Christine Rousseau

Mathieu Gonnet

Marc Le Romancer

Jacques Nicolas
email: jacques.nicolas@inria.fr

CRISPI: a CRISPR Interactive database

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.

INTRODUCTION

A remarkable regular structure made up of a skeleton of repeats holding a set of highly variable short sequences has been recognized several times in prokaryotic genomes under different names in the literature (TREP, SPIDR, SRSR...) and is called CRISPR since 2002 (for Clustered Regularly Interspaced Short Palindromic Repeats) [START_REF] Barrangou | CRISPR Provides Acquired Resistance Against Viruses in Prokaryotes[END_REF][START_REF] Sorek | CRISPR -a widespread system that provides acquired resistance against phages in bacteria and archaea[END_REF]. The structure contains generally 4 to 10 direct repeats ranging in size from 25 to 45, separated by spacers of similar length containing specific genomic material that is not present elsewhere in the genome and has been likely imported from plasmids or viruses. CRISPR are present in all but 6 archaeal species and half of bacteria. Since they are expected to play an important role in prokaryotic adaptative immunity and may serve as specific markers, it is highly desirable to have dedicated identification tools and regularly updated databases available. Several computational methods have been developed to predict CRISPR using a more or less explicit model introducing many parameters filtering the allowed number of elements, sizes and distances between elements of the structure, mismatches between units [START_REF] Bland | CRISPR Recognition Tool (CRT): a tool for automatic detection of clustered regularly interspaced palindromic repeats[END_REF][START_REF] Edgar | PILER-CR: Fast and accurate identification of CRISPR repeats[END_REF]Grissa et al., 2007)... The best source of data on CRISPR has been designed in 2007 by I. Grissa, G.Vergnaud and C. Pourcel (Grissa et al., 2007) with the most recent release in december 2008. We have tried to improve this setting with a simpler CRISPR model and several new utilities. * to whom correspondence should be addressed

IMPLEMENTATION

Identification of CRISPR

The usual specification of CRISPR, based on limited empirical data instead of biological functional constraints, remains too informal to be helpful in systematic studies: CRISPR are repeated structures composed of exact repeat sequences 24 to 48 bases long separated by unique spacers of similar length [START_REF] Victor Kunin | Evolutionary conservation of sequence and secondary structures in CRISPR repeats[END_REF].

In fact most CRISPR include altered repeats and spacers are occasionally repeated inside a same structure and sometimes even in different CRISPR inside a same chromosome. Some authors give more details on the structure: repeats are supposed to exhibit a kind of dyadic symmetry but as more data are available this characterization becomes questionnable; A leader sequence is often mentionned before the train of repeats, but it is only defined as an A/T rich region and seems to lack for some CRISPR. Since the existence of a skeleton seems the only tangible fact for CRISPR and since we try to minimize a priori assumptions, we have chosen to only base the search on the existence of a periodic spaced suite of units (at least four units) that is not a tandem repeat. Maximal repeats have largely been used for the detection of relevant repeats and applied on the search for units (Grissa et al., 2007). But short words such as those that appear in CRISPR can occur at a frequency comparable to random words of similar size. We have introduced locality restrictions on the notion of maximal repeat reflecting the kind of repeats that are found in CRISPR: first, each cluster of occurrences has a bounded size; second, only maximal repeats with at least one occurrence that is not covered by a larger repeat are kept. We produce putative units by clustering such overlapping local maximal repeats. Actually, we do not fix any value for the size of units or spacers, and we do not require units to be identical inside a given CRISPR (the minimal identity percentage to the consensus is however fixed to 60% in order to avoid spurious structures).

All bacterial and archaeal genomes have been downloaded from the NCBI FTP Server (ftp://ftp.ncbi.nih.gov/genomes/Bacteria/). The CRISPR have been searched for using the method sketched below implemented in C and Java (v. 1.5.0 12) and results have been stored into a MySQL (v. 4.1.12) database. All web pages are implemented using PHP (v. 4.3.9).

Access the CRISPI database

The main page of CRISPI offers three search forms: consult the content of the database, Blast a personal sequence against the database and find CRISPR structures in a personal sequence. be easily selected by accession number, by entering the genome name (or a part of it) or by selecting a genome in the genome list (alphabetical order) or in the taxonomy browser. Once the genome of interest has been selected, results are summarized in tables. Each CRISPR is highlighted and CAS genes found in its vicinity are displayed. These are identified by dedicated HMM profiles we have built from available genes. If new putative CAS genes were found, there are highlighted in red. Annotations contains various elements such as positions, sequence of the consensus unit, links to external NCBI information, links to graphical circular view of genome (thanks to CGView, see (Stothardet al., 2005)). Clicking on consensus jumps to the corresponding CRISPR's details and gives information such as units and spacers' coordinates, units and spacers' sequences, Pygram image [START_REF] Durand | Browsing repeats in genomes: Pygram and an application to non-coding region analysis[END_REF] and consensus WebLogo image (Fig. 1). Spacers, Units, CRISPR, flanking sequences, CAS genes may be downloaded in fasta format. The query sequence must be in fasta format (DNA or protein). One can either paste the query sequence into the input field or upload it from a file on the local machine (files with multiple sequences are allowed). Users have access to Blast parameters for fine-tuned comparisons. Moreover, it can be run against units instead of spacers for studies on the origin of such structures. The Blast results pages are cross-linked with the CRISPI database so that it is easy to return to the database by clicking on hyperlinks.

Consult the database

Find out CRISPR structures in personal sequence

People may want to check there own microbial sequence for annotation purpose. The query sequence must be in fasta format (only DNA sequences are allowed). One can either paste the query sequence into the input field or upload it from a file on the local machine files with multiple sequences are allowed). Results are summarized in a table with the option of being notified by email when available. These user-submitted genomes remain in confidential web pages that can be accessed for 10 days before deletion.

CONCLUSION

CRISPI is a dedicated environment on CRISPR in prokaryotic genomes that offers for the first time an up-to-date view of existing CRISPR (71 archaea totalling 291 CRISPR, and 987 bacteria totalling 2,103 CRISPR) including a complete repertory of CRISPR-associated genes -CAS genes-. The current version contains 1,173 archeal CAS genes and 4,396 bacterial CAS genes. We have not tried as in (Grissa et al., 2007) to keep very small structures (1 or 2 spacers) as it is not clear if they have any relevance or activity. In contrast, we have included a richer environment for practical works on CRISPR : access to extended queries via Blast parameters, multiple graphical views, etc. The next planned step in this work will be the automatic update of the database as new genomes will become available.

  CRISPI allows viewing all CRISPR found in Archaea and Bacteria genomes. Microbial genomes can c ⃝ Oxford University Press 2009.

Fig. 1 .

 1 Fig. 1. Typical graphical views in CRISPI 2.2.2 Blast a personal sequence against CRISPI Microbiologists or virologists can Blast private sequences to find out if a virus or plasmid sequence matches with one or more spacers in the database.The query sequence must be in fasta format (DNA or protein). One can either paste the query sequence into the input field or upload it from a file on the local machine (files with multiple sequences are allowed). Users have access to Blast parameters for fine-tuned comparisons. Moreover, it can be run against units instead of spacers for studies on the origin of such structures. The Blast results pages are cross-linked with the CRISPI database so that it is easy to return to the database by clicking on hyperlinks.

ACKNOWLEDGEMENTS

The necessary environment for all computations has been provided by the bioinformatics platform Biogenouest (http://biogenouest.org)

Funding: This work is supported by a grant from the ANR Agence Nationale de la Recherche through its MODULOME project.


Rémy Sun

Li Yang

Diane Lingrand

Frédéric Precioso

Mind the map! Accounting for existing map information when estimating online HDMaps from sensor data

Online High Definition Map (HDMap) estimation from sensors offers a low-cost alternative to manually acquired HDMaps. As such, it promises to lighten costs for already HDMap-reliant Autonomous Driving systems, and potentially even spread their use to new systems.

In this paper, we propose to improve online HDMap estimation by accounting for already existing maps. We identify 3 reasonable types of useful existing maps (minimalist, noisy, and outdated). We also introduce MapEX, a novel online HDMap estimation framework that accounts for existing maps. MapEX achieves this by encoding map elements into query tokens and by refining the matching algorithm used to train classic query based map estimation models.

We demonstrate that MapEX brings significant improvements on the nuScenes dataset. For instance, MapEXgiven noisy maps -improves by 38% over the MapTRv2 detector it is based on and by 16% over the current SOTA.

