Frédérik Detue

Charlotte Lacoste

What Testimony Does to Literature

Keywords: just art, documentary, poetics, justice, Testimony, Jean Norton Cru, Témoins, Primo Levi, witnessing

This article sheds light on a literary practice that critics began to reflect upon in the twentieth century: witnessing. This genre, by adopting a narrative model based on statements of evidence presented in the courtroom, distinguishes itself from other forms of expression practiced by witnesses. Survivors of political violence take up their pens and describe the situation they have been subjected to, so as to attest to historical facts and prevent erasure of the event through forgetting, denial or negation. This enterprise, which seeks to document lived experience and thereby pay homage to victims who did not survive, constitutes both a source of evidence for legal procedure and a contribution to the writing of history. Witnessing, however literary it may be, is founded on a pact of veracity, in which witnesses are bound to relate no more than their own experience and to do so with precision. Finally, witness accounts are addressed to society at large or even to humanity as a whole, in the hope of emancipating it from such violence by raising awareness of its intolerable nature. Though witnessing still lacks legitimacy within the literary field, the link it establishes between ethical, aesthetic and political positions makes this genre exemplary of what literature is capable of.

of political violence to write and publish detailed accounts of the events they have witnessed, to bring them to widespread attention. For acts of testifying to become a distinctive social phenomenon required the development of a democratic culture, from the nineteenth century onwards in the West. But the real expansion of such practices came in the following century, when the world wars and the numerous crimes against humanity and genocides forced so many to face what Miguel Abensour called the "modern terror" (231). 2 As Jean Norton Cru observed in 1929 in his analysis of the writings of First World War combatants, the practices of witnesses are diverse: diaries, reminiscences, reflections, letters and novels (War Books 45); and other forms should also be included, such as poetry or theatre. Yet among these testimonial practices, the one which particularly interests us here emerged as a new literary genre in the mid-twentieth century, at the same time as a new international law of human rights was being established: testimony which, in diary form (in medias res) or in the form of memoirs (after the fact), is written "as a judicial act" [START_REF] Levi Said | of If This Is a Man: "I saw this book as a judicial act. I wanted to testify[END_REF] and whose distinguishing feature is the use of a narrative model inherited from the legal deposition.

Testifying through literature: a judicial act

World War I marked an important step towards the establishment of testimony as a genre. Several factors combined to produce an unprecedented growth in testimonial practices at this time. The devastating effects of increased firepower, which led to new ways of "waging war" and dying from it, are not the only explanation. Also significant was that the shock of war affected massive numbers of civilians at a time when the average level of education was higher than in previous centuries. As such, the soldiers' ignorance of the realities of battle appeared all the more "inconceivable" (Cru, Témoins 411) to them at their first taste of action. The "need for truth" that compelled many of them to write their testimonies originated in their stupefaction at such unprecedented political violence, 4 which it was important to make known to as many people as possible. The same can be said, mutatis mutandis, of the crime perpetrated at the same time in the Ottoman Empire, which targeted the entire Armenian people and which was difficult to name. Both cases involved the social construction of an intolerable, [START_REF]On the intolerable as a social construction[END_REF] which in the 1940s led to the creation of the legal concepts of 'war crime,' 'crime against humanity' and 'crime of genocide.'

This was an historic recognition, and depended on three phenomena that emerged in the nineteenth century, besides the rise in literacy: the 'age of rights' ushered in by the American and French revolutions, which enshrined the universal idea of human rights; the gradual formation of the social sciences, at first in close association with literature, which led in particular to a renewal of the history discipline; and, finally, the unprecedented development of printing techniques, which encouraged the publication of all types of written material. The role played by the press should be stressed, first because newspapers published or supported the publication of survivor testimonies very early on, 6 and second because the rising figure of the reporter in the second half of the nineteenth century accustomed readers to a documentary standard based on witness accounts. WWI combatants and Armenian survivors had a cruel knowledge of the war or genocidal event that decimated them and recognised its significance for humanity; consequently, for the press to be drafted into the service of state propaganda and for the event, whether silenced or falsified, to escape the awareness of their contemporaries was quite simply intolerable.

This point is decisive. Never before the early twentieth century had the fear been so literally expressed that the reality of such historic violence might be obscured by a project of denial. This is as true for the Great War as it is for the genocide of the Armenians, which produced the same thirst to tell the story, the same necessity for the survivors to testify to the facts they had witnessed. In the case of the genocide, the act of bearing witness was encouraged by an appeal launched at the initiative of the Committee for Assistance to Deportees on 22 November 1918, in an Armenian newspaper in Constantinople. Entitled "Armenian Martyrdom Must be Proven," this appeal no doubt contributed to the "sudden and widespread emergence of deportation writing" in 1919. 7 As survivors of mass crimes had often been urged to remain silent and forget, this exhortation to testify was particularly important.

Faced with the world's deafness and strategies of denial, 8 some despaired at times of ever finding a sympathetic ear to listen and give credence to the narrative of their experience. Yet if "all Armenians who knew how to spell and who returned from deportation considered it their duty to describe what they saw" (Beledian "Le retour de la Catastrophe" 309), 9 it was because for the survivors of this genocide and, later, for the survivors of Auschwitz, "the need to tell our story to 'others,' to make 'others' share it, took on for us … the character of an immediate and violent impulse, to the point of competing with other elementary needs" (Levi, Preface n.p.). In this respect, the efforts that victims made to bear witness even before they were out of danger are particularly moving. Armenian journalist Chavarche Missakian, while fortunate enough to escape deportation, clearly felt this need. He risked his life by remaining as a clandestine in Constantinople in 1915 because he considered that there was nothing more vital at that time than to thwart, through his testimony, the law of silence imposed by the perpetrators of the genocide (see Missakian 47-59). In a different context -Japan after the bombing of Hiroshima-Ota Yôko was driven by a similar impulse to brave American censorship and write City of Corpses; as her French translator Maya Morioka Todeschini points out, "Ota feverishly recorded the events, writing on shreds of paper torn from the sliding doors typical of Japanese interiors or on toilet paper," while "terrified of dying from radiation before she could complete her story" (136). Remarkably similarly, though the stakes were different, WWI combatants had already felt the vital need to pass on their experience of war, "not to counter its being passively forgotten, but to counter its deliberate cover-up." [START_REF] Dulong | rightly points out that Jean Norton Cru's entire project in Témoins is based on this concern[END_REF] "When the humbug impresses us as too much, and is run off at the rate of millions of copies, a feeling of anger comes to us very quickly," observed Raymond Jubert in his memoirs (qtd. in Cru, War Books 43) regarding the false praise received in the press; and indeed many, like Maurice Genevoix, were angry at "the windjammers who manufacture their heroism, and the collectors of extraordinary deeds of prowess, and the concocters of exploits especially for the rear" (qtd. in Cru, War Books 97) and what Jean Drève called "the blatantly deceitful splendour in which the slaughter is disguised" (qtd. in Cru, Témoins 295).

As the war gave them "a horror of falsehood," many soldiers took up the pen, driven, as Jules-Émile Henches was, by "the more ardent desire for truth" (qtd in Cru, War Books 2).

