Tristram Shandy

Daniel Thomières

When Tristram Meets Nannette: An Inquiry Into Sexual Anxiety in Laurence Sterne's

Tristram and

I would like to return to the Nannette episode in Laurence Sterne's The Life and Opinions of Tristram Shandy Gentleman. I believe that this brief chapter (Chapter 43 of Volume VII, 377-379) offers a collection of symptoms which, if we succeed in interpreting them, should help us understand what Sterne was trying to achieve in the rest of his novel. 1 I hope that my readers will grant me that the work is something of an experiment in which, through his characters, Sterne asked himself what a crisis was. To a large extent, I hope to show that asking what a crisis is what Hamlet was doing when he exclaimed that "the time is out of joint". 2 Of course, plenty of other literary characters in other historical periods have displayed reactions not too far remote from Sterne's narrator. There will be always be crises, or, perhaps, we should say that there will always be people conscious that our world is going through a crisis. What is specific in Nannette scene? Ernest Hemingway would have 1 I am thinking of Gilles Deleuze's pronouncement when he explains that writers are (like) physicians. See his Essays Critical and Clinical, especially the first chapter, "Literature and Life." Deleuze briefly gives some examples: Herman Melville's "Bartleby," Thomas Wolfe, Franz Kafka, Louis-Ferdinand Céline, etc. I believe Laurence Sterne could safely be added to them. Deleuze considers that what matters in a great book is to be found in its details. Writers want their readers to organize assemblages of singularities in a critical way in order to try to discover problems, ruptures, evolutions, and thus produce a diagnosis. Let us recall here that the word 'diagnosis' means collecting symptoms and establishing distinctions between them (dia,) and then producing a body of knowledge (gnosis) that can later be used critically in order to enhance life. Following the French philosopher, my claim is that, among other functions, literature helps us discover for ourselves new possibilities to relate to myself, others and more generally the world and society. 2 Reference is to the Norton Critical Edition of Laurence Sterne's The Life and Opinions of Tristram Shandy, Gent., ed. Howard Anderson, New York: Norton, 1980, as it is easy to find in most university libraries around the world. I am, however, aware that there are dozens of other editions and that my (benevolent) readers may possess one of these instead of the venerable Norton. Although Tristram Shandy is not the Bible, I have taken the liberty of also referring, not to chapter and verse, but to volume and chapter. declared that it is the tip of an iceberg. The logic behind it -that is to say the seven eighths that need to be reconstructed -lies in the nine volumes of Tristram Shandy. It is also to found in Sterne's perception of history. That logic is anything but linear, not because the novel is rambling, but because it is about a crisis. All of sudden, reality no longer looks as it was. It has become a problem. Worse, it has become a problem without a solution.

The scene with Nannette constitutes a sort of paradox. In a novel which enjoys the universal reputation of being more than brimming with sexual innuendoes, a man suddenly finds himself faced with a woman who seems to be inviting him. 3 I have always supposed (perhaps wrongly…) that the average reader expects some kind of love scene, not to say something more pornographic. Nothing happens. That is the paradox. Tristam (our narrator cum character) runs away… To understand why, we have to reread the nine volumes of Tristram Shandy in the hope of being able to come up with a number of hypotheses. What becomes clear is that Tristram belongs to a certain family of male characters who are confronted to the question of manhood and who do not know how to respond to it. Hamlet is a good case in point. Something is decidedly rotten in the Shandy family, and in the kingdom they inhabit too… 4 3 It will probably come as a surprise to some readers who believe that there are literally hundreds of scholarly studies on the fascinating subject of Sterne and sex that that indeed is very far from the truth. A careful study of the articles included in the usual bibliographies (MLA, Extended ASAP, Project Muse, and JSTOR among others) reveals that actually very little has been published on the question. The problem was duly raised a long time ago by Robert Alter, A.R. Towers, and especially Frank Brady. The latter offers a most useful contribution which explores "the sexual and the scatological" in Tristram Shandy. After reading Brady's paper, the average reader no longer needs to feel guilty if he (or she?) believes that a nose or some other physical organ may possibly possess a second, hidden meaning. In addition, Brady teaches us quite a few things about sexual allusions that a great many mortals are probably not yet aware of (including this modest scholar…) More specifically, my hypothesis that the narrator displays an inordinately high interest in anal sex is more than corroborated by Brady's study whose only weakness is of course that it merely consists in a list of allusions. This essay which starts from a short excerpt tries on the contrary to connect series of details and discover a logic behind them that could help explain Sterne's achievement in the whole book. In other words, I am mainly concerned with interpretation and conceptualisation, and I hope that it will be clear that the problem raised by Stene has to do with the meaning of fatherhood and what is implied by the notion of crisis. More recent articles are often general pronoucements about 18th century culture, and in them sexual matters are by and large envisioned through themes like, for instance, irony or sensibility. The detail of Sterne's novel is largely ignored. These studies mainly include: Elizabeth Kraft, Ruth Perry, Dennis W. Allen, and James Kim, to which should be added the books Laurence Sterne as Satirist by Melwyn New, and Mother Midnight by Robert A. Erickson. (One could perhaps also mention here Michael Hardin's homosexual reading which posits that the reader (male presumably) is obsessed by his penis just like most of the characters in the novel…) After reading these essays, one has sometimes the feeling that poor little Nannette repelled not only the narrator, but also Sterne's critics. Janatone was perhaps a little luckier in that her name at least is mentioned a few times in scholarly articles, probably because she reappears in A Sentimental Journey. Maybe Nannette exhibits her fate in her name. Janatone can be construed as offer (ja) followed by refusal (na). Nannette, as for her, is twice negation. In colloquial French, her name has actually long been part of the childish phrase used to refuse to do something: "No, no, Nannette," before it became the title of a musical (on Broadway!) in 1927 under the title No No Nanette (in which she loses one n.) For Sterne's narrator, it would thus seem undeniable that woman carries within herself both time and negation… 4 It could be argued that Tristram's true heirs are to be found in America. In Love and Death in the American Novel, In this respect, Leslie Fiedler argues that classic American literature was born because of what Lovelace

a year in Languedoc

The scene between Tristram and Nannette is undoubtedly a key moment of the novel (VII/43 377-379). It is part of what the narrator calls his "PLAIN STORIES." What seems to be at stake in these four pages is the way the subject encounters the other. That is precisely the main problem raised in this chapter: how do I define my identity and my desire in an interpersonal fashion? As the narrator says, the countryside which might be supposed to be empty contains more life than London! What sort of relationships will Tristram establish with the people he comes across by chance on his road? Among these, there are a great many members of the opposite sex. Strangely enough (or not strangely enough?), strictly nothing happens. Maybe, readers are the victims of romantic clichés? When Tristram meets Nannette… What do we expect? We are sure than the scene will be pornographic… The answer is that it is erotic, but definitely not graphic. Everything is hidden and no sexual rapport is possible. 5 The whole scene is consistently ambivalent. It is about sex and at the same time it is not. At the beginning, the narrator first tells us that he meets plenty of women on the road and that he compliments them… on their legs. Admittedly, he also "tempts" them [sic]. However, that temptation involves only the offer of a pinch of snuff in order to start a conversation. It follows that our problem is made up of three components: a woman's legs, the notion of temptation, and a conversation. A lot of readers will imagine (which is what eroticism is about) that the narrator is attracted by the woman's whole body, or obviously by her sexual organs. What he is interested in here, however, is her legs and her conversation. A pattern emerges: fetishism and language. In this respect, Tristram shares a basic similarity with Don Giovanni: you collect as many women as possible, but you must never seduce the same woman twice. did to Clarissa in Richardson's novel. Maybe, after all, it is not Clarissa, but Tristram Shandy that started it all… In the United States, the same type of crisis occurred when the country became industrialised and urbanized in the 1850s, or rather when a number of people became conscious that they were simultaneously part of two temporalities, a past which looked familiar and a future which didn't seem to make sense to them. Is not Tristram a cousin of Melville's Pierre, Hawthorne's Young Goodman Brown, or (as the structure only belatedly appeared after WWI in a culturally backward South) Faulkner's Quentin Compson in The Sound and the Fury? Tristram is somewhat like Hawthorne's Young Goodman Brown one century later. Brown leaves Faith, his newly married wife for adventures in the forest that promise to look literally more exciting than "her bed". He finally returns to a home that is no longer a home and he has children who do not appear to mean anything to him. Herman Melville's Pierre also leaves his fiancée Lucy to embark upon a frightening journey into nightmare away from home not long after he fainted on catching sight by accident of Lucy's virginal bed. Still later, Quentin Compson also goes away from his home in Mississippi after considering castrating himself with a razor, the way they do in China… He eventually jumps to his death in the river Charles outside Harvard.