Introduction

Autonomous Driving [START_REF] Gao | VectorNet: Encoding HD Maps and Agent Dynamics From Vectorized Representation[END_REF][START_REF] Kuutti | A survey of deep learning applications to autonomous vehicle control[END_REF] represents a complex problem that promises to significantly change how we interact with transportation. While full vehicle automation still seems quite a ways away [START_REF] Teng | [END_REF], partially autonomous vehicles now populate a number of road systems in the world [START_REF] Kuutti | A survey of deep learning applications to autonomous vehicle control[END_REF]. These vehicles need to process a wealth of information to function, from the raw sensor data [START_REF] Gu | Vip3d: End-to-end visual trajectory prediction via 3d agent queries[END_REF] to elaborate maps of road networks [START_REF] Gao | VectorNet: Encoding HD Maps and Agent Dynamics From Vectorized Representation[END_REF][START_REF] Liang | Learning lane graph representations for motion forecasting[END_REF].

High Definition maps (HDMaps), in particular, represent a crucial component of the research on self-driving cars [START_REF] Elghazaly | High-definition maps: Comprehensive survey, challenges, and future perspectives[END_REF][START_REF] Gao | VectorNet: Encoding HD Maps and Agent Dynamics From Vectorized Representation[END_REF] (see Fig. 1 for a few simple examples of maps, with road boundaries represented by green polylines, lane dividers by lime polylines and pedestrian crossings by blue polygons). Although maps are not a typical input of neural networks, they contain necessary information to help the car understand the world it must navigate. As such, signif-Figure 1. We propose to use existing map information -even if inexact -to estimate better online HDMaps from sensor inputs. In doing so, we simplify the problem from generating maps using only sensors to re-using always available maps aided by sensors.

icant efforts have gone into incorporating this new type of data into proposed solutions [START_REF] Gao | VectorNet: Encoding HD Maps and Agent Dynamics From Vectorized Representation[END_REF][START_REF] Park | Leveraging future relationship reasoning for vehicle trajectory prediction (frm)[END_REF]. These efforts have in turn shown HDMaps have remarkable benefits both for fundamental problems like Object Detection [START_REF] Hausler | Displacing objects: Improving dynamic vehicle detection via visual place recognition under adverse conditions[END_REF] to precise trajectory forecasting problems [START_REF] Liang | Learning lane graph representations for motion forecasting[END_REF][START_REF] Park | Leveraging future relationship reasoning for vehicle trajectory prediction (frm)[END_REF].

These maps are however expensive to acquire and maintain, requiring precise data acquisition and exacting human labeling efforts [START_REF] Elghazaly | High-definition maps: Comprehensive survey, challenges, and future perspectives[END_REF][START_REF] Jeong | Tutorial on high-definition map generation for automated driving in urban environments[END_REF]. There has therefore been a strong push over the last year [START_REF] Baran Can | Structured bird's-eye-view traffic scene understanding from onboard images[END_REF][START_REF] Liao | MapTR: Structured modeling and learning for online vectorized HD map construction[END_REF] to approximate online HDMaps from sensor data. It is interesting to note that even seminal work on the subject has produced useful maps for trajectory forecasting [START_REF] Liu | Vectormapnet: End-to-end vectorized hd map learning[END_REF]. While recent methods like MapTRv2 [START_REF] Liao | Maptrv2: An end-to-end framework for online vectorized hd map construction[END_REF] have become proficient at generating online HDMaps from raw sensors, we feel they overlook very useful and nearly always available data: existing maps. We posit here that outdated or lower quality maps should usually be available and could significantly improve the acquired HDMaps as illustrated in Fig. 1. Indeed, even "map-free" models tend to use lowerquality satnav maps [START_REF]Learning to drive like a human[END_REF], and estimated maps could always be available as long as a vehicle went through a place once.

In this paper, we explore the central postulate that inaccurate maps can be used to improve the estimation of HDMaps from raw sensors as shown on Fig. 1. After providing some context on our method and the field in Sec. 2, we propose two distinct technical contributions. In Sec. 3, we outline reasonable scenarios under which an inaccurate map can be available along with practical implementations. In Sec. 4, we propose MapEX, an architecture that can generate HDMaps from sensor data while accounting for existing map information. Finally, we present results in Sec. [START_REF] Baran Can | Structured bird's-eye-view traffic scene understanding from onboard images[END_REF] with experiments on the nuScenes dataset [4]. Contributions We offer the following 3 contributions:

• We propose to account for existing Map information when estimating online HDMaps from sensor data. • We discuss reasonable scenarios under which existing maps are not perfect. We also provide realistic implementations of these scenarios and code for the nuScenes dataset. • We introduce MapEX, a new query based HDMap acquisition scheme that can incorporate map information when estimating an online HDMap from sensors. In particular, we introduce with MapEX both a novel way to incorporate existing map information with existing (EX) queries and a way to help the model learn to leverage this information by pre-attributing predictions to ground truths during training.

We demonstrate experimentally that our contribution lead to substantial improvements in online HDMap acquisition from sensors on the nuScenes dataset. In the scenario where we use HDMaps with noisy (or "shifted") map element positions for instance, MapEX reaches a 84.8% mAP score which is an improvement of 38% over the MapTRv2 detector it is based on and a 16% improvement over the current state-of-the-art as shown in Tab. 1.

Related Work

We provide here some brief context on HDMaps in autonomous driving. We begin by discussing HDMap's use in trajectory forecasting, before discussing their acquisition. We then discuss online HDMap estimation itself. HDMaps for trajectory forecasting Autonomous Driving often requires a lot of information about the world vehicles are to navigate. This information is typically embedded in rich HDMaps given as input to modified neural networks [START_REF] Gulzar | A survey on motion prediction of pedestrians and vehicles for autonomous driving[END_REF][START_REF] Park | Leveraging future relationship reasoning for vehicle trajectory prediction (frm)[END_REF]. HDMaps have proven critical to the performance of a number of modern methods in trajectory forecasting [START_REF] Deo | Multimodal trajectory prediction conditioned on lane-graph traversals[END_REF][START_REF] Park | Leveraging future relationship reasoning for vehicle trajectory prediction (frm)[END_REF] and other applications [START_REF] Hausler | Displacing objects: Improving dynamic vehicle detection via visual place recognition under adverse conditions[END_REF]. In trajectory forecasting in particular, it is remarkable that some methods [START_REF] Liu | LAformer: Trajectory Prediction for Autonomous Driving with Lane-Aware Scene Constraints[END_REF][START_REF] Liu | Multimodal motion prediction with stacked transformers[END_REF] explicitly reason on a representation of the HDMap and therefore absolutely require access to a HDMap [START_REF] Sun | Exploring the road graph in trajectory forecasting for autonomous driving[END_REF]. [START_REF] Liu | Vectormapnet: End-to-end vectorized hd map learning[END_REF] reports a 10% drop in performance for a common forecasting technique [START_REF] Liu | Multimodal motion prediction with stacked transformers[END_REF] when applied without an informative HDMap. [START_REF] Xu | Towards motion forecasting with real-world perception inputs: Are end-to-end approaches competitive?[END_REF] reports even more dramatic drops in performance for other well known methods. HDMap acquisition and maintenance Unfortunately, HDMaps are expensive to acquire and maintain [START_REF] Elghazaly | High-definition maps: Comprehensive survey, challenges, and future perspectives[END_REF][START_REF] Jeong | Tutorial on high-definition map generation for automated driving in urban environments[END_REF]. While HDMaps used in forecasting are only a simplified version containing map elements (lane dividers, road boundaries, ...) [START_REF] Li | Hdmapnet: An online hd map construction and evaluation framework[END_REF][START_REF] Liao | Maptrv2: An end-to-end framework for online vectorized hd map construction[END_REF] and foregoing much of the complex information in full HDMaps [START_REF] Elghazaly | High-definition maps: Comprehensive survey, challenges, and future perspectives[END_REF], they still require exceedingly precise measurements (on the scale of tens of centimeters) [START_REF] Elghazaly | High-definition maps: Comprehensive survey, challenges, and future perspectives[END_REF]. A number of companies have therefore been moving towards a less exacting Medium Definition Maps (MDMaps) standard [START_REF] Gupta | The mapping laritularity is near[END_REF], or even towards satellite navigation maps (Google Maps, SDMaps) [START_REF]Learning to drive like a human[END_REF]. Crucially, MDMaps -with their precision of a few meters -would be a good example of an existing map giving valuable information for the online HDMap generation process. Our map Scenario 2a explores an approximation of this situation. Online HDMap estimation from sensors Online HDMap estimation [START_REF] Baran Can | Structured bird's-eye-view traffic scene understanding from onboard images[END_REF] has therefore emerged as a promising alternative to manually curated HDMaps. While some works [START_REF] Baran Can | Structured bird's-eye-view traffic scene understanding from onboard images[END_REF][START_REF] Baran Can | Topology preserving local road network estimation from single onboard camera image[END_REF]45] focus on predicting virtual map elements, i.e. lane centerlines, the standard formulation introduced by [START_REF] Li | Hdmapnet: An online hd map construction and evaluation framework[END_REF] focuses on more visually recognizable map elements: lane dividers, road boundaries and pedestrian crossings. Probably because visual elements are easier to detect by sensors, this latter formulation has seen rapid progress over the last year [START_REF] Ding | Pivotnet: Vectorized pivot learning for end-to-end hd map construction[END_REF][START_REF] Liao | MapTR: Structured modeling and learning for online vectorized HD map construction[END_REF][START_REF] Liu | Vectormapnet: End-to-end vectorized hd map learning[END_REF]. Interestingly, the latest such method -Map-TRv2 [START_REF] Liao | Maptrv2: An end-to-end framework for online vectorized hd map construction[END_REF] -does offer an auxiliary setting for detecting virtual lane centerlines. This suggests a natural convergence towards the more complex settings comprising a multitude of additional map elements (traffic lights, ...) [START_REF] Li | Topology reasoning for driving scenes[END_REF][START_REF] Wang | Openlane-v2: A topology reasoning benchmark for unified 3d hd mapping[END_REF]. Nevertheless, the standard formulation from [START_REF] Li | Hdmapnet: An online hd map construction and evaluation framework[END_REF] remains the gold standard when evaluating the usefulness of additional information such as learned global feature maps [START_REF] Xiong | Neural map prior for autonomous driving[END_REF], satellite views [START_REF] Gao | Complementing onboard sensors with satellite map: A new perspective for hd map construction[END_REF], or SDMaps [2]. We thus keep to this problem formulation to demonstrate the use of existing map in-formation.