It is on the basis of this critical consciousness that testimony became established in literature as a "judicial act." While published testimony has sometimes led to the opening of a judicial enquiry or even been included in the prosecution's case in a trial, literary testimony is more commonly intended to prepare the ground for the court of history to judge the events it documents. After the Nazi occupation of Europe, Jewish survivors who had managed to produce and preserve testimonial writings entrusted them, with this aim in view, to the Jewish Historical Commissions that were formed at the time. Leon Weliczker's genocide diary, part of which was published in 1946 under the Polish title of Brygada śmierci [The Death Brigade] by the Central Jewish Historical Commission at Łódź, was used as evidence at the Eichmann trial in Jerusalem, in addition to Weliczker's testimony which it had made possible; but this use of his testimony illustrates precisely what helped make the Eichmann trial a trial for history. In 1929, Jean Norton Cru had endeavoured to advocate such use of testimonies in Témoins. This "Analytical and critical essay on soldiers' memoirs published in French from 1915 to 1928," which was the first corpus study based on the authors' status as witnesses, aimed to bring to light the truth content of the accounts and was intended "particularly" for historians (26). This was no mean challenge given that, as Cru pointed out, military historians had until then deemed the materials produced by troops unworthy of submitting to criticism and had dismissed them as potential sources. What Cru's work shows is that literary testimony as a "judicial act" entails not only telling the truth but also proving that it is true. Soldiers took so keenly into account the risk of being neither heard nor believed that their attitude as authors was often modelled on the oath of a witness testifying in court -who swears to tell 'the truth, the whole truth and nothing but the truth.' Cru hailed "this concern for scientific accuracy which is the honour of our century" (Témoins 412) and which, in his view, allowed those who fought in the Great War to "surpass by far any attempts of past generations to give those who did not fight an image of war" (Témoins 226). Indeed, one perceives in the corpus that Cru studied, and especially in the prefaces he signed himself, an approach that already outlined the contours of the testimonial contracta contract that exemplifies, in many respects, what testimony does to literature.

'The truth, the whole truth, and nothing but the truth'

The attestatory function of testimony determines the terms of the testimonial contract, which is fundamentally a pact of truthfulness. Its first requirement is an attestation of the witness's presence -"I was there," "I saw," "I lived it"-which not only lends factual weight to the author's words, but can at times be contentious. According to Cru, when Jean Bernier wrote that "The man who has not understood with his flesh cannot talk to you about it," he expressed "the alpha and omega of all war literature by witnesses" (Témoins 575). [START_REF] Bernier | Cru, who considered the genre of the novel "false[END_REF] For Cru, it was a question of contrasting the knowledge of the troops who "had [their] shoulder to the wheel" (War Books 16) and who, "from private to captain," were exposed to danger, with the ignorance of the high command who "could not know for only their intelligence was in contact with the war" (War Books 14). 12 Bearing witness to what one "understood with one's flesh" under bombardment thus amounted to testifying against the staff officers who were supposed to know but who, through blindness and/or ignorance (disinformation is denounced in many testimonies), were responsible for countless deaths. It is not immaterial that the testimonial genre originated as a protest from individuals who had no say in the war that was destroying them, directed against those most authorised to speak about it. The witnesses emphatically claimed the authority of experience while at the same time warning against all forms of deceit, especially those clothed in political, media or literary legitimacy.

The attestation of presence, which is the cornerstone of the witnesses' testimony and concern for accuracy, is therefore crucial. By stressing this aspect, Cru initiated, in the name of the WWI combatants, a materialist-inspired critique of culture: "What we see, what we live, 'is'; what contradicts our experience, 'is not', whether it comes from the general-in-chief, from the Memoirs of Napoleon, from the theories of the War College, or from the unanimous judgment of all the historians of war" (War Books 14). Testimonial writing relies on the empirical reality of events to assert what is, counter to both the most militant ideological discourses and the most insidious preconceptions. As Eric Hobsbawm explained, "unlike earlier wars, which were typically waged for limited and specifiable objects," the First World War "was waged for unlimited ends"; "the only war aim that counted was total victory: what in the Second World War came to be called 'unconditional surrender'" (30). What the testimonies attest to is that such a programme of destruction could only have been consistently based on a false representation of war, inherited in large part from the nineteenth century and the heroic representation of Napoleon's campaigns. Therefore, to describe war as it is, i.e., as a material, historical and political event, is at the same time to demystify all that Cru condenses into the word "legend" (War Books 27) and which tends to make a phantasmagoria of war.

Hence the requirement for testimonial concreteness and accuracy, which guarantees the text's truth value and serves to preclude abstraction. It is a matter of breaking with the tradition of idealism, from which stems an ideological blindness to the very principle of mass crime. Indeed, their terrible experience of the shock of war led many witnesses to a "resolute refusal of the concept of 'timeless truth'" (Benjamin 463) and to reduce the very idea of "truth" to more reasonable proportions. The truth the testimonies aim for, as Cru observes in Témoins, is not "dogmatic, absolute or transcendental truth, but an all-human truth, the truth of the sincere witness who says what he has done, seen and felt, a truth accessible to any intelligent man who knows how to see, reflect and feel" ( 661). Yet this materialist standpoint is not self-evident in literature; moreover, with few exceptions, witnesses who were already writers before going to the front and who wanted to get across the "truth of the war" preferred the historical fiction of the novel to the veracious narrative of the diary or memoir, convinced that they were reaching a higher truth. The rise of testimony brought with it a real literary schism.

More precisely, the materialist position which is at the heart of the testimonial genre and its value as a historical document, and which prompts the authors of testimonies to prove their presence, sincerity and good faith, leads them to make what we call, following Miguel Abensour, the "choice of the small." 13 The expression rightly emphasises the modesty of the testimonial undertaking as expressed in the oath to tell 'nothing but the truth.' This focus on experience, this choice to stick to what one has experienced -seen, heard, felt and thought-is a prerequisite for not speaking abstractly about war. Yet to most professional writer veterans who wrote a novel about the Great War, such a restriction seemed incompatible with their idea of literature, which entailed offering a panorama of the war that went beyond the limited perception of the witness. In Témoins, Norton Cru shows that these novelists sought to have it both ways: even though they "pride themselves on speaking as witnesses serving the cause of truth, revealing the war to the public as it really was" (War Books 51), they rejected the constraints of truthfulness that witnesses imposed on themselves-which did not stop them from being read and taken at their word.

These novelists doubtless still owed much to the naturalists' approach. While attached to the "documentary content" of their works, they nonetheless intended the "objectified facts," by the grace of the novelistic plot, to be "transfigured … into a 'vision,' which orders and organizes the present by plunging it back into the pathos of epic and theological, evolutionist and historicist rhetoric" (Chevrier and Roussin 5). This is clearly how the witness-novelists of the Great War continued to think of their art at the beginning of the 1930s when they claimed both the authority conferred by experience and the absolute freedom of the artist, and considered the experience of the witness as simply 'raw material' to be transcended. Heirs to the romantic theory of literature, these novelist witnesses were convinced that the liberty of artistic invention must surpass the constraint of experience, and that it is in this movement that the transubstantiation of the real into art takes place. "Why copy when you can create?" asked Roland Dorgelès (34), recalling Balzac's words on "truly philosophical writers" who "invent the true" (Balzac 52). The power to invent the true knowing no limits, Dorgelès could thus profess a "higher" goal:

"not to recount my war, but the war," (33) and aim to produce a synthesis of the war that gives access to a higher truth. This tradition has not disappeared. It is among these 'inventors of the true' that Jorge Semprún should be counted, according to François Rastier; in Literature or Life, Semprún claims "a narrative 'I' that draws on [his] experience but goes beyond it, capable of opening the narrative up to fiction, to imagination" (Rastier 118).

By aiming for quite the opposite, the testimonial 'choice of the small' critiques the main pillar of literature as defined by the romantics, namely the dogma of the independence of art. Cru helped clarify this criticism by highlighting the collusion between the dogma of aesthetic independence and the ideological blindness of which witnesses were victims and which they denounced in their writings. In particular, he demonstrated that despite their 'second sight' supposedly able to compete with the historian's gaze, the synthetic truth that novelists in fact produced was nothing but a fictitious web of errors of detail and fable -thereby doing a proud service to those who deny reality. What the 'choice of the small' brings to light, in contrast, is that the greatest challenge in art lies both in a living act of creation and a content of experience. It is the art of truth -in which, like Genevoix, one "refrains from any fabricated arrangement, any imaginative licence after the fact" (9)-that is most difficult.