The only difference with the Don is that Tristram doesn't try to have sex with them 6 .

The rest of the chapter follows the same logic. Its language is singularly saturated with sexual puns or connotations. The words look innocent enough, but the fact that too many of them may be considered to possess hidden pornographic connotations leads us to suspect that we are invited to produce some kind of bawdy interpretation. The young people the narrator sees are "running at the ring of pleasure" (a most innocent game in which you have to throw a stick into a hole), he gives his ass (his donkey…) "a prick," exclaiming "By saint Boogar, and all the saints at the backside of the door of paradise." Have we moved from women's legs to a serious consideration of the important question of anal sex? What is certainly worth noticing is that the perversion is purely verbal. The narrator once more is engaged in his love of wit. 7 Words is what he is interested in, not a woman's body.

Then comes Nannette. Tristram's attitude is once again ambivalent. On the one hand, as if by magic, he unties her hair. Here again, his desire is based on a synecdoche -the part for the whole8 . Hair is indeed a most traditional 6 Sterne did not need to read Søren Kierkegaard's Either/Or whose celebrated sub-part "The Diary of a Seducer" provides the ultimate compedium of all that there is to know about the logic behind Don Giovanni's desire in Mozart's opera. Kierkegaard, who most probably never heard of Tristram Shandy, opposed, just like Sterne, what he called the "ethical" posture (marriage and procreation) and the "aesthetic" posture (moments of personal pleasure and intensity). Kierkegaard knew perfectly well that these two postures cannot be reconciled (except by religious faith, a belief that the Church of England minister Laurence Sterne apparently does not entertain in his novel). 7 Howard Anderson's old article is still extremely worth reading in this respect. I have tried to develop some of his intuitions and see how they can be connected with the psychological implications of the Nannette episode. Sterne writes after Locke, and -just like David Hume -he develops in his own way a number of potentialities of British empiricism. The great invention of empiricism, as it was developed by Hume in his Enquiry Concerning Human Understanding, was not so much that ideas come from our sensations (as Locke said), but that our mind produces new operations all the time in order to connect ideas. What matters first and foremost has to do with these operations. They do not reproduce innate models. Hume's greatest contribution to philosophical thought is thus to have focused, not on sensations, but on the mental operations going on in our minds. In fact, he proved to be a revolutionary when he showed that (to quote Gilles Deleuze's own handy summary): "relations are external to their terms." It may be interesting to note that Deleuze, who is, with Henri Bergson, France's greatest empiricist, devoted his first published book in 1953 precisely to the philosophy of David Hume, Empirisme et subjectivité (translated asEmpiricism and Subjectivity). See also Deleuze's later, brief but pungent article "Hume," in François Châtelet's Histoire de la philosophie, 1972. Deleuze's presentation of what British empiricism really was about has never been clearer and more direct. Readers interested in that question can also look at the three following articles: Chinmoy Nanerjee, "Tristram Shandy and the Association of Ideas", Peter M. Briggs, "Locke's Essay and the Tentativeness of Tristram Shandy", and Duke Maskell, "Locke and Sterne, or Can Philosophy Influence Literature?" The problem, however, seems to me to lie in the elements of Tristram Shandy which are very close to Hume's breakthroughs rather than tracking down a possible influence of John Locke upon Sterne. The novelist go way beyond what Locke propounded, and of course he seizes upon a number of intuitions Locke had, but most certainly did not like. Sterne of the contrary was simply head over heels about them… I am thinking principally of wit and of the notion of the association of ideas. component of fetishism in many civilizations9 . On the other hand, his gaze is at the same time attracted and repelled by a metonymy, the slit in Nannette's petticoat. Metonymy or synecdoche? Of course, a great many readers will jump at the conclusion that the slit is a synecdoche, that is that it symbolically stands for an essential part of the young woman's body. It is as if her vagina was hidden and visible at the same time. The problem is, however, slightly more complex: the slit is undecidable. One is here tempted to ask ourselves whether the young woman belongs to an old tradition of English heroines which seems to have been started by Shakespeare's Sonnets. The fair-haired woman is a man's fantasy, whereas the dark-haired woman -like Nannette ("dark chestnut") -fully belongs to reality. Clearly, for Tristram, a woman with a body is not acceptable. Some deep-seated fear is awakened in his mind. After, a brief dance, he runs away, going "straightforwards, without digressions or parenthesis, in my uncle Toby's amours." Has the danger for Tristram's narcissism been too strong? For the first and only time in The Life and Opinions of Tristram Shandy, the narrator gives up the pleasures of digressions and chooses to follow a straight line.

The passage is important as it reveals a structure of desire. It shows precisely how perversion works, without telling us anything about Nannette. Nothing objectively suggests that she might have been sexually attracted by Tristram. Apparently, she is a young peasant girl simply enjoying herself after her day's work. The only textual detail mentioned in this respect concerns "a spark of amity" for the narrator. The problem raised by the slit is Tristram's problem and Tristram's only. "Nannette cared not for it." Nothing more. Besides, it is important not to forget that there is another couple present: a brother and her sister. Shall we assume that, for these young peasants, the whole episode is entirely innocent? The young man plays his flute. Well, in some cases, a nose is a nose… (Cf. the narrator's warning in his tentative "Chapter on Whiskers", V/1, 240-243). Here, a flute is a flute… In other words, everything is a question of point of view. For the Languedocian teenager and his sister, it is simply a flute. For the narrator, it is not a penis, but it could be one… The problem has nothing to do with anatomy, but with words and modal verbs.

The same could said of the "prick" mentioned above. The narrator speaks of the women he meets and associates them with a mulberry-tree. Going round it, as in the children's game? He speaks immediately after of the simplicity of the Languedocian dress and its plaits poets used to sing about "in better days" Who would dream of looking up a Languedocian skirt? (The suggestion is the narrator's…) Certainly not a poet. Virgil forbid! To put it differently, if someone is being seduced, it is the reader… Well, not all readers are poets of old. Some of us are just plain lechers... The passage is thus important in that it reveals what today we would call Tristram's unconscious. The narrator is systematically represented as a split self. Symbolically, before accosting Nannette, he "kicks off one boot into this ditch, and t'other into that." At the same time, he rebukes his mule who, curiously enough, is put off by the young peasant girl… Are we supposed to remember that, for Tristram's father, the word "ass" refers to a person's body? Nannette paralyses Tristram's unconscious. The narrator retorts to his mule, "'Tis very well, sir, said I -I never will argue a point with one of your family, as long as I live." We dutifully note that Walter spoke of an ass. We learned, however, earlier that his son's ass is actually a mule, by definition born of an ass and a mare. Mules are sterile. What "family" was then the narrator speaking of when he addressed the poor animal? The question of fatherhood is indirectly introduced. Its importance will increase.

The symptom is here. Nannette has a body. She is a body, the slit, the possibility of genital sexuality. To some men at certain periods of their lives, the body of women is a dark, unknown territory, which threatens to rob them of their identity and to carry them into relationships they won't be able to control. In addition, and perhaps foremost in Tristram's case, women are irretrievably linked to time. Tristram is running away from time and death. If he stops and stays with Nannette, which would be a fantasy since nothing suggests that she requires more than a dancing partner, he knows very well that time and death will immediately catch up with him. Unconsciously, Tristram understands that woman forces you to become part of two systems of differences: a vertical one, which says that you have a father and that you will be a father in your turn, and a horizontal one, which says that it takes a man and a woman to achieve procreation. (There is no pun intended here in the adjective "horizontal." We are most certainly not speaking of pleasure, the point of view here is not that of the individual, but that of society that will reproduce itself whether its members experience sexual pleasure or not in the process). Tristram's unconscious cannot accept either the sexual difference nor the difference between generations.