Our work is adjacent to the commonly studied change detection problems [START_REF] Bu | Toward map updates with crosswalk change detection using a monocular bus camera[END_REF]34] that aim to detect a change in a map (e.g. crossings). While rooted in more classical statistical techniques [34], a few efforts have been made to adapt them to deep learning [START_REF] Bu | Toward map updates with crosswalk change detection using a monocular bus camera[END_REF][START_REF] Heo | Hd map change detection with cross-domain deep metric learning[END_REF]. Notably, the Argoverse 2 Trust but Verify (TbV) dataset [START_REF] Lambert | Trust, but Verify: Crossmodality fusion for hd map change detection[END_REF] was recently proposed for this problem (see Appendix 8). This however differs substantially from our approach as we do not try to correct small mistakes on an existing map after aggregating from a fleet of vehicles [22,[START_REF] Pannen | How to keep hd maps for automated driving up to date[END_REF]. Instead we aim to generate accurate online HDMaps with the help of an existing -possibly very different -map, which is made possible by the modern online HDMap estimation problem. Therefore, we do not only correct small mistakes in maps but propose a more expressive framework that accommodates any change (e.g. distorted lines, very noisy elements).

What kind of existing map could we use?

We make the central claim that accounting for existing maps would benefit online HDMaps estimation. We argue here there are many reasonable scenarios under which imperfect maps can appear. After defining the HDMap representations we work with in Sec. 3.1 and our general approach in Sec. 3.2, we consider three main possibilities: only road boundaries are available (Sec. 3.3), the maps are noisy (Sec. 3.4), or they have changed substantially (Sec. 3.5).

HDMap representation for online HDMap estimation from sensors

We adopt the standard format used for online HDMaps generation from sensors [START_REF] Li | Hdmapnet: An online hd map construction and evaluation framework[END_REF][START_REF] Liao | MapTR: Structured modeling and learning for online vectorized HD map construction[END_REF]: we consider HDMaps to be made of 3 types of polylines, road boundaries, lane dividers and pedestrian crosswalks, with same colors as previously green, lime, and blue respectively, as represented on Fig. 2a.

We follow [START_REF] Liao | MapTR: Structured modeling and learning for online vectorized HD map construction[END_REF] by representing these polylines as sets of 20 evenly spaced points for our map generator, and using upsampled versions for evaluation. While true HDMaps are much more complex [START_REF] Elghazaly | High-definition maps: Comprehensive survey, challenges, and future perspectives[END_REF] and more intricate representations have been proposed [START_REF] Baran Can | Topology preserving local road network estimation from single onboard camera image[END_REF], the aim of this work is to study how to account for existing map information. As such we restrict ourselves to the most commonly studied formulation. The work in this paper will be directly applicable to the prediction of more map elements [START_REF] Baran Can | Topology preserving local road network estimation from single onboard camera image[END_REF], finer polylines [START_REF] Ding | Pivotnet: Vectorized pivot learning for end-to-end hd map construction[END_REF][START_REF] Qiao | End-toend vectorized hd-map construction with piecewise bezier curve[END_REF] or rasterized objectives [START_REF] Zhang | Online map vectorization for autonomous driving: A rasterization perspective[END_REF].

MapModEX: Simulating imperfect maps

As acquiring genuine imprecise maps for standard map acquisition datasets (e.g. nuScenes) would be costly and time consuming, we synthetically generate imprecise maps from existing HDMaps.

We develop MapModEX, a standalone map modification library. It takes nuScenes map files and sample records, and for each sample outputs polyline coordinates for dividers, boundaries and pedestrian crosswalks in a given patch, around the ego vehicle. Importantly, our library provides the ability to modify these polylines to reflect various modifications: removal of map elements, addition, shifting of pedestrian crossings, noise addition to point coordinates, map shift, map rotation and map warping. MapModEX will be made available after publication to facilitate further research into incorporating existing maps into online HDMap acquisition from sensors.

We implement three challenging scenarios, outlined next, using our MapModEX package, generating for each sample 10 variants of scenarios 2 and 3 (scenario 1 only admits one variant). We chose to work with a fixed set of modified maps to reduce online computation costs during training and to reflect real situations where only a finite number of map variants might be available.

Scenario 1: Only boundaries are available

A first scenario is one where only a bare HDMap (without divider and pedestrian crossings) is available as shown on Fig. 2b. Road boundaries are more often associated with 3D physical landmarks (e.g. edge of sidewalk) whereas dividers and pedestrian crossings are generally denoted by flat painted markings that are easier to miss. Moreover, pedestrian crossings and lane dividers are fairly commonly displaced by construction works or road deviations, or even partially hidden by tire tracks.

As such, it is reasonable to use HDMaps with only boundaries. This would have the benefit of reducing annotators costs by only asking annotators to label road boundaries. Furthermore, less precise equipment and less updates might be required to situate only road boundaries. Implementation From a practical standpoint, Scenario 1 implementation is straightforward: we remove the divider and pedestrian crossings from available HDMaps.

Scenario 2: Maps are noisy

A second plausible case is one where we only have very noisy maps as shown on Fig. 2c. A weak point of exist-ing HDMaps is the need for high precision (in the order of a few centimeters), which puts a significant strain on their acquisition and maintenance [START_REF] Elghazaly | High-definition maps: Comprehensive survey, challenges, and future perspectives[END_REF]. In fact, a key difference between HDMaps and the emergent MDMaps standard lies in a lower precision (a few centimeters vs. a few meters).

We therefore propose to work with noisy HDMaps to simulate situations where less precise maps could be the result of a cheaper acquisition process or a move to the MDMaps standard. More interestingly, these less precise maps could be automatically obtained from sensor data. Although methods like MapTRv2 have reached very impressive performance, they are not yet completely precise: even with very flexible retrieval thresholds, the precision of predictions falls far short of 80%. Implementation We propose two possible implementations of these noisy HDMaps to reflect the various conditions under which we might be lacking precision. In a first Scenario 2a, we propose a shift-noise setting where for each map element localization, we add noise from a Gaussian distribution with standard deviation of 1 meter. This has the effect of applying a uniform translation to each map element (dividers, boundaries, crosswalks). Such a setting should be a good approximation of situations where human annotators provide quick imprecise annotations from noisy data. We chose a standard deviation of 1 meter to reflect MDMaps standards of being precise up to a few meters [START_REF] Gupta | The mapping laritularity is near[END_REF].

