romantic love in young adults' future marriage goals[END_REF][START_REF] Wood | The normalization of violence in heterosexual romantic relationship. Women's narratives of love and violence[END_REF]. For instance, the romance narrative portrays women as needing to be rescued by man and as needing to be complete and fulfilled, while men are portrayed as naturally strong, full of power and sure of themselves [START_REF] Wood | The normalization of violence in heterosexual romantic relationship. Women's narratives of love and violence[END_REF][START_REF] Vincent | Sleeping with beauty: romantic love, sex, power and the construction of femininity in heterosexual young adult relationships[END_REF]). An important aspect of romantic love is therefore to contribute to the definition of gender roles in couple relationships [START_REF] Rudman | The social psychology of gender: How power and intimacy shape gender relations[END_REF], in particular by reducing women's identity to their feelings of love as well as making love into a destiny they must achieve [START_REF] Chung | Violence, control, romance and gender equality: Young women and heterosexual relationships[END_REF][START_REF] Power | Lovestruck: Women, romantic love and intimate partner violence[END_REF].

According to this literature, ambivalent sexism and domestic violence myths are two socio-cognitive constructs that should be theoretically linked to romantic love insofar as they contribute to defining traditional gender roles legitimizing male domination. The first construct brings together two co-existing forms of sexism whose common function consists in maintaining women in their gender role and legitimizing gender inequalities (Glick & Fiske, 2001). On the one hand, benevolent sexism is defined as a set of attitudes that lead to seeing women through perceived positive stereotypes (Glick & Fiske, 2001, p. 491). On the other hand, hostile sexism is based on the idea of domination and male superiority [START_REF] Dardenne | Structure latente et validation de la version française de l'Ambivalent Sexism Inventory: L'Échelle de Sexisme Ambivalent [Latent structure of the French validation of the Ambivalent Sexism Inventory: Échelle de Sexisme Ambivalent[END_REF]. Domestic violence myths were defined by Peters (2008) as stereotypical beliefs that are widely and persistently held to minimize or justify IPV against women. According to this author, the function of these myths is to support the patriarchal organization of society insofar as they are positively correlated to negative attitudes towards women and to certain restrictive visions of social gender roles.

Multiple contributions have shown that these two patriarchal ideologies are significant predictors of the justification of abusive behavior against women. For instance, it has been shown that domestic violence myths are linked to the attribution of victim responsibility, exoneration of the perpetrator and to non-recognition of IPV (see Giger et al., 2016;[START_REF] Lelaurain | Social Representations and Conditional Logics in Legitimization of Intimate Partner Violence[END_REF][START_REF] Yamawaki | Perceptions of domestic violence: The effects of domestic violence myths, victim's relationship with her abuser, and the decision to return to her abuser[END_REF]. In the same vein, ambivalent sexism has long been shown to affect attitudes toward violence against women such as minimization, victim-blame attribution, and excusing the perpetrator, (e.g., [START_REF] Craig | A study of male veterans' beliefs toward domestic violence in a batterers intervention program[END_REF][START_REF] Glick | Ambivalent sexism and attitudes toward wife abuse in Turkey and Brazil[END_REF][START_REF] Sakalh | Beliefs about wife beating among Turkish college students: The effects of patriarchy, sexism, and sex differences[END_REF][START_REF] Valor-Segura | Victim blaming and exoneration of the perpetrator in domestic violence: The role of beliefs in a just world and ambivalent sexism[END_REF][START_REF] Yamawaki | The functions of gender role traditionality, ambivalent sexism, injury, and frequency of assault on domestic violence perception: A study between Japanese and American college students[END_REF]. Thus, not only do ambivalent sexism and domestic violence myths help to define the traditional gender roles from which representations of romantic love are drawn, but these socio-cognitive constructs are also important predictors in the evaluation of IPV. This suggests that, behind the adherence to romantic love, the legitimization of IPV is likely to be determined by the internalization of patriarchal ideologies defining gender-symbolic roles and justifying male domination. Consequently, the potential effect of romantic love on the attitudes of individuals who face situations of IPV is likely to be mediated by the adherence to patriarchal ideologies. To our knowledge, this mediation has never been empirically tested.

Yet it is an important issue to the extent that romantic love is a relevant analytical framework for improving our understanding of ideologies underlying the acceptance of IPV.

The present study

In line with the literature, the first objective of the present study was to verify whether adherence to romantic love predicts different evaluations, such as victim blame, exoneration of the perpetrator and perceived violence severity. The second objective was then to examine how adherence to romantic love accounts for these evaluations that tend to legitimize IPV. As we have seen, several authors highlight the fact that romantic love may help to maintain gender inequalities [START_REF] Monckton-Smith | Murder, gender and the media[END_REF][START_REF] Singh | Women want love, man wives: The discourse of romantic love in young adults' future marriage goals[END_REF][START_REF] Wood | The normalization of violence in heterosexual romantic relationship. Women's narratives of love and violence[END_REF]. This suggests that adherence to patriarchal ideologies are mediators in the relationship between romantic love and the evaluation of IPV situations. We therefore hypothesized that: H1: The more individuals adhere to romantic love, the more they will blame the female victim for the violence she suffered.

H2:

The more individuals adhere to romantic love, the more they will exonerate the male perpetrator of the violence.