The obsession is systematic. In parts of his novel, Tristram expresses it in a very moving way when he evokes Jenny. Who is Jenny? Answers vary. Mistress? Lady friend? Muse? We will say, she is the Woman. He needs her, he possibly invents her in order to talk of Woman. He thus explain: "I will not argue the matter: Time wastes too fast: every letter I trace tells me with what rapidity Life follows my pen: the days and hours of it, more precious, my dear Jenny! than the rubies about thy neck, are flying over our heads like light clouds of a windy day, never to return more every thing presses on whilst thou art twisting that lock, see! it grows grey; and every time I kiss thy hand to bid adieu, and every absence which follows it, are preludes to that eternal separation which we are shortly to make." (IX/8, 430). For Laurence Sterne, one conclusion at least is perfectly unambiguous: woman is time.

The narrator speaks in virtually the same terms of the young Janatone, the inn-keeper's daughter at Montreuil, near Calais, in Northern France (VII/9, 343-344). This young woman teases the narrator with the stocking she is threading. Or does she? The occupation is fairly innocent -and for her probably necessary. Maybe the narrator is imagining things, or would like us to imagine things. He tells us that he is tempted to draw her in "the wettest of draperies." Then, he departs in a hurry without an explanation. Strangely enough (or logically?), the following chapter immediately broaches the subject of death that he is trying to shake off his scent. In the purest tradition of fetishism, it would appear that, for Tristram, Janatone is synonymous with a leg, or a stocking. Synecdoche or metonymy? In addition, like Nannette, whom she foreshadows, she hides and reveals -at least in the narrator's fantasypart of her sexual organs, viz. her breasts "in the wettest drapery." Nothing could be a clearer symbol of both sex and procreation than breasts… Finally, Tristram decides that he will not try to paint Janatone any further. He would very much prefer to describe the local church. It is made of stone and pretty impervious to the passage of time. On the contrary, as he says of that poor young woman, "thou carriest the principle of change within thy frame."

For Tristram, desire functions thanks to figures of speech. Women (and they are always French as if sexuality only became a problem once you have crossed the Channel…) are first seen through synecdoches and metonymies. Janatone is a stocking and a pair of breasts. Nannette is a tress of hair and a "slit"… In all these examples, the narrator is attracted and at the same time he is repelled. The movement freezes immediately (if I may be permitted to use a cinematographic simile), and these young women are then seen as metaphors. What is the logic at work? Why two (French) women? It is tempting to suggest that they offer the two representations of what a woman can be in Tristram's unconscious. The narrator dryly predicts that Janatone will successively become "a pumpkin" or "a flower," and then probably "a hussy." Nannette remains a "nymph" at the end of the scene. Pumpkins and flowers are undeniably metaphors. Are nymphs and hussies metaphors too? There is no reference to another species. Nymphs and hussies are women. Each stands for one pole of what a woman may represent for the narrator: she may be a body that is dirty and liable to defile him, or she may stop being a human being and turn into some sort of mythical creature that will take him to some Golden Age outside time.

Maybe we should return to the beginning of the "PLAIN STORIES" episode (VII/43). Laurence Sterne explains with perfect clarity the very special and defensive relationship he establishes between words and sex. "How far my pen has been fatigued like that of other travellers, in this journey of it, over so barren a track -the world must judge -but the traces of it, which are now all set o'vibrating together this moment, tell me 'tis the most fruitful and busy period of my life." Is the pen some sort of phallic symbol? Whatever the answer to that question, the pen is exhausted and the landscape will remain barren. Whether by choice or necessity, the narrator eschews sexual intercourse and procreation, that is to say the fundamental Law of human societies. On the other hand (no pun intended, it goes without saying…), the pen produces (sexual?) vibrations, words convey meaning and excitement, they connect with each other. In so doing, the narrator invents his own parallel world and of course his own personal law. Such is the basic structure of fetishism. I know what reality is and is not, yet I prefer to believe in my own mental constructions and I derive pleasure only from them. 10 The structure is once again ambivalent. It is highly likely that for Sterne it is bound up with the opposition between wit and judgment, an opposition he discovered in The Essay Concerning Human Understanding 11 . Sterne's opinion on the subject is very clearly put forward in the novel's "PREFACE" (which, as everyone knows, is placed chapter 20 right in the middle of Book III…) The author insists that both of these two operations are necessary, just like "the two knobbs […] upon the back of this self same chair on which I am sitting." Our problem -or rather Sterne's problem -is unavoidable. As all readers of the novel know perfectly well, Tristram, Sterne's narrator and character, prefers wit to judgment… Yet, the Preface insists, "they are made and fitted to go together"… (III/20, 146).

There would seem that the narrator has realized that he has reached a crisis. The crisis signifies an unbridgeable dissociation. It is not the dissociation 10 Sigmund Freud analysed the notion in his famous 1927 article on fetishism. One of the reasons why Freud devotes so much attention to fetishism is that its structure provides an abstract model enabling us to understand all perversions, and more particularly the role the subject's attitude towards society's Law and its two systems of differences (between sexes and between generations) plays in it. 11 In his Essay Concerning Human Understanding (Book II/11/2), John Locke, who unhesitatingly prefers judgment to wit, says that judgment "separating carefully, one from another, ideas wherein can be found the least difference, thereby to avoid being misled by similitude, and by affinity to take one thing for another" whereas wit as "lying most in the assemblage of ideas, and putting those together with quickness and variety, wherein can be found any resemblance or congruity, thereby to make up pleasant pictures and agreeable visions in the fancy". of sensibility T. S. Eliot so famously liked to talk about. It is a much more essential rift, as if the connection between wit and judgment had been lost, as if it had always been lost. When we become aware of the division, of the absence of one of the knobs, the crisis becomes visible, the time looks "out of joint" to us, and the world suddenly appears "ridiculous," as Sterne puts it. "Well, 'tis as miserable a sight as a sow with one ear." (ibid.)

Later, much later, Sigmund Freud will explain to us that perversion is the subject's ultimate defense against madness: Sterne had already guessed that much. There are at bottom three positions, and only three: i) sanity, psychological balance, social integration, procreation and the reproduction of society, a position most people inhabit. ii) madness and death, which is always a danger in the world of Tristram Shandy, just as it was in that ofHamlet. iii) perversion and wit, and in Tristram's case finding refuge in language in order to trying to ward off death and the horror of it. In his remarks on wit and judgment, Locke was perfectly clear. Judgment duplicates reality. (That is an essential component of the first conception of empiricism: knowledge derives from our senses). Sterne knows, however, that you cannot reproduce reality, and more specifically that you cannot always and only be a husband and a father. Wit, as for it, implies mental operations not necessarily connected with the world outside our minds, or for that matter with innate, immortal models. (That is the second conception of empiricism: knowledge is produced through new, original relationships constructed by our mind). Of course, these operations provide us with a lot of (selfish?) pleasure. With Sterne, perversion is always a matter of wit and language. And, with his famous endless sexual innuendoes, it has been giving readers a fair amount of personal pleasure for about two centuries and a half. 12 The Nannette episode is without any doubt a most fascinating passage. Most of it reads like a dream sequence. Causal links between actions in particular are conspicuously absent. How is that young woman's tress undone? Things appear and disappear, and…, and…, and… Is this vision a temptation? The fleeting temptation of normality? The temptation of a world which no longer exists, a world in which the dissociation between pleasure and society, wit and judgment had not yet taken place. It is certain that the narrator depicts some sort of Golden Age in the South of France, a pastoral universe such as the poets "in better days" would have painted. Nymphs and swains do not need to work, they play music and dance. Disease (the prevalent semantic field of Sterne's novel) is here completely absent. It is important to note too that, in the narrator's imagination, these four pages abound with circles: the mulberry tree, the ring of pleasure, the dance -a "roundelay," of course -with Nannette which lasts "seven years" (a most symbolic hyperbole and a most symbolic figure, especially if we believe that, in a cyclical conception of time, life starts again, not perhaps after the seventh year, but after the seventh day?). The narrator feels the temptation: "Why could I not live and end my days thus? Just disposer of our joys and sorrows, cried I, why could not a man sit down in the lap of content here -and dance, and sing, and say his prayers, and go to heaven with this nut brown maid?" The fantasy is as old as the world. The earth is a loving mother. On the other hand, happiness means enjoying pure and innocent relationships with a pretty young woman… It is almost a cliché… Womb and/or heaven: has Sterne rediscovered the oldest dream of mankind: regression as escape?