We then test our approach with a very challenging pointwise-noise Scenario 2b: for each ground truth point -keeping in mind a map element is made up of 20 such points -we sample noise from a Gaussian distribution with standard deviation of 5 meters and add it to the point coordinates. This provides a worst case approximation of the situation where the map was acquired automatically or provides very imprecise localization.

Scenario 3: Maps have substantially changed

The final scenario we consider is one where we have access to old maps that used to be accurate (see Fig. 2d). As noted in Sec. 3.3, it is fairly common for painted markers like pedestrian crossings to be displaced from time to time. Furthermore, it is not uncommon for cities to substantially remodel some problematic intersection or renovate districts to accommodate traffic increase by a new attraction [START_REF] Plachetka | Terminology and analysis of map deviations in urban domains: Towards dependability for hd maps in automated vehicles[END_REF].

It is therefore interesting to use HDMaps that are valid on their own but differ from the actual HDMaps in significant ways. These maps should often appear when the HDMaps are only updated by the maintainer every few years to cut down on costs. In that case, the available maps would still provide some information on the world but might not reflect temporary or recent changes. Implementation We approximate this by applying strong changes to existing HDMaps in our Scenario 3a. We delete 50% of the pedestrian crossings and lane dividers in the map, add a few pedestrian crossings (half the amount of the remaining crossings) and finally apply a small warping distortion to the map.

However, it is important to note that a substantial amount of the global map will remain unchanged over time. We account for that in our Scenario 3b, where we study the effect of randomly choosing (with probability p=0.5) to consider the real HDMap instead of the perturbed version.

MapEX: Accounting for EXisting maps

We propose MapEX (see Fig. 3), a novel framework for online HDMap estimation. It follows the standard query based online HDMap estimation workflow [START_REF] Liao | MapTR: Structured modeling and learning for online vectorized HD map construction[END_REF][START_REF] Liu | Vectormapnet: End-to-end vectorized hd map learning[END_REF] and processes existing map information thanks to two key modules: a map query encoding module (see Sec. 4.2) and a preattribution scheme of predictions and ground truths for training (see Sec. 4.3). We also propose an optional change detection module in Appendix 9 for cases where true maps are mixed with perturbed maps as in our Scenario 3b. Since our implementation is built upon the state-of-the-art Map-TRv2 [START_REF] Liao | Maptrv2: An end-to-end framework for online vectorized hd map construction[END_REF], it will translate to most methods [START_REF] Ding | Pivotnet: Vectorized pivot learning for end-to-end hd map construction[END_REF][START_REF] Liao | MapTR: Structured modeling and learning for online vectorized HD map construction[END_REF][START_REF] Liu | Vectormapnet: End-to-end vectorized hd map learning[END_REF]

Overview

The core of the standard query based framework is shown through gray elements on Fig. 3. It starts by taking sensor inputs (cameras and/or LiDAR), and encodes them into a Bird's Eye View (BEV) representation to serve as sensor features. The map itself is obtained using a DETR-like [START_REF] Carion | End-toend object detection with transformers[END_REF] detection scheme to detect the map elements (N at most). This is achieved by passing N × L learned query tokens (N being the maximum number of detected elements, L the number of points predicted for an element) into a transformer decoder that feeds sensor information to the query tokens using cross-attention with the BEV features. The decoded queries are then translated into map element coordinates by linear layers along with a class prediction (including an extra background class) such that groups of L queries represent the L points of a map element (L = 20 in this paper). Training is done by matching predicted map elements and ground truth map elements using some variant of the Hungarian algorithm [START_REF] David | On implementing 2d rectangular assignment algorithms[END_REF][START_REF] Harold W Kuhn | The hungarian method for the assignment problem[END_REF]. Once matched, the model is optimized to fit the predicted map elements to their corresponding ground truth using regression (for coordinates) and classification (for element classes) losses.

This standard framework has no way to account for existing maps, which necessitates introducing new modules at two key levels. At the query level, we encode map elements into non learnable EX queries (see Sec. 4.2). At the matching level, we pre-attribute queries to the ground truth map elements they represent (see Sec. 4.3).

The complete MapEX framework -shown on Fig. 3 -converts existing map elements into non-learnable map queries and adds learnable queries to reach a set number of

Translating maps into EX queries

There is no mechanism in current online HDMap estimation frameworks to account for existing map information. We therefore need to design a new scheme that can translate existing maps into a form understandable by standard querybased online HDMap estimation frameworks. We propose with MapEX a simple method of encoding existing map elements into EX queries for the decoder as shown on Fig. 4.

For a given map element, we extract L evenly spaced points, with L being the number of points we seek to predict for any map element. For each point, we craft an EX query that in the first 2 dimensions its map coordinates (x,y) and in the next three dimensions a one-hot encoding of the map element class (divider, crossing or boundary). The rest of the EX query is padded with 0s to reach the standard query size used by the decoder architecture.

While this query design is very simple, it presents the key benefits of both directly encoding the information of interest (point coordinates and element class), and minimizing collisions with learned queries (thanks to the abundant 0padding). A detailed discussion is provided in Sec. 5.3.2 with experimental comparisons to other possible designs.

Once we have N EX sets of L queries (for the N EX map elements in the existing map), we retrieve (N -N EX ) sets of L assorted learnable queries from our pool of standard learnable queries. The resulting N × L queries are then fed to the decoder following the base method we are working on: in MapTR the N × L queries are treated as independent queries whereas MapTRv2 uses a more efficient decoupled attention scheme that groups queries of a same map element together. After we predict map elements from the queries, we can either directly use them (at test time) or match them to the ground truth for training.

Map element attribution

While EX queries introduce a way to account for existing map information, nothing ensures these queries will be properly used by the model to estimate the corresponding elements. In fact, experiments in Sec. 5.3.1 show the net-work can fail to identify even fully accurate EX queries if left on its own. We thus introduce a pre-attribution of predicted and true map elements before the traditional Hungarian matching used at training as shown on Fig. 3.

Put plainly, we keep track for each map element in the modified map of which ground truth map element they correspond to: if a map element is unmodified, shifted or warped we can tie it to the original map element in the true map. To ensure the model learns to solely use useful information, we only keep matches when the average pointwise displacement score, between the modified map element m EX = {(x EX 0 , y EX 0 ), . . . , (x EX L-1 , y EX L-1 )} and true map element m GT = {(x GT 0 , y GT 0 ), . . . , (x GT L-1 , y GT L-1 )}:

s(m EX , m GT ) = 1 L L-1 i=0 x EX i y EX i - x GT i y GT i 2 (1)
is below 1 meter long. In case of deletions or additions, there are no corresponding map elements. This attribution process can be extended to most map modifications.

Given the correspondence between ground truth and predicted map elements, we can remove the pre-attributed map elements from the pool of elements to be matched. The remaining map elements (predicted and ground truth) are then matched using some variant of the Hungarian algorithm as per usual [START_REF] David | On implementing 2d rectangular assignment algorithms[END_REF][START_REF] Harold W Kuhn | The hungarian method for the assignment problem[END_REF]. As such, the Hungarian matching step is only needed to identify which EX queries correspond to non-existent added map elements, and to find standard learned queries that fit some of the true map elements absent from the real map (due to deletion or a strong perturbation).

Reducing how many elements must be processed by a Hungarian algorithm is important as even the most efficient variants are of cubical complexity O(N 3 ) [START_REF] David | On implementing 2d rectangular assignment algorithms[END_REF]. This is not a major weak point in most online HDMap acquisition methods currently as the predicted maps are small [START_REF] Gao | Complementing onboard sensors with satellite map: A new perspective for hd map construction[END_REF][START_REF] Liao | Maptrv2: An end-to-end framework for online vectorized hd map construction[END_REF] (30m × 60m) and only three types of map elements are predicted. As online map generation progresses further however, it will become necessary to accommodate an ever increasing number of map elements as predicted maps grow both larger [START_REF] Gao | Complementing onboard sensors with satellite map: A new perspective for hd map construction[END_REF] and more complete [START_REF] Li | Topology reasoning for driving scenes[END_REF].

