TopoLogic: An Interpretable  Pipeline for Lane Topology Reasoning on Driving Scenes
Authors: Yanping Fu
Wenbin Liao
Xinyuan Liu
Hang Xu
Yike Ma
Yucheng Zhang
Feng Dai
Venue: NeurIPS 2024 poster (2024)
Keywords: Autonomous Driving
Topology Reasoning
Lane Detection
High Definition Map Learning
Primary area: machine_vision
TL;DR: We proposed an interpretable pipline based on lane geometric distance and semantic similarity that has significantly enhanced the performance of lane topology reasoning on driving scenes.

Abstract: As an emerging task that integrates perception and reasoning, topology reasoning in autonomous driving scenes has recently garnered widespread attention.  However, existing work often emphasizes "perception over reasoning": they typically boost reasoning performance by enhancing the perception of lanes and directly adopt vanilla MLPs to learn lane topology from lane query. This paradigm overlooks the geometric features intrinsic to the lanes themselves and are prone to being influenced by inherent endpoint shifts in lane detection.
 To tackle this issue, we propose an interpretable method for lane topology reasoning based on lane geometric distance and lane query similarity, named TopoLogic. This method mitigates the impact of endpoint shifts in geometric space, and introduces explicit similarity calculation in semantic space as a complement. By integrating results from both spaces, our methods provides more comprehensive information for lane topology.  Ultimately, our approach significantly outperforms the existing state-of-the-art methods on the mainstream benchmark OpenLane-V2 (23.9 v.s. 10.9 in TOP$_{ll}$ and 44.1 v.s. 39.8 in OLS on subsetA). Additionally, our proposed geometric distance topology reasoning method can be incorporated into well-trained models without re-training, significantly enhancing the performance of lane topology reasoning. The code is released at https://github.com/Franpin/TopoLogic.

TopoLogic: An Interpretable Pipeline for Lane Topology Reasoning on Driving Scenes
Yanping Fu
Wenbin Liao
Institute of Computing Technology,
Institute of Computing Technology.
Chinese Academy of Sciences University of Chinese Academy of Sciences fuyanping23s@ictt.. ac
Chinese Academy of Sciences
University of Chinese Academy of Sciences
1iaowenbin2320ict.ed
Xinyuan Liu
Hang Xu
Institute of Computing Technology, Chinese Academy of Sciences University of Chinese Academy of Sciences liuxinyuan21s0ictt ac. cn
Hangzhou Dianzi University hxu@hdu. edu. cn
Yike Ma
Yucheng Zhang
Institute of Computing Technology,
Institute of Computing Technology, Chinese Academy of Sciences
Chinese Academy of Sciences ykma@ict.ace ac.icttt.coom
zhangyucheng@ict.cc ac en
Feng Dai
Institute of Computing Technology,
Chinese Academy Sciences fdai@i clai@ict.om ww..t.a.comm
Abstract
As an emerging task that integrates perception and reasoning, topology reasoning autonomous driving scenes has recently garnered widespread attention. However, existing works often emphasizes "perception over reasoning": they typically boost reasoning performance by enhancing the perception of lanes and directly adopt vanilla MLP to learn lane topology from lane query. This paradigm overlooks the geometric features intrinsic to the lanes themselves and is prone to being influenced by inherent endpoint shifts in lane detection. To tackle this issue, we propose an interpretable method for lane topology reasoning based lane geometric distance and lane query similarity. named TopoLogic. This method mitigates the impact endpoint shifts in geometric space, and introduces explicit similarity calculation in semantic space as a complement. By integrating results from both spaces, our method provides more comprehensive information for lane topology. Ultimately, our approach significantly outperforms the existing state-of-the-arr methods on the mainstream benchmark OpenLane- V2 (23.9 10.9 in TOPn and 44.1 v.s. 39.8 OLS on subser A). Additionally, our proposed geometric distance topology reasoning method be incorporated into well-trained models without re-training, significantly boosting the performance of lane topology reasoning. The code is released htttps:// ttttps://giln hwt.uub..oo///aiiaiiii wtt.tt/....o///aaai///oooo.oaao.
*Corresponding Author
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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(c)
(d)
Figure 1: Comparison of results with and without post-processing in TopoNet. We use post- processing based on geometric distance to improve the lane topology reasoning performance of TopoNet. (a) denotes the ground truth of lane topology reasoning. (b) denotes the endpoints of two connected lanes in prediction do not overlap (marked with yellow circle) as desired in ground truth. (c) denotes the lane topology reasoning result of TopoNet, the arrow denotes lane topology (marked with red arrow). (d) denotes the lane topology reasoning result of TopoNet using post poot-processing. significantly improves the reasoning precision of lane topology.
1 Introduction
In recent years, the field of autonomous driving has witnessed numerous milestone achievements and has progressively shifted from pure research to practical applications. In complex driving scenarios, vehicles need perceive lanes & traffic elements and reason their topological relationships (i.e., lane connectivity and correspondence with traffic elements), which provides comprehensive information for downstream path planning and motion control. Under the trend of end-to-end autonomous driving, abovementioned perception and reasoning are integrated into a single task, referred to as topology reasoning M in autonomous driving scenes. This challenge has attracted widespread attention within the ego planning 2 4 and high-definition map learning [5 6
communities.
The topology reasoning task has garnered significant attention recently, since it is closer to the real needs. Some works have explored lane centerline representation [ 9 [O] IT] and lane segment representation [12], while others have introduced SDMap (Standard-Definite
Map) [ to provide additional clues for learning. However, existing works primarily focus on enhancements in the perception part, with scarce modifications made to the reasoning part. Irrespective of the approach details, existing studies typical employ vanilla MLP to learn lane topology directly from lane query. This paradigm has its shortcoming: since each lane is encoded independently through distinct query, it is challenging to ensure strictly overlap at the endpoints of two connected lanes, as shown in Figure [b).. In contrast, it evident that the endpoints of two connected lanes in the ground truth actually overlap perfectly, as shown in Figure [[a.. Lanes with slightly shifted endpoints may be erroncously classified by MLP as disconnected. This leads MLP casily predicting fewer lane topology, as shown in Figure (c..
To tackle the aforementioned issues, introduce TopoLogic, an interpretable method for lane topology reasoning that is based on lane geometric distances and the similarity of lane query in semantic space. The geometric distance-based approach aims mitigates the impact of endpoint shift, thereby more robustly learning lane topology. This approach first calculates the geometric distance between lanes and then uses learnable mapping function to map the distance to connectivity probability. Notably, for two given lanes, their geometric distance is defined as the distance between the ending point of one lane and the starting point of subsequent lane. This distance itself can serve as a strong criterion: when this distance is within a certain range, the predicted endpoints should be considered overlapping, and the lanes connected; otherwise, they are not. In this way, the lane topology reasoning becomes more tolerant of endpoint shifts, thus becoming more accurate. It's worth noting that even when the geometric distance method merely applied as post-processe processsns without re- ve-training, the performance of SOTA model in lane topology reasoning is significantly improved, as shown Figure Moreover, reasoning lane topology completely based on geometric distances can lead to inaccuracies when lane detection is imprecise as is shown in Figure since the calculation of lane geometric distance heavily relies on the accuracy of lane detection. To make up for the deficiency of geometric distances approach, we design a extra topology approach based on the similarity of lane

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queries complement. This approach projects lane queries into a fiigh-dimesiooall semantic space, and involves explicitly computing the dot product between lane query determine similarity, and then mapping this similarity onto lane topology using sigmoid [14]. 'he approach for calculating lane query similarity complements the approach used for computing lane geometric distance topology and similarly boasts high interpretability. The final lane topology is obtained by fusing the topology matrix derived from both approachs. By the way, the lane topology also used in GNN to enhance lane learning through the aggregation of features from adjacent lanes. In summary, our contributions are as follows:
1. We identify the current state of research in topology reasoning as "perception over reasoning" and reveal that the lane topology is easily disturbed by the endpoint shifts in lane detection when MLP employed solely for lane topology reasoning.