Tristram is of course having a dream, and only a dream. The dancer are "carousing," that is to say dancing in a carrousel (if one stretches the etymology a little to add one additional circle to the text), or indulging in a bacchic orgy of sex and alcohol (to respect the correct etymology)?

The slit in Nannette's petticoat is still visible when the narrator runs away.

son but not lover.

Scattered throughout the nine volumes of the novel, there are a number of clues that will help us understand a little better Tristram's dysfunctioning in the Nannette episode. Why does he find it impossible to be a lover? The answer probably lies with the issue of fatherhood which is one of the key notions interrogated in the book. The problem hinges around Tristram's perception of his father whom he represents as a failed father. As is well known, out of sheer laziness, Mr. Shandy neglects his own coat of arms. His coach displays a bend sinister on its door even though the family is perfectly legitimate (IV/25). That was originally due to a mistake of the painter. A coat of arms is of course meant to be a sign whose meaning is manhood and aristocratic legitimacy. Your arms represent your identity in the eyes of others. Why on earth doesn't Mr. Shandy act? What is certain is that symbolically the Shandy family is a family in which the Name of Father 13 is no longer something children have to accept and cling to. Tristram appears to be a genuine bastard who will never learn the name of his real father. 14 Home disappears and for him life becomes synonymous with exile. Should we conclude that this rupture is ultimately caused by the weakness of a father who lives in the past and finds his only pleasure in quoting and repeating scraps of speeches made by famous ancient philosophers. Paradoxically, he keeps harping on traditional values, but he never puts them into practise. In other words, what Sterne seems to be telling us is that what is important is not what you say or think, but what you do. It is not your values, but your actions. Mr. Shandy never acts. The most he can do is curse the notorious Aunt Dinah. The aunt is part of the pattern the novel suggests: men talk, women act (and are associated to life and procreation). Mrs. Shandy, for instance, is presented as a proper 18 th century wife. She never asks questions, except once… in book I chapter 1 with the consequences one knows. She probably had a lover, she also looked after poor Tristram after his mishap with the sash window when her husband only launched into lofty pseudo philosophical speeches. Didn't Aunt Dinah do more or less the same when she slept with her coachman, and later married him after giving birth to their child? She certainly was concerned with life, pleasure and child-bearing. All Mr. Shandy could do was curse her at regular intervals for betraying her aristocratic lineage and defiling the Name of the Father. Certainly, Aunt Dinah is to be associated with one of the cracks that eventually destroyed the House of Shandy.

Apparently, the Shandy family has been unable to maintain a balance between what we might conveniently call the father's side and the mother's side. 15 The father preaches a complete negation of the body and the passions. His only refuge is language, preferably empty words out of touch with reality. 16 The mother, as for her, is conscious of the importance of sex, life and fertility. Of course, she is not allowed to express herself. How could their child find any 14 Is it necessary to recall that the beginning of the novel (I/ 1 to 4) lists a series of details that would indicate that materially Mr. Shandy cannot be Tristram's biological father? It is necessary to look very closely at the dates mentioned. In the two previous months preceding Tristram's conception, the two spouses could not have their monthly intercourse as Mr. Shandy was suffering from sciatica. Tristram, who was officially conceived on the first Sunday of March 1718, was born eight months later on November 5, "which to the aera fixed on, was as near nine kalendar months as any husband could in reason have expected." (I/5). 15 That question has received a number of very convincing studies. No-one now doubts the fact that Sterne was questioning (in his own way of course and with his own vocabulary) what we could call today phallocentrismwhich is made to especially ridiculous in Walter Shandy's most ineffective actions and reactions. On the other hand, the mother seems to stand for values which are on the side of life, love, and caring. That point is convincingly shown by Leigh A. Ehlers,Ruth Faurot,Juliet McMasters,and Paula Loscocco,together with Ralph Flores' book. 16 An extremely explicit passage concerning the father describes him as speaking of an idea of his "as notable and curious a dissertation as ever was engendered in the womb of speculation; -it was some months before my father could get an opportunity to be safely deliver'd of it." (II/7, 73). The metaphor recurs time and again in Tristram Shandy in connection with Walter. Such is his view of "engendering." We can thus see that the House of Shandy is the seat of two pregnancies: the mother's and the father's. The latter never needed a woman. Men can conceive on their own. An old immemorial (male) dream has come true. sort of stability to build his identity? 17 Tristram is thus characterized by an inability to connect the law and his desires. He is never supported by the Name of the Father, which certainly explains why he doesn't believe in his father and why he is constantly making him look ridiculous and inefficient. It is as if he did not have a father. It also looks as if he could not be a father himself. The last autobiographical passage of the novel (VII/43) ends with an alternative: Viva la Joia! versus Fidon la Tristessa! These Languedoc peasants surrounding Nannette enjoy life and its pleasures with complete innocence. Strangely, Tristram doesn't stay with them. He runs away as quickly as he can. His name is Tristram and his fate is tristesse… (That is to say something sinister, as the Latin etymology implies. He will never sit at the right hand of God. Like Cain, he will roam the earth until the day of his death). In addition, as Tristram is unable to effect the union of his desire and the Law, he can only enjoy pleasures that conform to his own private law. It is as if, long before Sigmund Freud, Laurence Sterne had discovered the aetiology of perversion. Unquestionably, the male Shandys -Tristram, his father and his uncle -cut a most strange figure in the 18th century. They steadfastly ignore sexual intercourse and procreation. For them, sex is mainly something that has to do with language and wit (at least for Mr. Shandy and his son). Do we need to remind ourselves that one of the key lessons a man of the world like Walter Shandy teaches (twice!) his brother Toby (III/31, 158) is that a woman possesses two sides, or rather two "crevices?" Which is the good one? Why this obsession for sodomy, which in fact is an obsession for the idea of sodomy? As far as Tristram is concerned, perversion seems to be a problem of fetishism. In the key scene with Nannette in France, the question is thus: the hair or the skirt? And, of course, the problem with the skirt is that there is a slit in it… A convenient way of describing the relationships between sexes in Tristram Shandy could be to borrow that famous pronouncement that the French psycho-analyst Jacques Lacan kept repeating ad nauseam: "Il n'y a pas 17 To a large extent, his novel is an attempt at answering a most crucial question: what is a couple? In it, couples in fact constitute a sort of formal system. It all starts with the preparations for Mrs. Shandy's confinement. Literally, there are two levels. We should in fact speak of the two floors (stories?) of the house: three men downstairs (Walter, Toby, and Dr. Slop) and three women above (Mrs. Shandy, the maid Susanna, and the midwife). These two antagonistic worlds have nothing in common. More generally, a most extraordinary characteristic of Sterne's novel in that there are no genuine heterosexual couples in it. The real couples are male. One is made up of the father and the uncle. It should never be forgotten that it is Uncle Toby who suggests to his brother to draw up the very constraining marriage contract. Understand that women's bodies are not to be trusted… In addition, the Uncle admittedly may seem to be constantly criticizing his brother's follies and 'hypotheses,' whistling "Lilliburlero" in order not to be obliged to listen to them, but in key moments he unobtrusively takes his brother's hand behind his armchair. Male solidarity never fails. The other couple is of course that of master and servant, Toby and Trim (T & T?) They share the same values. In this respect, there are few examples of male bonding as explicit as the scene in which T. and T. stand together outside the door of the Widow Wadman's cottage (IX/4, 425-426). de rapport sexuel"18 . Will we also say that there is no sexual rapport? In fact, Sterne is a hundred times more pessimistic than the French psychoanalyst. Lacan never intended to say that there is no sexuality. There are of course bodies connecting and interpenetrating each other. What he meant was that there is no rapport between genders, and more specifically that men and women will never communicate, let alone discover some sort of communion in the sex act. It is as if they were not on the same wave length (to use a trite 20th century phrase) when their bodies touch and give them sexual pleasure. The idea that the two partners see the same things or images at the same time is a myth, like for instance that of the androgyne in Plato's Symposium whose two halves could be reunited if only one could find the right partner. Individuals are isolated and exile is their inexorable fate away from a home that no longer exists and that perhaps never truly was a home. Do we need to add that love is an empty word? Did such a thing ever exist outside cheap 19 th century popular novels and very optimistic novels from the first half of the 18 th century? That is not all. There is something far worse in Tristram Shandy. Even sex doesn't exist… For the men in the novel at least, sexual intercourse never ever succeeds. That indeed could be a general law which we might deduce from the book. One of the consequences of that failure is that society will no longer be able to reproduce itself. Such is the crux of the crisis: people no longer believe in society.