In one sense, it is true, witnesses' knowledge is limited and their accounts are partial; but they Nevertheless, to share this knowledge, witnesses must work on writing without sacrificing anything in artistic quality for the sake of factual precision. The very transmission of the testimonial voice is at stake here, as the documentary value of testimonies depends on their literary value. The difficulty lies in how to balance the 'whole truth' of the testimonial oath with the 'nothing but the truth.' Far from getting around the difficulty by confusing, as some novelists do, 'the whole truth' with the absolute truth, the witness who makes the 'choice of the small' aspires to nothing more than to tell "the truth about his war" (Cru, Témoins 36). Thus, the ethical duty to "work well" (Broch 63) takes precedence above all else.

Ethics, aesthetics and politics of testimony

Telling 'the whole truth' does not mean telling the whole of one's experience; it means telling what, in that experience, is most representative of what others subjected to the same treatment have also undergone. To avoid distorting the perspective, and so as not to fuel the imagination of readers eager for sensationalism, singular extremes are excluded. But some of the abominations recounted in testimonies nonetheless appear implausible. The art of testimonial truth therefore contrasts squarely with the art of novelistic verisimilitude as theorised by Maupassant. 14 The attestation of presence and recurrent references to places and dates (in memoirs as well as in diaries) are also there to counter the reader's disbelief-so bitterly feared by the witnesses. As the dates act as "a reminder to honesty" for the authors themselves (Cru, War Books 45), these precise and precious references often guarantee the reliability of their testimonies. The space-time framework is especially important because it helps to make reality felt in its materiality and to convey, as André Pézard does in Nous autres à Vauquois, "the facts -not bare, but with their atmosphere" (Cru Témoins 226).

Testimony, which is a personal document, should therefore not be confused with that other documentary practice: the report. 15 It was by setting out to express "the war in its most intimate, concrete, human and essentially observable aspects" that the best witnesses of the Great War succeeded, according to Cru, in capturing the "atmosphere of the front which gave things all their value, strength, charm and horror" (Témoins VIII and 226), and thereby conveying a "psychological" truth that had never before got through. This is essential for "turning what had affected [the witness] into something that could affect [readers]" because, as Georges Perec wrote in an article on testimony, "facts do not speak for themselves. It is a mistake to think they do" (142). In Là-bas, 16 First World War veteran Guy Hallé gives a palpable sense of the terrible anguish he experienced before the attack on Douaumont on 22 May 1916, and enables us to better understand that "the hell of the soldiers [was] above all a hell of ideas" (Témoins 161).

More precisely, testimonial writing is dialectical; it differs both from the report, based on a positivist conception of the facts, and from novelistic technique which aims to immerse the reader.

Testimonial narrative rejects the pathos of action that gives readers the illusion of participating and lets them take refuge in easy emotion. On the contrary, the psychological truth of testimony is developed through distance, which reflects the distance between the witness who saw and experienced the events and the survivor who produces the retrospective account of them. Even if he or she relives the events while narrating them (sometimes very shortly afterwards), the witness "interposes [between his experience and us] the entire grid of a discovery and a memory and a consciousness which carry things through to the end" (Perec 143), following a writing process which, Perec asserted, led Robert Antelme to provide, with The Human Race, "the finest example ... of what literature can be" (150).

If the intention to attest to the facts one has witnessed so as to give readers the means to rightly understand the event is not incompatible -far from it-with literary craft, if -indeed-"the testimony of survivors remains the honour of literature" (Rastier, "Témoignages inadmissibles" 127), it is based on a sparse eloquence. Stylistically speaking, the 'choice of the small' results in a form of sobriety. Those who drafted the appeal of 22 November 1918 urging all survivors to bear witness and "prove the Armenian martyrdom" understood this perfectly, as they instructed authors to write "incisively (gdroug) and without embellishments (ansetheveth)" (qtd. in Beledian, "Traduire un témoignage" 111). 17 Against exaggeration in all its forms (stylistic ornaments, retrospective embellishments, sensationalism), witnesses professed a "rejection of the gigantic and the apocalyptic" (Perec 142) that opened up new perspectives for literature. Whereas through spectacular fictions, as Jacques Rivette has observed, "everyone surreptitiously grows used to the horror" (54), restraint is exercised in testimony so that the reader does not become used to what witnesses have to say.

Commenting in 1976 on his writing of If This Is A Man, Levi states:

[…] I deliberately assumed the calm and sober language of the witness, not the lament of the victim nor the outrage of the avenger: I thought that my words would be most credible and useful the more they appeared objective and the less they sounded fervent. Only in this way does a witness fulfil his function, which is to prepare the ground for the judges. The judges are all of you. ("Appendice" 187) This choice of sobriety can be found in an author such as Marcel Cohen, who clearly expressed "the feeling [that writers of his generation have] of having been altogether swindled by a great deal of the literature of their century: too much 'fine work', charm, ego, stylistic effects, 'little airs' and great organ" (220). They are even less inclined to the literature of effects because they see it as a sinister sign of complicity. The work of the collaborationist writer Louis-Ferdinand Céline represents an exemplary deterrent since, in his post-1945 novel trilogy, the author used his "little airs" to deny the testimonies of deportation to the Nazi camps. 18 More generally, testimonial sobriety determines the "mental attitude" that Rithy Panh believes is part of the legacy of the finest witnesses of the twentieth century , 19 and which is not unrelated to what Levi says about the "theme of indignation" (La Zone grise 63). This "mental attitude," which stems from a search for accuracy as a corollary of the desire for justice, harmonises with the three main functions of the genre -to attest, to pay homage and to educate -which are inseparable. Testimonies are more often written using "we" than "I," not least because, as Panh does in his L'Élimination, witnesses dedicate their works to their missing 'peers' in an effort to pay off the debt they have incurred towards them. The homage function of testimonies, which gives them a quality akin to a tomb, should not be confused with the all-too-familiar 'duty of remembrance.' This point must be stressed, as it concerns the politics of testimony and therefore, also, its legacy. If witnesses find it important to relate the real agony experienced by their dead friends or relatives, it is because sounding out the depths of this suffering might allow for the motives and nature of the crime to be rigorously determined. This means that the fight against denial involves not only attestation (against the criminals) and paying homage (to the other victims) but also education (for future generations). In this regard, witnesses are 'messengers,' to borrow the title of Laëtitia Tura's and Hélène Crouzillat's documentary film on the violence of contemporary migration policies (Crouzillat and Tura). Witnesses seek knowledge of the past in the hope of averting the perpetuation or repetition of the crime they suffered, and thus argue in favour of a form of literature viewed as a warning device. In doing so, witnesses initiated an art of writing that encourages us to rethink the relationship between artistic freedom and the ethics of responsibility, renews the notions of both author and creation, and redefines the forms of 'engagement' in literature.

The history of the reception -both public and critical-of the genre reveals that the literary schism brought about by testimony resulted in its long being poorly received. It still often remains "on the edge of literature," as sociological research on literary fields in particular has shown. 20 It is our hope, however, that the work we and others are doing will help, apart from its establishment as a genre, to substantiate it as literature-not only in law but in fact.