H3:

The more individuals adhere to romantic love, the less they will perceive the male violence suffered by the female victim as severe.

H4:

The effect of romantic love on the evaluation of IPV will be mediated by the adherence to ambivalent sexism and domestic violence myths.

Method

Participants

Two hundred and thirty-five participants (51.1% women), aged between 18 and 80 (M = 38.31, SD = 16.23), were recruited for this study. One hundred and twenty-one participants (51.9%) were engaged in a professional activity while 81 (34.5%) were students and 20 (8.5%) were retired. Finally, 48 (20.4%), said that they had ever experienced IPV and 120 (51.1%) reported knowing someone who was a victim of IPV.

Procedure

Participants were approached in various public places such as university libraries, train stations, and main streets of a city in the south of France. The research was presented to participants as a questionnaire on couple relationships and as individual, anonymous, and confidential. It was made clear that they could refuse to participate and that they could stop at any time without any explanation and without any consequences. A questionnaire was given to participants only after receiving their verbal consent. They completed it in the public places where they were recruited. A debriefing was offered to them after completion.

Data collection

Evaluation of IPV. Based on the procedure of Giger et al. (2016), participants were asked to evaluate an IPV situation presented in a short scenario (see Appendix) through a 12-item questionnaire measuring three sub-scales: the perceived responsibility of the female character (Victim Blame), the perceived exoneration of the male character (Exoneration of the perpetrator), and the perceived severity of the violence perpetrated by the male character on the female character (Perceived Severity of Violence). Responses were given on a 7-point Likert scale, and overall scores could range from 1 to 7, with higher scores representing higher victim responsibility, aggressor exoneration and perceived violence severity.

Romantic Love. We used the Attitude Towards Love Scale [START_REF] Knox | Conceptions of love at three developmental levels[END_REF]; see also [START_REF] Knox | Attitudes of college students toward love[END_REF]. This is a 30-item scale measuring the degree to which one holds romantic versus realistic attitudes toward love. Participants answered items on a 5-point Likert scale, and overall score could range from 1 to 5 with higher scores representing a greater degree of romantic love. Items were averaged so that higher scores reflected stronger romantic attitudes toward love. Internal consistency (α = .87) in the present study was good. Ambivalent Sexism. Sexism was measured with the Ambivalent Sexism Inventory [START_REF] Dardenne | Structure latente et validation de la version française de l'Ambivalent Sexism Inventory: L'Échelle de Sexisme Ambivalent [Latent structure of the French validation of the Ambivalent Sexism Inventory: Échelle de Sexisme Ambivalent[END_REF]Glick & Fiske 1996). This 22-item questionnaire is composed of two dimensions: hostile sexism which is composed of negative feelings towards women; and benevolent sexism which reflects a chivalrous ideology of being sympathetic and protective towards women who agree with conventional gender roles. As allowed by the different validations of this scale, we used its unidimensional version which groups together the two forms of sexism. Responses were given on a 6-point Likert scale, and overall scores could range from 0 to 5, with higher scores representing a greater degree of ambivalent sexism.

Internal consistency (α = .94) in the present study was better to those reported by Glick and Fiske (2001;α = .81 in Study 1; α = .83 in Study 2). Domestic Violence Myths. We used the Domestic Violence Myth Acceptance Scale (Lelaurain, Fonte, Graziani, & Lo Monaco, in press;Peters, 2008). This 18-item questionnaire measures stereotypical attitudes and beliefs contributing to the minimizing, denial, and even justification of IPV. Responses were given on a 7-point Likert scale, and overall score could range from 1 to 7 with higher scores representing greater endorsement of myths surrounding IPV acceptance. Internal consistency (α = .88) in the present study was similar to those reported by Peters (2008; α = .81 in Study 1; α = .88 in Study 2) and by Giger (2016;α = .86 in Study 1; α = .90 in Study 2).

Results

Descriptive statistics and correlations for the relevant measures are reported in Table 1. Pearson correlations were performed to examine whether Romantic Love, Ambivalent Sexism, Domestic Violence Myths and evaluations of IPV were correlated. These analyses revealed that all correlations were significant (all ps < .05), except for the relationship between Romantic Love and Perceived Severity of Violence. Then linear regression analyses were performed to examine the predictive ability of romantic love on the evaluation of IPV.

Results showed that, the more participants adhered to Romantic Love, the more they blamed the victim (β = .31, t(1, 233) = 4.94, p < .001). Thus, our hypothesis H1 was not rejected.

Then, the more participants adhered to Romantic Love, the more they exonerated the perpetrator (β = .29, t(1, 233) = 4.66, p < .001). Thus, our hypothesis H2 was not rejected. However, romantic love was not a predictor of Perceived Severity of Violence (β = -.06, t(1, 233) = -.87, p = .39). Our hypothesis H3 was rejected.