Interestingly enough, when Sterne writes about his male characters, there is always something that remains indecidable. Are they sexually impotent? The question is repeatedly asked in relation to Uncle Toby. The father is another case in point. It seems clear that Tristram is not his biological son. What about Bobby? We will never know. The only thing that seems to be certain is that the Shandy bull is impotent, which constitutes a bit of a problem in a story that on its last page claims to be a "cock and bull" story... In Tristram Shandy, they shoot cocks and bulls, don't they? And when a bull is no longer a symbol, a man is no longer a man. Perhaps, one of the central objectives Sterne probably had in writing his book becomes clearer: what is that anxiety surrounding sexuality and all that that notion implies?

A consequence of that is that Tristram Shandy can be read as a long collection of instances of coituses interruptus. Things start at the beginning when Mrs. Shandy asks her famous question. As if she wanted to destabilize her husband so that they would not go through with their monthly duty? Then examples accumulate. Maybe we should not include the mad Maria of Book IX (445). It is, however, true that she became mad because she was prevented from marrying the man she wanted. Uncle Toby helps Le Fever, a dying soldier, who lost his wife one night when he was having sex with her… (VI/7, 297) The Roman General Cornelius Gallus suffered the same misadventure, except that it was not his wife, but he who died (V/4, 250). Later, in France, the Shandy family hears the story of two lovers separated by "cruel parents, and by still more cruel destiny," Amanda and Amandus. When they were at long last reunited, they both fell dead… (VII/31, 365). Lastly, Book IV begins with the long tale of Julia and Diego who finally become reconciled in Lyons after a long exile away from each other. What can they possibly do when they meet again? They stare into each other's eyes, but if they look up, their chins clash, and when they look down, so do their foreheads… (IV/1, 198). Their eyes try to reach some kind of communion, but their bodies won't allow it. This technical (and symbolic) problem is of course caused by Diego's nose which is inordinately long. Julia originally went away because she could bring herself to believe that that nose was real. She thus brought about the crisis. (A nose is a nose, the narrator insists. No-one of course ever imagined it could be a metaphor for another bodily organ… Bis repetitam… Cf. V/1, 243). Crises are always brought about by a lack of trust, an inability to believe and build a relationship. It is the crisis which renders love impossible. And in Sterne's universe, the crisis is so severe that even sexual intercourse is impossible. Would Trim then be the exception that confirms the rule? He admittedly does not belong to the gentry, and consequently he does not have to follow aristocratic principles such as starting a family and perpetuating his name. In any case, he certainly does not start a family with Bridget, and, in his first sexual adventure in Belgium, the Béguine nun's hand seems to stop short of his groin. Always the groin…

the time is out of joint

The Nannette episode is a crisis, which is why Tristram's actions and motivations do not make sense. The scene is a symptom. Sterne writes about an individual. He also writes about a society. All historical periods have their times of crisis. Not everybody is affected, but some individuals are. Why them and not the rest of society? It is literally impossible to explain. As a matter of fact, it would seem that Sterne tries to represent what is impossible to explain. It is as if some individuals were able to ask these questions because they are dimly conscious of fissures in the world. Things no longer appear to fit. Time no longer is seen as running smoothly. These individuals begin to embody the crisis. From an etymological point of point, the Greek "krinein" means a turning point in a disease. Nothing will be the same ever after. More precisely, and as a consequence, the word points to the fact that you can now discern, distinguish, separate (that is the meaning of the word) two things, two levels, and of course two temporalities. Writing about a crisis is writing critically, a word that shares the same root as crisis. A crisis always implies that it is no longer possible to connect. The fissures in society and in people's minds take hold of time and produces discontinuities. Hamlet is of course the most famous example of that state of anxiety. Tristram Shandy is not far behind him.

The problem is probably linked to a wound. In its own way, the wound appears as a primal cause. And yet, in itself it is nothing, it is a mere accident, a chance happening. Let us think of Uncle Toby's wound: a rock that flew when a wall was shattered by a cannon ball at the battle of Namur. Yet the wound reverberates throughout the novel. It is exceedingly contagious, not in a medical sense, but symbolically. The accident that cannot be explained was at first physical. It then became mental. We could perhaps suggest that it is in the nature of a 'crack-up.' 19 A fissure is slowly bringing about the fall the House of Shandy. The family is sick, as is probably the whole society too. And apparently, as a consequence, poor Tristram is regularly wounded: his nose is smashed when he is born, part of his penis (which part? how much? et cetera and et cetera…) is severed by a sash window, his lungs are consumptive, and he appears to be sexually impotent. (Jenny, his lady-friend, is very understanding in that respect. Cf. VII/29, 363). Even the name intended for him suffers a blow when he is christened Tristram instead of Trismegistus (the Greek equivalent of the Egyptian Thoth, the God of Truth, who incidentally also invented writing) 20 . The name and the penis… They are placed exactly on the same level. It is a sort of curse. These people will not inherit a name, only impotence and the wound. 19 Our lives are always caught in processes of becoming. We are not necessarily conscious of it, but we are changing all the time, whether we like it or not. What happens when you become conscious of change? In 1936, the American novelist Francis Scott Fitzgerald relates what that mental event represented for him in a brief essay, The Crack-up. What were the causes of the 'crack-up'? In fact, in his case, there are so many of them that they become irrelevant: alcoholism and the deterioration of his body, the economic crisis of the 30s, etc. What matters is that a series of tiny fissures (meaningless in themselves) end up one day producing a rupture, that is to say an event situated in my consciousness. There are then two possibilities open to me. Either I ignore the change and go on living (not a very good word… surviving?) in a fossilized manner (like Toby or Walter in Sterne's book), or I cross the frontier, I develop a new identity, I invest new territories, I run away in another direction. For it undeniably will have to be a flight away from my former certainties which have suddenly proved to be illusions. (Gilles Deleuze and Felix Guattari analyse Fitzgerald's essay in Chapter VIII of Mille Plateaux. Cf. Capitalisme et schizophrénie 2 (Engl. transl., A Thousand Plateaus: Capitalism and Schizophrenia.) 20 Some of these ideas (you write after a/the wound) are alluded to, but not developed the same way, in Ross King, "Tristram Shandy and the Wound of Language." I fully agree with King that words, and more generally, discourse will never bridge the gaps that I suddenly find yawning in my life and in the world at large. Dennis W. Allen in his paper on "Sexuality/Textuality" broadly offers the same conclusion when he studies the relationship between language and reality in Sterne's book.

Perhaps, we should say it in more philosophical terms: they know that they will never be complete. Only the mythical Trismegistus was complete.