Translated from the French by Jessica Edwards

Works Cited

Abensour, Miguel. "Le choix du petit." Postface to Theodor. W. Adorno, Minima Moralia. Réflexions sur la vie mutilée, Paris: Payot, 1991, pp. 231-243. 16 This testimony was published in 1917 with cuts made by military censors. In the issue of Europe that we edited, we published three chapters of this work, restoring for the first time the passages that had been redacted in the original edition. See Hallé (16-36). 17 The adjective ansetheveth, Beledian specified, "means at once ornate, affected, mannered, and invented, embellished" (111). 18 On this subject, see Hartmann in the special issue of Europe. 19 Rithy Panh is the author, in collaboration with Christophe Bataille, of L' Élimination (2012), in which he recounts his experience of the genocide perpetrated by the Khmer Rouge in Cambodia from 1975 to 1979. The quotation is taken from the interview he gave us about the book (Panh 171). 20 See, for example, Tristan Leperlier's study of the reception of Algerian testimonies on the "black decade" in France (178-191) in the special issue of Europe.

  at least know what they are doing: The fighter has short views. … But because his views are narrow, they are sharp; because they are restricted, they are clear. He doesn't see a lot, but what he does see he sees plainly. Because his own eyes and not those of others inform him, he sees what 'is.' (Georges Kimpflin qtd. in Cru, War Books

	16)


Pr

-Émond

Julie Hlavacek-Larr

Kathryn Grasha

Typeset using

Keywords: Machine Learning, ISM, Galaxies

, we demonstrated that neural networks can robustly and efficiently estimate kinematic parameters for optical emission-line spectra taken by SITELLE at the Canada-France-Hawaii Telescope. This paper expands upon this notion by developing an artificial neural network to estimate the line ratios of strong emission-lines present in the SN1, SN2, and SN3 filters of SITELLE. We construct a set of 50,000 synthetic spectra using line ratios taken from the Mexican Million Model database replicating H ii regions. Residual analysis of the network on the test set reveals the network's ability to apply tight constraints to the line ratios. We verified the network's efficacy by constructing an activation map, checking the [N ii] doublet fixed ratio, and applying a standard k-fold cross-correlation. Additionally, we apply the network to SITELLE observations of M33; the residuals between the algorithm's estimates and values calculated using standard fitting methods show general agreement. Moreover, the neural network reduces the computational costs by two orders of magnitude. Although standard fitting routines do consistently well depending on the signal-to-noise ratio of the spectral features, the neural network can also excels at predictions in the low signal-to-noise regime within the controlled environment of the training set as well as on observed data when the source spectral properties are well constrained by models. These results reinforce the power of machine learning in spectral analysis.

INTRODUCTION

Emission-line nebulae are a critical part of our understanding of galactic evolution and radiative processes; thus, they are a primary targets of observation in extragalactic astronomy (Kennicutt 1984;Veilleux & Os-terbrock 1987;Kewley et al. 2019). H ii regions form from clumps of gas in the interstellar medium (ISM) when young O/B stars irradiate the surrounding environment (e.g. Franco et al. 2000;[START_REF] Osterbrock | Astrophysics of gaseous nebulae and active galactic nuclei[END_REF][START_REF] Shields | [END_REF]). The region becomes either partially or fully ionized depending on the budget and hardness of ionizing photons, the morphology and the total mass of the mother cloud. H ii regions are primarily composed of Hydrogen and Helium; however, they contain non-negligible amounts of metals (e.g. Shields & Tinsley 1976;Garnett & Shields 1987;Kennicutt & Oey 1993;Oey & Kennicutt 1993). Through recombination and collisonal processes between the ionized atoms and the free electrons, the nebula emits characteristic strong emission-lines which indicate their underlying chemical structure (e.g. Baldwin et al. 1981;Crawford et al. 1999;Kewley et al. 2001;Kewley et al. 2006;Kewley et al. 2019). In the optical, the primary emission lines include, but are not limited to, the Balmer series (i.e. H αλ6563, and H βλ4861), ionized oxygen (i.e.

[O ii]λλ3726, 3729, and [O iii]λλ4959, 5007), ionized nitrogen (i.e. [N ii]λλ6548, 6583), and ionized sulfur (i.e. [S ii]λλ6716, 6731). By studying the relative ratios of these lines, the primary emission and ionization mechanism can be determined. Sources that power ionized emission differ and the regions themselves are categorized into several distinct classes: classical H ii regions (e.g. Viallefond 1985;Melnick et al. 1987), shock induced regions such as supernova remnants (e.g. Fesen et al. 1985;Danziger & Dennefeld 1976), and planetary nebulae (e.g. Miller 1974;Oserbrock 1964). Several diagnostics exist to categorize emission nebulae based off their line ratios (e.g. Baldwin et al. 1981;Kewley et al. 2019;Constantin & Vogeley 2006;D'Agostino et al. 2019). Nevertheless, these different diagnostics have limitations due to the multi-parameters physical nature of these objects which is not exempt of degeneracy. With that in mind, we want to test the hypothesis that fitting multiple strong lines directly using model predictions (e.g. CLOUDY, MAPPINGS; Ferland et al. 2017Allen et al. 2008) that covers typical physical conditions in the gas could help minimize the errors associated on the line parameters (intensity, broadening and velocity), provide a pathway to classification of the nebulae directly from the fit, and potentially significantly increase the computational efficiency of the procedure as well as providing a new angle to estimate uncertainties.

The recent advent of integral field spectroscopy is expanding our knowledge of emission-line nebulae with their increased spatial and spectral resolution; these instruments are pushing the ability of existing analysis tools due to their resolution. (e.g. [START_REF] Sánchez | [END_REF][START_REF] Leroy | [END_REF]Bundy et al. 2014;Martins et al. 2010). SITELLE, an Imaging Fourier Transform Spectrograph (IFTS) located at the Canada-France-Hawai'i Telescope, is one such instrument. SITELLE has an unrivaled field of view of 11 ×11 and produces data cubes containing over 4 million pixels. Each pixel contains a spectrum. (e.g. Baril et al. 2016;[START_REF] Drissen | [END_REF]. SITELLE has a spectral resolution between 1 and 20,000. It's in-strumental line shape is described by a cardinal sinc function. It can be convolved with a Gaussian [START_REF] Martin | [END_REF] to account for natural broadening of the observed lines. Spectral fits must be done cautiously to accurately model the line shape and capture the effects of sidelobes of the sinc, which can greatly influence the estimated flux of an emission-line (e.g. [START_REF] Martin | Software and Cyberinfrastructure for Astronomy II[END_REF]. In many field of astrophysics, it is necessary to model resolved and unresolved (blended) lines accurately. Emission line parameters are the root information used to infer physical properties of locally-resolved nebulae as well as classifying them, but they are also crucial for proper characterisation of galaxies at different redshift. For the later, the line parameters are essential to fully understand how internal and external processes affect galaxies as one cannot disentangle active galactic nucleus, stellar winds, supernovae, etc, multiple feedback processes that affect the whole galaxy in different ways and at different scales.

In this paper we apply an artificial neural network to SITELLE spectra in order to obtain the strong emissionline ratios and validates its results by comparing with the line ratio derived from a standard line fitting techniques. We demonstrate the capability of the machine learning algorithm in low signal-to-noise regimes. In §2, we describe the synthetic data used to train and test the algorithm. It is important to note that although the method is tested here on well resolved objects, it could as well be used on galaxy at higher redshift and on integrated spectra. Additionally, we dissect the neural network and its hyperparameters. In §3, we describe how the network was trained and how it compares with the standard fitting procedure. In §4, we explore the impact of the signal-to-noise on the algorithm in addition to applying it on a real observation of M33, a well resolved local galaxy. We conclude in §5.

METHODOLOGY

In the first article of the series, Rhea et al. (2020), we explored the application of a convolutional neural network to calculate the kinematic parameters from SITELLE spectra. In this paper we expand the use of machine learning to calculate another critical set of physical parameters, the line ratios of strong emissionlines. As in the previous paper, the initial step in any machine learning application is to assemble the appropriate training set.