Two successive structural equation models were performed from a confirmatory perspective to test our theoretical model according to which patriarchal ideologies mediate the effect of Romantic Love on the evaluation of IPV. Structural equation modelling was used because it allows complex mediation models to be tested in a single analysis [START_REF] Gunzler | Introduction to mediation analysis with structural equation modeling[END_REF][START_REF] Mackinnon | Introduction to statistical mediation analysis[END_REF]. In the first step, we tested a model in which Romantic Love, Ambivalent Sexism and Domestic Violence Myths were related to Victim Blame, Perceived Severity of Violence and Exoneration of the Perpetrator (Figure 1). This analysis revealed that all standardized path coefficients were significant (all ps < .01), except for the relationship between Domestic Violence Myths and the Perceived Severity of Violence (β = -.09, p = .284). A non-significant path was also revealed for the relationship that Romantic Love maintains with Victim Blame (β = .08, p = .155), Perceived Severity of Violence (β = .11, p = .121), and Exoneration of the perpetrator (β = .07, p = .229).

In order to check for the significance of the indirect mediated effect of these nonsignificant direct effects, bootstrap tests were performed (mean of 5000 bootstrap samples with bias-corrected 95% confidence intervals). These analyses revealed a significant indirect effect for the relationship that Romantic Love maintains with Victim Blame (β = .08, p < .001, 95% CI = .17; .30), Perceived Severity of Violence (β = .10, p < .001, 95% CI = -.22; -.11), and Exoneration of the perpetrator (β = .07, p < .001, 95% CI = .16; .29). This suggests that ideologies legitimizing patriarchy are significant mediators in the relationship between Romantic Love and the evaluation of IPV. The goodness-of-fit tests yielded a significant chi square (χ 2 (3) = 29.02, p <. 001), which means that the model did not fit the observed data. The model's baseline fit was inadequate (RMSEA = .193, SRMSR = .050, CFI = .940, TLI = .698). In the second step, we rectified our theoretical model to decrease the chi-squared index:

The non-significant direct effects were withdrawn, and, on the basis of the modification indices, a covariance was added between Perceived Severity of Violence and Victim Blame, and between Victim Blame and Exoneration of the perpetrator (Figure 2). The analysis of this new model revealed that all standardized path coefficients were significant (all ps < .01).

Goodness-of-fit tests yielded a non-significant chi square (χ 2 (5) = 7.15, p = .210), which meant that the new model fitted the observed data. The model's baseline fit was adequate (RMSEA = .043, SRMSR = .030, CFI = .995, TLI = .985). Comparing the models using Δχ 2 revealed a significant difference between the final model and the initial model (Δχ 2 (Δdf = 2) = 21.87, p < .001), which indicates that the model fitted the observed data better when Romantic Love was only related to the evaluation of IPV via patriarchal ideologies. Thus, our hypothesis H4 was not rejected.

Discussion

This research provides an original contribution to the understanding of the mechanism by which an IPV situation could be legitimized. The findings showed that romantic love was associated with evaluations that tend to legitimize IPV, confirming the relationship suggested by some qualitative research (see [START_REF] Gius | I loved her so much, but I killed her" Romantic love as a representational frame for intimate partner femicide in three Italian newspapers[END_REF][START_REF] Wood | The normalization of violence in heterosexual romantic relationship. Women's narratives of love and violence[END_REF]. More specifically, the adherence to this ideology predicts significantly victim blame and exoneration of perpetrator of a case of IPV. They also showed that patriarchal ideologies mediated the relationship between romantic love and the evaluation of IPV, which is consistent with the assumption that romantic love is underpinned by stereotypes legitimizing gender inequalities and violence against women (see [START_REF] Chung | Violence, control, romance and gender equality: Young women and heterosexual relationships[END_REF][START_REF] Singh | Women want love, man wives: The discourse of romantic love in young adults' future marriage goals[END_REF][START_REF] Wood | The normalization of violence in heterosexual romantic relationship. Women's narratives of love and violence[END_REF]. Thus, IPV is legitimized insofar as the adherence of individuals to romantic love also leads them to adhere to ambivalent sexism and domestic violence myths; in return, the adhesion to these two ideologies leads individuals to perceive the male aggressor as less accountable and the female victim as more accountable. In others words, this suggests that, behind the adherence to romantic love, the legitimization of IPV is determined by the internalization of patriarchal ideologies defining gender-symbolic roles and justifying male domination. These results stand out from those of other studies exploring the relationships between romantic love and IPV, which have focused more on love as a reason to stay and not seeking help (see [START_REF] Anderson | Why doesn't she just leave?": A descriptive study of victim reported impediments to her safety[END_REF][START_REF] Dziegielewski | Domestic violence: Focus groups from the survivors' perspective[END_REF][START_REF] Towns | If I loved him enough, he would be okay": Women's accounts of male partner violence[END_REF] or to justify early signs of IPV [START_REF] Frías | Between support and vulnerability: Examining family support among women victims of intimate partner violence in Mexico[END_REF][START_REF] Power | Lovestruck: Women, romantic love and intimate partner violence[END_REF][START_REF] Pyles | Building bridges to safety and justice: Stories of survival and resistance[END_REF]. Indeed, we shed light on another aspect of adherence to romantic love ideology: how romantic love favors the acceptance of IPV by reinforcing the adherence to patriarchal ideologies.

Our findings led us to conduct an ideological and macro-social [START_REF] Doise | Levels of explanation in social psychology[END_REF] level analysis in order to question the social functions of romantic love in Western cultures.