You write because of the wound, you feel a compulsion to make sense of it. Because of it, you suddenly possess a heightened perception of all these small things which now don't seem to be fulfilling their usual role in society. For instance, Sterne was confronted with an almost imperceptible socio-economic evolution. He obviously could not name it. The phrase 'Industrial Revolution' only appeared in the 1840s under the pen of Friedrich Engels, then later of Arnold Toynbee. Yet, Mr. Shandy is a small, impoverished country squire lost somewhere in the middle of Yorkshire who simply somehow knows that he needs to enclose the common known as Ox-Moor (IV/31, 232) in order to exploit it… The Industrial Revolution has begun. Mr Shandy is the man who started it. Laurence Sterne did not know the phrase, but he shows its symptoms to us and connects them to a number of personal and social problems. For Mr. Shandy is like for his son, things have changed for him, they no longer connect, it is as if they had been displaced. I offer that maybe we still read Tristram Shandy today because in our way we too feel that our relationship to time has become problematic, that our identity is a problem and not a certainty, and that simply "the times, they are changing…" and so are we.

As for Tristram, it would seem that for us time is no longer was a colorless medium. It has become a problem, which means that Tristram doesn't live in any sort of regular chronological temporality. His minds keeps constructing connections between the future (into which he is literally running away in an attempt to escape the hand of death) and the past (into which he plunges in an endless quest to try and seize his origin). He is virtually never in the present... Walter Shandy, his father, is a failure. Elizabeth Shandy, née Mollineux, chooses resistance in her own unassuming manner. Tristram, as for him, tries to escape -as if exile was now the fate of modern man.

The problem can perhaps be briefly explained by means of a well-known example. To put it in 18th century terms, Tristram Shandy is not Tom Jones. The explanation is admittedly simplistic, but it points to an opposition which is essential if one wants to understand the logic at work in the Nannette episode. Sterne doesn't believe in the stability of reality. For him, it is most unlikely that self or world were given once and for all. Tom Jones on the contrary possesses an essence. As a matter of fact, Fielding's novel relates the discovery of that essence. Its hero perceives -correctly or not -situations, obstacles, and then he reacts to them, and thus acts. What matters is always what is achieved next. Indeed, the plot of the novel lists a series of items Tom lacks, and, at the end of the book, he is in full possession of his rightful name, identity, house, fortune, etc. He also enjoys social recognition and of course he has gained a wife, love, and happiness. It also goes without saying that his children will perpetuate his name. He will have played his allotted "normal" role in the reproduction of society. Tristam reaches none of these things at the end of Sterne's novel. Indeed, at least on one point, the conclusion of Tristram Shandy is perfectly clear: Tristram is a problem. He never understands the present situation. He never really acts. The only possibility for him is to keep running away. We don't even know where he physically is, apart from the fact that he has been given some sort of hospitality near Toulouse in the South of France where he is in the course of writing volume VII of his book. We only know that he is (still) alive. Barely… He no longer has a home. Exile is the only world the adult Tristram knows. Sterne unquestionably refuses to write a novel which describes the discovery of a hidden truth. For him, neither our bodies, nor our identity are stable. The same is true of space, objects, and more generally of society and history. If asked, we may suppose that Hume would explain that Tom Jones relies on habits. He possesses an intuitive advance knowledge of what he has to connect in order to achieve a result. Tristram Shandy just doesn't know what comes next. His life cannot proceed by means of sensor-motor mechanisms as his perception of the world has become problematic. In fact, he rarely looks towards the future. When he does, it is to try to ward off death. On the contrary, he plunges into the past. He does so in a completely non-teleological manner, never conscious of what he is going to find -if anything…

In his case, plunging into the past means embarking upon an ending process of exile. The scene with Nannette is in fact Tristram's least appearance as a character. The narrator will continue to write the last two volumes of the novel, but it would seem that the character cannot go any further. Tristram vanishes when he is faced with the possibility of sexual intercourse and its consequence, procreation. It is of course only a possibility. It is likely that Nannette's invitation has nothing amorous about it, but the protagonist's unconscious (the hidden part of the iceberg) conjures up a terrible anxiety. Joia vs Tristessa? There are times when there are forces in you that are stronger than your mind. Nannette's slit spells out tristessa in Tristram's mind.

How can we distinguish between these notions? There are in fact three of them. A tradition attributes the following -possibly apocryphal -definitions to Jean-Paul Sartre. Eroticism refers to the photo of a beautiful woman in her bathing suit. Pornography refers to the photo of the same beautiful woman without her bathing suit. Obscenity refers to a photo of a piece of meat on a butchers's stall.

Curiously enough, British empiricism is historically based on a similar system. In his Enquiry Concerning Human Understanding, David Hume explains that there are basically three mental operations: cause, contiguity (metonymy and also, one supposes, synecdoche?) and resemblance (metaphor?).

Do we need to mention these Muslim women who hide their hair behind scarves? Closer to us, in Nathaniel Hawthorne's The Scarlet Letter, Hester Prynne removes her grey cap in the wilderness of the forest and for a very brief moment recovers her feminity. At the same period too, Charles Baudelaire wrote one of his most erotic poems, "La Chevelure," in which that specific part of his mistress's body hides the whole universe which is itself a metaphor standing for another whole, that is the beloved mistress…

Sigmund Freud said basically the same thing: wit is something you share with your listeners or readers, these being males usually (which doesn't mean that women cannot enjoy it, and indeed a lot of them seem to derive a lot of pleasure from that peculiar form of humour which strangely enough is fundamentally directed against them.) Freud repeatedly explained that wit implies (mentally) "undressing" a woman. Do we need to add that most men find the activity extremely amusing, even if they won't acknowledge it publicly? See Sigmund Freud's Wit and its Relation to the Unconscious.

The concept of the Name of the Father is borrowed from French psychoanalyst Jacques Lacan. Lacan kept returning to his "Nom du père" all along his life in an attempt to develop all its implications. Its first official appearance seems to have been in his Seminar devoted to psychoses("Les Psychoses," 1956[START_REF] Towers | Sterne's Cock and Bull Story[END_REF].

"Il n'y a pas de rapport sexuel". As with the Name of the Father, Jacques Lacan all along his life never stopped analysing this formula. Readers interested in its implications and developments are advised to turn to the published version of his Seminar XX, Séminaire XX: "Encore"(1973)(1974)(1975), pp. 131-132. Lacan adds by way of explanation: "Le rapport sexuel est ce qui ne cesse pas de ne pas s'écrire." (Sexual rapport is what which never stops not writing itself.) There is little doubt that Laurence Sterne would have heartily approved: he literally never stopped writing about sexual relationships in order to tell us that no such thing will ever take place.


Guillaume Renton
email: guillaume.renton@univ-rouen.fr

Pierre Héroux

Sébastien Adam

Benoit Gaüzère

Graph Neural Network for Symbol Detection on Document Images

Keywords: Graph Neural Network, Graphs, Floorplans

In this paper, we propose a new method to simultaneously detect and classify symbols in floorplan images. This method relies on the very recent developments of Graph Neural Networks (GNN). In the proposed approach, floorplan images are first converted into Region Adjacency Graphs (RAGs). Within those graphs, each node corresponds to a white region in the original image, and each edge indicates an adjacency relationship between two regions encoded by incident nodes. Nodes are attributed using Zernike moments, and edges are characterised using the distance between centers of gravity of connected components. Then, graphs are fed to a dedicated neural network which has been learned to classify the nodes of unknown graphs using both node attributes and topology. The method is evaluated on the ILPIso dataset and obtains very promising results. These results show the interest of using graphs for such a task, especially when input data are noisy.

I. INTRODUCTION

In pattern recognition community, most of existing approaches embed images to well-suited euclidean spaces to profit from efficient pattern recognition methods existing. These methods use the numerous mathematical properties associated to euclidean spaces, which allow to solve complex and challenging problems. However, despite euclidean spaces can encode numerical data, they fail to encode all the available information when the data include some structural information such as molecular compounds, networks, complex patterns, etc.

