Diane Zarzoso-Lacoste

Pierre-Loup Jan

Lisa Lehnen

Thomas Girard

Anne-Laure Besnard

Sebastien J Puechmaille

Eric J Petit

P-L Jan

A-L Besnard

Combining noninvasive genetics

Keywords: noninvasive genetics, molecular sexing, Chiroptera, parentage assignments, Rhinolophus hipposideros

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Introduction

Monitoring wild populations is crucial for their effective management [START_REF] Mcmahon | Improving assessment and modelling of climate change impacts on global terrestrial biodiversity. Trends in Ecology Accepted Article relation to their biogeographic patterns[END_REF]Pereira et al. 2013). Yet, developing robust monitoring protocols is challenging (Nichols & Williams 2006), particularly regarding detection probability issues [START_REF] Vos | A framework for the design of ecological monitoring programs as a tool for environmental and nature management[END_REF][START_REF] Yoccoz | Monitoring of biological diversity in space and time[END_REF]Pollock et al. 2002). While extrinsic factors (related to observer identity, time, climate, habitat, or site) that lead to detection probability variation can be accounted for using covariates, this is not the case when variation results from inter-individual variation in behaviour. A common source of intra-specific variation is sex, with males and females displaying different behaviour that leads to large differences in detection probabilities (e.g. Ogutu et al. 2006;[START_REF] Christy | Modelling detection probabilities to evaluate management and control tools for an invasive species[END_REF][START_REF] Singh | Evaluating heterogeneity of sex-specific capture probability and precision in camera-trap population estimates of tigers[END_REF]. This observation lead to the development of statistical frameworks accounting for specific forms of intra-specific variation (e.g. [START_REF] Veech | Intrinsic heterogeneity in detection probability and its effect on N -mixture models[END_REF]), but the most obvious and efficient way of correcting potential bias is to a priori identify subsets of populations that differ in detection probabilities.

Numerous bat species are threatened by human induced perturbations and global change, and their loss could dramatically impact ecosystem functions and services (Mickleburgh et al. 2002;[START_REF] Jones | Carpe noctem: the importance of bats as bioindicators[END_REF]Rebelo et al. 2010). Monitoring programs that are set up to assess bat population trends most often use visual counts or, more recently, passive acoustics. One important caveat of these approaches is that different categories of individuals, which are not identifiable during census, may differ in detection probabilities.

For example, sexual segregation varies both spatially and temporally in bats and many other organisms [START_REF] Wearmouth | Sexual segregation in marine fish, reptiles, birds and mammals: behaviour patterns, mechanisms and conservation implications[END_REF][START_REF] Angell | Sexual segregation and flexible mating patterns in temperate bats[END_REF]. Different behaviour may even occur between individuals of the same sex [START_REF] Senior | Sex and segregation in temperate bats[END_REF], potentially leading to differences in detection probabilities [START_REF] Marescot | Capture-recapture population growth rate as a robust tool against detection heterogeneity for population management[END_REF]. Moreover, visual counts may cause disturbance to roosting bats, especially during the parturition and hibernation periods Accepted Article [START_REF] Kunz | Methods for assessing colony size, population size, and relative abundance of bats[END_REF]. Despite these limitations, visual counts are widely used in maternity colonies to study bat population structure and dynamics, either by assuming that males are not a substantial component of maternity colonies [START_REF] Johnson | Nocturnal Activity Patterns of Northern Myotis (Myotis septentrionalis) during the Maternity Season in West Virginia (USA)[END_REF]Olson & Barclay 2013) or by acknowledging that the unknown amount of males within colonies does not permit to correctly estimate essential parameters such as fecundity [START_REF] Seckerdieck | Alternative use of two different roost types by a maternity colony of the lesser horseshoe bat (Rhinolophus hipposideros)[END_REF].

When unverified, the first assumption is particularly likely to lead to incorrect inferences on population structure and dynamics. Furthermore, because females are the most important contributors to population dynamics in bats and many other animals, it is crucial to be able to differentiate both sexes when estimating colony sizes.

Capture-mark-recapture (CMR) techniques deliver individual level data which allow insights into bat life history and ecology, including longevity, physiology, social organization, movement behaviour, reproduction, sex ratio, and, to some degree, survival and population size (O'Shea et al. 2004;[START_REF] Ellison | Summary and analysis of the US Government bat banding program[END_REF]). However, CMR methods have generally proven unsuccessful for reliably estimating bat population size due to bias associated with the need to capture individuals multiple times, heterogeneity in individual detection probability, low recapture rates, trap happiness or shyness, or mark loss [START_REF] Kunz | Censusing bats: challenges, solutions, and sampling biases[END_REF][START_REF] Schorr | Estimating sample size for landscape-scale markrecapture studies of North American migratory tree bats[END_REF].

Therefore, CMR is difficult to apply to bats, which are elusive and sometimes rare organisms that are usually small-sized, nocturnal, cryptic, highly mobile and capture-sensitive. Superior censusing methods should minimize disturbance and sampling bias [START_REF] Yoccoz | Monitoring of biological diversity in space and time[END_REF][START_REF] Kunz | Methods for assessing colony size, population size, and relative abundance of bats[END_REF].

Noninvasive genetic methods have become a well-established tool to study free-ranging animals by identifying each individual through its unique DNA fingerprint, without having to capture or disturb them. DNA is extracted from noninvasive samples (hair, faeces, urine) and amplified at genetically informative markers. As a drawback, noninvasive samples often contain only low amounts of degraded target DNA, resulting in genotyping errors (Broquet et al. 2006). Previous work has proven that high quality genotypes can be efficiently obtained from bat feaces (Puechmaille et al. 2007). Multilocus genotypes are then treated as individual molecular marks, and identical genotypes are considered as recaptures. This information can be used in CMR models to estimate demographic parameters [START_REF] Lukacs | Research notes: estimating population size from DNAbased closed capture-recapture data incorporating genotyping error[END_REF]. The data provided can also be analysed using population genetic tools to gather critical information on sex-ratio (using a sex-linked genetic marker), relatedness, pedigrees, population structure or genetic diversity within or between populations [START_REF] Waits | Noninvasive genetic sampling tools for wildlife biologists: a review of applications and recommendations for accurate data collection[END_REF].

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Rhinolophus hipposideros is the Palearctic bat species whose population decline is best documented. During the last century, it became rare or extinct at the northern edge of its range in Northern Europe, likely due to pesticides use, food shortage, and habitat loss [START_REF] Bontadina | The lesser horseshoe bat Rhinolophus hipposideros in Switzerland: present status and research recommendations[END_REF][START_REF] Weiner | Roosting ecology, population development, emergence behaviour and diet of a colony of Rhinolophus hipposideros (Chiroptera: Rhinolophidae) in Bavaria[END_REF][START_REF] Farcy | Activité et terrains de chasse du Petit rhinolophe (Rhinolophus hipposideros Bechstein, 1800) en Bretagne, France[END_REF]. Females are known to return to their natal roost in late spring or early summer to give birth and raise their single young [START_REF] Gaisler | Reproduction in the lesser horseshoe bat (Rhinolophus hipposideros hipposideros Bechstein, 1800)[END_REF]. Males are usually assumed to live alone or to gather in small groups throughout the year but their presence in maternity roost has already been reported [START_REF] Gaisler | Mark-recapture results and changes in bat abundance at the cave of Na Turoldu, Czech Republic[END_REF][START_REF] Bontadina | Radio-tracking reveals that lesser horseshoe bats (Rhinolophus hipposideros) forage in woodland[END_REF]. Pregnant and lactating females have stricter roost requirements than others [START_REF] Speakman | Physiological ecology and energetics of bats[END_REF]. Such possible intra-specific variations in roosting requirements and behaviour depending on sex or reproductive status could result in intrinsic heterogeneity in detection probabilities, and therefore, affect colony size (i.e. total number of adults) and fecundity (i.e. ratio juveniles/adults) measurements when estimated by visual counts [START_REF] Safi | Sex differences in population genetics, home range size and habitat use of the parti-colored bat (Vespertilio murinus, Linnaeus 1758) in Switzerland and their consequences for conservation[END_REF][START_REF] Veech | Intrinsic heterogeneity in detection probability and its effect on N -mixture models[END_REF]. Here, we provide evidence that genetic approaches, including molecular sexing, are of great interest to elucidate the population structure of bat maternity colonies and to investigate possible differences in sex-and/or status-related behaviours.

The main goals of this study were to investigate population size, sex ratio and sex-

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related behaviour in R. hipposideros maternity colonies with a noninvasive genetic CMR approach combined with parentage assignment. We developed a robust molecular protocol, using 8 polymorphic microsatellites and one sexual marker which we applied on samples from 19 R. hipposideros colonies situated in Northern France, assessing the importance of taking into account sex and reproductive status when monitoring populations.

Material and Methods

Study site and sampling protocol

19 colonies located in Northern France (Picardie) were investigated (Fig 1). Bat faeces were collected during two successive sessions conducted before and after parturition in 2013.

Newspaper was spread on the ground under the main hanging sites of each colony to gather bat faeces. After approximately 10 days, faeces were collected and stored on containing silica gel fragments to prevent DNA degradation until analysis (Puechmaille & Petit 2007). The number of visible adults was recorded during each visit.