Specifically, this would allow us to understand the ambivalence between the strong condemnation of violence in society, perceived as "intolerable" [START_REF] Herman | Lutter contre les violences conjugales [Combating domestic violence[END_REF], and its persistence as well as its social acceptance. While romantic love depicted in popular culture is conflated with the idea of control [START_REF] Bonomi | Double crap!" Abuse and harmed identity in Fifty Shades of Grey[END_REF][START_REF] Deller | Reading the BDSM romance: Reader responses to Fifty Shades[END_REF], this type of love remains highly socially valued and seems harmless on the surface [START_REF] Papp | The dark side of heterosexual romance: Endorsement of romantic beliefs relates to intimate partner violence[END_REF]. Such a conception of love is therefore symptomatic of a culture of male dominance perceived as natural and unproblematic [START_REF] Dobash | Violence against wives: A case against the patriarchy[END_REF]. This ideology thus appears as a hegemonic construct that could help to facilitate the negotiation of social norms outlawing IPV against women. A recent study aiming at exploring the representations that emerge in communications when French individuals discuss an IPV situation illustrates this strategy [START_REF] Lelaurain | Social Representations and Conditional Logics in Legitimization of Intimate Partner Violence[END_REF]. Romantic love has been shown to be a salient conditional parameter for legitimizing the deviation from the norm of "one doesn't slap a woman" to which all participants spontaneously refer. Specifically, they discussed different aspects of a situation of male violence against a woman in order to estimate its severity or its justification. The violence thus appeared as more justified and less severe if the couple were in a long-term relationship or if they were in love.

These considerations finally invite us to take a greater interest in consensual and apparently insignificant cultural objects but which nevertheless play an essential role in the legitimization of IPV against women. Such cultural objects therefore present a particular challenge for researchers who are in close axiological proximity between their own values and those of the society in which they live. The latter always face the risk of being "blinded" by ideologies whose dominant character lies precisely in not being perceived as such. [START_REF] Bourdieu | Masculine domination[END_REF] considerations about love in the post-scriptum of his book on male domination are illustrative of this risk. Although this work is part of a perspective of systematically distancing and deconstructing common sense evidence on gender relations, his specific reflections on heterosexual love mark a break with this line of conduct. Love is therefore thought of by Bourdieu as a feeling that suspends male domination, and not as a vector of this domination as the feminists of his time already conceptualized it.

Limitations and future directions

This work has one main limitation concerning the correlational analyses used. Therefore, it invites us to be cautious when interpreting and generalizing the findings since further research is needed in order to provide causal evidence for our hypotheses. From this perspective it could be relevant to use experimental procedures in order to deepen our knowledge of the effect of romantic love on IPV evaluation. One perspective of testing the causal effect of romantic love on the adherence to ideologies legitimizing male dominance and the evaluation of IPV situations could be to use the autobiographical recall technique (see [START_REF] Galinsky | Power reduces the press of the situation: Implications for creativity, conformity, and dissonance[END_REF]. Specifically, this technique would consist in asking participants to write about a life event in which they felt in love and then to measure the variables mentioned above. We finally suggest that the development of this kind of research would be useful for enhancing sex education programs, especially for adolescents and young adults, for whom love being essential and eternal are dominant ideas [START_REF] Singh | Women want love, man wives: The discourse of romantic love in young adults' future marriage goals[END_REF]. Thus, instead of just trying to change individuals' attitudes and behaviours, these programs could also be directed toward the deconstruction of the dominant representation of love which contributes to the perpetuation of hierarchical gender constructions and to the acceptation of IPV. The knowledge produced by gender studies is an important matter here on which such programs should be based. They are conceptual tools that allow us to initiate a reflection on the problems stemming from gender relationships and to denaturalize certain shared evidence on these relationships, but also to raise young people's awareness of the existence of all the diversity of possible relational ways between men and women.

Figure 1 .

 1 Figure 1. Initial structural equation model with standardized path coefficients (RMSEA =

Figure 2 .

 2 Figure 2. Final structural equation model with standardized path coefficients (RMSEA = .043,

This research was financed by National Funds provided by the FCT-Foundation for Science and Technology through project UID/SOC/04020/2013 and by the region of Provence-Alpes-Côte d'Azur (PACA).

Appendix

Mary is telling Ann what happened to her with her boyfriend: "You know, yesterday I was sitting on the couch with John, and we were watching TV. Someone rang me, but I hung up, so we wouldn't be bothered. John asked who it was. I replied that it was nobody important. He picked up my mobile phone and began to check my calls and he saw that it was Peter. He got furious and threw the mobile phone against the wall. The phone broke into pieces. I told him he had no right to do so. He grabbed my wrist with full force, insisting that I tell him who Peter was. I told him he was hurting me, but he didn't let go of my wrist. I replied that it was my new colleague, with whom I was working on an important project and I had already spoken about him. He looked at me angrily and said: 'Why are you doing everything to make things go badly for us and make me angry?' When I didn't answer him, he continued, saying, 'If I get angry it's because I love you so much,' and he hugged me."

Conflict of Interest

The authors declare that they have no conflict of interest.

Research Involving Human Participants and/or Animals

The study was carried out in accordance with the 1964 Helsinki declaration and its later amendments, the ethical principles of the French Code of Ethics for Psychologists, and the World Health Organization ethical recommendations for research on violence against women.