A nice and efficient way to encode such structural information is to use graphs. A graph G is defined as a pair G = (V, E). The set of nodes v i ∈ V defines a set of elements which are connected or not through the set of edges E ∈ V × V . Two elements are said to be connected if there exists an edge (v i , v j ) ∈ E. This set of connections is used to define the neighbourhood N vi of each node v i . This neighbourhood corresponds to all nodes connected to v i , ie. v j ∈ N vi ⇔ (v i , v j ) ∈ E. Note that we talk here about undirected graphs, where edges have no direction. This leads to (v i , v j ) ∈ E ⇔ (v j , v i ) ∈ E. Nodes and edges can carry there own information. This information is carried out by a node labelling function µ : V → L v which associates each node of the graph to a particular label of the set L v . Similarly, an edge labelling function ξ : E → L e associates a label to each edge of a graph. Using such structure, we can now encode topological relationships between elements of a set. Graphs have been widely used to encode structured information such as networks, RAG, molecules and shapes.

Floorplans, as the ones included in the dataset ILPIso [START_REF] Le Bodic | An integer linear program for substitution-tolerant subgraph isomorphism and its use for symbol spotting in technical drawings[END_REF], [START_REF] Héroux | Datasets for the Evaluation of Substitution-Tolerant Subgraph Isomorphism[END_REF], are originally encoded as images. These images are directly extracted from data produced by architects. However, since they represent a building floor, the underlying information includes some important structural relationships between the elements of the floorplan. Each building floor is composed of rooms and furniture elements which are interconnected by their topological relationships: A table is inside a kitchen, a bed is inside a bedroom, and bedroom and kitchen are connected together by a door. This structural information is not explicitly encoded within the original image, but it requires to be extracted from the former. Then, a graph representation of this floorplan may allow to encode this structural information.

A particular strength of euclidean based pattern recognition methods consists in using machine learning framework to perform the recognition and prediction task. However, most of machine learning methods are defined on euclidean spaces, where they benefit from well defined optimisation problems and efficient mathematical tools. Using such methods on graph data is not straightforward since graph space is more general than euclidean spaces, and thus more complex to manipulate. Using graph based methods, such as graph edit distance, we often face a complexity problem due to possible permutations of node order and different number of nodes. Considering a very basic problem such as determining if two graphs are an unique and same one is a NP-Hard problem, which forbids its exact solving in most of real world applications. To overcome this drawback, many methods are devoted to compute descriptors from graphs, and then embed graphs into an euclidean space to benefit from all machine learning methods. However, selecting and computing these descriptors reduce the versatility of graph representation and the encoded structural information. The set of descriptors is generally defined using an a priori expert choice, which doesn't allow to control the loss of information.

An alternative strategy is neural network based methods.

In the last decade, these methods helped the community to break a performance bottleneck by determining and computing optimal features thanks to deep architectures and thousands of examples. These particularities bring deep neural networks to the state of the art on most of pattern recognition and computer vision datasets. Nonetheless, one strong limitation of deep neural networks is that they are restricted, in their native definition, to euclidean data encoded as vectors, these vectors having a fixed and predefined size.

To benefit from the expressive power of graphs, one needs to connect graph representations and deep neural networks. This challenge requires to define new architectures, but it may allow to automatically compute optimal features according to a particular task.

The recent emergence of different Graph Neural Networks [START_REF] Gori | A new model for learning in graph domains[END_REF], [START_REF] Scarselli | The graph neural network model[END_REF], [START_REF] Li | Gated graph sequence neural networks[END_REF], [START_REF] Gilmer | Neural message passing for quantum chemistry[END_REF], [START_REF] Peter W Battaglia | Relational inductive biases, deep learning, and graph networks[END_REF], [START_REF] Zhou | Graph neural networks: A review of methods and applications[END_REF], [START_REF] Wu | A comprehensive survey on graph neural networks[END_REF] is dedicated to bridge the gap between neural networks and graphs. Through different approaches to tackle dimension and permutation problems, these methods have shown good prediction performances, hence proving they are able to exploit the structural information included within graphs.

In this paper, we propose to exploit graph neural networks methods to address the task proposed by ILPIso [START_REF] Héroux | Datasets for the Evaluation of Substitution-Tolerant Subgraph Isomorphism[END_REF], [START_REF] Le Bodic | An integer linear program for substitution-tolerant subgraph isomorphism and its use for symbol spotting in technical drawings[END_REF] dataset. This task consists in identifying the class and the location of different furniture symbols which appear regularly within floorplan images. Transforming images to graphs will allow our prediction model to use the topological information around each furniture symbol, and thus to include some contextual information during learning process. The use of graph neural network approaches avoids the definition of ad-hoc features, and thus the hard choice of a predefined set of features. Combining these two approaches may lead to robust and accurate prediction of symbol classes.

This paper is structured as follows. First, we review in Section II the different neural network architectures proposed to process graphs within a classification scheme. Second, Section III-A details how we pass from floorplan images to graphs. Then, Section III-B presents our proper graph neural network model, adapted to the particular classification task associated to ILPIso dataset. Finally, our contribution is tested in section IV through some experiments on ILPIso dataset to evaluate its accuracy and robustness against some noise.

II. RELATED WORKS A. Original graph neural network

Graph Neural Networks (GNN) have firstly been theorised by Gori et al. in [START_REF] Gori | A new model for learning in graph domains[END_REF] and then extended in [START_REF] Scarselli | The graph neural network model[END_REF]. In those papers, authors want to update state of a node by aggregating information contained in its labelling, its neighbourhoods labelling and the labelling of the edges linking the node to its neighbourhood. This defines the very idea of graph neural network. More specifically, each node in the graph is updated according to equation 1. In this equation and for the rest of

v 2 h v 1 h v 4 h v 3 h v 5 h v 6 h v 8 h v 7 h v 9 h v 10 h v 11 h v 2 h v 1 h v 4 h v 3 h v 5
Figure 2: Example of how a node is updated depending on its neighbourhood. On the left is the original graph. On the right, the node h v2 is updated depending on its neighbourhood h v1 , h v3 , h v4 , h v5 , and the edges between h v2 and its neighbour (in bold).

this paper, the following notation are defined : h v the hidden state of the node v, l v is still the attributes of node v, e vw the edge between node v and node w, N (v) is also still the neighbourhood of v, and thus l N (v) and e N (v) respectively the nodes and edges attributes of v neighbourhood. Finally, f defines an arbitrary function. This function is iterated T times, and thus, each

h t+1 v is updated depending on h t v . h t+1 v = f (l v , l N (v) , h t v , e N (v) ) (1)
Finally, a decision o v is taken for each node v following equation 2:

o v = g(h t v , l v ) (2)
where g w is an arbitrary function which take into account the actual node state h t v and the original node label l v . Figure 2 shows an example of how a node is updated depending on its neighbourhood.

Finally, both functions f and g are neural network.

B. General graph neural network model

More recently, [START_REF] Gilmer | Neural message passing for quantum chemistry[END_REF] proposed a more general approach, where a message m t+1 v is computed following equation 3 where M t is an arbitrary function.

m t+1 v = w∈N (v) M t (h v , h t w , e vw ) (3)
Finally, each node is updated depending on an arbitrary function U t , which take as input the actual node state and the computed message, as expressed in equation 4.

h t+1 v = U t (h t v , m t+1 v ) (4)
As shown in [START_REF] Gilmer | Neural message passing for quantum chemistry[END_REF], this model generalises multiple models, such as [START_REF] Duvenaud | Convolutional networks on graphs for learning molecular fingerprints[END_REF], [START_REF] Li | Gated graph sequence neural networks[END_REF], [START_REF] Battaglia | Interaction networks for learning about objects, relations and physics[END_REF], [START_REF] Kearnes | Molecular graph convolutions: moving beyond fingerprints[END_REF], [START_REF] Kristof T Schütt | Quantumchemical insights from deep tensor neural networks[END_REF], and both functions M t and U t are generally neural networks.