2. We propose interpretable method, referred to TopoLoggic, which conducts lane topology reasoning by calculating lane geometric distances and semantic similarity of lane query high- dimensional semantic space.
3. Extensive experiments on the mainstream benchmark OpenLane- V2 for topology reasoning task indicate that our method significantly outperforms existing state-of-the-art methods, especially in lane topology metric. Even employed solely as a post-proce proceesooss step without re- t--raanning, proposed geometric distance approach can significantly enhance well-trained lane topology reasoning models.
2
Related Work
2.1 Lane Detection
Lane detection plays an important role in autonomous driving, which has been fundamental aspect of lane topology reasoning. In the realm of lane detection, some works [15] 16 17 attempt to perform lane detection on a segmentation map. Morcover, some researchers use vector-based methods to perform 3D lane detection [18 19 20 (2]). however, these methods rely on a predetermined series of Y-axis coordinates within the query for forecasting 3D lanes, thereby lacking the capability to exclusively predict 3D lane positions along the Y-axis. In recent study, TopoNet [1] leverages Graph Neural Network (GNN) 22 enhance the perception of lane centerline, while TopoMLP utilizes PETR 23 for centerline detection. LaneSegNet [12] designs Lane Attention mechanism to reinforce the perception of lane segment, and SMERF [3] introduces Standard (SD) Map an additional input to bolster the perception of lane centerline. In our work, we enhance lane learning by aggregating features of adjacent lanes through GNN, which involves computing lane geometric distance and lane query similarity.
2.2 Lane Topology Reasoning
In lane topology reasoning, accurate comprehension of lane topology is imperative for effective
navigation and decision-making in autonomous driving. Some methods [24 25 26 27 28 have been proposed to address this. The STSU (29) model drew inspiration from DETR (30 and employed neural network architecture, complemented by multi-layer perceptron (MIP) to establish line connectivity. Building upon this foundation, Can et al. [31] introduced minimal cycle queries to refine centerline, ensuring accurate ordering of overlapping lines and thereby enhancing precision. Further ad advancements include the perception of centerline [3] [1] 9 and the perception of lane segment [12. Among them, CenterLineDet [I]] and [e... Both treat lane line as vertices and leverage an graph-based model to update lane representation and lane topology. While these methods have predominantly relied on MLP for generating adjacency matrices represent lane topology. In our work, we calculate the lane topology matrices based on the geometric distances between lanes and the similarity of lane query within high-dimensional semantic space, respectively, and then fuse them to form the final lane topology. The fusion of geometric and semantic space enriches the model's 's understanding of lane topology, thereby culminating in improved performance in driving scene analysis and pecciionnmmkingg
3

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Feature Encoder
TugoLogic Lane Decuder Layer x
BEV
K.V
Festurre
Lase Debin. Deceder
Coss Newwok
BEY
Similarity Topology
Geometric Tepology
Sigeokd Farction
Malis-ien view Imsage
Mapplag Functlen
Lune Query
Edllonoed Lass Query
MLP
MLF
Senilanty Adjooney Mazis
151
Adposecy
Manit
Figure 2: Pipeline of TopoL.gic.. The overarching structure of TopolLogic comprises main components: an image encoder for feature extraction and transformation, and a lane decoder respon- sible for end-to-end topology reasoning. This decoder utilizes the proposed lane geometric distance topology and lane similarity topology, and fuse them into the final lane topology, which is facilitated through GNN augment lane learning in the decoder layer.
Method
3.1 Problem Definition
Given images captured by the surround-view cameras of a vehicle, lane topology reasoning needs to perceive lane instances BEV(Bird's Eye View) and then infer the topology between these lane instances. The enhancement of lane instance perception assists in the reasoning of lane topology. Lane instances are described as a set of directed lane lines which denoted as [lo..... In-1] Each lane line is composed of a series of ordered points, and it is denoted as [po. ... Pn- p (x,, y, 2) E R The topology between lane instances signifies the connectivity the directed lanes and it depicted
topology graph EV, where the edge set E C V V. An entry (i, )) in E is positive if and only if the ending point of lane lend connects to the starting point of lane 1start.
3.2 Overview
As is depicted in the Figure 2, our proposed TopoLogic takes multi-view images from onboard cameras as input. These images are processed by backhone generate multi-scale image features. Multi-scale image features are transformed into BEV features through a view transformation module, and then passed to lane deformable decoder generate lane query Qi for lane detection. The proposed lane geometric distance approach and the lane similarity approach compute the lane topology respectively. Ultimately, the two topologies fused and fed into GNN augment the learning of lane line in the next decoder layer.
3.3 Lane Geometric Distance Topology
Lane Geometric Distance Matrix. Lane query QI can generate multiple directed lane lines through lane head. We can assess the connectivity between these lanes by computing the geometric distance between the ending point of one directed lane line and the starting point of the following lane line.
lg 1o...... 4n-1 1 LLneHHedd(
dij = gnnd .start
D {di j.jj 0...
(3)

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Topalogy Score
fauzz
finn
0.3m
Distancu
4397 10
Figure 3: Comparison of various mapping functions. fgau represent Gaussian func- tion, [sig represent sigmoid function, and Stan represent tanh function. Compared to gaau: fsigs Stans our proposed function fours has greater tolerance for endpoint shift.
Figure 4: Influence of inaccuracies in lane detection. Blue denotes correct prediction lane line, yellow denotes incorrect prediction lane line, green denotes correct prediction of lane topology. and red denotes incorrect prediction of lane topology.
where D is the lane geometric distance, 4 and l represent preceding and subsequent lane lines, di denotes the geometric distance between 4, and lj. 1end signifies the last point of lane line 4, and Ishart indicates the first point of lane line ly.
Distance to Topology Mapping Function. After obtaining the geometric distance matrix D for the lanes, necessary to map the lane geometric distance into the lane topology. The lane topology can be represented by matrix ranged in 0~1 Zero indicates that there is no connection between two lanes, while one indicates that there a connection. This mapping function needs capture the following notion:
when the input 0, it meaning the two lanes are very close to each other, the output y > 1, suggesting that these two lanes are very likely to be connected. Conversely, as æ + oc. y + 0. Inspired by the Gaussian function, we design a learnable mapping function as follows:
fours = Xeo
(4)
where x = d.y. a is the standard deviation the geometric distance matrix D. a, À are learnable parameters. With the help of such mapping, get lane topology follows:
Gass {forrs (d. = O... -1
(5)
There also exists some common alternative functions that meet the criteria, for example Gaussian function, sigmoid-based function and tanh-based function Equation [gquation[]a...c.. b...).). We make compari- son between them with fours Figure 3 Obviously, fours sets larger geometric distance threshold for determining topological connectivity compared to Sgaus fsig and Stans which makes the lane topology more robust to the endpoint shifts. Ablation study in Table 3 also verifies this opinion.