Santiago Cuervo

Maciej Grabias

Jan Chorowski

Grzegorz Ciesielski

Adrian Łańcucki

Paweł Rychlikowski

Ricard Marxer

CONTRASTIVE PREDICTION STRATEGIES FOR UNSUPERVISED SEGMENTATION AND CATEGORIZATION OF PHONEMES AND WORDS

Keywords: self-supervised learning, Contrastive Predictive Coding, unsupervised phoneme segmentation, unsupervised word segmentation, phoneme classification

We identify a performance trade-off between the tasks of phoneme categorization and phoneme and word segmentation in several self-supervised learning algorithms based on Contrastive Predictive Coding (CPC). Our experiments suggest that context building networks, albeit necessary for high performance on categorization tasks, harm segmentation performance by causing a temporal shift on the learned representations. Aiming to tackle this trade-off, we take inspiration from the leading approaches on segmentation and propose multi-level Aligned CPC (mACPC). It builds on Aligned CPC (ACPC), a variant of CPC which exhibits the best performance on categorization tasks, and incorporates multi-level modeling and optimization for detection of spectral changes. Our methods improve in all tested categorization metrics and achieve state-of-the-art performance in word segmentation.

INTRODUCTION

Speech self-supervised learning (SSL) without linguistic labels is aimed at producing representations that are useful for downstream problems such as transcription, classification or understanding. The prior work focuses mainly on either automatic boundary detection of phonemes or words [START_REF] Kreuk | Self-Supervised Contrastive Learning for Unsupervised Phoneme Segmentation[END_REF][START_REF] Bhati | Segmental Contrastive Predictive Coding for Unsupervised Word Segmentation[END_REF][START_REF] Kamper | Towards unsupervised phone and word segmentation using self-supervised vector-quantized neural networks[END_REF], or learning representations which expose phonemic information [START_REF] Van Den Oord | Representation learning with contrastive predictive coding[END_REF][START_REF] Chorowski | Aligned Contrastive Predictive Coding[END_REF], and facilitate phoneme prediction with linear transformations. Even though the tasks seem related, an approach which performs well on the former may do poorly on the latter. An extreme example is an encoding that alternates between only two labels at every phone change. This representation has the full information about the boundaries, yet no information about the sequence of phonemes. On the other The authors thank the Polish National Science Center for funding under the OPUS-18 2019/35/B/ST6/04379 grant and the PlGrid consortium for computational resources. We also thank the French National Research Agency for their support through the ANR-20-CE23-0012-01 (MIM) grant. hand, we may imagine an encoding with no abrupt changes at phoneme boundaries, in which every frame maps to the correct phoneme through some unknown linear projection.

Contrastive Predicting Coding (CPC) [START_REF] Van Den Oord | Representation learning with contrastive predictive coding[END_REF] and its variants are popular methods of approaching these tasks. CPC is an SSL algorithm which extracts latent representations from sequential data by learning to predict future states of the model. An encoder g enc maps consecutive overlapping chunks of data to latent representations z, producing sequences of codes. An autoregressive model g ar is then applied to the latent representations and trained to predict M upcoming latents. The model is trained using Noise-Contrastive Estimation (NCE): the prediction p t of the latent code z t at time t must be closer to z t than to randomly sampled latent codes, termed negative samples. When applied to speech, CPC produces acoustic representations which are useful for phoneme prediction and low-resource speech recognition.

Different variations of CPC have been proposed in the literature and have shown improvements on various downstream tasks. Chorowski et al. [START_REF] Chorowski | Aligned Contrastive Predictive Coding[END_REF] presented Aligned CPC (ACPC), in which rather than producing individual predictions for each future representation, the model emits a sequence of K < M predictions which are aligned to the M upcoming representations. In this way, g ar solves a simpler task of predicting the next symbols, but not their exact timing, while g enc is incentivized to produce piece-wise constant latent codes. ACPC exhibits higher linear phone prediction accuracy and lower ABX error rates than CPC, while being slightly faster to train due to the reduced number of prediction heads.

CPC-based techniques have also been applied to unsupervised phoneme and word segmentation. Kreuk et al. [START_REF] Kreuk | Self-Supervised Contrastive Learning for Unsupervised Phoneme Segmentation[END_REF] proposed a model that omits the prediction network g ar and is instead trained to discriminate between adjacent and nonadjacent representations. The model learns to detect spectral changes in the signal and tends to produce piece-wise constant latent codes. Boundaries are obtained as peaks in cosine dissimilarity between consecutive latent representations.

Segmental CPC (SCPC) [START_REF] Bhati | Segmental Contrastive Predictive Coding for Unsupervised Word Segmentation[END_REF] improves upon [START_REF] Kreuk | Self-Supervised Contrastive Learning for Unsupervised Phoneme Segmentation[END_REF] by adding a standard CPC feature extractor with M =1 to model the signal at the level of segments of frames. A differentiable imple-arXiv:2110.15909v2 [cs.LG] 25 Feb 2022 mentation of the boundary detector used by [START_REF] Kreuk | Self-Supervised Contrastive Learning for Unsupervised Phoneme Segmentation[END_REF] is applied to the frame-level latent representations and those within boundaries are averaged to produce a sequence of segment representations that is fed as input to another feature extractor. The segment-level feature extractor is meant to operate roughly at phoneme level and act as a language model. At test time the boundary detector from [START_REF] Kreuk | Self-Supervised Contrastive Learning for Unsupervised Phoneme Segmentation[END_REF] is used at the frame-level to predict phoneme boundaries and at the segment level for word boundaries. SCPC reported state-of-the-art performance in both phone and word unsupervised segmentation.