Synthetic Data

In order to facilitate the training of the network used to estimate strong-line ratios, we rely on carefully constructed synthetic spectral data. Synthetic data for emission-line sources must account for both the instrumental line shape (ILS) of an instrument for a given spectral resolution and the relative intensities and broadening of the lines available through observations. The network was developed for use in the SIGNALS program, which uses SITELLE to observe in three bands: SN1 (365-385 nm), SN2 (480-520 nm), and SN3 (651-685 nm). The synthetic data, and observed data, contain approximately 841 channels in SN3, 219 channels in SN2, and 171 channels in SN1. Each strong emission-line's ILS (Hα(6563

) Å, [O ii]λ3726, [O ii]λ3729, Hβ(4861) Å, [O iii]λ4959, [O iii]λ5007, [N ii]λ6548, [N ii]λ6583, (Hα(6563) Å, [S ii]λ6716
, and [S ii]λ6731, was separately modeled using the routine orb.fit.create cm1 lines model [START_REF] Martin | Software and Cyberinfrastructure for Astronomy II[END_REF]; ORB is the software kernel written for SITELLE, the imaging Fourier Transform Spectrometer on the Canada-France-Hawaii Telescope [START_REF] Martin | [END_REF]Martin & Drissen 2017;Baril et al. 2016). ORBS and ORCS build upon the ORB kernal and are used for data reduction and data analysis, respectively.

Following the SIGNALS large program instrumental configuration for the observations, we set the maximal spectral resolution in SN1 and SN2 to R∼1000 and in SN3 to R∼5000 (Rousseau-Nepton et al. 2019) to create the training set. Since the resolution varies as a function of location in a SITELLE spectral cube, we allow for variations within our spectral resolution to R∼200 less than the maximal value (e.g. Martin & Drissen 2017). Previous work reveled that this is a key parameter for an accurate training of the algorithm (Rhea et al. 2020). To fully sample the velocity and broadening space expected in the SIGNALS catalog (and in keeping with our previous study), we randomly select the velocity parameter from a uniform distribution between -200 and 200 km s -1 and the broadening parameter between 10 and 50 km s -1 . These values represent expected values for typical HII regions (e.g. Epinat et al. 2008); additionally, at R∼5000 SITELLE is unable to resolve the broadening parameter below 10 km s -1 (Rousseau-Nepton et al. 2019). The resolution, broadening, and velocity were randomly selected with replacement for each synthetic spectra so that we sample the entire parameter space (e.g., [START_REF] James | An Introduction to Statistical Learning: with Applications in R, 1st edn[END_REF]. Furthermore, the signal-to-noise ratio varied randomly between 5 and 30 with respect to the Halpha emission -meaning that Halpha emission is at least 5 times over the noise. However, this does not ensure that all lines are above the noise. The noise was assigned to each spectral channel individually and was randomly sampled from a normal distribution centered around the chosen signal-to-noise ratio with a sigma of 1.

The last element required to create synthetic spectra is the relative amplitude of the strong emission-lines. For each type of nebulae, we used different databases. Following the methodology described in detail in Rhea et al. (2020), relative line amplitude of the HII regions were sampled from the Mexican Million Models database (3MdB; Morisset et al. 2015) BOND simulations (Vale Asari et al. 2016). Following standard procedure, we use 70% of the synthetic data for the training set, 20% for the validation set, and 10% for the test set (e.g., Breiman 2001).

In contrast with our previous study, Rhea et al. 2020, we require all strong lines sampled in the SIGNALS observations to be present. We also add the restriction that all strong emission-lines must have an amplitude equal to or greater than 12% of the Hα amplitude. This threshold corresponds to a signal-to-noise ratio of 3 for the faintest targets in the SIGNALS sample whose Hα surface brightness is approximately 8 × 10 -17 erg s -1 cm -2 arcsec -2 (Rousseau-Nepton et al. 2019). While the impact of this threshold is discussed more in-depth in § 4.2, note that consistently, the training, validation, and test sets for the primary CNN used in this paper all adhere to this signal-to-noise constraint. Moreover, we select a Balmer decrement by randomly sampling a value between 2 and 6 from a uniform distribution with a sampling increment of 0.01. We then apply reddening at each wavelength sampled in our spectra following the procedure outlined in § 2.5.

We create 50,000 mock spectra in the form of FITS files which contain the emission-line information (e.g. velocity, broadening, resolution, emission-line fluxes) in addition to the spectrum itself.

Artificial Neural Networks

In this paper, we study the application of an artificial neural network to the problem of strong emission-line ratio estimation. Using the synthetic spectra described in §2.1, we train a network to approximate the function which maps SITELLE spectra to their corresponding line ratios.

The Algorithm

Feed Forward artificial neural networks (ANN) contain three principal layers: the input layer, the hidden layer(s), and the output layer (e.g. Hansen & Salamon 1990). The input layer consists of the preproccessed data that will be used to train the network and eventually be fed unseen inputs to make predictions. In this case, the input layer is the combined SN1, SN2, and SN3 SITELLE observations described previously. The output layer consists of line ratio estimates. The hidden layers contain an ensemble of nodes which are parametrized

[S ii]λ6731/[S ii]λ6716 [S ii]/Hα [N ii]/Hα [N ii]/[S ii] [O iii]/Hβ [O ii]/Hβ [O ii]/[O iii]
Hα/Hβ* 0.73-0.79 0.27-1.18 0.27-2.03 0.14-6.97 0.33-2.47 0.24-6.97 0.60-30.89 1.93-5.99

Table 1: Ranges of line ratio parameters from synthetic spectra. The distribution of the parameters are all skewed heavily to the lower values (with the exception of the [S ii] doublet ratio which is evenly distributed over a small range) which represents the likelihood of finding those parameters in the simulations from which these values are obtained. After applying an arcsinh transformation, the variables are normally distributed. * The wide range is due to artificially injected dust redenning following the prescription described in §2.5.

by a linear function that takes the input, x, multiplies it by a weight matrix, w, and adds a bias, b. The node is then activated by a predetermined function. A common activation function, the Rectified Linear Unit (ReLU), is employed in every layer of the network used in this paper except for the final layer (e.g. [START_REF] Chen | Non-linear system identification using neural networks[END_REF]). The ReLU function, g(w

× x + b) = max(0, w × x + b)
, takes the value of the node unless the value is negative; in that case, it takes the value 0. The result is a non-negative value for each node in a layer where the vector-valued function of each layer, l, is denoted as h l (x,b,w). In traditional neural networks, such as the network applied in this work, the layers are fully-connected ; thus, each node in a layer is connected to all nodes in the previous and subsequent layer.

After calculating h l (x,b,w) sequentially for each layer, we have a vector-valued output f (x,b,w). We can calculate the loss between the final predictions, f, and the correct outputs, y. We adopt the Huber loss function which is defined as:

k δ (f, y : w, b)) =    1 2 (y -f (w, b)) 2 |y -f (w, b)| ≤ δ δ|y -f (w, b)| -1 2 δ 2 otherwise (1)
where δ is a tune-able parameter and initialized as 1. The Huber loss function is often employed since it reduces the effects of outliers on the final cost calculation (e.g. Huber 1964).

We then minimize the loss function through backpropagation in which we alter the weights and biases (Hecht-Nielsen 1989):

arg min w,b k(f, y; w, b) (2)
We apply the Adam implementation of the stochastic gradient descent algorithm in order to minimize the loss function (Lechevallier & Saporta 2010; Kingma & Ba 2017). In this manner, we are able to train the network by updating the weights and biases until the loss function is minimized on the training set.

The Network and Hyper-Parameters

In order to determine the structural parameters of the network, we first constructed four networks; The first network had two hidden layers, the second network three hidden layers, and so on. Since the problem is nonlinear, we did not test a single hidden layer network. We note that the training, validation, and test sets used to determine the structural parameters contain only 10000 synthetic spectra. These spectra were not re-used in the final training, validation, and testing ensemble. Initially, each hidden layer contained 1000 nodes. This number is sufficient to test the optimal number of layers (e.g. [START_REF] Sheela | Review on Methods to Fix Number of Hidden Neurons in Neural Networks[END_REF]. Figure 1 demonstrates that the MAPE plateaus for the training set at four layers. However, since the mean squared error (MSE) increase in both the validation and test sets between three and four layers, we chose three layers as the optimal value. Although the figure is not included, the same patterns hold for the mean absolute error. Next, we applied a grid search on the number of hidden neurons allowing each to vary from 64,128,256,512, and 1024 nodes. The MSE was minimized for all sets when the first layer has 1024 nodes, the second layer has 1024 nodes, and the third layer has 512 nodes. Figure 2 We determined the optimal hyperparameter values by using the grid search and random search cross-validation techniques implemented in sklearn. The batch size's optimal value was determined to be four. Additionally, we adopt a normal random distribution as the initialization of the hidden layer neurons [START_REF] Thimm | From Natural to Artificial Neural Computation[END_REF][START_REF] De Castro | Proceedings 5th Brazilian Symposium on Neural Networks (Cat. No.98EX209[END_REF]. The data are normalized using to the maximum value in the the SN3 filter which corresponds to the maximum value in the combined filter. We note that this is not necessarily the amplitude of the Hα line. We use the tensorflow implementation of the ADAM optimization algorithm.