2 1 c
8gau = e
(a),
Jeig
(b),
Jran c +1
(c)
3.4 Lane Similarity Topology
Lane topology reasoning based on the geometric distance of lane lines can achieve commendable results when the detection of lane lines accurate. However, since this topology reasoning method heavily relies on the detected lane lines, inaccuracies in lane line detection can interfere with the geometric approach and lead to erroneous reasoning outcomes, as demonstrated in the Figure In light of this situation, we reason lane topology by calculating the similarity between lane query Q within high-dimensional semantic space, higher similarity between Qi indicates greater likelihood of connectivity between the lanes, while lower similarity suggests absence of connectivity, We
5

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initially encode Qi using two distinct MLP, and then represent the similarity by computing the inner product between the two encoding results. Finally, we require function to map the similarity between Qi to lane topology. Given the correlation between lane similarity and lane topology, we employ sigmoid to map the lane similarity onto lane topology. This process as follows:
Q embi Qembz MLLP(QQ))) MLP2(())
(7)
S matmuu ( Q Qemb, transpose(Qenal
(8)
Gstnn sigmoid(S)
(9)
where Qi E RNXCC S represents the similarity of Qi. Gaim E RNIN,, while Ni represents the number of lane query.
3.5 Lane-Lane Topology
Both the lane topology reasoned from the geometric distance between lane lines and the lane topology reasoned from the similarity of lane query Qi in the high-dimensional semantic space can indicate the connectivity of lanes. These two methods are complementary in the task of lane topology reasoning. In this context, merge the two lane topology reasoning results together the final and more accurate lane topology using learnable coefficients as follow:
G A1 Gdis + A2 Gsim
(10)
where A X2 are learnable parameters, and G is the final lane topology prediction.
3.6 Learning
Similar to Transfomer- basedd networks (2) the supervision is applied each decoder layer to optimize the query feature iteratively. The overall loss of TopoLogic is:
C= Ltop
(11)
The lane detection loss Ldst consists of a focal loss (33 for lane classification and an LI loss for lane regression. The lane topology reasoning loss Ltop includes only the loss computed for Gsim- As for the calculation Gais, since it is enhanced by GNN to facilitate lane learning, we update its learnable parameters through Ldet.
4
Experiment
4.1 Dataset and Metric
Dataset. We have evaluated Topoloogic the SpennLane-V
which is currently the only large-scale perception and topology reasoning dataset devised for autonomous driving scenarios. This dataset was developed by Argogorse2 [35] and nuScenes (36) respectively. provides annotations for both lane centerline tasks and lane segment detection tasks. OpenLane-V V2 consists of two subsets: subset_A A and subset B, each comprising 1000 scenes with 2Hz multi-view images and annotations. Each subset includes annotations for the lane centerline, traffic element, lane topology, as well as the topology between traffic element and lane. subset A, there are seven views as input, together with additional Standard-definition Map input, and the annotations for lane segment have been expanded; subset_ B contain only six views as input.
34
Metric. Openl Lnne V2 evaluates perception tasks for both lane centerline and lane segment.
(1) In the task of lane centerline perception, the metrics include DET, DET,, TOP and TOP DET, quantifics similarity by averaging the Frechet distance at matching thresholds of 1.0, 2.0. 3.0. DET, uses Intersection over Union (IoU) measure of similarity and calculates the average across different traffic categories. TOPn and TOP;, respectively compute the topology matrix similarity between lanes and between lanes and traffic elements, with the overall evaluation metrie for lane centerlines being denoted as OLS. The OLS is carried out as OLS = [DET, + DET, + f(OOp,) ((TOPu)), where / is the square root function.
(2) In the task of lane segment perception, we adopt the metric proposed by LaneSegNet for evaluating lane segment perception. These include the lane segment distance Die, the corresponding Average

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Precision A and AP ped, with the mAP calculated as the average of AP and AP APped. segment topology metric is denoted as IsPs
ped,
ped. The lane
(3) For centerline, OpenI Openlanne-2 a2 has two versions available for evaluation on TOP TOP and OLS: v1.0.0 and v2.1.0. For lane segment, V2 has versions v2.0.0 and v2.1.0 TSP Since the ultimate goal of perception is reasoning, we believe that topology metrics are what should be paid more attention. Moreover, our modifications mainly involve lane topology reasoning, so we primarily focus on the lane topology metric TOP and 1SP
2
4.2 Implementation Details
Feature Extractor. All images are resized into the same resolution of 1550 2048. For reproducibil- ity, we utilize the official implementations of TopoNet, SMERF, and LaneSegNet models. Both models use ResNet-50 [37] backbone pretrained on ImageNet [8 paired with a Feature Pyramid Network (FPN) 39 to extract multi-scale features. The number of output channels is set to 256. We employ the view transformer from BEVformer [40] encoder to transform multi-scale features into BEV features. The size of BEV grids is set to 200 100. TopoLogic is configured identically.
Lane Detector. We employ Deformable DETR 32 for the detection of lane line. The number of query set to 200. After passing through each decoder layer of Deformable DETR, the query undergo GNN using the lane topology matrix. We predict the offset of the lane lines by setting reference points, with each lane line consisting of 11 prree-dimensioall points. For LaneHead, the classification head adopts three-layer MLP with LayerNorm and ReLU predict the confidence score of the lane line. The regression head a three-layer MLP combined with ReLU, used to predict the 11 x3 offset of the lane line. For lane detection loss Ldet, the weight of the classification part is 1.5, and the weight of the regression part is 0.025.
Lane Topology Head. The Lane Topology Head consists of lane geometry distance predictor and a lane similarity predictor. For lane geometry distance predictor, we first calculate the geometric distance between the terminating point of the previous lane line and the starting point of the subsequent lane line to obtain a 200 200 distance matrix. Then the distance matrix is mapped to a lane topology
matrix through a learnable mapping function (<x e X where the size of a, X, is 1x1, a is the standard deviation of x, ar À are learnable parameters, a is initialized to 2, À is initialized to 0.2. For the calculation of lane similarity, given a 200x lane query, it is encoded through two different three-layer MLP. The we compute the similarity between the encoded results, resulting in a x00x200 lane similarity matrix. The similarity matrix is transformed into lane topology matrix through sigmoid. The two lane topology matrices are fused into the final lane topology using learnable coefficients, which are initialized to I and have size of 1.
Training. We train Logic utilizing the AdamW optimizer +. with a weight decay of 0.01 with an initial learning rate of 2 x 10 and employ a cosine annealing schedule for the learning rate. All experiment is trained for 24 epochs on NVIDIA RTX 3090 GPUs with batch size of 16.
4.3 Comparison to State-of-the-art
Centerline. We compared Topol with existing state-of-thh-ar methods such as STSU, Vec- torMapNet, MRpTR, TopoNet, SMERF on centerline. Table [ shows the results on the subset_A A and subset_B B datasets. Without any additions, our method achieves state-of-the-ar performance. Compared with TopoNet, our method achieves decent detection accuracy (29.9 v.s. 28.6 on subset_A. 25.9 v.s. 24.4 on subset B), especially with significant improvement in TOP (18.6 v.s. 4.1 on subset A for vl.0.0, 23.9 v.s. 10.8 on subset A for v2.1.0), which is the lane topology reasoning score. There is also an improvement in OpenLane- V2 overall score OLS (41.6 v.s. 35.6 on subset A for v1.0.0, 44.1 v.s. 39.8 on subset for v2.1.0). Even when using SDMap. our proposed TopoLogic still manages to achieve state-of-the-ar performance and realizes significant improvement in TOPn (23.4 v.s. 7.5 for vl.0.0, 28.9 v.s. 15.4 for 12.1.