We investigate the performance of ACPC on phoneme segmentation, and of [START_REF] Kreuk | Self-Supervised Contrastive Learning for Unsupervised Phoneme Segmentation[END_REF] and SCPC on phoneme classification accuracy and ABX. The results suggest a trade-off between segmentation and categorization performance. We then explore the variations to the standard CPC model to understand the causes of this conflict. We also propose a multi-level ACPC model aiming to obtain gains in segmentation performance similar to SCPC [START_REF] Kreuk | Self-Supervised Contrastive Learning for Unsupervised Phoneme Segmentation[END_REF], and explore the effect of multi-level modelling on phoneme classification and the ABX task. Finally, we show that including an auxiliary contrastive loss between adjacent frames as in [START_REF] Kreuk | Self-Supervised Contrastive Learning for Unsupervised Phoneme Segmentation[END_REF] in ACPC models consistently improves segmentation and categorization performance. The mACPC model has two main modules: framelevel and segment level. The frame-level module works on raw waveforms and extracts latent representations. These are processed by the boundary detector, which predicts boundaries and averages latents within those boundaries to produce segment representations. Finally, the segment-level module learns to predict higher-level features.

AUGMENTING ACPC FOR SEGMENTATION

We propose multi-level ACPC (mACPC; Fig. 1), which extends the ACPC architecture with a second ACPC feature extractor to model the signal at the level of frame segments, similarly to [START_REF] Bhati | Segmental Contrastive Predictive Coding for Unsupervised Word Segmentation[END_REF]. At the frame level, a strided convolutional encoder g enc maps the input sequence x 1 , . . . , x T to a sequence of encoded frames z 1 , . . . , z T . The encoded frames are used to determine the position of the segment boundaries. Following [START_REF] Kreuk | Self-Supervised Contrastive Learning for Unsupervised Phoneme Segmentation[END_REF], we calculate the score for placing a boundary at the position t as -sim(z t-1 , z t ), where sim(•) denotes cosine similarity. Peaks in the dissimilarity scores indicate boundaries. Frames within two consecutive boundaries are considered as segments and their constituents are averaged. We obtain the final segment representations s 1 , . . . , s J by feeding the averages to a segment-level encoder s enc . While the frame-level auto-regressive model g ar summarizes all encoded frames up to time t into a context vector c t = g ar (z ≤t ), the auto-regressive model s ar does it at the segment level c sj = s ar (s ≤j ). Finally, K and K s predictions are made at frame and segment levels conditioned on the corresponding context vectors, which are then aligned to M and M s upcoming encoded frames and segments respectively. The ACPC prediction loss, as described in [START_REF] Chorowski | Aligned Contrastive Predictive Coding[END_REF], is applied at both levels. The two prediction losses from frames and segments are summed into the total loss to be optimized.

Additionally, we also consider variations of ACPC and mACPC in which we add to their total loss the contrastive loss between adjacent representations proposed by Kreuk et al. in [START_REF] Kreuk | Self-Supervised Contrastive Learning for Unsupervised Phoneme Segmentation[END_REF] to optimize for detection of spectral changes in the signal. The loss is applied to the output of g enc .

EXPERIMENTS

We perform two phone classification evaluations: frame-wise classification, and an alignment-insensitive evaluation using Connectionist Temporal Classification (CTC) [START_REF] Graves | Connectionist temporal classification: Labelling unsegmented sequence data with recurrent neural networks[END_REF]. The classifiers are trained on the LibriSpeech train-clean-100 dataset [START_REF] Panayotov | Librispeech: An asr corpus based on public domain audio books[END_REF] for 10 epochs. For the frame-wise case, a linear classifier is optimized with a cross-entropy loss and we report accuracy. The model used for the CTC evaluation is a single-layer bidirectional LSTM network with 256 hidden units, followed by a 1D convolution with 256 filters, kernel width 8 and stride of 4, trained using the CTC loss in which emission of the blank character is forbidden to force classifying each frame as a phoneme. Performance is evaluated using Phoneme Error Rate (PER).

Phoneme segmentation experiments are run on both TIMIT [START_REF] Garofolo | Darpa timit acoustic phonetic continuous speech corpus cdrom[END_REF] and Buckeye [START_REF] Pitt | The buckeye corpus of conversational speech: labeling conventions and a test of transcriber reliability[END_REF]. Word segmentation is only run on Buckeye as in [START_REF] Bhati | Segmental Contrastive Predictive Coding for Unsupervised Word Segmentation[END_REF]. Segmentation quality was measured with precision, recall, F1-score and over-segmentation robust R-value [START_REF] Räsänen | An improved speech segmentation quality measure: the rvalue[END_REF], with a 20ms tolerance [START_REF] Kreuk | Self-Supervised Contrastive Learning for Unsupervised Phoneme Segmentation[END_REF][START_REF] Bhati | Segmental Contrastive Predictive Coding for Unsupervised Word Segmentation[END_REF].