Experimental results

We now verify experimentally that existing maps are useful for online HDMap estimation. After providing a general overview of MapEX results in relation to the literature in Sec. 5.1, we highlight the improvements from using existing map information over the baseline in our different scenarios (see Sec. 5.2). We then provide deeper understanding of the MapEX framework through careful ablations in Sec. 5.3. Setting We evaluate our MapEX framework on the nuScenes dataset [4] as it is the standard evaluation dataset for online HDMap estimation. We base ourselves on the MapTRv2 framework and official codebase. Following usual practices, we report the Average Precision for each of the three map element types (divider, boundary, crossing) at different retrieval thresholds (Chamfer distance of 0.5m, 1.0m and 1.5m) along with overall mean Average Precision over the three classes. To be comparable to results in the literature [START_REF] Ding | Pivotnet: Vectorized pivot learning for end-to-end hd map construction[END_REF][START_REF] Liao | Maptrv2: An end-to-end framework for online vectorized hd map construction[END_REF][START_REF] Liu | Vectormapnet: End-to-end vectorized hd map learning[END_REF], we show results on the nuScenes val set but conduct no hyper-parameter tuning on the val set to avoid overfitting to it. We directly get training parameters from MapTRv2 without tuning (using standard learning rate scaling heuristics [START_REF] Granziol | Learning rates as a function of batch size: A random matrix theory approach to neural network training[END_REF] to adapt to our 2 GPU infrastructure). Our code, along with the standalone MapModEX package will be made available upon publication. A complete description of the setting is provided in Appendix 7.

For each experiment, we conduct 3 experimental runs using three fixed random seeds. Importantly, for a given seed and map scenario combination, the existing map data provided during validation is fixed to facilitate comparisons. We report results as mean ± std, up to a decimal point even if standard deviation exceeds that precision, in order to keep notations uniform.

Performance of MapEX

We provide in Tab. 2 an overview of results from the literature along with MapEX performance in the 5 existing map scenarios outlined in Sec. 3: maps with no dividers or pedestrian crossings (S1), noisy maps (S2a for shifted map elements, S2b for strong pointwise noise), and substantially changed maps (S3a with only those maps, S3b with true maps mixed in). We contextualize MapEX's performance by comparing it both to an exhaustive inventory of existing online HDMap estimation on comparable settings (Camera inputs, CNN Backbone) and to the current state-of-the-art (which uses significantly more resources).

First and foremost, it is clear from Tab. 2 that any sort of existing map information leads MapEX to significantly outperform the existing literature on comparable settings regardless of the considered scenario. In all but one scenario, existing map information even allows MapEX to perform much better than the current state-of-the-art MapTRv2 [START_REF] Liao | Maptrv2: An end-to-end framework for online vectorized hd map construction[END_REF] model trained over four times more epochs with a large vision transformer backbone pretrained on an extensive depth estimation dataset [START_REF] Park | Is pseudo-lidar needed for monocular 3d object detection?[END_REF]. Even the fairly conservative S2a scenario with imprecise map element localizations leads to an improvement of 11.4 mAP score (i.e. 16%).

In all scenarios, we observe consistent improvements over the base MapTRv2 model in all 4 metrics. Understandably, Scenario 3b (with accurate existing maps half of the time) yields the best overall performance by a large margin, thereby demonstrating a strong ability to recognize and leverage fully accurate existing maps. Both Scenarios 2a (with shifted map elements) and 3a (with "outdated" map elements) offer very strong overall performance with good performance for all three types of map elements. Scenario 1, where only road boundaries are available, shows huge mAP gains thanks to its (expected) very strong retrieval of boundaries. Even the incredibly challenging Scenario 2b, where Gaussian noise of standard deviation 5 meters is applied to each map element point, leads to substantial gains on the base model with particularly good retrieval performance for dividers and boundaries.

Improvements brought by MapEX

We now focus more specifically on the improvements that existing map information brings to our base MapTRv2 model. For reference, we compare MapEX gains with those brought by other sources of additional information: Neural Map Prior with a global learned feature map [START_REF] Xiong | Neural map prior for autonomous driving[END_REF], Satellite Maps with geolocalized Satellite views [START_REF] Gao | Complementing onboard sensors with satellite map: A new perspective for hd map construction[END_REF], and P-MapNet which uses geolocalized SDMaps [2]. Importantly, MapModEX relies on a stronger base model than these methods. While this makes it harder to improve upon the base model, it also makes it easier to reach high scores.

To avoid having an unfair advantage, we provide in Tab. 3 the absolute ∆AP = AP Base+Inf o -AP Base score gain. We see from Tab. 3 that using any kind of existing map with MapEX leads to overall mAP gains larger than any other source of additional information (including a more sophisticated P-MapNet setting). We generally observe very strong improvements to the model's detection performance on both lane dividers and road boundaries. A slight exception is Scenario 1 (where we only have access to road boundaries) where the model successfully retains map information on boundaries but only provides improvements comparable to previous methods on the two map elements it has no prior information on. Pedestrian crossings seem to require more precise information from existing maps as both Scenario 1 and Scenario 2b (where a very destructive noise is applied to each map point) only provide improvements comparable to existing techniques. Scenarios 2a (with shifted elements) and 3a (with "outdated" maps) lead to strong detection scores for pedestrian crossings, which might be because these two scenarios contain more precise information on pedestrian crossings.

Ablations on the MapEX framework

We conduct here extensive experiments on the impact of MapEX inputs in Sec. 5.3.1. We then propose specialized experiments on relevant scenarios regarding our EX queries (Sec. 5.3.2) and our attribution scheme (Sec. 5.3.3).

Contribution of inputs in MapEX

Tab. 4 shows how the different types of inputs (existing maps, map element correspondences, and sensor inputs) impact MapEX. As discussed in Sec. 5.1, results demonstrate clearly that existing maps strongly improve performance.

As much as MapEX benefits from maps however, we can see from lines 1 and 3 of Tab. 4 that it still relies significantly on the sensor inputs. Indeed, models solely based on map inputs are substantially worse than complete MapEX models. This indicates sensor inputs help MapEX improve upon its imperfect existing map inputs.

Ground truth correspondences (for pre-attribution of predictions and ground truths) seem to lower the variance of MapEX as indicated by lines 1 and 2 of Tab. 4. This demonstrates pre-attribution is indeed necessary to properly leverage existing map information. A good way to understand this is to consider our Scenario 1. In this scenario, we have access to the exact boundary elements. With preattribution this consistently leads to near perfect retrieval of those elements (see Tab. 2). This is not the case without pre-attribution unfortunately: in two out of three runs, the network only reaches a score below 80% AP. This suggests pre-attribution helps ensure MapEX consistently learns to utilize the information provided by existing maps.

On EX query encoding

We use in Sec. 4.2 a simple encoding scheme to translate existing map elements into EX queries. This might be surprising, as one might expect learned EX queries to be more useful (e.g. by projecting a 5-dimensional vector description of the element into a query). Tab. 5 shows learned EX queries perform much worse than our simple non-learnable EX queries. Interestingly, initializing learnable EX query with the non-learnable values might bring very minor improvements that do not justify the added complexity. 6. Influence of ground attribution schemes on results (Scenario 2a). Discarding existing map elements too far from the corresponding ground truth significantly improves results.

Discussion

We propose to improve online HDMap estimation by taking advantage of an overlooked resource: existing maps. To study this, we outline three realistic scenarios where existing (minimalist, noisy or outdated) maps are available and introduce a new MapEX framework to leverage these maps. As there is no mechanism in current frameworks to account for existing maps, we develop two novel modules: one encoding map elements into EX queries, and another ensuring the model leverages these queries.

Experimental results demonstrate that existing maps represent a crucial information for online HDMap estimation, with MapEX significantly improving upon comparable methods regardless of the scenario. In fact, the median scenario (in terms of mAP) -Scenario 2a with randomly shifted map elements -improves upon the base MapTRv2 model by 38% and upon the current state-of-the-art by 16%.

We hope this work will lead new online HDMap estimation methods to account for existing information. Existing maps -good or bad -are widely available. To ignore them is to forego a crucial tool in the search for reliable online HDMap estimation.

Mind the map! Accounting for existing map information when estimating online HDMaps from sensor data

Supplementary Material

We provide in this Appendix some additional details to understand our work:

• We provide more details on our experimental setting in Sec. 7. • We discuss how the Argoverse 2 Trust but Verify relates to our problem in Sec. 8. • We study how the model behaves with exact map inputs in Sec. 9. • We give pseudocode overviews of our two original MapEX modules in Sec. 10.

Detailed setting and codebase

We introduce here the detailed experimental details used for our experiments along with in-depth explaination of how existing maps are obtained for our various scenarios.

Our code is largely based on the official MapTRv2 code 1 , and will be made available along with our standalone Map-ModEX libray upon acceptance of this paper.