DNA isolation

All pre-PCR procedures were carried out with aerosol barrier tips and single-use non-talc gloves, and pre-and post-PCR procedures were performed in separate rooms to avoid crosscontamination. For each colony, the desired number of faeces (twice the number of bats visually counted during colony sampling; see Table 2) was randomly picked. Faeces were individually homogenized using two glass beads (2 mm diameter) for 2 × 30 s at 30 Hz (Tissuelyser, Retsch). DNA was extracted using the NucleoSpin® 96 Plant II Kit (Macherey-Nagel) with slight modifications from the original protocol (Appendix A).

Development of a new polymorphic sex-linked marker

A primer pair was designed to target a pseudo-autosomal portion of the 8 th intron of the sex-

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linked DEAD-box helicase 3 gene (DDX3). This gene was previously amplified in bats, with amplicon lengths suitable for degraded DNA analyses [START_REF] Hellborg | Y chromosome conserved anchored tagged sequences (YCATS) for the analysis of mammalian male-specific DNA[END_REF]. The new primer pair (DDX3X/Y-Mam-F: CAGATCTATGAGGAAGCCAGAAA; DDX3X/Y-Mam-R: TCATACCGCTCTAGAGTTCGC) targets a locus that exhibits different length on the X (154 bp from the DDX3X gene, also called DBX) and Y (131 bp from the DDX3Y gene, also called DBY) chromosomes, respectively.

The suitability of this marker for R. hipposideros sex identification was tested using 22 male and 17 female pure DNA samples extracted from postmortem biopsies following a salting out protocol (Petit et al. 1999). PCR reactions were conducted in a final volume of 15μL containing 1 µL of template DNA, 10X PCR Buffer (20 mM Tris-HCl ph 8.4, 50 mM KCl; Promega), 0.2mM dNTPs (Invitrogen), 1.5mM MgCl2 (Promega), 0.3μM of forward and reverse primer, 0.05U/μL Taq DNA polymerase (Promega). The cycling conditions included an initial denaturing step of 95°C for 15 min followed by 45 cycles of 94°C for 45 s, 56°C for 45 s, and 72°C for 1 min and a final extension step of 72°C for 1 h. The PCR products obtained from two female and two male were cloned and purified (Strataclone PCR Cloning Kit, Agilent). Consensus sequences for DDX3 fragments amplified from both X-and Y-chromosomes were obtained by forward/reverse sequencing seven clones from each individual (Sanger technology).

In silico PCR (ecoPCR programme: [START_REF] Ficetola | An In silico approach for the evaluation of DNA barcodes[END_REF]) was conducted to assess the theoretical coverage (Bc) of our sex-linked primer pair. To do so, we compiled a customized sequence database by blasting (Blastn) our consensus X-linked amplicon on the entire EMBL database, and by retrieving from GenBank the mRNA sequences of each available mammalian (sub)species (taxid: 40674). We then filtered out those that (i) did not align correctly, (ii) were too short to cover the entire length of the corresponding amplicon (i.e partial sequences) and (iii) contained ambiguous nucleotides (e.g. N). We randomly kept one

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sequence per (sub)species to reduce overrepresentation of a few species. Sequences were trimmed to contain only the amplicon (including primer binding sites), and internal insertions were removed. Our customized mRNA sequence database, containing 91 unique mammalian (sub)species (Appendix B), was used with ecotaxstat [START_REF] Ficetola | An In silico approach for the evaluation of DNA barcodes[END_REF] to compute Bc (allowing 3 mismatches).

We also looked for length polymorphism of our sex-linked marker in Mammalian species. We first compiled a customized sequence database by blasting (Blastn) our consensus X-linked amplicon on all available mammalian reference genomic sequences (refseq_genomic) and by retrieving the sequences (and corresponding chromosome, gene and sex annotations) from each matching (sub)species. We then filtered out those that did not align correctly, as well as partial sequences, and trimmed the sequences to contain only the amplicon (including primer binding sites). Finally, we calculated the theoretically amplified amplicon length for all the 162 sequences, belonging to 85 unique mammalian (sub)species, contained in our customized genomic sequence database (Appendix B).

Multilocus genotyping

Bat DNA was amplified and genotyped using 9 polymorphic molecular markers including a panel of 8 microsatellites selected from the literature, and our new sex-linked maker (Table 1, Appendix C). These 9 markers were optimized into a single 8 μl multiplexed reaction containing 3.5 μl Multiplex PCR buffer mix (Qiagen), 0.0875 μM of each primer (Table 1) and 2 µl DNA templates.

A touchdown thermal cycle program was used to prevent non-specific amplification, which included an initial denaturation at 95°C for 15 min followed by 16 cycles each of denaturation at 94°C for 45 s, 58°C with 0.5°C decrease per cycle for 45 s, and extension at 72°C for 1 min, and completed with 20 additional cycles with an annealing temperature of 50°C. A final extension at 72°C for 1 hour was included at the end of the cycles before

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holding at 4°C. Amplifications were replicated three times to allow for genotyping error detection and to build robust consensus genotypes. Alleles were scored using GeneMapper v.5 from electrophoreses run on a 3730xl DNA Analyzer sequencer with GeneScanTM-500LIZ size standard (Applied Biosystems).

Bioinformatic pipeline and genotyping quality

An automatic procedure that scores genotypes and determines consensus genotypes was developed to avoid problems associated with subjective/inconsistent scoring of alleles and human errors and minimize the time necessary for scoring alleles. This bioinformatic pipeline is based on a comparison between alleles obtained from different scoring parameters for each replicate, and a comparison between replicates. A first scoring mode, "stringent", only considered peaks high enough to avoid genotyping errors associated with small peaks, with a threshold depending on the fluorescent dye (200 for PET, 100 for others). A second scoring mode, "non-stringent", employed peak height thresholds of 20, 40, 50, and 60 for FAM, VIC, NED, and PET, respectively. This allowed the recovery of peaks that were not detected with the first thresholds. Thresholds for stringent and non-stringent analyses were chosen after careful observation of randomly selected samples to account for the different markers' propensities to generate higher peaks or smaller artefacts. Peaks detected with the nonstringent analysis were only scored if they were detected in at least two of the three PCR replicates. Automated scoring with GeneMapper tends to not consider peaks obviously high enough when another peak is drastically higher. To overcome this issue, in a third approach, we scored our data as Amplified Fragment Length Polymorphisms (AFLP) instead of microsatellites. This allowed the detection of all the peaks within defined bins independently of the height of other peaks, retaining only those that had already been detected in previous scorings in at least one other replicate. When more than two alleles per locus were scored by the software, only the two highest were kept.

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The three replicates obtained from each sample were then used to create a consensus genotype by applying the following rule: one allele of the consensus must appear at least twice over the three replicates. In the rare case of problematic consensus (three alleles seen twice), the smallest peak was discarded. To rule out that distinct genotypes actually corresponded to the same individual because of genotyping errors, we manually checked every consensus that differed from others by one or two loci (mismatch 1 and 2 -Puechmaille & Petit 2007). If there was any evidence for distinct genotypes originating from the same individual (i.e. if a particular allele was present in at least one replicate of the genotype of the individual scored as homozygous for that locus) this allele was retrospectively validated, in order to create a common genotype and merge samples.

Samples with missing data on at least one locus were discarded for subsequent analyses, except the juvenile dataset for parentage assignment (see below). Allelic Drop Out (ADO) and False Allele (FA) rates, as well as the Quality Index (QI), were estimated by comparing consensus genotypes to PCR replicates [START_REF] Broquet | Quantifying genotyping errors in noninvasive population genetics[END_REF]Miquel et al. 2006). The expected heterozygosity of each locus was computed with unique genotypes (i.e. individuals) using the adegenet package [START_REF] Jombart | adegenet: a R package for the multivariate analysis of genetic markers[END_REF] to evaluate the markers' polymorphism.

Deviations from Hardy-Weinberg proportions were quantified and tested with FIS and the corresponding permutation test using the software GENETIX [START_REF] Belkhir | GENETIX 4.05, logiciel sous Windows TM pour la génétique des populations[END_REF]. Only individuals encountered before parturition (adults) were used in these two tests.

Parentage assignment

To identify mothers, parentage was assigned using the software Colony 2 with a full-pedigree likelihood method [START_REF] Jones | COLONY: a program for parentage and sibship inference from multilocus genotype data[END_REF]. Males were designated as polygamous, and mothers as monogamous with only one possible offspring because samples were taken over a single reproductive event [START_REF] Gaisler | Reproduction in the lesser horseshoe bat (Rhinolophus hipposideros hipposideros Bechstein, 1800)[END_REF]. Individuals sampled before parturition were considered as

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potential parents while those only sampled after parturition were considered as potential juveniles. Only individuals successfully genotyped at 9 loci were considered, except potential juveniles for which the selection threshold was lowered to 7 loci since these individuals, only sampled after parturition, were less likely to represent a clean genotype due to the lack of comparison between sampling sessions. We ran analyses ten times to assess the robustness of the results. Only individuals assigned at least five times out of ten runs were considered as parents.