III. MODEL

A. From images to graphs

Region Adjacency Graphs are well suited for representing symbols and technical drawings since they enable to model the adjacency relations between the regions extracted by a segmentation process. Working on technical documents, the digital images are mainly binary images where white components denote the background while black components stand for the drawings. Segmenting such kind of images can be achieved using component labelling [START_REF] Fu Chang | A linear-time componentlabeling algorithm using contour tracing technique[END_REF]. However, aiming at finely modelling adjacency relations between two regions, a binary image can be firstly thinned [START_REF] Gaüzère | Skeltonization algorithm running on path-based distance maps[END_REF]. The obtained image is then morphologically the same than the initial image of the document but the thickness of the drawing components is reduced to a single pixel. Using this image, each white component is mapped to a vertex of the graph. Then, the skeleton branches represent frontiers and adjacency relations between two regions. An edge is then build between two vertices representing regions separated by a skeleton branch. Figure 3 illustrates the overall process on an extract of a document image.

To enrich such a description, attributes have to be assigned to each vertex and edge. Many features have been proposed to characterize shapes and spatial relations [START_REF] Terrades | A review of shape descriptors for document analysis[END_REF]. Among them, Zernike Moments (ZM) [START_REF] Teague | Image analysis via the general theory of moments[END_REF] yield interesting results for pattern recognition tasks when invariance to affine transforms and robustness to degradations are required. Hence, a feature vector corresponding to a set of ZM is assigned to each vertex in order to characterize shapes. Concerning the edges, a single attribute is used : the relative distance between gravity centers of adjacent regions which is computed with respect to the overall area of the two regions. d e (g source , g target )

A(source) + A(target)

where d e denotes the Euclidean distances between gravity centers.

We finally get a graph-based representation G = (V, E, µ, ξ) of a document where V stands for the set of vertices (regions) and E ⊆ V × V stands for the edges (adjacency relations). µ and ξ are mapping functions :

• µ : V → R 24 describing the morphology of a region (a vertex), • ξ : E → R expressing the geometrical properties of an adjacency relation (an edge).

B. Graph Neural Network Model

As stated in introduction, our method relies on the recent graph neural network developments which have been introduced in the literature. In section 2, we presented a general model of a GNN. In this subsection, we focus our definition on the particular GNN we use. One of the simplest way to compute a GNN is probably the one defined in equation 5, where a node and its neighbourhood are updated independently. In this equation, W is a neural network.

h t+1 v = m t+1 v = (h t v + w∈N (v) h t w ) • W (5)
More particularly, this GNN is interesting by the way it is computed when working with tensors (equation 6). One can notice the similarity with neural networks.

H t+1 = (A + I) • H t • W (6)
One problem with this simple way comes with the fact that it makes no difference between the central node and its neighbourhood. For example, in Figure 4, the simplest GNN will update the node v similarly in both cases, while intuitively, one would probably update them in a different way.

To tackle this limitation, one solution could be to use two different neural networks, one for the central node, and another one for the neighbourhood. This is defined by equation 7.

h t+1 v = h t v • W 0 + ( w∈N (v) h t w ) • W 1 (7)
This last equation defines our general model. However, it does not use the possible edges attributes. For this case, we use the edge network proposed in [START_REF] Gilmer | Neural message passing for quantum chemistry[END_REF], which is defined by equation 8, where W A is a neural network applied to the edges attributes which computes a matrix.

Case 1

Case 2

h v 2 h v 1 h v 4 h v 3 h v 5 h v 2 h v 1 h v 4 h v 3 h v 5
Figure 4: During the hidden state update of vertex h v , the simplest GNN that considers the central node the same way as neighbouring node can not distinguish Case 1 and Case 2 since this update is based on 3 orange nodes and 1 green node in both cases. These two cases can be distinguished when the central node is considered differently from the neighbouring nodes

h t+1 v = h t v • W 0 + ( w∈N (v) (h t w • e vw • W A )) • W 1 (8)
In our experiments, models defined by equation 7 and 8 are both tested.

IV. EXPERIMENTS

A. Dataset presentation

To evaluate our model, we experiment it on the ILPIso dataset, a dataset made of 200 floorplans like the plan of Figure1. We apply our graph conversion strategy to each of the floorplan images, and thus get 200 graphs. After this conversion, we count 24281 nodes and 105110 edges, which give us a mean of 121 nodes and 525 edges per graph. Each node is labelled with the 24 first Zernike moments of the connected component he represents. Each edge is labelled with the distance between the center of gravity of the two nodes the edge is linking. Finally, each node is associated to one of the 17 classes corresponding to the different objects in the original floorplan images. The 17 classes are the 16 kinds of symbols to be found in floorplans (Figure 5), plus a dummy class, for the case where the node do not correspond to any of the 16 symbols.

B. Evaluated models

We evaluated 3 different models: the first model, which corresponds to our baseline, is a neural network which takes as input and classify each node independently and only using its original features. The neural network is made of two dense layers, with the second one used for decision. Thus, with this instance, no topological relationships between any node is taken into account (see Figure 6).

The second model is a graph neural network (GNN), made of two layers. Similarly to the baseline, the second layer is used for decision. With this model, we are only able to use the existence of an edge between a pair of nodes, but not the labels associated to this edge (see Figure 6). The third experimented model uses the edge network (EN) defined in section III-B. This model uses both the existence of an edge and its labels (see Figure 6).

To be able to compare the three models, we make them as similar as possible. Thus, both the neural networks of the baseline and the two GNN produce 200 features for each node.

C. Experimental protocol and results

In this section, we describe the protocol used to conduct our experiments. First, our 200 graphs are randomly divided into 3 sets. 160 graphs are used in training, 20 in validation and 20 in test. Each node's and edge's attribute is normalized to have a value either between 0 and 1 or -1 and 1, depending on the minimum value of the attribute. Each model is then trained using the Adam optimizer with an initial learning rate of 5.10 -3 . Each model is trained for 100 epochs using the crossentropy loss and the best model in validation is used for test. We run this experiment 10 times per model and compute the mean and standard deviation for the node classification of those 10 experiments. We computed the results obtained in table I.

As one can see, results for both GNN and EN are pretty similar and close to 100%. The difference between the two results comes from one run which failed on GNN, while the 9 others obtained perfect scores, as for EN. To be able to compare the methods more rigorously, and evaluate their ability to generalize, we decided to add some noise on the tested data. We added a Gaussian noise centered in 0 with different variances. We tried 3 different values for this variance : 0.05, 0.1 and 0.2. Results are given in table II. First thing we notice is that results for the baseline collapse quickly. This shows how useful the structural information is in decision. Second is that GNN behave better than EN with low variance (0.05 and 0.1), but are dropping quickly when the variance becomes higher (0.2), while EN results are dropping in a more regular way. This can be explained by the fact that at first, the existence or not of edges are not influenced by the noise, but when the noise on nodes is too important, the presence of attributes on edges, even if they are noised, helps the network for the decision.

V. CONCLUSION

In this paper, a new approach for floorplans segmentation is proposed. The approach firstly transform the floorplans images into Region Adjacency Graphs. Graph Neural Network are then applied on those graphs to take a decision on each node.

Two different models of graph neural networks are studied. Both of them presents great results on the evaluated dataset, and improve results obtained without structural information. Especially, we show that this structural information is really important with noised data. Future works will explore more flexible ways to convert images to graphs and try different GNN models on new data. Another outlook would be to find subgraph symbols inside the floorplans, instead of classifying nodes.

Figure 1 :

 1 Figure 1: Summary of our method. First, a floorplan image is converted into a Region Adjacency Graph, where each node corresponds to a connected component. Then, a graph neural network is used to predict the label of each node.

  h

  (a) Initial image (b) Skeleton image of (a) (c) Components labels of (b) (d) Corresponding RAG

Figure 3 :

 3 Figure 3: Raster to Region Adjacency Graph.

Figure 5 :

 5 Figure 5: Symbol models

Table II :

 II Results obtained with noised test data.

	Gaussian noise of variance 0.05
	Base	68.3 ± 2.44
	GNN	99.7 ± 0
	EN	97.4 ± 1
	Gaussian noise of variance 0.10
	Base	46.4 ± 3.7
	GNN	98.9 ± 0
	EN	94.8 ± 2.2
	Gaussian noise of variance 0.20
	Base	27.2 ± 2.44
	GNN	81.3 ± 3.8
	EN	89.1 ± 2.2