Training details We largely reprise the 24 epochs training settings from our MapTRv2 [START_REF] Liao | Maptrv2: An end-to-end framework for online vectorized hd map construction[END_REF] base, which were described in the original paper as: "ResNet50 is used as the image back-bone network unless otherwise specified. The optimizer is AdamW with weight decay 0.01. The batch size is 32 (containing 6 view images) and all models are trained with 8 NVIDIA GeForce RTX 3090 GPUs. Default training schedule is 24 epochs and the initial learning rate is set to 6 × 10-4 with cosine decay. We extract ground-truth map elements in the perception range of ego-vehicle following [...] The resolution of source nuScenes images is 1600 × 900. [...] Color jitter is used by default in both nuScenes dataset and Argoverse2 dataset. The default number of instance queries, point queries and decoder layers is 50, 20 and 6, respectively. For PV-to-BEV transformation, we set the size of each BEV grid to 0.3m and utilize efficient BEVPoolv2 [77] operation. Following [START_REF] Gulzar | A survey on motion prediction of pedestrians and vehicles for autonomous driving[END_REF], λ c = 2, λ p = 5, λ d = 0.005. For dense prediction loss, we set α d , α p , α b to 3, 2 and 1 respectively. For the overall loss,

β o = 1, β m = 1, β d = 1."
1 https://github.com/hustvl/MapTR/tree/maptrv2

Our own training setting solely differs from MapTRv2's in the fact that we train on 2 NVIDIA Quadro RTX 8000 GPUs. This in turn mean we need to reduce the batch size by 4 and scale learning rates by 2 following standard scaling heuristics for Adam optimizers [START_REF] Granziol | Learning rates as a function of batch size: A random matrix theory approach to neural network training[END_REF].

Scenario 1 implementation

We remove the divider and pedestrian crossings from available HDMaps.

Scenario 2a implementation

For each map element localization, we add noise from a Gaussian distribution with standard deviation of 1 meter. This has the effect of applying a uniform translation to each map element (dividers, boundaries, crosswalks).

Scenario 2b implementation

For each ground truth point -keeping in mind a map element is made up of 20 such points -we sample noise from a Gaussian distribution with standard deviation of 5 meters and add it to the point coordinates.

Scenario 3a implementation

We delete 50% of the pedestrian crossings and lane dividers in the map, add a few pedestrian crossings (half the amount of the remaining crossings) and finally apply a small warping distortion to the map. The warping distortion is composed of first trigonometric warping with horizontal and vertical amplitudes 1, and inclination 3. We then perform triangular warping following a slightly perturbed grid where each point on the regular grid is shifted according to random Gaussian noise with standard deviation 1.

Scenario 3b implementation

For each map, we draw a uniform random value between 0 and 1. If it is below p=0.5 we keep the true HDMap, otherwise we perturb it in the same way as in Scenario 3a.

On the Trust but Verify dataset

The Argoverse 2 Trust but Verify (TbV) dataset [START_REF] Lambert | Trust, but Verify: Crossmodality fusion for hd map change detection[END_REF] offers situations where the HDMap does not fit sensor inputs for change detection. While TbV is an excellent dataset for change detection, it unfortunately contains a limited number of real scenarios to train model for online HDMap acquisition. Moreover, a number of the change scenarios are indiscernible for our HDMap representation (e.g. change in the type of divider). Interestingly, the limited number of hand curated change situations is reserved for the validation and test sets with the train set generated from synthetic data. Where TbV chooses to generate synthetic views that differ from the available HDMap, we take the opposite view of modifying the HDMaps. While this is likely less desirable for change detection, it is of no consequence for online HDMap acquisition and much lighter computationally.

Map change detection 9.1. Map change detector

There are a number of situations where fully accurate HDMaps might be mixed in with the imperfect HDMaps (e.g. our Scenario 3b). As such, we propose a lightweight change detection module to leverage these situations.

We introduce a learned change detection query token and perform cross-attention between this token and intermediate map element queries at different stages of the decoder. This token is then decoded by dense layer into a change prediction c ∈ [0, 1] (with a sigmoid activation). At training time, we train this token with a binary cross entropy loss (with target ĉ = 1 if the map is not fully accurate and ĉ = 0 if it is): we minimize

L = L Base + L BCE (c, ĉ), (2)
with L Base the loss of the base online HDMap estimator. At test time, if no change is detected we output the existing HDMap instead of the prediction (and we output the decoder predictions as usual if a change is detected).

Using the existing HDMap has two distinct benefits: it provides a very precise HDMap (something most methods struggle with [START_REF] Ding | Pivotnet: Vectorized pivot learning for end-to-end hd map construction[END_REF]), and it provides a way to stop the map estimation process early. Indeed, returning the existing map removes the need for further decoding of the query tokens which can be expensive.

Processing accurate existing maps

Finally, we take a closer look at how MapEX deals with perfectly accurate existing maps as it can sometimes happen in scenarios like Scenario 3b. To this end, we compare MapEX to variants that use an explicit map change detection module (described in Appendix 9) and substitute the predicted map with the input existing map if no change is detected. Tab. 7 shows MapEX does not need a change detection module: it recognizes and uses accurate existing map elements on its own. In fact, training a change detection module jointly with MapEX appears to deteriorate performance. 7. Usefulness of the change detection module (Scenario 3b). MapEX seems to recognize and leverage existing maps without the need for an explicit change detection scheme.

Pseudo code

We provide here pseudo code for our two additional modules: the EX query encoding module (Alg. 1) and the preattribution code (Alg. 2). * / a = Merge(p p , a n , split inds); return a; Algorithm 2: Hungarian matching with pre-attribution.

  (a) Ground Truth. (b) Scenario 1. (c) Scenario 2a. (d) Scenario 3a.

Figure 2 .

 2 Figure 2. Examples of HDMaps generated by MapModEX.

Figure 3 .

 3 Figure 3. Overview of our MapEX method (see Sec. 4). We add two modules (EX query encoding, Attribution) to the standard query based map estimation pipeline (in gray on the figure). Map elements are encoded into EX queries, then decoded with a standard decoder.

Figure 4 .

 4 Figure 4. Encoding map elements into EX queries. For each point of the element, we encode the (x,y) coordinates along with the element class. (div=divider, ped=crossing, bnd=boundary)

Data:

  Map element m EX = {(x EX 0 , y EX 0 ), . . . , (x EX L-1 , y EX L-1 )} of class c (among divider, crossing and boundary). Result: list query list of L H-dimensional EX queries. query list = []; for i ← 0 to L-1 do / * Encode position * / pos vec = array([x EX i vec = one hot(c, num class=3); / * Build query * / pad vec = zeros(H -5); query i = concatenate([pos vec, class vec, pad vec]); query list.append(query i); end return query list; Algorithm 1: Encoding map elements into EX Queries. Data: Predictions p = {p i } i=0,...,49 , (Padded) ground truths g = {g i } i=0,...,49 , correspondence list c = {c i } i=0,...,49 where c i = -1 if there is no correspondence Result: Assignment a = {a i } i=0,...,49 where a i is the index of the ground truth associated to the i-th prediction. / * Split off pre-attributed pairs * / p p , g p , c p , p n , g n , c n , split inds = Split(p,g,c); / * Perform Hungarian matching * / a n = Hungarian(p n , g n ); / * Merge c p with a n

Table 1 .

 1 MapEX strongly improves on existing online HDMap estimation methods and beats the current state-of-the-art mean average precision (mAP) by 16% in the median scenario on nuScenes.

	Method	Backbone Epochs	Extra info	mAP
	MapTRv2 (Base)	R50	24	✗	61.5
	MapTRv2 (SOTA)	V2-99	110	Depth pretraining 73.4
	MapEX-S2a (Ours)	R50	24	Inaccurate map	84.8

Table 2 .