Population size estimates

Population sizes were calculated using a Bayesian estimator based on single session CMR data (Petit & Valière 2006). This method, adapted to noninvasive genetic data, considers every population size between a minimum (the number of genotypes detected) and a maximum size (set to 10 times the visual count) and determines the most probable population size given the distribution of recaptures (i.e. the number of faeces corresponding to the same individual). This method assumes a homogenous detection probability and a closed population. The homogeneity of detection probability was tested with the method developed in Puechmaille & Petit (2007), which consists in simulating the sampling process under an assumption of homogeneous capture probability, and to compare the observed with the expected number of captures per individual. Population closure is highly likely since samples were deposited over a maximum of two weeks. Population size estimates were computed when considering adult (i) females and males and (ii) females only. Individuals assigned as juveniles were removed from population size estimates. To compare visual and genetic estimation methods, we performed a generalized linear mixed model (glmm) with population size as a response variable (following a Poisson distribution) and with the estimation method and sampling session as fixed effects. Colonies were considered a random effect. Fixed effect significances were tested with a Wald chi square test followed by post-hoc pairwise least-

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square means test. Glmm and Chi-square tests were performed in R 3.2.2 (R Core Team 2016). For comparison, we also estimated the population size with the Capwire package (Pennell et al. 2013), by performing either the "Equal Capture Model" or the "Two-Innate Rates Model" (depending on the likelihood ratio test included in the package) before performing the same glmm and subsequent tests. To validate the suitability of our molecular markers to discriminate among a large number of individuals, population size estimates were compared with the reciprocal of the probabilities of identity computed for unrelated individuals (PID-rand) and full siblings (PID-sibs) using Gimlet [START_REF] Valière | GIMLET: a computer program for analysing genetic individual identification data[END_REF]) and for samples collected before parturition.

Sex related behaviour

The overall and offspring sex-ratio of each colony (i.e. the ratio of males to total number of individuals genotyped) was estimated separately before and after parturition. To investigate the capture probability of females and males depending on the sampling session, we performed a generalized linear mixed model (glmm) with the number of recaptures for each individual as a response variable (following a Poisson distribution) and with sex and sampling session as fixed effects. Because the same individual could be sampled before and after parturition, we considered individuals as a random effect. The fixed effect significance was tested with a Wald chi-square test followed by a pairwise least-square means post-hoc test. A Chi-square test was performed to investigate if the inter-session recapture rate (number of individuals captured before and after parturition) differed between sexes and with female reproductive status.

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Results

Molecular protocol validation and sex ratio

The results of the amplification tests carried out with the DDX3X/Y-Mam sex-linked marker on 37 known R. hipposideros males and females confirmed its reliability for sex identification (100% were correctly sexed). Sequenced amplicons provided one allele from the X-Chromosome (154 bp) and two from the Y-Chromosome (129 and 131 bp).

Furthermore, in silico PCRs confirmed the reliability of the DDX3X/Y-Mam marker for sex identification, its length polymorphism between and within 85 unique mammalian (sub)species, and the wide taxonomic coverage of the corresponding primer pair that theoretically amplified 88% of the 91 tested (sub)species belonging to all described placental mammal super-orders (detailed results are available in Appendix B).

In this study, 3544 samples out of 5099 (69.5%) were genotyped at all 9 loci. Mean ADO and FA rates over loci were 6.7% and 2.5% respectively, resulting in a QI of 91.6%. The average expected heterozygosity of the eight microsatellite loci was 70% (range 43-83%). Over all loci and colonies, the minimal number of individuals that could be discriminated for unrelated individuals (1/PID-rand) and assuming full siblings (1/PID-sibs) was above 1.46 x 10 6 and 2.77 x 10 4 , respectively, and was always clearly greater than the corresponding colony sizes estimated visually or genetically (Table 2).

We distinguished 1337 unique genotypes, inferred to correspond to different individuals, 345 (25.8%) of which were males. The number of unique genotypes identified for each colony and sampling session ranged from 4 to 200 with a mean of 43.7, and was in the range of corresponding visual counts (Table 2). F IS values were variable between colonies, with four significantly positive values (Pic4, Pic5, Pic6, Pic19) and one significantly negative (Pic8). Males were sampled in each colony and at each sampling session, except in the smallest colony (Pic1) before parturition. The mean overall sex-ratio of

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the sampled colonies was 0.22 (range 0 -0.5) and varied between colonies and sampling sessions (Table 2).

Population size estimates

Population sizes estimated from all individuals ranged from 8 to 235, with a mean of 64.16 (SD = 46.16) individuals before parturition, and 60.28 (SD = 34.49) after parturition (Table 2). When only considering females, average population sizes decreased to 47.9 (SD = 28.71) and 44.56 (SD = 24.49) before and after parturition, respectively. However, capture probabilities were not homogenous in half of the colonies (in 9 to 11 colonies depending on male presence and sampling session, see Table 2). Because no recapture occurred at Pic1 after parturition, we were unable to estimate its population size.

Mean population sizes calculated from all individuals, before and after parturition, were greater than those estimated from females only. Mean adult population sizes estimated through visual counts were closer to those calculated from females only (Fig. 2) and no significant difference was observed between them before parturition (Least-square means, pvalue = 0.22). Independently of the estimation method, adult population sizes decreased after parturition. Capwire estimates gave similar results, with no significant differences between visual counts and female population size before and after parturition, with a p-value of 0.25 and 0.32, respectively (data not shown).

Sex ratio and sex related behaviour

Among the 662 females sampled before parturition and the 670 potential juveniles, only 174 were assigned as mother-juvenile pairs at least 5 times among 10 Colony runs. Motherjuvenile assignments were possible for all 19 sampled colonies, but with very heterogeneous proportions of mothers, varying from 8% to 80% (31.4% on average). This analysis allowed us to distinguish mothers and unassigned females (hereafter, non-mother females).

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The number of samples collected from individuals assigned as mothers was significantly higher than for males for both sampling sessions (Least-square means, p-values < 0.05). The number of recaptures for mothers was particularly high after parturition, and significantly higher than for non-mothers (Fig. 3). There were significantly more inter-session recaptures for mothers (63.8%) than for non-mothers (34.2%), and more for both types of females than for males (20.6%) (Chi-square test; p-values < 0.001).

Discussion

Molecular protocol validation

We developed a widely applicable noninvasive molecular protocol, involving eight microsatellite loci and one sex-linked marker, for population genetic studies conducted on R. hipposideros. Our results confirmed the suitability of the DDX3 sex-linked marker for reliable molecular-sexing from DNA extracted from different sources, including noninvasive samples. Indeed, the amplification of different pseudo-autosomal DNA fragment sizes (i.e. length polymorphism) from both X and Y chromosomes in a single PCR reaction allowed the unequivocal distinction between sexes by avoiding misidentification due to PCR failure (i.e. false negative results) when using chromosome-specific markers. We showed that this interchromosomal length polymorphism, which is linked to an indel located in the 8 th intron of the DEAD-box helicase 3 gene, is observed in 85 mammalian (sub)species, making it a potentially widely applicable molecular sexing tool (Appendix B.2).

Despite the challenging low concentration and degraded nature of noninvasive DNA samples, our protocol allowed the complete genotyping of 70% of analysed faeces and provided high quality genetic data (QI 91.6%) with low genotyping error rates (ADO <7% and FA <3%). When including the samples with missing data, the Quality Index dropped to 73.3% but ADO and FA rates remained relatively stable (6.6% and 3.2%, respectively). These

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values are among the best recorded when compared to other studies directly amplifying nuclear DNA from faeces [START_REF] Broquet | Noninvasive population genetics: a review of sample source, diet, fragment length and microsatellite motif effects on amplification success and genotyping error rates[END_REF], but are lower than those obtained in Puechmaille et al. (2007), where microsatellites markers were only genotyped if mtDNA was previously amplified in a given sample. This suggests that directly performing three PCR replicates per sample can represent a good compromise between sufficiently reducing genotyping error rates while keeping the cost of large scale studies as low as possible.

Here, 1337 unique genotypes were obtained from 19 colonies, which, in combination with the low PIDs calculated for our data set (even assuming full siblings), demonstrates that our molecular marker set is variable enough to discriminate a large number of individuals.

F IS spanned a wide range of values around zero, with the most extreme ones being significantly different from zero (Table 2). No particular locus was involved in these extreme values (data not shown), excluding potential experimental artefacts. These F IS values may rather be related to different underlying structures (e.g. Wahlund effect or family structures, see Parreira & Chikhi 2015) in the different colonies, a topic that will require further investigation.

Extrinsic factors affecting detection probability and population size estimates

Mean bat colony sizes estimated visually were always closer to the genetic estimates of female population sizes than to those of the total population (Fig. 2). Hence, visual counts, which do not allow sex differentiation, underestimate the total number of individuals that occupy colonies. Indeed, individuals which are not present when the visual count occurs are missed. Individuals with the highest philopatry, i.e. females, are more likely to be detected.

Beyond sex, individual detection probability may be heterogeneous due to a multitude of time-or site-dependent extrinsic factors affecting the observation process itself (observers' skills, timing and duration of censusing) and/or conditions (environmental factors restraining visibility or observers' proximity to the animals and/or factors related to species biology and Accepted Article ecology) [START_REF] Kunz | Methods for assessing colony size, population size, and relative abundance of bats[END_REF][START_REF] Veech | Intrinsic heterogeneity in detection probability and its effect on N -mixture models[END_REF]. Our results confirm that visual counts represent a reliable and cost effective method for censusing the more settled individuals within colonies (i.e. adult females, see below) when only interested in bat demographic trends.

However, when more detailed demographic data are required (e.g. population structure, reproduction or vital rates), sampling noninvasively over several consecutive days combined with CMR approaches represents a powerful alternative. Genotypes were obtained at a cost of 7.25€ per sample (consumables only) and approximately two months of lab work and data analysis were required to obtain clean consensus genotypes for all 19 colonies. This investment provided high quality data at the individual level and while minimizing both disturbance of colonies and the effects of extrinsic factors on individual detection probability and population size estimates (Petit & Valière 2006;Puechmaille & Petit 2007;[START_REF] Kunz | Methods for assessing colony size, population size, and relative abundance of bats[END_REF]).