Initial testing of the algorithm revealed a systematic bias of approximately 10% in the residuals (see §3 for more details). In order to account for the bias, we applied two techniques: a transformation of the target variables and a regularization parameter. Initially, the distributions of the target variables (i.e. the line ratios the network is predicting) were skewed positive;

we thus applied several transforms on the target variables (e.g. log10, ln, arcsinh, etc.). Experimentation showed that applying an arcsinh transformation resulted in normalized target variable distributions. Furthermore, this reduced the systematic bias considerably (e.g. [START_REF] Zheng | Feature Engineering for Machine Learning[END_REF][START_REF] Kuhn | Feature Engineering and Selection: A Practical Approach for Predictive Models[END_REF]. Additionally, we applied a simple l2 regularization technique with λ = 5 × 10 -4 (e.g. [START_REF] Phaisangittisagul | 2016 7th International Conference on Intelligent Systems, Modelling and Simulation (ISMS)[END_REF]van Laarhoven 2017).

In order to increase the accuracy of the method and provide error estimates, we employ a technique known as deep ensembling [START_REF] Lakshminarayanan | [END_REF]). This method leverages the fact that each neural network is independent of the other. We train ten individual networks with the same architecture but with different weight initializations. We then apply each network to the test data individually. We average the classification probabilities and allow the standard deviation to act as an uncertainty estimate.

SITELLE Data

SITELLE observations of the Southwest Field of M33 led by P.I. Laurie Rousseau-Nepton were taken during the Queued Service Observation Period 18B (Program 18BP41). The galaxy was imaged in the three primary filters: SN1, SN2, and SN3. Both the SN1 and SN2 observations were taken at a spectral resolution R ∼ 1000, while the SN3 observation was taken at a spectral resolution R ∼ 5000. Although we do not analyse the data from the following two galaxies in detail in this paper, we demonstrate the feasibility of applying the network to two additional SIGNALS galaxies: M95 (Program 19A) and NGC4214 (Program 18A). These observations represent a subsample of the SIGNALS survey. We note that the authors are members of the SIGNALS science team. The raw data were reduced and calibrated using SITELLE's Level-1 reduction software, ORBS (version 3.1.2 [START_REF] Martin | Software and Cyberinfrastructure for Astronomy II[END_REF]).

Dereddening

Since we are using emission-line ratios spanning a large range of wavelengths, we must include the effects of dust attenuation by reddening the spectra (Calzetti et al. 1994;Buat & Xu 1996;[START_REF] Pettini | [END_REF]. We calculate dereddening following the standard procedure of postulating an effective dust screen attenuation to obtain the intrinsic emission-line fluxes (F 0,λ ),

F 0,λ = F obs,λ e τ λ = F obs,λ e τ V q λ , (3)
where F obs,λ is the observed flux, τ λ is the optical depth at a given wavelength, τ V is the optical depth in the V -band, and the shape of the dust attenuation curve is parametrized by q λ ≡ τ λ /τ V . We adopt the Cardelli et al. ( 1989) attenuation law with a total-to-selective extinction R V = 3.1. We use the Balmer decrement, defined as B d = F obs,Hα /F obs,Hβ , to calculate τ V :

τ V = 1 q Hβ -q Hα ln B d B d,in , (4)
where B d,in is the intrinsic Balmer decrement. We assume this value to be 2.87, which is appropriate for the Case B, an electronic temperature of 10 000 K and low density (e.g. [START_REF] Osterbrock | Astrophysics of gaseous nebulae and active galactic nuclei[END_REF]). Dereddening is applied to the line ratios post calculation by the neural network.

3. RESULTS

Optimal Synthetic Data

In this section we discuss the primary results of the paper and address the efficacy of the ANN when applied to optimal SITELLE HII regions sythethic spectra in order to predict the following strong emission-line ratios :

[N ii]λ6548/[N ii]λ6583, [S ii]λ6731/[S ii]λ6716, ([S ii]λ6716+[S ii]λ6731)/Hα, [N ii]λ6583/Hα, Hα/Hβ, [N ii]λ6583/([S ii]λ6716+[S ii]λ6731), [O iii]λ5007/Hβ, ([O ii]λ3726+[O ii]λ3729)/[O iii]λ5007, and ([O ii]λ3726+[O ii]λ3729)/Hβ.
We train and validate the network using the synthetic data described in §2.1. The mean absolute errors ( N i abs(y truei -y predi ); N is the number of training and validation input) on the training and validation are 0.0555 and 0.1207, respectively. The algorithm is applied to the test set; Figure 3 shows the relative errors achieved by the network when recovering each emission-line ratio. We note that all line-ratios recovered from SN3 have a low residual standard deviation; this is attributed to the higher spectral resolution in SN3 compared to SN1 and SN2. All error plots reveal approximately Gaussian error distributions with a positive skew. In order to validate these results using the standard fitting techniques, we use the ORB routine fit.fit lines in spectrum. We individually fit each filter; however, within a given filter, we fit all emissionlines simultaneously and supply the routine with the correct velocity and broadening parameters initially in order to retrieve the best possible fits. The lines were fit with a sincgauss function [START_REF] Martin | [END_REF]. Table 2 displays the comparison between the relative errors obtained using standard fitting routines and our ANN on the training set. In these conditions, the network outperforms the standard method for line ratios in all three filters. It is important to note that the relatively high errors in the fits are largely due to signal-to-noise effects (see §4.2 for the discussion). Appendix A contains the residuals binned by signal-to-noise for both the neural network and standard fits. These plots illustrate that the neural network is capable of outperforming a fitting routine in the low SNR (signal-to-noise) regime when compared within the training set environment. Importantly, the Hα/Hβ errors have the potential to be reduced significantly which will lead to higher fidelity dereddening estimates.

Noise Classification

In this section we evaluate the network used to classify a spectrum as noisy or clean; we define a spectrum clean if the SNR of all strong emission-lines is above a certain pre-determined threshold -in this case 5% that of Hα. This value was determined by running our network on the SN3 spectra of varying thresholds (from 1%-20%). The results indicated that below 5%, the ability of the network to recover the line ratios becomes inhibited.

Synthetic spectra for all filters were created in a method identical to that described in § 2.1 except that we removed the requirement that all strong emissionlines have an amplitude equal to at least 12% that of Hα. Spectra were classified as noisy if any emission-line had an amplitude less than 5% that of Hα; otherwise, the spectrum was classified as noiseless. In spectra where a single strong emission-line amplitude was below the chosen threshold, several other lines were also beneath the threshold; thus, this constraint accurately categorizes data into noisy and noiseless. We created 1,000 noisy and 1,000 noiseless spectra with signal-to-noise ratios of Hα varying between 5 and 30.