 2 Comparison of MapEX to the current state-of-the-art. In all possible scenarios, MapEX improves upon the base MapTRv2 model. In Scenarios 1, 2a, 3a and 3b it even beats the state-of-the-art obtained with a much stronger backbone. Best results are highlighted in bold, second best are underlined, third best are in italic. (

	Method	Backbone Epoch		Extra info	Average Precision at {0.5m, 1.0m, 1.5m}
							AP divider	AP ped	AP boundary	mAP
						Previous methods
	HDMapNet [26]		EB0	30		✗	27.7	10.3	45.2	27.7
	... + P-MapNet * [2]		EB0	30		Geoloc. SDMaps	32.1	11.3	48.7	30.7
	VectorMapNet [33]		R50	110		✗	47.3	36.1	39.3	40.9
	... + Neural Map [43]		R50	110		Learned map feats	49.6	42.9	41.6	44.8
	MapTR [29]		R50	24		✗	51.5	46.3	53.1	50.3
	... + MapVR [46]		R50	24		✗	54.4	47.7	51.4	51.2
	... + Satellite Map * [13]	R50	24	Geoloc. Satellite views	55.3	47.2	55.3	52.6
	PivotNet [10]		R50	24		✗	56.2	56.5	60.1	57.6
	BeMapNet [39]		R50	30		✗	62.3	57.7	59.4	59.8
	MapTRv2 * , † [30]		R50	24		✗	62.4	59.8	62.4	61.5
	MapTRv2 * [30]		V2-99	110		Depth pretrain	73.7	71.4	75.0	73.4
						Our method
	MapEX-S1		R50	24	Map w/ only boundaries 66.1 ± 0.6	62.5 ± 0.4	99.9 ± 0.1	76.2 ± 0.1
	MapEX-S2a		R50	24		Map w/ element shift	82 .5 ± 1 .0	78.4 ± 0.8	93.5 ± 0.4 84 .8 ± 0 .3
	MapEX-S2b		R50	24		Map w/ point noise	78.4 ± 0.1	62.1 ± 0.6	72.4 ± 0.4	70.9 ± 0.3
	MapEX-S3a		R50	24		Outdated maps	84.6 ± 0.3 74 .1 ± 0 .6	99.1 ± 0.1	85.9 ± 0.2
	MapEX-S3b		R50	24		50% outdated maps	92.8 ± 0.1 87.2 ± 0.1	99.3 ± 0.2	93.1 ± 0.1
	Previous methods
	Neural Map	+02.3	+06.8	+02.6	+03.9
	Satellite Map *	+03.8	+00.9	+02.2	+02.3
	P-MapNet *	+04.4	+01.0	+03.5	+03.0
	P-MapNet * ,+	+08.4	+11.1	+06.8	+08.8
		Our method
	MapEX-S1-onlybounds	+03.7	+02.8	+37.5	+14.7
	MapEX-S2a-shift	+20.1	+18.6	+31.1	+23.3
	MapEX-S2b-point	+16.0	+02.3	+10.0	+09.4
	MapEX-S3a-fullchange	+22.2	+14.3	+36.7	+21.4
	MapEX-S3b-halfchange	+30.4	+27.4	+36.9	+31.6

* : Concurrent work, † : Same codebase and setting as our experiments.) Method Improvement ∆AP = AP Base+Inf o -AP Base ∆AP divider ∆AP ped ∆AP bound ∆mAP

Table 3 .

 3 Improvements from additional information. In all considered scenarios, existing map information substantially improves results compared to other sources of information. (

* : Concurrent work, + : MAE

[START_REF] He | Masked autoencoders are scalable vision learners[END_REF]

pretraining, Camera+LiDAR inputs)

Table 4 .

 4 ± 0.1 84.8 ± 0.3 70.9 ± 0.3 85.9 ± 0.2 93.1 ± 0.1 ... w/o Attribution 64.5 ± 1.9 84.7 ± 0.7 72.0 ± 1.9 80.3 ± 9.6 93.1 ± 0.2 Influence of MapEX inputs (sensors, maps, map element correspondences) on mean Average Precision. All MapEX inputs appear crucial to consistent overall precision.

	Method		Mean Average Precision
		S1	S2a-shift	S2b-noise	S3a-full	S3b-half
	MapEX 76.2 ... w/o Sensors 54.7 ± 0.9	69.5 ± 0.5	43.5 ± 0.4	73.3 ± 0.3	85.9 ± 0.3
	... w/o Map (Base)	61.4	61.4	61.4	61.4	61.4

Table 5 .

 5 Influence of map query design on results (Scenario 1). ± 1.0 78.4 ± 0.8 93.5 ± 0.4 84.8 ± 0.3 ... w/o sim. threshold 79.5 ± 1.6 76.4 ± 0.9 91.9 ± 0.2 82.6 ± 0.7

	Method		Average Precision at {0.5m, 1.0m, 1.5m}
		APdivider	APped	APboundary	mAP
	MapEX encoding	66.1 ± 0.6 62.5 ± 0.4 99.9 ± 0.1 76.2 ± 0.1
	Linear encoding	63.4 ± 0.3 61.1 ± 0.3	100 ± 0.1	74.8 ± 0.1
	Linear encoding w/ MapEx init. 66.6 ± 0.1 62.5 ± 0.9	100 ± 0.1	76.4 ± 0.3
	Our non-learnable EX query encoding does not perform any worse
	than learnable EX queries while requiring no extra training.
	5.3.3 On ground truth attribution
	Since pre-attributing map elements is important to consis-
	tently use existing map information (see Sec. 5.3.1), it might
	be tempting to pre-attribute all the corresponding map ele-
	ments instead of filtering them like we do in MapEX. Tab. 6
	shows that discarding correspondences when the existing
	map element is too different (see Sec. 4.3) does lead to
	stronger performance than indiscriminate attribution. In
	essence, this suggests it is preferable for MapEX to use a
	learnable query instead of EX queries when the existing
	map element is too different from the ground truth.
	Method	Average Precision at {0.5m, 1.0m, 1.5m}
	AP divider	AP ped	AP boundary	mAP
	MapEX 82.5 Table

  MethodAverage Precision at {0.5m, 1.0m, 1.5m} AP divider AP ped AP boundary mAP MapEX 92.8 ± 0.1 87.2 ± 0.1 99.3 ± 0.2 93.1 ± 0.1 ... w/ substitution 92.5 ± 0.3 87.3 ± 0.3 99.4 ± 0.1 93.0 ± 0.1 ... w/ sub. & optimization 92.5 ± 0.2 87.2 ± 0.2 99.3 ± 0.1 93.0 ± 0.1

	Table

Acknowledgements This work was realized by the Mul-tiTrans project funded by the Agence Nationale de la Recherche under grant reference ANR-21-CE23-0032. The authors are grateful to the OPAL infrastructure from Université Côte d'Azur for providing resources and support.


Comment

The potential of wealth taxation to address the triple climate inequality crisis

Lucas Chancel, Philipp Bothe & Tancrède Voituriez

The triple climate inequality crisis, or disparities in contributions, impacts and capacity to act within and between countries, is a central issue in addressing climate change. This Comment advocates for progressive wealth taxation as a viable solution to the finance gap.

The climate crisis impacts human societies profoundly, especially in regions with low historical emissions and income levels 1,2 . Such impacts exacerbate economic disparities within countries, with climate-related losses primarily affecting the economically vulnerable 3,4 . Research finds that a small fraction of the global population in emerging and high-income countries is responsible for a disproportionate share of greenhouse gas emissions 5,6 . This group also controls a substantial portion of global wealth and holds the key to effective global climate finance and meaningful adaptation strategies [START_REF] Chancel | Climate Inequality Report 2023, Fair Taxes for a Sustainable Future in the Global South (World Inequality Lab[END_REF] . Better understanding the joint distribution of carbon emissions, climate-related losses and capacities to finance the transition is pivotal to accelerating societies' response to climate change.

       

Mapping out the triple climate inequality crisis

All individuals contribute to emissions, but not in the same way. Society is faced with triple climate inequality, including emissions, income loss and capacity. At the global level, the top 10% of the population (ranked according to income, consumption or emissions) emit between 43% and 49% of global emissions based on recent studies, while the bottom 50% emit 7% to 13% of the total 5,6 . Therefore, the global top 10% of emitters generates three to five times as much carbon as the bottom half of the world, albeit they are five times less numerous. By contrast, the   exposure of the top 10% of emitters to climate-induced relative income losses appears to be very limited-only 3% of relative income losses are borne by this group. The capacity to finance climate action of the global top 10% of wealth owners, proxied by their share of global wealth, also reveals an extreme level of inequality. The comparison of the global bottom 50%, middle 40% and top 10% in terms of losses, emissions and capacity to finance global climate action provides a clear snapshot of three intertwined climate inequality crises and a reasonable guide to identify the key contributors to the funding of climate policies (Fig. 1).