Half of the population size estimates did not meet the assumption of homogeneous detection probability, and this heterogeneity can alter population size estimates [START_REF] Link | Nonidentifiability of population size from capture-recapture data with heterogeneous detection probabilities[END_REF].

Therefore, population size estimates taken at the colony level should be treated carefully. Indeed, in most wild animal populations, standardizing sampling effort is helpful to reduce biases due to extrinsic factors, but will not totally eliminate heterogeneity, because other intrinsic variables, like inter-individual behavioural variations, will influence their detection probability through space and time [START_REF] Yoccoz | Monitoring of biological diversity in space and time[END_REF][START_REF] Veech | Intrinsic heterogeneity in detection probability and its effect on N -mixture models[END_REF]. It is thus crucial to define subsets of populations that differ in detection probability for a more accurate evaluation of key parameters such as population sizes or vital rates.

Intrinsic factors affecting detection probability and demography

Within a population, individuals may exhibit distinct types of behaviour that will make them more or less detectable. This heterogeneity in detection probability can be related to one or several intrinsic factors including age (e.g. [START_REF] Crespin | Increased adult mortality and reduced breeding success with age in a population of common guillemot Uria aalge using marked birds of unknown age[END_REF], sex (e.g. [START_REF] Tavecchia | Sex-biased survival and breeding dispersal probability in a patchy population of the Rock Sparrow Petronia petronia[END_REF], breeding or social status (e.g. Ogutu et al. 2006).

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Although intrinsic heterogeneity remains difficult to measure and to control for statistically [START_REF] Veech | Intrinsic heterogeneity in detection probability and its effect on N -mixture models[END_REF], its underlying factors are important to identify and consider whenever possible, because behaviour is often the primary force responsible for changes in density, genetic diversity, and sex or age structure.

Sex related behaviour

The set of molecular markers used allowed us to assess variation of bat maternity colony structure over time. Our results show that these colonies are indeed mainly composed of females but also that the number of males is substantial (25.8%). This is in agreement with sex-ratios recorded in other European maternity colonies [START_REF] Bontadina | Radio-tracking reveals that lesser horseshoe bats (Rhinolophus hipposideros) forage in woodland[END_REF], though our results demonstrate that sex-ratio is not homogenous between colonies and through time within the same colony.

Unsurprisingly, a greater number of samples was analysed per female than per male before and after parturition (Fig 3). This number significantly increased in females while it decreased in males after parturition, suggesting that most males leave or spend less time in the roost and are not recaptured (Table 3). This is supported by the fact that our female population size estimates were slightly lower (13.7% on average) than visual counts, which only encompass the most settled individuals independently of their sex. Such behaviour has been observed in many other temperate bats where females segregate from males in spring and summer to form maternity colonies and raise their young [START_REF] Mccracken | Bat mating systems[END_REF][START_REF] Senior | Sex and segregation in temperate bats[END_REF][START_REF] Safi | Sex differences in population genetics, home range size and habitat use of the parti-colored bat (Vespertilio murinus, Linnaeus 1758) in Switzerland and their consequences for conservation[END_REF][START_REF] Ibáñez | Sexual segregation in Iberian noctule bats[END_REF]. Indeed, during this period of low mating willingness, the lower fidelity of males to maternity colonies may reduce local resource competition with pregnant and lactating females that display more stringent foraging and roosting requirements [START_REF] Senior | Sex and segregation in temperate bats[END_REF][START_REF] Safi | Sex differences in population genetics, home range size and habitat use of the parti-colored bat (Vespertilio murinus, Linnaeus 1758) in Switzerland and their consequences for conservation[END_REF].

These results highlight the potential of molecular approaches to investigate sex-related

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behaviour, in relation to species biology and ecology, and to evaluate how it could affect individual detection probabilities during population surveys. Such sex-specific information can inform conservation programs, especially in social and/or colonial species in which females, which are key individuals for population growth, form isolated groups to give birth and raise their young, a period in which they are particularly vulnerable.

Female reproductive status

The combination of our noninvasive CMR approach with parentage analysis allowed deeper insights into the structure of maternity colonies, revealing that female roost fidelity can change over time according to reproductive status, and providing fecundity estimates.

Only 26.3 % of the females sampled before parturition were assigned a mother status. This is surprisingly low considering previously reported values of this species' fecundity (e.g. 0.38 and 0.5 in [START_REF] Schofield | The ecology and conservation biology of Rhinolophus hipposideros, the lesser horseshoe bat[END_REF]Petit et al. 2014, respectively). A possible explanation would be that we failed to assign a significant number of mothers due to insufficient sampling, or because of genotyping failure of some mothers before parturition and/or some juveniles after. The latter is particularly likely because sex-ratios of assigned juveniles, which are supposed to be balanced [START_REF] Gaisler | Reproduction in the lesser horseshoe bat (Rhinolophus hipposideros hipposideros Bechstein, 1800)[END_REF], were biased towards females in our study (21.8% males, data not shown). This could be explained by an unexpected difficulty to sample juveniles (e.g. particular composition and/or frequency of deposition of juvenile faeces, coprophagy behaviour of the mother), or by a significant part of the assigned juveniles actually corresponding to philopatric adult or subadult females sampled only after parturition. Nevertheless, variation in offspring sex-ratio has been reported in numerous mammal species including bats [START_REF] Barclay | Variable variation: annual and seasonal changes in offspring sex ratio in a bat[END_REF], and different adaptive explanations have been proposed [START_REF] Clutton-Brock | Sex ratio variation in mammals[END_REF].

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We cannot currently accept or reject one of those two hypothetical explanations for the low number of assigned mothers observed, the reality being probably a mix of both. If low juvenile sampling prevails in shaping the observed patterns, sampling twice in a single year might not be optimal for correctly identifying all mothers of that year, or to estimate fecundity. Sampling colonies twice a year over multiple years would enhance both adult and offspring sample sizes and could help elucidating the causes of the observed low parentage assignment and female-biased offspring sex ratios.

Differences between the fecundity observed in bibliography, estimated from visual counts, and our molecular approach could also be related to intrinsic heterogeneity in individual detection probabilities due to behavioural differences in roost occupancy between individuals of different reproductive status. Indeed, the mean number of samples analysed per individual after parturition was higher for females assigned as mothers than for any nonmother in both sampling sessions (Fig. 3). For mothers, the number of samples analysed per individual increased after parturition, suggesting a smaller mobility of females that gave birth. This number did not vary for non-mother females between sampling sessions, suggesting a stable behaviour over this period. Furthermore, the proportion of females resampled after parturition was higher for females assigned as mothers (Tab. 3). These results clearly show that all females seem to frequent the maternity colony before the permanent settlement of mothers. Because the costs and benefits of site fidelity for females may change with reproductive conditions and associated energetic requirements, we hypothesize that nonmothers are less faithful to their colony because of intra-specific competition for local resources with mothers (see [START_REF] Anthony | Night roosting and the nocturnal time budget of the little brown bat, Myotis lucifugus: effects of reproductive status, prey density, and environmental conditions[END_REF][START_REF] Kunz | Methods for assessing colony size, population size, and relative abundance of bats[END_REF]Ngamprasertwong et al. 2014).

Finally, our results highlight the suitability of our approach (involving a well conserved polymorphic pseudo-autosomal sexual marker) to (i) gather high quality data at the

Accepted Article

individual level, (ii) decipher complex inter-individual behavioural variations that may influence individual detection probability, and (iii) consider these factors for more precise population size and reproduction rate estimates, which are fundamental for efficient management of wild populations.

Conclusion

With noninvasive genetic sampling and an analysis method adapted to large datasets, we obtained high quality genetic data with minimal disturbance of the colonies. We showed that distinguishing males from females, using a sex-linked marker, offers unique opportunities to more reliably determine different categories of individuals (males, females, potential breeders, reproductive individuals), to identify extrinsic and intrinsic factors of heterogeneity in individual detection probabilities, and to estimate population sizes, which is critical for understanding population dynamics and optimise wildlife management. By combining parentage with CMR analyses, we showed that the population structure of R. hipposideros in maternity colonies changes dynamically during the summer. Parentage assignment provided valuable insights into female behaviour revealing that, after parturition, maternity colonies are mainly composed of mothers and their offspring while males and non-mother females continue to frequent them without residing there permanently. Because reproductive females crucially contribute to the establishment and long-term persistence of social animal colonies, disentangling behaviour specific for these different categories of individuals is essential for an effective monitoring and conservation of wild populations. Finally, our study highlights that noninvasive genetic samples, when analysed both as individual marks (CMR) and genetic fingerprints (parentage) instead of as allelic frequencies only, allow to investigate both individual (behaviour, mating, etc.) and population (genetics and dynamics) level processes.

When combined with information on other biotic or abiotic factors, such data offer unprecedented information to better understand population dynamics and the underlying responsible

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processes [START_REF] Jan | Which temporal resolution to consider when investigating the impact of climatic data on population dynamics? The case of the lesser horseshoe bat (Rhinolophus hipposideros)[END_REF]. This knowledge is urgently needed for conservationists, managers and policy makers to understand how species are responding to global environmental change (e.g. climate, habitat) and to make long-term predictions.