We use a Decision Tree Classifier, but in order to reduce bias and probabilistic errors, we aggregate several trees into a Random Forest. The data were randomly shuffled; 90% were set aside for training, and 10% for testing. Using 10 estimators (or 10 decision trees), the Random Forest Classifier reports 100% accuracy in classifying the two spectral types resulting in a diagonal confusion matrix. Although reaching perfect accuracy is relatively rare in machine learning scenarios, the welldefined and simple task allow the Random Forest Classifier to achieve 100% accuracy. Furthermore, if instead 70% of the data is taken for training, the power of the algorithm allows us to simply increase the number of estimators in order to obtain the same perfect accuracy. A future paper will dig deeper into the Noise classification problem.

Fitting Procedure [S ii]λ6731/[S ii]λ6716 [S ii]/Hα [N ii]/Hα [N ii]/[S ii] [O iii]/Hβ [O ii]/Hβ [O ii]/[O iii
4. DISCUSSION

Verification of the Network

Although neural networks trained on synthetic data are notoriously difficult to verify, we explore several methods to test whether the network is accurately learning the line ratios and is portable to real data (e.g. Bishop 1994; [START_REF] Krogh | Advances in Neural Information Processing Systems 7[END_REF]. We apply the following three techniques: k-fold cross-validation, tracking the static [N ii]λ6548/[N ii]λ6583 ratio, and a saliency map.

We apply a standard k-fold cross-validation by partitioning our synthetic data set into ten equal-sized allotments. We then train and validate the network with nine of the ten partitions allowing the final partition to serve as the test set. This process is repeated until each partition has been served as a test set (e.g. Bengio & Grandvalet 2004;[START_REF] Picard | [END_REF]. This method validates the network's estimates by testing the network for overfitting. Overfitting occurs when the network learns the training set but is unable to generalize to new data. If the network is susceptible to overfitting, then the final accuracy scores of the k-fold cross-validation model will differ significantly. A k-fold cross-validation analysis of our network indicates no overt overfitting in the model since the accuracy are all within several percentage points of one another (Molinaro et al. 2005;Cawley & Talbot 2010).

Additionally, we estimate the line ratio [N ii]λ6548/[N ii]λ6583 which is expected to be constant throughout all emission-line nebula and is frequently set to 3 in fitting code (e.g. Schirmer et al. 2013). This is reflected in the synthetic data set. Figure 4 reveals that the calculated [N ii] doublet ratio relative error between the true and network-estimated value is between 0 and -1% while the standard deviation is approximately 0.27%. Therefore, the network accurately replicates the static relation between the [N ii] lines.

Subsequently, we calculate the saliency map of the network. In order to calculate the saliency map, we calculate the derivative of the input with respect to the output of the neural network: ∂[input] ∂ [output] . By multiplying the gradients together, we are left with our desired partial derivative (e.g. [START_REF] Simonyan | Workshop at International Conference on Learning Representations[END_REF]. We normalize the values to unity in order to compare their relative importance with ease. In this manner, input nodes with a saliency value of zero do not affect the neural network, while input nodes with a saliency value of 1 have the most importance in affecting the neural network's estimation. In Figure 5, we show the saliency values plotted over a reference spectrum with a signal-to-noise of 20; we note that saliency values less than 0.05 are not included in the figure. The saliency map clearly shows that the network prioritizes the amplitude of the emission lines. However, the map also reveals the importance of the regions adjacent to the emission-lines and the areas of the spectrum in between emission-lines. This reflects the importance of the sidelobes of the ILS on the flux ratio estimates.

Effects of Varying Signal-to-Noise

Signal-to-noise constrains the efficacy of traditional fitting methods (e.g. Campbell et al. 1986;Endl & Cochran 2016). In this section, we compare the effects of signal-to-noise on the standard fitting techniques implemented in ORB compared to the artificial neural network described in this paper.

In order to study the effects of the signal-to-noise on the efficacy of line ratio estimates, we bin the line ratio residuals as a function of signal-to-noise. A signal-tonoise bin is created at each integer value of the sampled signal-to-noise used to create the synthetic data (5-030). Residuals were calculated by taking the estimated value and subtracted the ground truth and dividing that value by the ground truth value; the value was then multiplied by 100 to make it a percentage. We then removed all outliers; outliers are defined as residual values more than 3-σ off the median value. We then calculated the median value of the remaining set of residuals in each signal-tonoise bin. Errors were calculated as the 1-σ deviations from the median. The plots are shown in appendix A. Figure 7 demonstrates that the residuals do not change as a function of the signal-to-noise when calculated by the neural network. Conversely, the residuals and their associated errors are greatly reduced in high signal-tonoise regimes (R > 20) when calculated using standard fitting techniques.

Application to M33

Having demonstrated the feasibility of using a neural network to estimate strong emission-line ratios, we apply our methodology to the Southwest field of M33 studied in our previous article (Rhea et al. 2020). This field contains several previously identified emission region types (classic H ii regions, supernova remnants, and planetary nebulae; e.g. Zaritsky et al. 1989;[START_REF] Hodge | [END_REF]Viallefond et al. 1986); additionally, this field is a SIG-NALS target. All fits (both from the algorithm developed here and ORCS) were run using a computing server located at the CFHT headquarters in Waimea, Hawaii named iolani. The server has 2 Intel XEON E5-2630 v3 CPUs operating at 2.40GHz with 8 cores each. The configuration also has 64 GB of RAM available for computing purposes.

To compare our results with those from the ORCS fitting pipeline, we fit each cube seperately using ORCS. We use the fit lines in region function to fit the strong emission-lines present in a given filter. Within a filter, the lines are fit simultaneously with a single sinc function convolved with a Gaussian which returns each line's flux, velocity, and broadening (Martin & Drissen 2017). ORCS fits the observed data to a sinc function convolved with a Gaussian using the Levenberg-Marquardt least squares optimization algorithm. Velocity and broadening priors were determined by fitting a binned (8×8) data cube. The final unbinned fits (∼ 4 million spaxels) of SN3 took approximately 11 days, SN2 took 5.5 days, and SN1 took 1.8 day. We note that these calculations are done in parallel. Additionally, we applied the trained neural network to the cube. By comparison, the machine learning methodology requires approximately 18 computing hours, non-parallelized, to complete the entire cube (all three filters). This represents a reduction in computation time by approximately 2 orders of magnitude. Additionally, we applied the network outlined in Rhea et al. (2020) to calculate the velocity and broadening in order to have a more robust timing analysis. We report that the addition of this network did not add any significant amount of time to the overall fitting of the data cube. These results reinforce the notion introduced in Rhea et al. (2020) that by taking a machine learning approach to the analysis of IFU data cubes we can greatly reduce the time required for computation while retaining the accuracy of the results with a proper training.

Although there does not exist a known ground-truth value for these line ratios, we calculate the residuals between the machine learning predictions and standard ORCS fits in order to quantify the accuracy of the algorithm. Normalized residual plots for each line ratio can be found in appendix B. A visual inspection of the residual plots reveal that the machine learning algorithm returns similar values to those calculated by ORCS. Results deviate most strongly in regions which we show in Rhea et al. (2020) to be best described by multiple emission profiles, regions identified as non-H ii regions, and those with a low signal-to-noise ratio. We note, however, that the normalized residual plots (Figures 9 and10) show general agreement between the standard ORCS fits and those calculated by the neural network. Furthermore, discrepancies between the ORCS and neural network estimates illustrate the limitations of such an approach when used as a replacement to global fitting algorithms such as ORCS. These results further indicate the importance of taking multiple emission profiles into account when modeling -this is the topic of the following paper in the series.

CONCLUSIONS

Applications of machine learning in astronomy are broad: from the estimation of stellar spectral parameters (e.g., Fabbro et al. 2018) to the discovery of objects of interest in extensive astronomical surveys (e.g., Škoda et al. 2020). In this work, we apply an artificial neural network to combined-filter (SN1, SN2, and SN3) SITELLE data representing typical SIGNALS large program observations. The network is designed to calculate important emission-line ratios for H ii-like regions which are present in the primary SITELLE filters. We train, validate, and test the algorithm using synthetic data created with the ORBS software package. We adopt physically-derived line amplitudes from the Million Mexican Model Database (Morisset et al. 2015). Our results indicate that the network can potentially constrain the line ratios with greater precision than the standard line fitting technique implemented in ORCS if the source spectral properties are well represented in the training set. To demonstrate the applicability of the method beyond synthetic data, we apply the network to the Southwest field of M33. Timing analysis indicates that the network can analyze the entire cube approximately 100 times faster than the standard methods.