We follow the methodology from [START_REF] Kreuk | Self-Supervised Contrastive Learning for Unsupervised Phoneme Segmentation[END_REF][START_REF] Bhati | Segmental Contrastive Predictive Coding for Unsupervised Word Segmentation[END_REF] for the train/test split and pre-processing of the corpora, and train our mod- All models read single channel raw waveforms sampled at 16kHz, chunked into sequences of 20480 samples. Encoder g enc applies five 1D convolutions with internal dimension 256 and filter widths (10; 8; 4; 4; 4). Convolutions are followed by channel-wise magnitude normalization and all but the last by ReLU activations. Convolutions are strided by (5; 4; 2; 2; 2), resulting in a 160-fold rate reduction, yielding a 256dimensional latent vector extracted every 10ms. The segment is a network with a single fully connected hidden layer of 512 units and ReLU activation. Context-building models g ar and s ar are two-layer LSTM networks [START_REF] Hochreiter | Long Short-Term Memory[END_REF] with 256 units. We use K =6, M =12, K s =2 and M s =4 for (m)ACPC models. Each prediction head accesses all past contexts through a single transformer layer [START_REF] Vaswani | Attention is all you need[END_REF] with 8 scaled dot-product attention heads with internal dimension 2048 and dropout with p = 0.1.

Our implementation is available at https://github. com/chorowski-lab/CPC_audio.

RESULTS AND DISCUSSION

Shifted predictions due to context building

Upon visual inspection of CPC and ACPC segmentations, we observed that predicted boundaries are often shifted in the same direction and by a similar amount. We hypothesize that the use of a context building network in the CPC model promotes pushing into the future the representation of the underlying signal. This would ease prediction of several steps ahead especially when the recurrent layer of the context builder is capable of exploiting the increased past context.

To test this possibility we re-evaluate the segmentation performance of the different methods by offsetting the pre- dicted boundary positions by several fixed values. Note that each offset evaluates on different amount of data due to border effects, however scores are averaged across whole utterances limiting the consequences of this difference. Figure 2 shows how ACPC and mACPC exhibit an optimal offset value at 1 frame step (-10ms), while other methods peak at 0ms as expected from predictions without misalignment issues. To ensure this effect is due to the context builder and not other changes in ACPC (or mACPC), we also run a CPC model with and without it (dotted lines). It is worth noting that the optimal offset for both of these techniques is the same for the two datasets, however further investigation is needed to know whether this value is independent from the data. This consistent offset can be considered as a hyperparameter of the model. For comparison purposes, in the following experiments we report segmentation scores at a fixed offset of -10ms for models with a context builder.

Comparative study on segmentation and classification of phonemes

Tables 1 and2 show the performance of the studied methods on phoneme segmentation and classification, respectively. Segmentation performance increases by adding to the model in [START_REF] Kreuk | Self-Supervised Contrastive Learning for Unsupervised Phoneme Segmentation[END_REF] a second CPC at the segment level (as in [START_REF] Bhati | Segmental Contrastive Predictive Coding for Unsupervised Word Segmentation[END_REF]). Interestingly ACPC [START_REF] Chorowski | Aligned Contrastive Predictive Coding[END_REF] and mACPC do not attain the same segmentation performance level despite their similarities and the offset correction. On the other hand they do achieve much better phoneme prediction rates, both frame synced (frame-wise accuracy) and through alignment (CTC PER). This points to an apparent compromise between ensuring proper boundaries and retaining phonemic information.

In order to assess which factors influence this trade-off, we perform a study in which each of the identified changes to CPC are tested * (Table 3). The one step ahead prediction used by [START_REF] Kreuk | Self-Supervised Contrastive Learning for Unsupervised Phoneme Segmentation[END_REF] and SCPC is not in itself enough to improve segmentation performance. The key aspect, as hinted in [START_REF] Kreuk | Self-Supervised Contrastive Learning for Unsupervised Phoneme Segmentation[END_REF], is the removal of the frame level context builder and the use of the encoded frames themselves as predictors.

Furthermore, the models in which we augment the ACPC loss with an auxiliary contrastive loss between adjacent representations show consistent improvements on segmentation and classification metrics, motivating its use as a method to tackle the performance trade-off. Moreover, the representations obtained by these models did not present a time shift even when using a context builder. This indicates that optimizing for detection of spectral changes penalizes representation shifting, and at least partially explains the better segmenting ability of [START_REF] Kreuk | Self-Supervised Contrastive Learning for Unsupervised Phoneme Segmentation[END_REF] and SCPC.

The ZeroSpeech ABX task

Phoneme segmentation and classification are often targeted due to their potential use in applications such as the ABX task from the ZeroSpeech challenge [START_REF] Nguyen | The zero resource speech benchmark 2021: Metrics and baselines for unsupervised spoken language modeling[END_REF], in which the objective is to match a speech example to its equivalent by choosing from two others that differ in a single phone. In this situation conserving the phonemic content is crucial since it is the discriminant factor. Results in Table 4 confirm that methods such as mACPC that excel in frame-wise accuracy and CTC PER also do so in ABX.