Figure 1 :Figure 2 :Figure 3 :

 123 Figure 1: Location of the 19 monitored colonies (Picardie, France)

Table 3 :

 3 Number of adults sampled only before parturition vs in both sessions, depending on their sex and, for females, their assignment as a mother. *: significant Chi square-test (pvalues < 0.001)

		Sampled only	Sampled before and
		before parturition	after parturition
	Males Unassigned females Mothers	170 321 63	44 167 111	* *	*

Acknowledgements:

The National Forest Office, PROCOPE/DAAD and Research Training Group -DFG RTG 2010 provided funding. J. Lefèvre, P. Janin, J. Jaminon, V. Berger and B. Marette from the National Office Forest, as well as M. Georges, D. Top, A. Pierroux and T. Cheyrezy from the Conservatory of natural areas provided field and logistical support. E. Meglecz and V. Dubut provided support in taxonomic coverage analysis. E. Hartmann and A. Monchaux provided informatics support. S. Dool and E. Teeling from University College Dublin provided us with an unpublished R. hipposideros DBY8 sequence used for primer design.

Accepted Article

& Evolution, 26, 249-259. Mickleburgh SP, Hutson AM, Racey PA (2002) A review of the global conservation status of bats. Oryx, 36. Miquel C, Bellemain E, Poillot C et al. (2006) Quality indexes to assess the reliability of genotypes in studies using noninvasive sampling and multiple-tube approach. Molecular Ecology Notes, 6, 985-988. Ngamprasertwong T, Piertney SB, Mackie I, Racey PA (2014) Roosting habits of Daubenton's bat (Myotis daubentonii) during reproduction differs between adjacent river valleys. Acta Chiropterologica, 16, 337-347. Nichols J, Williams B (2006) Monitoring for conservation. Trends in Ecology & Evolution, 21, 668-673. Ogutu JO, Piepho H-P, Dublin HT, Reid RS, Bhola N (2006) Application of mark-recapture methods to lions: satisfying assumptions by using covariates to explain heterogeneity. Journal of Zoology, 269, 161-174. Olson CR, Barclay RMR (2013) Concurrent changes in group size and roost use by reproductive female little brown bats (Myotis lucifugus). Canadian Journal of Zoology, 91, 149-155. O'Shea TJ, Ellison LE, Stanley TR (2004) Survival estimation in bats: historical overview, critical appraisal, and suggestions for new approaches. In: Sampling rare or elusive species: concepts, designs, and techniques for estimating population parameters (ed Thompson W), pp. 297-336. Island Press, Washington, District of Columbia. Parreira BR, Chikhi L (2015) On some genetic consequences of social structure, mating systems, dispersal, and sampling. Proceedings of the National Academy of Sciences, 112, E3318-E3326. Pennell MW, Stansbury CR, Waits LP, Miller CR (2013) Capwire: a R package for estimating population census size from non-invasive genetic sampling. Molecular Ecology Resources, 13, 154-157. Pereira HM, Ferrier S, Walters M et al. (2013) Essential Biodiversity Variables. Science, 339, 277-278. Petit E, Excoffier L, Mayer F (1999) No Evidence of Bottleneck in the Postglacial Recolonization of Europe by the Noctule Bat (Nyctalus noctula). Evolution, 53, 1247-1258. Petit E, Le Texier E, Farcy O (2014) Suivi démographique de quatre espèces patrimoniales en Bretagne : analyse statistique de 11 années de comptage. Symbioses, 32, 63-67. Petit E, Valière N (2006) Contributed papers: Estimating population size with noninvasive capture-mark-recapture data: noninvasive capture-mark-recapture data. Conservation Biology, 20, 1062-1073. Pollock KH, Nichols JD, Simons TR et al. (2002) Large scale wildlife monitoring studies: statistical methods for design and analysis. Environmetrics, 13, 105-119. Puechmaille S, Mathy G, Petit E (2005) Characterization of 14 polymorphic microsatellite loci for the lesser horseshoe bat, Rhinolophus hipposideros (Rhinolophidae, Chiroptera). Molecular Ecology Notes, 5, 941-944. Puechmaille SJ, Mathy G, Petit EJ (2007) Good DNA from bat droppings. Acta Chiropterologica, 9, 269-276. Puechmaille SJ, Petit EJ (2007) Empirical evaluation of non-invasive capture-mark-recapture estimation of population size based on a single sampling session: Non-invasive capturemark-recapture. Journal of Applied Ecology, 44, 843-852. R Core Team (2016) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria. https://www.R-project.org/. Rebelo H, Tarroso P, Jones G (2010) Predicted impact of climate change on European bats in

Data Accessibility:

DNA sequences: Genbank accessions KY793696-KY793699

Accepted Article

This article is protected by copyright. All rights reserved. R scripts and genotypes used in this study were deposited at DRYAD entry doi:10.5061/dryad.8fh54

Author contributions:

This project was designed by EJP with input from SJP and fundraising was conducted by EJP. Lab experiments were performed by DZL, PLJ, ALB and LL. Data were analysed by DZL, PLJ, TG, ALB, LL, SJP and EJP. The paper was written by DZL, PLJ, SJP and EJP. Both co-first authors contributed equally to the study. All authors were involved with data interpretation and draft corrections.

Supporting Information:

Appendix A: DNA isolation using the NucleoSpin® 96 Plant II Kit (Macherey-Nagel). Appendix B: In silico validation of our sex-linked primer pair. Appendix C: Example of genotype profiles obtained from one male (A) and one female (B) (three replicates each).

ccepted Article ccepted Article


Thibaut Marty

Tomofumi Yuki

Steven Derrien

Algorithm Level Timing Speculation for Convolutional Neural Network Accelerators

Keywords: Algorithm Based Fault Tolerance, Timing speculation, High-level synthesis, Convolutional Neural Network Tolérance aux fautes au niveau algorithmique, spéculation temporelle, synthèse de haut niveau, réseaux de neurones convolutifs

In this paper, we propose a technique for improving the efficiency of hardware accelerators based on timing speculation (overclocking) and fault tolerance. We augment the accelerator with a lightweight error detection mechanism to protect against timing errors, enabling aggressive timing speculation. We demonstrate the validity of our approach for the convolution layers in Convolutional Neural Networks (CNN). We present an implementation of a fault-tolerant CNN accelerator combined with the lightweight error detection for convolution layers. The error detection mechanism we have developed works at the algorithm level, based on algebraic properties of the computation, allowing the full implementation to be realized using High-Level Synthesis tools. We use a set of Zybo boards to experimentally demonstrate that overclocking boosts the frequency by 17-36% with low chances of error, and that the infrequent errors can be detected with a negligible overhead (only 1000 LUTs).

Introduction

The use of embedded systems for various computing tasks is already widespread, and will continue to grow. The key challenge for hardware designers is to produce designs that are efficient, in terms of many metrics such as speed, energy, area cost, and so on, under limited time (short time-to-market). In combination with the increasing maturity of High-Level Synthesis tools, we have the opportunity to explore many system-level design choices in search for efficient designs.

Circuit-level timing speculation, also known as overclocking, is one possible approach to boost the efficiency of such hardware. However, timing speculation may lead to incorrect/corrupted results due to timing anomalies that typically occur within long combinational paths. For carrychain based arithmetic circuits, these long paths contribute to the most significant bits of the results of an operation. As a consequence, such timing errors cause large numerical errors in the computation [START_REF] Chaudhuri | Timing speculation in FPGAs: Probabilistic inference of data dependent failure rates[END_REF], [START_REF] Li | Understanding Error Propagation in Deep Learning Neural Network (DNN) Accelerators and Applications[END_REF], [START_REF] Shi | Accuracy-Performance Tradeoffs on an FPGA through Overclocking[END_REF]. Although many applications are known to be robust to noise (i.e., frequent errors with small amplitude), occasional large errors can have devastating effect even for such applications.

Furthermore, the frequency of error depends on a number of factors, including the intensity of overclocking, operating temperature, variability within and across boards, input data, and so on. This makes it extremely difficult to determine a "safe" overclocking speed analytically or empirically. Therefore, overclocking must be applied conservatively or the infrequent large errors must be tolerated by the application.

In this work, we propose to combine timing speculation with lightweight error-detection to make overclocking a viable option. Error-detection is necessary to prevent the high impact errors from affecting the final output, and it must be lightweight so that the gains by overclocking is not nullified. Although many low level error detection techniques exist, they either have prohibitive area or performance overhead [START_REF] Ernst | Razor: A Low-Power Pipeline Based on Circuit-Level Timing Speculation[END_REF], [START_REF] Reis | SWIFT: Software Implemented Fault Tolerance[END_REF] or do not provide enough error coverage [START_REF] Nakahara | A deep convolutional neural network based on nested residue number system[END_REF]. We therefore propose a higher level error detection scheme by building on earlier results on Algorithm Based Fault Tolerance [START_REF] Huang | Algorithm-Based Fault Tolerance for Matrix Operations[END_REF]. ABFT offer lightweight error detection techniques, and are widely used in High Performance Computing as a protection from both soft and hard errors [START_REF] Chen | Online-ABFT: An Online Algorithm Based Fault Tolerance Scheme for Soft Error Detection in Iterative Methods[END_REF], [START_REF] Du | Algorithm-based Fault Tolerance for Dense Matrix Factorizations[END_REF].