These results not only have an impact on the computational aspects of line ratio calculations, but they also carry scientific implications. Although our knowledge of galactic dynamics has expanded considerably over the past several decades, spectroscopic conclusions are restricted by the rigor of the fitting schemes employed and precision of the results. In this paper, we have demonstrated that machine learning algorithms can considerably increase the precision of emission line ratios in both low and high signal-to-noise regimes. This has profound implications on the study of these regions since it will allow stricter categorization using methods such as lineratio diagnostics in conjunction with BPT diagrams (e.g. Baldwin et al. 1981;Kewley et al. 2006;Kewley et al. 2019). These methods require concise measurements in order to accurately categorize the emission-region type and break any model degeneracies.

Following up on the success of our first report, the work presented here represents the second article in a series of articles covering the application of machine learning algorithms to SITELLE data cubes. Our re-sults have been encouraging in mapping out emission line ratios in pixels dominated by H ii region emission serves as a proof-of-concept that using machine learning to identify line fluxes is a viable methodology. We note this work is not meant to be a replacement to global line fitting algorithms. Identifying regions containing multiple, blended emission components, as well as multiple sources of emission with spectral features not represented in a training set remains to be explored. Additionally, example code can be found at https://github.com/sitelle-signals/Pamplemousse.

Figure 1 :

 1 Figure 1: Final mean absolute percentage error after five epochs of training as a function of the number of layers in the neural network. Each layer contains 1000 nodes and is activated by a relu function. The graphics show the curve for the mock training, validation, and test sets. We emphasize that the synthetic data used in the structural parameter tuning were not used again.

Figure 2 :

 2 Figure 2: Graphical depiction of the artificial neural network employed in this paper. The spectrum vectors for SN1, SN2, and SN3 are combined to form a single input vector which is then passed through a series of three fully connected layers. A linear activation function takes the final layer and compresses it into a final prediction for each line ratio.

Figure 3 :

 3 Figure3: Density plots of line ratio relative errors calculated using the ANN described in §2.2. We note that the errors follow an approximately Gaussian distribution with a non-negligible positive skew.

Figure 4 :

 4 Figure 4: Relative error as a function of signal-tonoise for the [N ii] doublet: [N ii]λ6548/[N ii]λ6583. The black dots represent the median relative error in a given signal-to-noise bin while the grey bars are the 1-σ errors associated with a given bin.

Figure 5 :

 5 Figure 5: Activation Map of the SN1, SN2, and SN3 filters using the reference spectrum. The relative weights are centered on emission line peaks and surrounding regions reflecting the importance of amplitude and side-lobes on flux ratio estimations. The signal-to-noise of this sample spectrum is approximately 20.

Figure 6 :

 6 Figure 6: Coadded Hα and [N ii]λ6583 emission map.The image illustrates the density of emission-line regions in the outskirts of M33. All pixels with an Hα flux less than 2 × 10 -17 erg s -1 cm -2 are masked out which corresponds to a signal-to-noise ratio of approximately 5.

Figure 7 :

 7 Figure7: Signal-to-noise ratio vs relative errors for the estimations obtained on the test set using the artificial neural network described in this paper. The signal-to-noise bins were taken at integer intervals. The black dots are the mean residuals. The grey bars represent the 1-sigma errors in a given signal-to-noise bin.

Figure 8 :

 8 Figure 8: Signal-to-noise ratio vs relative errors for the estimations obtained on the test set using the software package ORBS. The black dots are the mean residuals. The signal-to-noise bins were taken at integer intervals. The grey bars represent the 1-sigma errors in a given signal-to-noise bin. Baril, M., Grandmont, F., Mandar, J., et al. 2016, International Society for Optics and Photonics, 9908 Bengio, Y., & Grandvalet, Y. 2004, Journal of Machine Learning Research, 1089 Bishop, C. M. 1994, IEE Proceedings -Vision, Image andSignal Processing, 141, 217, doi: 10.1049/ip-vis:19941330 Breiman, L. 2001, Machine Learning, 45, 5 Buat, V., & Xu, C. 1996, Astronomy and Astrophysics, 306, 61. http://adsabs.harvard.edu/abs/1996A%26A...306...61B

Figure 9 :

 9 Figure 9: Residual Plots created by taking the difference between the ORCS fits and the values calculated by the artificial neural network for the Southwest Field of M33 normalized by the ORCS fit values. As discussed in the text, regions with large discrepancies between the ORCS and ANN fits are generally either not classic H ii regions or are described best by multiple components.

Figure 10 :

 10 Figure 10: Extension of Figure 9.

  graphically depicts the entire network. The structure of the algorithm is as follows:

	1. Concatenate spectral vectors from SN1, SN2, and
	SN3 as input
	2. Fully Connected Layer with ReLU Activation
	(1x1024)
	3. Dropout (25%)
	4. Fully Connected Layer with ReLU Activation
	(1x1024)
	5. Dropout (15%)
	6. Fully Connected Layer with ReLu Activation
	(1x512)
	7. Fully Connected Output Layer with Linear Acti-
	vation (1x8)

Table 2 :

 2 Standard deviation calculations for relative errors of strong emission-line ratios. The top row reports values calculated using the standard ORB routine while the second row calculates the same values for test set spectra with a signal-to-noise ratio greater than ten; comparatively, the bottom row contains values obtained using our ANN. [S ii] refers to the addition of the [S ii] doublets: [S ii]λ6713 and [S ii]λ6731; similarly, [O ii] refers to the addition of the two primary [O ii] lines: [O ii]λ3726 and [O ii]λ3729. Note that [O iii] refers only to a single line: [O iii]λ5007.As expected, the values calculated can be significantly elevated because the test set contains spectra in the extremely low signal-to-noise regime. We discuss the effects of signal-to-noise in detail in §4.2.

ACKNOWLEDGMENTS

The authors would like to thank the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Research Council (NRC) of Canada, the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii. The observations at the CFHT were performed with care and respect from the summit of Maunakea which is a significant cultural and historic site. C. R. acknowledges financial support from the physics department of the Université de Montréal, the MITACS summer scholarship program, and the IVADO doctoral excellence scholarship. J. H.-L. acknowledges support from NSERC via the Discovery grant program, as well as the Canada Research Chair program. NVA acknowledges support of the Royal Society and the Newton Fund via the award of a Royal Society-Newton Advanced Fellowship (grant NAF\R1\180403), and of Fundação de Amparo á Pesquisa e Inovação de Santa Catarina (FAPESC) and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq).

APPENDIX

A. SIGNAL-TO-NOISE AND RESIDUALS

In this section we display the signal-to-noise vs residual plots described in §4.2. Figure 7 displays the signal-to-noise vs residual plots for each line ratio calculated using the machine learning algorithm described in §2.2. Figure 8 shows the signal-to-noise vs residual plots for each line ratio calculated using ORB as described in §3.

B. LINE RATIO RESIDUAL PLOTS

This section contains the line ratio residual plots (ORCS fits -ANN estimates; Figures 9 and10). The two methods are in agreement in regions found to be best described by a single emission profile for each strong-line (see Rhea et al. (2020) for details); in regions best described by two emission profiles, the results differ significantly. In the subsequent paper, we will explore machine learning techniques to determine whether or not emission regions are best described by a single or double emission profile.


Victor Garric

Kimberly Colas

Patricia Donnadieu

Marie Loyer-Prost

Frederic Lepretre

Véronique Cloute-Cazalaa

Benedicte Kapusta

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