Lane Segment. Concurrently, we compared TopoLogic with existing state-of-the-art methods such as TopoNet, MapTR, Map2Rv2, LaneSegNet on lane segment. In Table 2 it indicates that our method exhibits improvements in the Mean Average Precision (mAP) for lane segment detection compared
See the official repository for version differences of metrics: OpenLane- V2/1ssues/76d
https: htt///gttthuchccc htwpthhhhhccmmmmpmrrriie..aaa
7

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Table 1: Performance comparison with statc-of-the-art methods on OpenLane-V2 benchmark on centerline. Results for existing methods are from TopoNet, TopoMLP and SMERF. "SDMap" indicates the use of Standard-deffnition Map. "." denotes the absence of relevant data. We are more focused on u
v1.0.0
v2.1.0
Data
Method
SDMap DET, 1 DET;
TOPn
TTOP TOLS 1TOP tOLSt
STSU [16]
X
12.7
43.0
0.5
15.1
25,4
2.9
19.8
29.3
VectorMapNeet 6
X
11.1
41.7
0.4
5.9
20.8
2.7
9.2
24.9
MapTTR 41
X
17.7
43.5
1.1
10.4
26.0
5.9
15.1
31.0
subser_
TopoNet
X
28.6
48.6
4.1
20.8
35.6
10.9
23.8
39.8
TopoMLP
9
X
28.3
50.0
7.2
22.8
38.2
19.0
23.4
42.2
TopoLogic
X
29.9
47.2
18.6
21.5
41.6
23.9
25.4
44.1
SMERF 13
33.4
48.6
7.5
23.4
39.4
15.4
25.4
42.9
TopoLogic
34.4
48.3
23.4
24.4
45.1
28.9
28.7
47.5
STSU [6
8.2
43.9
0.0
9.4
21.2
VectorMapNNe [6
X
3.5
49.1
0.0
1.4
16.3
subset B MapTR 41
X
15.2
54.0
0.5
6.1
25.2
TopoNet
24.3
55.0
2.5
14.2
33.2
6.7
16.7
36.8
TopoMLP
X 26.6
58.3
17.8
38.7
Topol.ogic
X
25.9
54.7
15.1
15.1
39.6
21.6
17.9
42.3
Table 2: Performance comparison with state-of-the-ee methods on OpenLane- benchmark on lane segment. Results for existing methods are from LaneSegNet. "." denotes the absence of relevant data. We are more focused on TOP
v2.0.0
v2.1.0
Method
MAPt
APts
AP APped ped
TOPist f
TOP:ss 1
TopoNet 1
23.0
23.9
22.0
1.0
MapTR 41
27.0
25.9
28.1
MapTRR2
42
28.5
26.6
30.4
LaneSegNet
12
32.6
32.3
32.9
8.1
25.4
TopoLogic
33.2
33.0
33.4
22.0
30.8
with LaneSegNet (33.2 v.s. 32.6). Moreover, there is a significant enhancement in topology reasoning score TOPtata (22.0 v.s. 8.1 on v2.0.0, 30.8 v.s. 25.4 on v2.1.0).
4.4 Alation Study
We have studied several important components of TopoLogic and conducted ablation experiments on the OpenLane- V2 subset_At A. In the following text, we employ evaluation metrics from the latest 1.. release for assessment.
The design mapping function. We have studied the effect of different mapping functions in the transformation from lane geometric distances to lane topology. Table S suggests Subgeess that our designed lane lines to
learnable mapping function performs better at mapping the geometric distances lane topology compared to sigmoid-based tanh-based, and Gaussian functions. It exhibits the best performance in terms of both the lane topology reasoning score and the centerline score (29.9 v.s. 28.9 v.s. 28.7 v.s. 27.6 on DET, and 23.9 v.s. 21.7 v.s. 19.1 v.s. 15.1 on TOP,).
The approach of lane topology reasoning. We have investigated the impact of various lane topology computation approaches on lane topology reasoning, specifically using MLP, lane query similarity, and geometric distance. The results the Table indicate that the integration of lane topology method, combining both lane geometric distance and lane query similarity calculations, yields optimal results on TOP,, (23.9 v.s. 20.1 v.s. 12.9 v.s. 10.8) and also performs best terms of lane line detection scores indicated by DET, (29.9 v.s. 28.6 v.s. 28.1 v.s. 27.8). This demonstrates that

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Table 3: Ablation study on different mapping functions from lane geometric distance lane topology on centerline.
Table 4: Ablation study on different lane topol- ogy reasoning approaches on centerline. Ours indicate Similarty+GGeoDist.
Function DET,
DET, 1 T
TTOP:
TOLSt
Approach DET, DET, TTOP; FTOP tOLS
tan
27.6
47.2
15.1
24.8
40.9
MLP
27.8
46.8
23.9
39.1
foig
28.7
44.1
19.1
24.1
41.4
Similarity
28.1
46.4
12.9
23.7
39.8
f gau 28.9
46.8
21.7
23.2
42.6
GeoDist
28.6
44.1
20.1
23.1
41.4
Foure 29.9
47.2
23.9
25.4
44.1
Ours 29.9
47.2
23.9
25.4
44.1
Table 5: Ablation study on using MLP to encode lane query computing lane similarity topology. Ours indicate using two indepent MLPs.
Approach
DET;
DET, 1
TOPμ
TOP
OLS
No MLP
25.6
46.5
18.7
20.8
40.2
Single MLP
27.5
46.8
21.2
23.8
42.3
Ours
29.9
47.2
23.9
25.4
44.1
the topology obtained from the fusion of these two methods can also improve the learning of lane centerline through GNN feature enhancement.
The approach of similarity topology. We investigated the impact of using MLPs to encode lane queries for computing lane similarity lane topology reasoning. As Lane similarity topology, its subtlety lies in that it uses two independent MI.Ps to map the lane query rather than a single MIP, which decouple lane into queries of start and end point, achieving the geometric distance approach in semantical space. The results presented in Table indicate that encoding lane query with two independent MLPs to obtain features for the starting and ending points of lanes allows for better computation of lane similarity topology. This approach exhibits the best performance in terms of both lane centerline detection score and lane topology reasoning score (29.9 v.s. 27.5 v.s. 25.6 on DET, and 23.9 v.s. 21.2 v.s. 18.7 on TOP;)-
analogous effect to
The post-processing mode of geometric distance approach. We have investigated the effectiveness of geometric distance approach as a post-processing module on well-trained model. In Table 6 conducted experiments by adding post-processing the already trained TopoNet, SMERF, and LateSegNet, respectively. The results indicate that our proposed approach, which calculates lane topology based on lane geometric distances, can be integrated into well-trained models with- out any additional modifications and can significantly enhance the performance of lane topology reasoning (22.3 10.9 on TopoNet, 26.2 v.s. 15.4 v.s. on SMERF).
4.5 Qualitative Analysis
As shown in Figure 5 we presents qualitative comparison between TopoLogic and TopoNet. Specifically, two traffic scenes are selected for analysis, and the results of lane line detection and topology reasoning are visualized. The first row displays multi-view inputs of realistic scenes, while the second row shows the lane detection results of TopoLogic and TopoNet alongside the ground truth. Notably, TopoLogic demonstrates superior accuracy in lane line detection compared to TopoNet.
Lane Graph. The inherent complexity of topology reasoning makes intuitive representation of results challenging. To address this issue, as shown in third row in Figure we construct lane graph where nodes represent lane lines, and their relative positions in the graph correspond one-to-one with the relative positions of lane lines. This layout enhances the connection between lane line detection results and facilitates subsequent analysis. Additionally, we use directed edges to represent the lane topology, with red indicating error predictions and blue indicating missing predictions. Topo- Logic consistently exhibits proficient lane topology reasoning across various intersection scenarios, showcasing significantly enhanced performance in the topology graph compared to TopoNet.