We use Convolutional Neural Networks as a case study to demonstrate our approach. CNN is a variant of multi-layered neural networks that are known to work well for image/video processing where the main idea is to construct features from local information through convolutions. CNN models used in state-of-the-art applications are computation intensive and often need to be accelerated on GPUs or FPGAs to achieve high performance and/or obtain better energy efficiency [START_REF] Nakahara | A deep convolutional neural network based on nested residue number system[END_REF], [START_REF] Farabet | Hardware accelerated convolutional neural networks for synthetic vision systems[END_REF], [START_REF] Suda | Throughput-Optimized OpenCL-based FPGA Accelerator for Large-Scale Convolutional Neural Networks[END_REF], [START_REF] Sankaradas | A Massively Parallel Coprocessor for Convolutional Neural Networks[END_REF], [START_REF] Aydonat | An OpenCL™ Deep Learning Accelerator on Arria 10[END_REF], [START_REF] Zhang | Optimizing FPGA-based Accelerator Design for Deep Convolutional Neural Networks[END_REF], [START_REF] Krizhevsky | ImageNet Classification with Deep Convolutional Neural Networks[END_REF]. The core computations of CNNs have abundant parallelism, both task-level and fine-grained, that can be efficiently mapped to these accelerators. Furthermore, CNNs are known to be tolerant to noise. The reasons above make CNN an interesting class of computation to target.

Specifically, our contributions are the following:

• An in-depth quantitative analysis of the impact of overclocking on the performance and accuracy of CNN accelerators on FPGAs.

• A low overhead error detection for convolution layers in CNNs based on algorithmic properties.

• An implementation taking advantage of the above.

The remainder of this paper is organized as follows. Section 2 provides background on timing speculation techniques and CNNs. We describe our proposed accelerator with lightweight error detection in Section 3. We demonstrate the approach with a prototype implementation in

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Section 4, and then discuss our results and related work in Section 5. We conclude and give directions for future work in Section 6.

Background

In this section, we introduce the background of our work.

Timing Speculation through Overclocking in FPGAs

The minimum clock period at which a given FPGA design is expected to work is obtained from a static timing analysis. This analysis assumes the worst case scenario, and hence the design may be operated on a slightly higher operating frequency without much risk of observing an incorrect behavior. However, this technique, widely known as overclocking or timing speculation, also has many pitfalls:

• Variability among chips and operating conditions makes it difficult to determine how much overclocking can be tolerated. The fact that errors do not manifest often (or the inability to observe errors in a given setup) does not mean that an error will never happen.

• The impact of timing errors on the circuit output is difficult to evaluate a priori. Unlike errors arising from truncation/quantization, the impact is not limited to least significant bits. Thus, it may result in large numerical errors, which may compromise the design functionality.

There is little work on the impact of overclocking on FPGA performance, and its consequences to the circuit output. A notable exception is the work by Shi et al. [START_REF] Shi | Accuracy-Performance Tradeoffs on an FPGA through Overclocking[END_REF] that compares the performance/accuracy trade-off obtained by reduced arithmetic precision (through quantization) with that by overclocking. They have shown that overclocking can give gains competitive to quantization. However, the quality metric used was a statistical measure (SNR) that can mask the difference between frequent, low amplitude, error; and infrequent, high amplitude, error. Li et al. [START_REF] Li | Understanding Error Propagation in Deep Learning Neural Network (DNN) Accelerators and Applications[END_REF] show that even a single bit flip in higher order bits can cause CCNs to missclassify images. We have confirmed this result with out prototype impementation as reported in Section 4.6. These results show that infrequent large errors have large impact on CNN outputs, necessitating error detection to be combined with overclocking.

Convolutional Neural Networks

In this paper, we are interested in the forward pass of CNNs, i.e., when a trained network is applied to new inputs. Accelerating the training of NNs is an interesting topic on its own, and is not in the scope of this paper.

In a typical configuration, a forward pass of CNNs process three-dimensional matrices in a pipelined manner through multiple layers. The input is usually an image, having its height and width plus the color being the third dimension, often called depth. For classification, the final output is a one-dimensional vector of length M indicating the likelihood of each category, which can be viewed as a 1 × 1 × M matrix.

Layers can be of two different types:

Convolution layers These act as local feature extractors. Given a P × Q × N input matrix x, it computes a R × C × M output y. Each of the M two-dimensional outputs are computed as a three-dimensional convolution over x with a kernel (weights) of size K × K × N . The convolution Inria may be strided by some factor S. The R and C dimensions of the output matrix may become smaller than the input for a non-unit stride, or depending on the padding of the boundaries (and also as a result of sub-sampling layers mentioned below). Different layers take different values of the parameters described -the output R × C × M , called feature maps, can be viewed as an "image" where the depth is replaced with extracted features.

Fully-Connected layers These are usually employed as the last stages of the pipeline where the size of the input matrix has become significantly smaller than the original image. They perform a collection of dot-products with weights and produce a one-dimensional vector as outputs.

They are identical to the hidden layers in regular ANNs and can be computed as matrix-matrix products.

Additionally, activation functions (e.g., rectifier) or sub-sampling (e.g., max-pooling) may be considered as layers in CNN. Since these layers are inexpensive and can be merged with the preceding layer, we do not discuss them in this paper.

State-of-the-art CNN model are known to be computationally demanding (a single run of a VGG16 model requires more than 30 GOP), with more than 90% of the computational workload spent on the convolutions layers. Our approach aims at accelerating the convolution layer.

Given a P × Q × N input matrix x and K × K × N × M matrix holding the weights w, a convolution layer outputs a R × C × M matrix y through the following equation:

y r,c,m = N -1 ∑ n=0 K-1 ∑ i=0 K-1 ∑ j=0 x Sr+i,Sc+j,n • w i,j,n,m (1)

Proposed Approach

In this section, we first describe our accelerator from a system level perspective, and explain how we use timing-speculation (overclocking) to improve its computational performance. We then describe our lightweight error detection algorithm-the corner stone of our speculation technique-and describe how the error detection is mapped to hardware.

Algorithm Level Timing Speculation

Our approach builds on our ability to detect errors impacting the result of a convolution layer. This error detection mechanism uses two checksums, one computed from the output, and another computed directly from inputs, which we refer to as output-checksum and input-checksum, respectively. Note that it uses only two checksums, unlike matrix multiplication ABFT. This allows to reduce the checksum computation complexity, thus reducing the error detection overhead. We use the same system level architecture as described by Zhang et al. [START_REF] Zhang | Optimizing FPGA-based Accelerator Design for Deep Convolutional Neural Networks[END_REF] that use a decoupled access/execute model in the form of macro-pipelining. The actors pipeline the computation in blocks called tiles that partition the computation into smaller chunks to fit on-chip memory. Our speculative execution scheme therefore also operate at the tile level.

Our modified architecture is depicted in Figure 1 where the notables differences from the original [START_REF] Zhang | Optimizing FPGA-based Accelerator Design for Deep Convolutional Neural Networks[END_REF] are:

• Data exchange between our accelerator and the rest of the system is based on asynchronous FIFOs to enable a different clock domain for our convolution accelerator. Note that datatransfers to/from memory are not overclocked, and are therefore error free. The convolution kernel has three sources of parallelism. The main convolution (or dot-product) has ample parallelism, which is used as the fine-grained parallelism (unrolling in HLS). This datapath is also aggressively pipelined to process different inputs. Furthermore, this datapath itself is replicated for convolutions by different weights to the same input. The factor of unrolling and/or replication controls the throughput of the accelerator.

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• Two additional components are used to compute the input-checksum and output-checksum on the data stream flowing into/out of the accelerator. How the checksums are computed is described later in this section.

• Overclocking is enabled through a clocking wizard component which is managed in software.

In our setup, the clock wizard offers a 0.1 MHz resolution.

The efficiency of speculation depends on two factors:

• The overhead (in terms of area/latency) of error detection.

• The performance penalty caused by a misspeculation, which corresponds to the re-computation cost weighted by its probability of occurrence.

We show in Section 4 with our prototype implementation that the error detection itself does not incur any performance overhead, and has negligible area overhead. We discuss the cost of misspeculation in the next section.

Failure Recovery Cost

Once tile computation has completed, the accelerator compares the input-checksum with the output-checksum. If checksums do not match, the tile is recomputed at normal (safe) frequency. An important point is that the execution of all tiles can be done in parallel (and therefore in any order). A faulty tile does hence not stall the accelerator macro-pipeline : its output is simply discarded. The faulty tile only needs to be later fed back to the pipeline for a safe re-execution.

When the faulty tile is reprocessed, the clock wizard must be reprogrammed twice to run the tile at some lower frequency. On our system, the total reprogramming T p cost is less than T p = 80 µs while the execution of a tile (without overclocking) T s ranges from 100 µs to 3300 µs. The total cost of failure recovery in our design is 2T p + T s , we can conclude that the cost of misspeculation is negligible as long as the error rate is low. The rest of the section describes our checksum computation technique. We start with a simpler case for 2D convolution kernel, and then generalize to convolution layers in CNNs.

Inria K C K R (a) 2D convolution without zero- padding K C K R w 2,2 w 2,1 w 2,0 w 1,2 w 1,0 w 0,2 w 0,1 w 0,0 (

Intuition with 2D Convolution

The 2D case is missing the depth dimension in the processed matrices, but the main ideas carry over to the 3D case. Given the 2D output y, the output-checksum is: The reuse between two input groups corresponding to weights w 0,0 and w 0,1 . The sum of all elements in group w 0,1 can be computed by addition/subtraction of columns from that of w 0,0 , instead of repeating R × C additions.