While

 
there is a delay in tackling climate inequalities head on, climate change contributes to economic and material deprivation in a myriad of ways, now well documented. Climate-related disasters and slow-onset events aggravate low agricultural productivity in poorer countries, as well as water scarcity and security [START_REF]IPCC Climate Change 2022: Impacts, Adaptation, and Vulnerability[END_REF][START_REF] Ortiz-Bobea | [END_REF] . Heatwaves have substantial impacts on mortality, particularly in vulnerable urban centres 10 . Tropical cyclones and floods will continue to displace millions of people, mostly in low-income countries, and rising sea levels will make large swaths of coastal land uninhabitable 11 . While such events will affect regions as a whole, studies point to a strong socioeconomic relationship between exposure (and especially vulnerability) and current living conditions, whereby the worst off are more affected than the rest 3 . The wide set of already visible climate change impacts reveal that every fraction of a degree matters. It follows that every tonne of carbon matters as much as every dollar of adaptation funding.

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in perspective, climate finance flows from rich countries to developing countries amounted to US$83 billion in 2020. A look at cumulative historical greenhouse gas emissions reveals that most affluent nations in the Global North have exceeded their population-weighted carbon budgets, thereby disproportionately consuming the global 1.5 °C carbon budget. Consequently, the compelling question of compensating countries that have preserved their rightful share of the 1.5 °C budget emerges as a focal point of public discourse about funding the net-zero transition in developing countries.

Recent research proposed that countries in the Global South, which have not overshot their carbon allocations, should be entitled to a total of US$192 trillion in climate compensation by 2050-this is calculated using marginal abatement costs of carbon from IPCC Sixth Assessment Report scenarios consistent with 1.5 °C, and a monetization of overshoot emissions since 1960 [START_REF] Fanning | [END_REF] . If this compensation were to be paid between 2020 and 2050, an annual compensation of around US$6.4 trillion from the over-emitters would thus be required to support the countries that have kept within their carbon limits. Translated into palpable terms, we find that this compensation mirrors a 2% yearly tax on the total assets held by the Global North in 2022 (equivalent to 12% of their national income every year) spread across three decades. Alternatively, this amount could be sourced through a 3.5% yearly wealth tax targeting the richest 10% in the Global North, sparing the rest of the population. Tweaking rates within this top echelon could distribute the burden more fairly. Harnessing revenues from a top-up rate on multinational corporate profits could also help go in this direction [START_REF] Chancel | Climate Inequality Report 2023, Fair Taxes for a Sustainable Future in the Global South (World Inequality Lab[END_REF] .

These figures might appear staggering, especially when contrasted against the current official development aid (typically around 0.6% of annual national income of rich countries, or 0.1% of their wealth).

Why inequalities in emissions matter

Understanding how groups may win and lose from the transition to net-zero emissions is key to accelerating it. Established environmental policies such as emissions trading schemes are somewhat agnostic to distributional concerns. We argue instead that modern climate policy needs to live up to empirical realities and consider inequality more systematically in policy design, as certain countries have started to do.

The different pathway of each group to net zero within countries will matter for political and economic reasons. Knowing the triple inequalities of different groups is paramount to providing an equitable answer to questions such as: at what pace should various actors bring down their emissions? Efficiency questions are also at stake: the 'marginal effort' required to mitigate emissions might be lower for high-emitting and high-wealth groups, which could create an incentive for policies that target this group first. Last, as top emitters are likely to be (although not always) relatively well protected from the adverse consequences of climate change, their incentives to reduce emissions are not necessarily aligned with the damage those emissions cause. Quantifying inequalities in carbon emissions, exposure to damages and capacities to act allows to be more explicit about these issues and can help accelerate the transition to net zero.

A 1.5% wealth tax for 1.5 °C

To tackle these challenges, it is necessary that rich countries fulfil their climate finance commitments from the Paris Agreement. However, this condition is not sufficient to decrease inequality both in capacities to adapt and in climate-induced losses. The Loss and Damage Fund initiated at Sharm el-Sheikh COP27 represents a step in the right direction. Yet the timeline for operationalizing the fund is short (COP28) and politically sensitive questions remain on who benefits and who pays.

Similarly, the adaptation funding gap remains yawningly wide open. The Summit for a New Global Financing Pact held in Paris in June 2023 gave renewed impetus to reform development banks, with a plan to draw on more of their current assets. However, the financing commitments and debt relief plans agreed on are marginal compared with the true financing needs in the face of the looming climate collapse [START_REF] Songwe | Finance for Climate Action: Scaling up Investment for Climate and Development[END_REF] . New resources need to be mobilized, and Fig. 1 illustrates where these resources could be found. Adaptation funding needs in developing countries have been estimated at nearly US$   200 billion per year while funding flows were US$29 billion in 2020 [START_REF] Songwe | Finance for Climate Action: Scaling up Investment for Climate and Development[END_REF] . Our estimations suggest that a very small annual wealth tax of 0.06% of the value of assets owned by the residents of rich countries would entirely close this gap. While such a proposal considers inequality between countries, it considers neither within-country inequalities in wealth ownership nor inequality in contributions to climate change. A progressive wealth tax targeted at very top wealth holders can be envisaged to factor in such inequalities to some extent. As an illustration, we consider a '1.5% wealth tax for 1.5 °C on the world's very richest individuals (that is, a tax base of roughly 65,000 centimillionaire individuals globally) with tax rates increasing from 1.5% of net personal wealth, to a top rate of 3%. Such a tax scheme, if implemented successfully, could raise about US$300 billion every year globally, and thus entirely close the current adaptation funding gap [START_REF] Chancel | Climate Inequality Report 2023, Fair Taxes for a Sustainable Future in the Global South (World Inequality Lab[END_REF] (Fig. 2).

Factoring in inequality in climate policy design

Fig. 1 |

 1 Fig. 1 | The triple climate inequality crisis. Distribution of climate-related relative income losses, carbon emissions and wealth across the global population.The graph shows that the bottom 50% of the world population, ranked by emissions level, contributes to 12% of global emissions but is exposed to 75% of relative income losses due to climate change. Emissions inequality data are based on the World Inequality Database for 2019. Losses can be measured in many different ways. In this simple representation, we use country-level gross domestic product losses (in 2030 and relative to a world without climate change) from existing studies. We attribute, to each emitter group within each country, a per capita percentage income loss score. We assume that the bottom 40% of the distribution is 20% more exposed to losses than the average population in a given country, a conservative estimate based on recent studies (see ref.3). The sum of these loss scores, weighted by population, gives a total global relative income loss burden, which is distributed across groups of emitters. These estimates of the global inequality in income losses should be interpreted with great care given the stylized approach taken to construct them. They nonetheless provide a useful representation of the large global inequality in climate change impacts found in the literature. Capacity to finance is here proxied by the distribution of net wealth across the world population, ranked by net wealth. Figure adapted from ref. 7, under a Creative Commons license CC BY 4.0.

Fig. 2 |Lucas Chancel 1 , 2 , 3 , Philipp Bothe 3 & Tancrède Voituriez 4 1

 212334 Fig. 2 | Potential revenues from progressive taxation of global centimillionaires versus current adaptation funding flows and needs. Adaptation finance flows to developing countries reached US$29 billion. Finance needs amount to about US$200 billion. A wealth tax on centimillionaires could generate US$295 billion per year, enough to close the gap and generate additional revenues. Finance needs are based on ref. 12. Annual wealth tax revenues for 2021 are from the World Inequality Database. Wealth tax rates are as described in the text. Figure adapted from ref. 7, under a Creative Commons license CC BY 4.0.

  The sum of these loss scores, weighted by population, gives a total global relative income loss burden, which is distributed across groups of emitters. These estimates of the global inequality in income losses should be interpreted with great care given the stylized approach taken to construct them. They nonetheless provide a useful representation of the large global inequality in climate change impacts found in the literature. Capacity to finance is here proxied by the distribution of net wealth across the world population, ranked by net wealth. Figure adapted from ref. 7, under a Creative Commons license CC BY 4.0.

Distribution of climate-related relative income losses, carbon emissions and wealth across the global population. The graph shows that the bottom 50% of the world population, ranked by emissions level, contributes to 12% of global emissions but is exposed to 75% of relative income losses due to climate change. Emissions inequality data are based on the World Inequality Database for 2019. Losses can be measured in many different ways. In this simple representation, we use country-level gross domestic product losses (in 2030 and relative to a world without climate change) from existing studies. We attribute, to each emitter group within each country, a per capita percentage income loss score. We assume that the bottom 40% of the distribution is 20% more exposed to losses than the average population in a given country, a conservative estimate based on recent studies (see ref.

3

).

  Turning to the overall climate finance gap, estimates indicate that finance for the Global South should escalate to an additional US$1.8 trillion annually by 2030, from public or private sources. To put this number

Competing interests

The authors declare no competing interests.

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