---

Table 6: Ablation study on incorporating lane geometric distance into post-processing for well-trained model under different task settting (centerline /eMterlnne+S lane segment).
Centerline
TOP
SenerrlnneSSDMap
TOPμ
Lane Segment
TOP t
TopoNet R
10.9
SMERF [3
15.4
LaneSegNet [2]
25.4
TepoNet+GeoDist
22.3
26.2
LaneSegNet+GeoDist
29.6
Mullii-vew Ingaat
I Lane' Topolooy
Lane Graph
Figure 5: Qualitative result about lane topology reasoning result of TopoNet and our TopoLogic. The first row denotes multi-view inputs. The second row denotes lane detection result and lane topology reasoning result. The third row denotes graph form of lane topology reasoning (node indicates lane line, edge indicates lane topology), where green color indicates the right prediction, while red color indicates the error prediction and blue color indicates missing prediction.
Conclusion
In this paper, we reveal the limitation of using vanilla MLP in lane topology reasoning task and propose TopoLogic, which is the first to employ interpretable approach for lane topology reasoning. TopoLogic fuses the geometric distance of lane line endpoints mapped through designed function and the similarity of lane query in high-dimensional semantic space to reason lane topology. Experiments on the large-scale autonomous driving dataset OpenI.ane- V2 benchmark demonstrate that Topol.ogic significantly outperforms existing methods in topology reasoning in complex scenarios.
Limitations. Due the GNN's role in merely aggregating features from adjacent lanes to enhance the learning of the current lane, our proposed method significantly improves the performance of lane topology but does substantially elevate lane detection.
Impact. Based on the previous sections, research purposes. It should not be directly used in deployed within any actual autonomous driving application. Notably, we cannot provide any guarantee in safety-critical situations.
evident that our proposed method is intended for
6
Acknowledgements
This work supported by National Key R&D Program of China (2023YFD2000303) and National Natural Science Foundation of China (62372433).
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Reviews:
[{"review_id": "KZtQIC4gJ3", "reviewer": "Reviewer_8GTK", "summary": "This paper proposes an interpretable method for lane topology reasoning based on lane geometric distance and lane query similarity. The authors reveal that the lane topology is easily disturbed by the endpoint shifts. Based on this, the proposed post-processing module improves the robustness and performance of lane topology reasoning, which can be plugged into other methods without re-training. And it also alleviates the influence of inaccuracies in lane detection on topology reasoning. Extensive experiments on OpenLane-V2 demonstrate its state-of-the-art performance.", "questions": "- As can be seen in Figure 3, compared to other mapping functions, the final result of the learnable Gaussian mapping function has a much higher threshold. Therefore, compared to the present comparison experiments ($f_{gau}, f_{sig}, f_{tan}$), it may be better to manually set the hyperparameters for a series of gradients to observe its effect on the final performance. And I'm wondering why $f_{gau}, f_{sig}, f_{tan}$ are very close but differ dramatically on $TOP_{ll}$ in Table 3.\n\n- According to L146-149, the motivation of Lane Similarity Topology is to alleviate the influence of inaccuracies in lane detection on topology reasoning. However, the proposed method as a post-processing step does not significantly change the lane line detection results. In addition, the comparison results of the Lane Similarity Topology module should be added to Figure 4 to increase its persuasiveness.\n\nThere are many typos in the paper, which should be further checked and polished.  \nFor example:  \nL6: \"are prone to\" -> \"is prone to\"  \nL12: \"our methods provides\" -> \"our methods provide\"  \nL17: \"boost\" -> \"boosting\"  \nFigure 1 caption: \"reasoing\"", "limitations": "This paper is limited in the post-processing for topology reasoning.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- The authors reveal the phenomenon that topology reasoning is highly susceptible to lane line endpoint shifts, providing a solid foundation and motivation for subsequent research.\n- The proposed post-processing module improves the robustness and performance of lane topology reasoning, which can be plugged into other methods without retraining.\n- The entire paper is easy to understand. The lane graph in Figure 5 shows very clearly the topological relationships between lanes and the differences from previous methods, which should be followed by other subsequent work.", "weaknesses": "- The proposed method is relatively simple and involves only post-processing modules, which at the same time leads to limited contributions and incremental improvements.\n\n- Considering that TopoNet is just a simple baseline model, the boost in topological reasoning is not surprising. Moreover, as can be seen in Table 1, the improvement of $TOP_{lt}$ is very small and $DET_{t}$ even decreases, which needs further analysis and discussion.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Thanks for your careful reading of our paper. We hope our response and clarifiction can ease some of your concerns.**\n\n**Q1:** The proposed method is relatively simple and involves only post-processing modules, which at the same time leads to limited contributions and incremental improvements.\n\n**A1:** Thanks for your comments. \n\n- The proposed method, TopoLogic, is an end-to-end trained model with two key modules (i.e., Similarity & GeoDist) instead of just one simple post-processing. **The modules are plugged at each layer of the decoder, so that the lane topology is enhanced geometrically and semantically at each layer and  refined layer by layer.**  Once trained, the GeoDist module can be utilized as a plug-and-play post-processing component for any pre-trained lane topology reasoning model to enhance TOP$\\_{ll}$.\n\n- Although the model is relatively simple, the performance improvement is significant (**10.9** to **23.9** (**+13.0**) on TOP$\\_{ll}$ in Table 1) after end-to-end training. **The improvement in itself** is a valuable contribution to the field, and its **theoretical basis** (endpoint-connection characteristics of the lane topology) is another contribution to the field.\n\n----\n\n**Q2.1:** Considering that TopoNet is just a simple baseline model, the boost in topological reasoning is not surprising. \n\n**A2.1:** Thank you for your feedback. We are to blame for the ambiguity, and we will add more clarification in the final version. **TopoNet is the official recommended baseline evaluated on OpenLane-V2 benchmark, and recently many new model (e.g., SMERF, LaneSegNet) are actually based on TopoNet, so we claim vaguely that our TopoLogic is based on TopoNet.** We conducted experiments with TopoNet, SMERF, and LaneSegNet. As demonstrated in Table 1 and Table 2, TopoLogic consistently achieves superior performance compared to these approaches. \n\n**Q2.2:** The improvement of is very small and even decreases, which needs further analysis and discussion.\n\n**A2.2:** Thanks for your comments, and we will add more clarification in the final version.\n\n- It is **reasonable** that the improvement on TOP$_{lt}$ is smaller the improvement on TOP$\\_{ll}$, as our method **mainly affects the lane-lane topology** and **does not deal with traffic elements specifically**.\n\n-  For the same reason, DET$_t$ has not improved. As for decrease sometimes, it seems to be **a bug in baseline's official code**. When we reproduced the DET$_t$ of baseline, it was always **unstable and lower** than the value reported in the original paper. We also found that the DET$_t$ 's reproduced result in other papers (e.g. SMERF) were lower.\n\n----\n\n**Q3.1:** It may be better to manually set the hyperparameters for a series of gradients to observe its effect on the final performance. \n\n**A3.1:**  Thank you for your feedback. We tested a series of manually set $\\alpha$  and $\\lambda$ values to observe their effects on performance. As is shown in following table, automatically learned hyperparameters $\\alpha=1.3, \\beta=0.23$ are actually superior to other manually set value, which frees us from the hassle of tuning parameters.