σ = R ∑ r=0 C ∑ c=0 y r,c w 0,1 w 0,0 K C K R (

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Substituting the definition of y (Eqn. 1 without m, n and S = 1) gives the direct computation from the inputs:

ρ = R ∑ r=0 C ∑ c=0 K-1 ∑ i=0 K-1 ∑ j=0 (x r+i,c+j • w i,j )
The goal is to simplify the computation of ρ so that the checksum comparison can be performed with reduced cost. The additional two-dimensional summation provides two sources for simplification. The combination of the two simplifications described below reduces the cost of computing the checksum for 2D case from O(RCK 2 ) to K 2 multiplications and O(RC) additions.

Factorization

Multiplications can be factored out to eliminate RC multiplications. This may be viewed as a reordering of the summations followed by factorization:

ρ = K-1 ∑ i=0 K-1 ∑ j=0 w i,j ( R ∑ r=0 C ∑ c=0 x r+i,c+j )
A graphical illustration is given in Figure 2. This reduces the number of multiplications from K 2 RC to K 2 .

Reuse in Summations

The groups of summations after factorization have significant overlaps, which can be used to reduce the number of additions. This simplification concerns the computation of the inner two summations:

X i,j = R ∑ r=0 C ∑ c=0 x r+i,c+j
Note that each value of X is a summation over slightly different regions of x due to the offsets by i and j. These values of X takes K 2 RC additions when computed naïvely. However, once a value of X for a specific instance of i, j is computed, the remaining instances can be computed by only O(C) or O(R) additions as explained in Figure 3.

There are multiple ways to rewrite the definition of X to take advantage of this reuse. One example is as follows:

X i,j =                        R ∑ r=0 C ∑ c=0 x r,c : i = 0 j = 0 X i-1,j + C ∑ c=0 x R-1+i,c+j - C ∑ c=0 x i-1,c+j : i > 0 X i,j-1 + R ∑ r=0 x r+i,C-1+j - R ∑ r=0
x r+i,j-1 : i = 0 j > 0

In the above, the R × C summation for X 0,0 is performed first. Then the remaining instances of X i,j is computed by addition and subtraction of one row/column. The R × C summation is not repeated for all each X i,j (K × K instances) reducing the complexity by O(K 2 ) in exchange for 2R or 2C additions.

Inria

Lightweight Checksum for 3D Convolution Layers

For the 3D case, the output y has the third dimension corresponding to the different kernels applied to the input. The checksum is over all three dimensions of the output:

σ = M -1 ∑ m=0 R-1 ∑ r=0 C-1 ∑ c=0 y m,r,c (2)
Substituting Eqn. 1 (again, assuming unit stride) gives the direct checksum computation from the inputs:

ρ = M -1 ∑ m=0 R-1 ∑ r=0 C-1 ∑ c=0   N -1 ∑ n=0 K-1 ∑ i=0 K-1 ∑ j=0 x n,r+i,c+j • w m,n,i,j  
Reordering of the summations permits the factorization of the multiplication by weights:

ρ = N -1 ∑ n=0 K-1 ∑ i=0 K-1 ∑ j=0 (( R-1 ∑ r=0 C-1 ∑ c=0 x n,r+i,c+j ) • M -1 ∑ m=0 w m,n,i,j )
Note that in the 3D case, the different convolution kernels applied to the same input (the m dimension) can be first added together, since m is invariant to the expression involving x.

ρ = N -1 ∑ n=0 K-1 ∑ i=0 K-1 ∑ j=0 ( X n,i,j • M -1 ∑ m=0 w m,n,i,j ) (3)
where X takes the same form as the 2D case, except for the additional n dimension, which does not have any reuse.

We have assumed unit stride to simplify the presentation. We do not give the full detail due to space reasons, but the same principles apply to non-unit strides as well. The main difference is in the simplification of the summations. With non-unit strides, the input groups (Figure 2c) also becomes strided. This reduces the reuse across the input groups, but this is natural since non-unit stride essentially corresponds to sub-sampling, i.e., the number of uses of each input for computing the output is reduced.

Implementation of Checksum Calculations

The output-checksum is implemented as a simple accumulator over convolution outputs, with a small area overhead compared to the rest of the datapath. The hardware component responsible for computing the input-checksum (Eqn. 3) is more costly, as it involves a multiplier, storage for partial sums, and non-trivial control logic. As depicted in Figure 1a, this component operates directly on the input stream.

Both of these components are significantly less complex compared to the main kernel. The main performance constraint is to ensure that the data processing rate matches that of the convolution kernel. The amount of parallelism in the convolution kernel affects the rate of input consumption as well as output production. The checksum calculations need sufficient parallelism to keep up with this rate. This ensures that the input-checksum, computed in parallel with the main convolution computation, do not impact the overall latency of the accelerator.

The rates of inputs/outputs may be viewed as the number of data in a single FIFO element. As the throughput of the convolution kernel increases, the input/output elements become wider vectors holding more values. The checksum calculations must then operate on vectors of inputs and outputs.

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The output-checksum has a trivial parallelization to process the output vectors. Since the output-checksum is an accumulation, the computation is independent except for the aggregation at the end.

Proof-of-Concept

We present our empirical study in this section. The study consist of two parts: (i) quantifying area overhead in contrast to adding more parallelism (ii) study of variability.

Experimental Platform

The whole accelerator was designed using SDSoC (2016.3), demonstrating the suitability of our approach to modern FPGA tools that operate at higher level of abstractions.

We targeted two boards from the Xilinx Zynq-7000 family in our experiments: Zybo and ZC706 (XC7Z045). The motivation for using Zybo is because we have more than 8 boards available for our experiments. This allowed us to perform a large number of experiments to quantify the error rate with different frequencies in high resolution, and to study the degree of variability across boards. ZC706 is significantly larger than Zybo, providing design points that are more relevant for use cases that require high throughput.

The hardware designs used in this section targets the fifth layer in the AlexNet [START_REF] Krizhevsky | ImageNet Classification with Deep Convolutional Neural Networks[END_REF] CNN architecture with the following configuration: N = 192, M = 128, R = C = 13, K = 3, and S = 1. A preliminary experience showed that this layer was the one that most impact classification rate when impacted by timing errors. Note that the third and fourth layers of AlexNet also have similar configurations with bigger N and/or M .

Accelerator Design Space

The accelerator design have a number of parameters:

• Tile size (T n , T m , T r , T c ). As explained in Section 3.1, our CNN accelerator processes convolution layers in smaller units called tiles. These parameters define the subset of the output calculation to be executed by a single execution of the accelerator. The corresponding indices in Eqn. 1 are partitioned by the values specified by these parameters to define a tile. These parameters control the computation to communication ratio of the accelerator.

• Unrolling Factor (U n , U m ). These factors control the degree of parallelism. The pipelined datapath performs U n instances of the multiplication each cycle, which is controlled as the unroll factor of the innermost loop in HLS. This datapath is replicated U m times to process convolutions by different kernels in parallel.

• Word Length (WL). We use fixed-point arithmetic in our accelerator, which naturally give rise to another tuning parameter: number of bits used to represent each number. We use the same word length for all variables.

All designs are synthesized with highest target frequency that can be met. This ensures that excessive slacks in the timing are avoided. We explored various combinations of word lengths and unroll factors. They both have significant influence on the area cost of the convolution accelerator without our proposed error detection. The tile sizes were selected to be the largest tile that can accommodate the unroll factors we tried. Having larger tiles increases BRAM usage forcing some of our designs to not fit on the target board.

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Table 1: Area results for different design parameters on ZC706 and Zybo. ABFT enabled designs include the cost for all components: the convolution kernel, input-checksum, and outputchecksum. The area overhead of ABFT is negligible across all designs -at most 3.7% additional LUTs for ZC706 and 5.9% for Zybo. BRAM/DSP/GOP are unaffected. GOPS is giga operations per second for executing 96 tiles, including the latency of read/write actors.

WL Um×Un

Area Overhead

In our approach, we add additional hardware for detecting errors to enable more aggressive overclocking. Thus, the area overhead must be smaller than simply increasing the parallelism using the additional resource spent on error detection. Otherwise, it will be simpler and better to use this additional hardware to improve the accelerator performance by adding more parallelism without relying on overclocking and error detection. We can expect significantly lower cost compared to the main computation due to the algorithmic simplifications presented in Section 3. In particular, the simplification eliminates a factor of R × C multiplications that translates to 169 times less multiplications for Alexnet's layer 5.

These multiplications are computed by a single multiplier implemented with LUTs, as other operators. LUTs are also used for needed memories. Thus, no BRAM or DSP are used for the input-checksum computation.

As expected, the area overhead is extremely small on all the designs across a number of designs we have synthesized, reported in Table 1. For ZC706 that can fit larger tiles than Zybo, the overhead is at most 3.7%. This is negligible in contrast to the proportional area requirement by simply adding additional parallelism, which corresponds to higher unroll factors (Um and Un).

Cost of Miss-speculation

Study of Variability

In this section, we report our empirical study on two sources of variability. The main message is that due to many different sources of variability, statically selecting an overclocking frequency must be done conservatively. Our online error detection mechanism provides an opportunity to perform overclocking more aggressively.

Inter-Board Variability

Process variation is a well-known phenomenon that causes the same circuit to behave differently across boards. This gives significant variations across boards with respect to timing errors as well. As illustrated in Figure 4,

Data Variability

Timing errors are expected to be sensitive to data. This is because the critical path is data dependent. For typical arithmetic operations, inputs with small absolute values (i.e., high order bits are zero) have shorter critical paths. We empirically quantify this variability by executing our accelerator with input data masked to have higher order bits set to zero.

The precise setup is as follows. We take the design for Zybo synthesized for 16 bits input data and ran with varying frequencies for 400 images each. The input data were masked to have varying effective width (dynamic range). We collect the number of erroneous values in the output image with respect to the error-free execution using masked input data.