Integration of higher-level structure

We observe that the addition of higher level information using the second head in mACPC improves the results. SCPC showed an improvement in the case of phoneme segmentation, here we show the benefit of such strategy in phoneme discrimination with mACPC. Furthermore, it enables the detection of word boundaries using the technique from [START_REF] Bhati | Segmental Contrastive Predictive Coding for Unsupervised Word Segmentation[END_REF]. Word boundary experiment results in Table 5 indicate that * We do not report variations for the number of negative samples because they did not have a significant effect on any of the metrics We also analyse topline performance in phoneme categorization and word-segmentation of SCPC and mACPC by using ground-truth phoneme boundaries during training. For mACPC, oracle segmentations improve PER on encoded frames from 21.15 (Table 2) to 20.12 and word segmentation R-value from 47.40 (Table 5) to 49.20. This contrasts with SCPC where use of ground-truth segments marginally affects results (31.62 to 31.93 PER and 45.39 to 46.1 R-value), suggesting that the representations obtained by the contrastive loss on adjacent frames [START_REF] Kreuk | Self-Supervised Contrastive Learning for Unsupervised Phoneme Segmentation[END_REF] are insufficient for language modelling. The improved performance of mACPC when using ground-truth segmentation should motivate further work on improving estimated segmentation.

CONCLUSIONS AND FUTURE WORK

We investigate the applicability of CPC-based models to unsupervised phoneme segmentation and classification. As in [START_REF] Bhati | Segmental Contrastive Predictive Coding for Unsupervised Word Segmentation[END_REF] we propose a two-level model acting simultaneously on time synchronous frames and on variable-length segments, to capture linguistic regularities. We discover a performance compromise between phoneme segmentation and classification, and find that it stems from a roughly constant prediction shift induced by CPC's context modeling. We show that this issue can be alleviated by manually removing the offset from the representations or by using an auxiliary contrastive loss between consecutive latent representations. After accounting for the prediction shift, our model achieves competitive segmentation performance and outperforms existing approaches in phoneme classification, transcription, word boundary detection and ABX tests. Furthermore, the use of oracle phonemic alignments indicate that improvements on segment estimation may lead to even better performance in these tasks.

Fig. 1 .

 1 Fig.1. The mACPC model has two main modules: framelevel and segment level. The frame-level module works on raw waveforms and extracts latent representations. These are processed by the boundary detector, which predicts boundaries and averages latents within those boundaries to produce segment representations. Finally, the segment-level module learns to predict higher-level features.

Fig. 2 .

 2 Fig. 2. Segmentation performance for different predicted boundary shifts on TIMIT (left) and Buckeye (right). Models with context builders perform better with an offset, indicating a representation shift.

Table 1 .

 1 Phone segmentation on TIMIT (top) and Buckeye

	(bottom) test sets
	Model	Precision Recall F1 R-val
	Kreuk et al. SCPC ACPC ACPC + Kreuk et. al. loss mACPC mACPC + Kreuk et. al. loss 84.63 84.79 84.70 86.86 84.80 85.77 85.27 87.35 85.31 85.36 85.31 87.38 83.41 83.15 83.26 85.64 83.68 84.74 84.69 86.86 82.53 83.05 82.78 85.26
	Kreuk et al. SCPC ACPC ACPC + Kreuk et. al. loss mACPC mACPC + Kreuk et. al. loss 74.70 76.81 75.72 78.97 76.27 78.42 77.31 80.35 77.21 78.95 78.03 80.90 74.44 76.28 75.32 78.66 74.68 76.59 75.59 78.88 74.00 76.04 74.98 78.34

Table 2 .

 2 Phone classification on the test split of LibriSpeech train-clean-100 On z vectors On c vectors

	Model	Acc. PER Acc. PER
	Kreuk et al. SCPC ACPC	44.87 32.46 43.79 31.62 47.62 24.34 67.87 18.10 ----

ACPC + Kreuk et. al. loss 47.82 25.93 67.99 18.15 mACPC 50.98 21.15 69.97 16.91 mACPC + Kreuk et. al. loss 51.64 21.69 70.25 16.65

Table 3 .

 3 Classification and phone segmentation performance of CPC variants. Frame-wise accuracy is calculated on en-

	coded frames.
			R-value
	Model	Frame Acc. Buckeye TIMIT
	CPC, M =1 CPC, M =12, no g ar CPC, M =12	17.28 38.11 47.90	66.98 70.77 75.17 84.20 78.89 86.11

Table 4 .

 4 ABX scores on ZeroSpeech 2021 dev set. For models using context-networks the values are calculated on con-

	text vectors.
	Model	ABX within ABX across
	Kreuk et al. SCPC ACPC ACPC + Kreuk et. al. loss mACPC mACPC + Kreuk et. al. loss	10.93 20.18 5.78 5.67 5.28 5.13	19.11 16.26 7.93 7.78 7.13 6.84
	Table 5. Word segmentation on Buckeye test set
	Model	Precision Recall F1 R-val
	SCPC mACPC mACPC + Kreuk et. al. loss 40.36 30.86 34.83 47.11 36.23 32.75 34.33 45.39 42.06 30.32 35.05 47.40
	mACPC outperforms SCPC. We hypothesize that the supe-
	rior phoneme representations of mACPC improve the quality
	of the pseudo-language model.