The result presented in Figure 5 shows the expected behavior; input data with smaller effective width result in errors at a much higher frequency.

Importance of Dynamic Adjustment

We have empirically study two sources of variability. The timing error behavior changes due to many factors such as temperature, data dynamic range, tile size, and target frequency set during Each bar correspond to the highest overclocking rate achievable of a given Zybo board (a given overclocking rate is considered achievable if it translates as a tile error rate lower than 0.2%). In addition, we also illustrate how this maximum overclocking is impacted by data variability by plotting the best-case vs worst case interval for different data masking scenarios qqqqqqqqqqqqqq qq q q q q q q q q q q qq qq qq q q q q q q q q q q qq qq qq q q q q q qq qqqqqqq q qqqqqqqqq qqq qqq qqq qqq qqq qq qq qq qq qq qqq qqqqq qqqqq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 20 Effective Data Width of n means 16 -n most significant bits were set to zero. Data points with zero observed error are not plotted -the bottom points have small but non-zero error rate.

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HLS to name a subset. The static timing analysis gives a frequency where the timing can be guaranteed to be met. However, the analysis is necessarily conservative due to the variability and also because it must consider worst case scenarios. Our approach allows for run-time adjustment of the frequency to overclock as much as possible, without risking timing errors to influence the final output. It may seem possible to perform an off-line calibration step before-hand for certain sources of variability, such as inter-board variation. However, the probabilistic behavior of timing errors that depends on many parameters makes it extremely challenging to find a "safe" frequency. The number of samples that needs to be collected to statistically select frequencies are likely to be prohibitively high, forcing conservative choices to be made.

In constrast, our approach enables much more aggressive overclocking for a very low area overhead (ony a few percent additional LUT utilization).

Impact on Classification Accuracy

Since neural networks are known to be tolerant to noises-frequent, low amplitude errors-one may question if the timing errors cause notable impact on the final quality of the CNN or not. Li et al. [START_REF] Li | Understanding Error Propagation in Deep Learning Neural Network (DNN) Accelerators and Applications[END_REF] have performed an extensive study for various networks including AlexNet [START_REF] Krizhevsky | ImageNet Classification with Deep Convolutional Neural Networks[END_REF] in the context of soft-errors. They show that errors in the higher order bits significantly degrades the accuracy of neural networks.

We measured the frequency of flips for each bit while processing AlexNet images with publicly available model1 on our accelerator. The accelerator was overclocked to produce a small number of errors per image (in the order of 100 corrupted values per image). By using overclocking frequencies with small error rates, we avoid having multiple timing errors while computing a single output. We confirmed that most of the corrupted values are different from the error-free execution by one and only one bit. This gives us an empirical estimate of the likelihood of bits being flipped under moderate overclocking beyond error-free frequencies.

The empirical probability of each bit being flipped derived from 5124k erroneous values collected are summarized below: MSB (bit 15) bit 14 bit 13 bit 12-0 combined 27% 16% 24% 33% This shows that there are significant chances for the high order bits to be flipped through timing errors. This makes sense as timing errors are expected in critical paths that commonly affect high order bits (e.g., carry chains).

We used a software implementation2 to simulate the impact on classification results based on the above probability. The final impact on the result depends on the layer where the error occurs. The last two layers (4th and 5th) have the most significant influence. We observed that injecting a small number of errors (20 per image) to the last layer causes more than 10% miss-classifications when compared to error-free execution.

We have also observed that extreme overclocking basically produces random values as outputs. The impact on classification accuracy is much higher in such situations.

Note that the probability reported above is only a rough empirical estimate. We can expect them to change due to various factors: variability due to data, temperature, etc.; the low-level decisions during HLS and/or P&R; and so on. It is difficult to have precise analytical models as we do not have full control over low-level designs synthesized by HLS tools.

Discussion and Related Work

Comparison with Existing ABFT Techniques

Our approach builds on the ABFT technique for matrix operations [START_REF] Huang | Algorithm-Based Fault Tolerance for Matrix Operations[END_REF]. In fact, the convolution layer and the fully-connected layer can be viewed as a collection of matrix products, making the classical ABFT directly applicable. Most ABFT extensions employ a variant of the original method by identifying pieces of computations that can be viewed as matrix operations [START_REF] Roy-Chowdhury | Algorithm-based error-detection schemes for iterative solution of partial differential equations[END_REF], [START_REF] Bosilca | Composing resilience techniques: ABFT, periodic and incremental checkpointing[END_REF].

We emphasize that the lightweight checksum calculation proposed in this paper is not a direct application of the classical ABFT. We use algorithmic invariants in collections of convolutions to further reduce the cost of checksums. This is evident in the fact that we reduce the algorithmic complexity by two-fold, exploiting reuse in two-dimensions, whereas the original ABFT brings one-degree savings.

The algebraic properties used in ABFT relies on associativity and commutativity. Since floating-point operations are not commutative, the application of these techniques requires additional care. For instance, a small threshold value to decide that the checksums match may be needed. This is not a concern for hardware CNN accelerators, since the clear trend is to use short integers encodings for data and/or weights [START_REF] Qiu | Going Deeper with Embedded FPGA Platform for Convolutional Neural Network[END_REF].

Other Techniques for Timing Error Detection

The potentially high impact of timing errors has led to several circuit-level techniques for its detection and correction.

The Razor technique [START_REF] Ernst | Razor: A Low-Power Pipeline Based on Circuit-Level Timing Speculation[END_REF] uses a dual flip-flop scheme to detect timing violation. The idea consists in delaying the clock signal by a small offset at the input of the second flip-flop and compare the two sampled values. If these two values differ, then a timing error has occurred. This approach is however not well suited to modern FPGA design flows since it often requires manual floor-planning to obtain the expected behavior [START_REF] Ragavan | Adaptive Overclocking and Error Correction Based on Dynamic Speculation Window[END_REF], [START_REF] Brant | Safe Overclocking of Tightly Coupled CGRAs and Processor Arrays using Razor[END_REF]. Another issue is that the error detection overhead can be significant when the number of flip-flops that needs to be protected in fine-grain FPGA pipelined datapath is large.

Other error detection techniques, such as those based on Residue Numbering Systems could be used. RNS protection provides low overhead error detection [START_REF] Piestrak | Design of Fault-Secure Transposed FIR Filters Protected Using Residue Codes[END_REF] for convolution kernels. However, they only offer limited protection against typical timing errors that impact several outputs at a time.

Conclusions and Future Work

In this paper, we propose timing speculation coupled with lightweight error detection as an approach to further improve the performance of hardware accelerators for CNNs. We have demonstrated the efficacity of our approach with a prototype implementation and an extensive empirical study. In addition, our approach is very well-suited for implementation in high-level design tools such as Vivado HLS/SDSoC, which is becoming more and more attractive for productivity reasons.

We believe that similar techniques can be applied to many other application domains (bioinformatics, iterative solvers, etc.) by taking advantage of existing ABFT techniques or by devising new algorithms tailored for this task. This is part of our ongoing work.

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  The convolution kernel based on the design by Zhang et al.[START_REF] Zhang | Optimizing FPGA-based Accelerator Design for Deep Convolutional Neural Networks[END_REF]

Figure 1 :

 1 Figure 1: Timing-Speculative Convolution Accelerator. At the system-level, we have a macropipeline decoupling the I/O with the main kernel, equipped with a clock management hardware.The convolution kernel has three sources of parallelism. The main convolution (or dot-product) has ample parallelism, which is used as the fine-grained parallelism (unrolling in HLS). This datapath is also aggressively pipelined to process different inputs. Furthermore, this datapath itself is replicated for convolutions by different weights to the same input. The factor of unrolling and/or replication controls the throughput of the accelerator.

Figure 2 :

 2 Figure2: Illustration of the factorization for 2D case. As depicted in Figure2a, 2D convolution can be viewed as a dot-product between the weights and the neighboring inputs with a sliding window. An alternative view shown in Figure2bis that an input value is used to compute K 2 output values, contributing to each of them through multiplication by different weights. We can thus group the input data into (overlapping) subsets based on the weights, which is what is shown for three weight values in Figure2c. Since sum of convolution outputs is completely linear, the multiplication can be factorized to save work.

Figure 3 :

 3 Figure 3: The reuse between two input groups corresponding to weights w 0,0 and w 0,1 . The sum of all elements in group w 0,1 can be computed by addition/subtraction of columns from that of w 0,0 , instead of repeating R × C additions.

  (a) ZC706 area results for tiles of size 128 × 192 × 13 × 13.

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Figure 4 :

 4 Figure 4: This figure shows how inter-board variability impacts the achievable overclocking rate.Each bar correspond to the highest overclocking rate achievable of a given Zybo board (a given overclocking rate is considered achievable if it translates as a tile error rate lower than 0.2%). In addition, we also illustrate how this maximum overclocking is impacted by data variability by plotting the best-case vs worst case interval for different data masking scenarios

Figure 5 :

 5 Figure 5: Percentage of corrupted outputs as a function of operating frequency over 400 images.Effective Data Width of n means 16 -n most significant bits were set to zero. Data points with zero observed error are not plotted -the bottom points have small but non-zero error rate.

https://github.com/BVLC/caffe/tree/master/models/bvlc_alexnet

https://github.com/tiny-dnn/tiny-dnn Inria

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Acknowledgment

This work was partially supported by European project ARGO. Ce projet bénéficie du soutien financier de la Région Bretagne.