\n\n| $\\alpha$ | $\\lambda$ | TOP$\\_{ll}$ |      | $\\alpha$ | $\\lambda$ | TOP$\\_{ll}$ |\n| -------- | --------- | ----------- | ---- | -------- | --------- | ----------- |\n| 2.0      | 0.23      | 20.4        |      | 1.3      | 0.06      | 16.0        |\n| 1.8      | 0.23      | 21.0        |      | 1.3      | 0.10      | 19.7        |\n| 1.6      | 0.23      | 21.8        |      | 1.3      | 0.14      | 21.6        |\n| 1.4      | 0.23      | 22.5        |      | 1.3      | 0.18      | 22.7        |\n| **1.3**  | **0.23**  | **23.9**    |      | **1.3**  | **0.23**  | **23.9**    |\n| 1.2      | 0.23      | 22.8        |      | 1.3      | 0.26      | 23.1        |\n\n----\n\n**Q3.2:** Why $𝑓_{𝑔𝑎𝑢}$,$𝑓_{𝑠𝑖𝑔}$,$𝑓_{𝑡𝑎𝑛}$ are very close but differ dramatically on TOP$_{𝑙𝑙}$ in Table 3?\n\n**A3.2:** Thank you for your thoughtful question. We believe the counterintuitive phenomenon is primarily due to **the sensitivity of these functions to the threshold values**. To investigate this hypothesis, we conducted additional analyses by plotting Gaussian function curves with varying $\\alpha$ and $\\lambda$ parameters, as illustrated in Figure 1 and 2 of the Rebuttal PDF. **These figures and table in A3.1 show that while the threshold values do not exhibit significant changes, the TOP$\\_{ll}$ scores vary substantially**, which is another reason why we adopt learnable mapping functions in TopoLogic.\n\n----\n**Q4.1:** The motivation of Lane Similarity Topology is to alleviate the influence of inaccuracies in lane detection on topology reasoning. However, the proposed method as a post-processing step does not significantly change the lane line detection results. \n\n**A4.1:** Nice question. We are to blame for the ambiguity, and we will add more clarification in the final version. Our motivation is indeed to alleviate the influence of inaccuracies lane detection on topological reasoning, however, our strategy is **not to directly improve lane detection**, but to **robustly improve lane topological reasoning** through the geometric and semantic information of the lane **in the case of inaccurate detection**, which is a brand new perspective  first proposed by us for the topological reasoning task .\n\n----\n\n**Q4.2:** In addition, the comparison results of the Lane Similarity Topology module should be added to Figure 4 to increase its persuasiveness.\n\n**A4.2:** Thanks for your valuable suggestions, and we will add the module's visualized results to Figure 4. Since OpenReview's reply cannot directly attach pictures, please go to Rebuttal PDF Figure 3 to view.\n\n----\n\n**Q5:** Typos\n\n**A5:** Thank you for carefully pointing out these typos. We will diligently correct these issues.\n\n**We hope this response could help address your concerns, and wish to receive your further feedback soon.**", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Lq53yNaotd", "reviewer": "Reviewer_FMUS", "summary": "The authors claim previous topology reasoning methods typically boost reasoning performance by enhancing the perception of lanes and directly adopt MLP to learn lane topology from lane query. In this work,  the authors propose to make full use of lane geometric distance and lane query similarity for topology reasoning. The proposed method, named TopoLogic, mitigates the impact of endpoint shifts in geometric space, and introduces explicit similarity calculation in semantic space as a complement. The method achieves SOTA results in OpenLane-V2 dataset.", "questions": "When compared with previous methods (like TopoNet, SMERF), what about the computation overhead and the difference in network architecture?", "limitations": "Refer to the Weaknesses part.", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The idea of paying more attention on geometry and similarity to help topology reasoning makes sense. It makes the reasoning process more interpretable and robust.\n2. The performance gain brought by the proposed method is significant. The authors provide adequate ablation experiments to validate the design.\n3. Many qualitative results are presented to show the effectiveness of the proposed method. The conection between lane endpoints are obviously improved.", "weaknesses": "1. Like an incremental work based on TopoNet. The contribution is limited. The contributed part is only a similarity module for mapping lane line endpoints. But the design is simple and straightforward, not surprising enough.\n2. The proposed GeoDist module is a post-processing algorithm. It's like an engineering improvement rather than academic contribution.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Thanks for your careful reading of our paper. We hope our response and clarifiction can ease some of your concerns and you could reconsider your rating.**\n\n**Q1:** Like an incremental work based on TopoNet. The contribution is limited. The contributed part is only a similarity module for mapping lane line endpoints. But the design is simple and straightforward, not surprising enough.\n\n**A1:** Thanks for your comments. Compared to TopoNet, our modification looks like small, but that doesn't mean the contribution is small. \n\n- We clearly point out that TopoNet and other methods ignore the endpoint-connection characteristics between the lanes when topological reasoning, and design **a module based geometric distance** and **a module based on semantic similarity** to **significantly improve** the topological performance (**+13.0** TOP$\\_{ll}$  in Table 1) in the case of **reducing the number of parameters and the amount of computation**. Therefore, the contributed part is not limited in similarity module.  \n- As similarity module, its subtlety lies in that it uses **two independent MLPs** to map the lane query **rather than a single MLP**, which can **decouple a lane into two queries of start and end point**, achieving an **analogous** effect to the (endpoint) geometric distance module **in semantical space**. This opinion can be verified by the following experiments, so it is not simple and straightforward.\n\n|                      | DET$_l$ | DET$_t$ | TOP$\\_{ll}$ | TOP$_{lt}$ | OLS  |\n| -------------------- | ------- | ------- | ---------- | ---------- | ---- |\n| No MLP               | 25.6    | 45.9    | 18.7       | 20.8       | 40.0 |\n| Single MLP           | 27.5    | 46.8    | 21.2       | 23.8       | 42.3 |\n| Two independent MLPs |**29.9**    | **47.2**    | **23.9**       | **25.4**       | **44.1** |\n\n----\n\n**Q2:** The proposed GeoDist module is a post-processing algorithm. It's like an engineering improvement rather than academic contribution.\n\n**A2:** Thanks for your comments, but we don't think it's just an engineering improvement.\n\n- The GeoDist module is not just used as post-processing after training. This module can be used (in conjunction with Similarity module) at each layer of the decoder, so that the lane topology is enhanced geometrically and semantically at each layer and  refined layer by layer. In addition, lane topology  in  layer is also facilitated  by GNN to augment lane learning  in   layer through aggregating features from adjacent lanes. Using GeoDist module in an integrated training manner provides more performance gains (**+13.0** TOP$\\_{ll}$  in Table 1) than just post-processing (**+11.4** TOP$\\_{ll}$  in Table 5). \n\n- This improvement is not an accident attempt,  but comes from our **accurate and highly interpretable understanding**  of **the endpoint-connection characteristics** of the lane topology, which makes it apart from simple engineering improvements. \n\n  All in one, **reasonable analysis** and **effective verification** are our academic contributions.\n\n----\n\n**Q3:** When compared with previous methods (like TopoNet, SMERF), what about the computation overhead and the difference in network architecture?\n\n**A3:** Thank you for your valuable question. The key distinction between TopoLogic and both TopoNet and SMERF is that **TopoLogic introduces similarity module and geometric distance module for lane topology reasoning, whereas TopoNet and SMERF only use MLP for lane topology reasoning.** Here, we provide some computational benchmark as follows, and we will include the experiment result in the final version of the paper.\n\n|                         | SDMap | #PARAMS | FLOPS  | FPS  |\n| ----------------------- | ----- | ------- | ------ | ---- |\n| TopoNet                 | false | 38.6M   | 712.1G | 10.5 |\n| TopoLogic(TopoNet ver.) | false | 37.8M   | 665.0G | 10.8 |\n| SMERF                   | true  | 39.4M   | 720.1G | 15.3 |\n| TopoLogic(SMERF ver.)   | true  | 38.7M   | 678.2G | 15.8 |\n\n\n\n**We hope this response could help address your concerns, and wish to receive your further feedback soon.**", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "DT0rG7AZLO", "reviewer": "Reviewer_SnEK", "summary": "Reasoning about lane topology is becoming more and more important for the autonomous driving community. Current methods mostly focus on improving the perception performance and ignore the reasoning part of the task. The authors raise the importance of the relationship between lanes, namely the lane distance and lane similarity. The lane distance is determined by the geometry distance between the starting and ending points of the lanes. Then, the connectivity is decided based on the result of a learnable threshold function. The lane similarity is calculated based on the lane queries, and a large similarity indicates a large possibility of connectivity. Both lane distance and lane similarity modules serve as plug-in modules to existing networks. Experimentally, both modules have significantly improved the existing methods.", "questions": "- The two proposed modules are plug-in modules on current networks, and the proposed pipeline is trained in an end-to-end manner. However, as these two modules focus on topology reasoning, and the final topology prediction is decided by these two modules, it is curious to know how these two modules benefit existing networks. Namely, only parameters in the proposed modules are trained, and the remaining weights of the existing networks are frozen.\n- For the second proposed module, the lane similarity module. Logically, the lane queries usually encode positional information of lanes. It is curious to know why improving the similarity between two connected lanes would improve topology reasoning performance. That is, the only similar thing between two connected lanes is the ending point of one lane and the starting point of another. Two parallel lanes should have a larger similarity than two connected lanes.", "limitations": "N/A", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "- The authors observed that current methods on lane topology reasoning mostly focus on improving perception accuracy but ignore topology reasoning. The proposed modules serve as a good posting-processing technique for topology reasoning.\n- The proposed modules are effective and can be placed in existing networks.", "weaknesses": "- In the experiment session, the authors provide scores on lane segment prediction. However, the lane segment is different from the lane centerline. Only the lane centerline is discussed in the methodology session.\n- It is not stated which split of the dataset is used for experiments.\n- The mixture of using different versions of the metric is confusing (vx.0 and vx.1). As stated in the repository of the dataset, this difference leads to different TOP scores. For instance, in Table, metrics in v2.0 and v2.1 are both listed, which is unreasonable.\n- The two proposed modules focus on topology reasoning. However, experimentally, the detection scores of the proposed pipeline also improved compared to other methods. This improvement is not discussed.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Thanks for your careful reading of our paper. We hope our response and clarifiction can ease some of your concerns and you could reconsider your rating.**\n\n**Q1:** Lane segment is not discussed in the methodology session.\n\n**A1:** Thanks for your attention to this detail, which is indeed omitted from the Methods section. However, lane segment is just **another more refined representation of the lane**, and the centerline can still be **easily extracted** from the lane segment, so that our algorithm does not need any special processing for the lane segment.\n\n----\n\n**Q2:** It is not stated which split of the dataset is used for experiments.\n\n**A2:** Thanks for your mind. Perhaps we should  this information in the caption of tables, even although these information can be found on line 233-234 and 183-185 (SOTA comparison, Table 1 on subset_A/B & Table 2 on subset_A)  and line 248-250 (ablation study, Table 3-5 on subset_A).\n\n----\n\n**Q3:** The mixture of using different versions of the metric is confusing (vx.0 and vx.1).\n\n**A3:** It is indeed unusual to using two versions of metric, but it is a legacy issue in the lane topology field, as can be seen in the Openlane-V2 official repository ([Update on OpenLane-V2 Metric · Issue #76 · OpenDriveLab/OpenLane-V2 · GitHub](https://github.com/OpenDriveLab/OpenLane-V2/issues/76)). We provide two versions of the metric **for comparison with more methods**. Moreover, it should be noted that our method has a **significant advantage** over each other **regardless of which version of metric**.\n\n----\n\n**Q4:** Why detection scores of the proposed pipeline also improved compared to other methods?\n\n**A4:** The reason for this can be found in the caption of Figure 2 and Introduction (Line 61-62), and we will add further explanation in the experiment section. Note that the proposed modules serve in **each** layer of the decoder, where geometric distance topology and lane similarity topology are fused into the final lane topology. This lane topology is facilitated  to augment lane learning **by GNN aggregating features from adjacent lanes** in the **next** decoder layer. Thus, Improvement on TOP$\\_{ll}$ corresponds to increased DET$_l$（**28.6** to **29.9** (**+1.3**) in Table 1). \n\n----\n\n**Q5:** How these two modules benefit existing networks?\n\n**A5:**  Thank you for your valuable suggestions. We carried out experiments by freezing the network parameters of TopoNet and incorporating the similarity and geometric distance modules for end-to-end training. The results in the table indicate that the two modules introduced in TopoLogic significantly enhance TopoNet. Additionally, training TopoLogic end-to-end yields better performance compared to freezing a portion of the parameters.\n\n| Method                                | DET$_l$  | DET$_t$  | TOP$\\_{ll}$ | TOP$_{lt}$ | OLS      |\n| ------------------------------------- | -------- | -------- | ---------- | ---------- | -------- |\n| TopoNet (baseline)                    | 28.6     | **48.6** | 10.9       | 23.8       | 39.8     |\n| TopoLogic (freeze TopoNet parameters) | 29.2     | 46.9     | 22.8       | 24.8       | 43.4     |\n| TopoLogic                             | **29.9** | 47.2     | **23.9**   | **25.4**   | **44.1** |\n\n----\n\n**Q6:** Why improving the similarity between two connected lanes would improve topology reasoning performance? \n\n**A6:** Thank you for your valuable question; it is very meaningful. The similarity module proposed in TopoLogic calculates the similarity of **lane endpoints** rather than **the entire lane itself**. As shown in Figure 1, the lane query passes through **two independent MLPs** to encode representations, computing the similarity between **the starting and ending points** of two directed lanes. Additionally, to address your inquiry, we conducted experiments with MLPs as shown in the table. **The \"No MLP\" configuration does not encode the lane query, calculating the similarity of the entire lane. In contrast, the \"Single MLP\" configuration computes the similarity of the same endpoint across two lanes.** The table indicates that employing two independent MLPs to encode lane queries for calculating the similarity between the starting and ending points of directed lanes yields the best performance, thereby validating the effectiveness of the TopoLogic design.\n\n| Method               | DET$_l$  | DET$_t$  | TOP$\\_{ll}$ | TOP$_{lt}$ | OLS      |\n| -------------------- | -------- | -------- | ---------- | ---------- | -------- |\n| No MLP               | 25.6     | 46.5     | 18.7       | 20.8       | 40.2     |\n| Single MLP           | 27.5     | 46.8     | 21.2       | 23.8       | 42.3     |\n| Two independent MLPs | **29.9** | **47.2** | **23.9**   | **25.4**   | **44.1** |\n\n\n\n**We hope this response could help address your concerns, and wish to receive your further feedback soon.**", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "dTrjzaLeBz", "reviewer": "Reviewer_E2Wq", "summary": "The paper investigates topological reasoning for lane graph prediction for autonomous driving. The paper focuses on improving the prediction of the topological structure of the lane graph. Therefore, they propose two new mechanisms, the first is a geometric approach that estimates connectivity based on the distance between the end point and starting point of center lines. Secondly, they propose a semantic approach which uses the similarities of lane queries in a high dimensional space. These two approaches stand in contrast to existing works which mainly use MLPs to predict the connectivity of the lanes. They show how these approaches can be interleaved into a lane graph network and how it improves results, especially the topological reasoning results. Even adding only the geometric approach to existing methods improves the topological reasoning results.", "questions": "- Given that f_ours is just a gaussian function with an adapted decision boundary. I think the fair comparison would be with a hand tuned decision boundary, for example by looking at end point errors of a trained model. \n- f_tanh in equation 6 seems to map to [0, 2] and not to [0, 1]\n- Equation 10 is not a [0, 1] probability anymore, to remain this property you would need to take a convex combination of the two values. Do you perform some sort of normalization?\n- If you say a variable is 1x1 do you mean it is a real number? If so just write \\in R\n- The batch size of 2 on 8 GPUs seems strange, is it a batch size of 2 per GPU, so an actual batch size of 16?\n- How do you handle traffic elements?\n\n- Typos: \n- L90: . some methods - not capitalized after full stop\n- L204: Both models - three models are listed before\n- L236: ),especially \n- L259: Table 4 Indicate show", "limitations": "Has been discussed", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "The paper is well written and easy to follow. The paper and results highlight the importance of geometric cues when predicting conductivity. Or in other words, the fact that the geometric approach works so well shows that there is a lot of potential in current methods. Furthermore, the geometric approach can be integrated into existing networks or combined with other approaches and allows for competitive lane topology prediction. \n\nBoth the geometric and semantic prediction branches are clear and make sense and are able to improve results for topological metrics.", "weaknesses": "- It is not clear to me why the paper does not compare with TopoMLP, the numbers for Table 2 v1.0.0 can just be taken out of the paper.\n- When comparing with TOP_lt TopoMLP outperforms TopoLogic and overall performance is very similar, in this case both methods use the same backbone.\n- The paper highlights that geometric cues in predicting the topology of the lane graph are underutilized which is interesting, but I am not fully sure if this is a Neurips paper, since technical contributions are marginal.\n- See questions", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Thanks for your careful reading of our paper. We hope our response and clarifiction can ease some of your concerns and you could reconsider your rating.**\n\n**Q1:**  Why the paper does not compare with TopoMLP?\n\n**A1:** Thank you for your insightful question. I will respond to it in detail. Although both TopoMLP and TopoLogic use ResNet-50 as their backbone, TopoMLP is implemented using PETR, while TopoLogic, TopoNet, SMERF, and LaneSegNet are based on DETR. **Unfortunately, TopoMLP could not be run on the NVIDIA RTX 3090 GPU due to its high memory consumption. As a result, we were unable to perform a comparative analysis with TopoMLP at that time due to equipment limitations.** We apologize for this inconvenience. To address this issue, **we have implemented TopoLogic based on PETR and conducted experiments on Tesla A100 GPU**. The experimental results are provided below, and we will include these results in the final version of the paper.\n\n| Method     | DET$_l$  | DET$_t$  | TOP$_{ll}$ | TOP$_{lt}$ | OLS      |\n| ---------- | -------- | -------- | -------- | -------- | -------- |\n| TopoMLP    | 28.3     | **50.0**     | 19.0     | 23.4     | 42.2     |\n| TopoLogic  | **29.9** | 47.2     | 23.9     | 25.4     | 44.1     |\n| TopoLogic\\* | 29.7     | 49.5 | **25.4** | **26.8** | **45.3** |\n\nThe experiments were conducted on subset_A, OpenLane-V2 version 2.1.0. In this context, **TopoLogic\\* denotes the version of TopoLogic implemented using PETR.** \n\n----\n\n**Q2:** TopoMLP outperforms TopoLogic on TOP$_{lt}$?\n\n**A2:** As indicated in the table in A1, TopoMLP does not outperform TopoLogic on TOP$\\_{lt}$ (25.4 v.s. **26.8**). We implemented TopoLogic using PETR, and it shows improved performance on TOP$\\_{lt}$ (**26.8** v.s. 25.4 v.s. 23.4).\n\n----\n\n**Q3:** Not fully sure if this is a Neurips paper, since technical contributions are marginal.\n\n**A3:** Thanks.  The performance can **significantly improved** (**+11.4** TOP$\\_{ll}$ in Table 5) even if it is only used as post-processing, and can be **further improved** (**+13.0** TOP$\\_{ll}$ in Table 1) after integrated training. Such an improvement exceeds the improvement of previous works in a large margin, which **in itself** is a valuable contribution to the field. **reasonable analysis** and **effective verification** are our academic contributions, which will be beneficial to promote the development of the field.\n\n----\n\n**Q4:** Fair comparison about mapping function.\n\n**A4:** Thank you for your insightful feedback. We appreciate your suggestion to ensure a fair comparison by considering a hand-tuned decision boundary. In response to your concern, we conducted additional experiments to further validate the performance of $f_{ours}$ Gaussian function with its adaptive decision boundary.\n\nTo determine the decision boundary, we explored two hyperparameters: $\\alpha$ and $\\lambda$. We evaluated the TOP$\\_{ll}$ metrics across various combinations of these hyperparameters. The results are presented in the following table:\n\n| $\\alpha$ | $\\lambda$ | TOP$\\_{ll}$ |      | $\\alpha$ | $\\lambda$ | TOP$\\_{ll}$ |\n| ---------- | --------- | ---------- | ---- | -------- | ----------- | ---------- |\n| 2.0        | 0.23      | 20.4       |      | 1.3      | 0.06        | 16.0       |\n| 1.8        | 0.23      | 21.0       |      | 1.3      | 0.10        | 19.7       |\n| 1.6        | 0.23      | 21.8       |      | 1.3      | 0.14        | 21.6       |\n| 1.4        | 0.23      | 22.5       |      | 1.3      | 0.18        | 22.7       |\n| **1.3**    | **0.23**  | **23.9**   |      | **1.3**  | **0.23**    | **23.9**   |\n| 1.2        | 0.23      | 22.8       |      | 1.3      | 0.26        | 23.1       |\n\nAs the table illustrates, **the decision boundary with $\\alpha=1.3$ and $\\lambda=0.23$ yielded the best performance in terms of the TOP$\\_{ll}$ metric.** This finding aligns with our original experimental results and underscores the optimization effectiveness and advantages of the $f_{ours}$ Gaussian function. We hope these additional results address your concerns regarding fair comparison and demonstrate the robustness of our approach. \n\n----\n\n**Q5:** $f_{tan}$ in equation 6 seems to map to [0, 2] and not to [0, 1].\n\n**A5:** Thank you for your detailed consideration. In fact, since $f$ maps endpoint distances, so $x$ is always greater than or equal to 0 rather than unbounded, ensuring that the range of these functions is always within [0, 1].\n\n----\n\n**Q6:** Equation 10 is not a [0, 1] probability, and do you perform some sort of normalization?\n\n**A6:** Thank you for your attention. We did not perform normalization. The two coefficients, λ₁ and λ₂, in Equation 10 are learnable and can be trained to range between [0,1]. In other words, λ₁ + λ₂ approaches 1.\n\n----\n\n**Q7:** If you say a variable is 1x1 do you mean it is a real number? If so just write \\in R.\n\n**A7:** Yes, it's not necessary to say 1x1 shape for scalars, and we're going to modify the expression.\n\n----\n\n**Q8:** The batch size of 2 on 8 GPUs seems strange, is it a batch size of 2 per GPU, so an actual batch size of 16?\n\n**A8:** Your understanding is correct.  To be precise, the batchsize of each GPU is 2, so the total batchsize of 8  GPUs is 16. It's our fault to make it unclear.\n\n----\n\n**Q9:** How do you handle traffic elements?\n\n**A9:** For the traffic element treatment, we adopt  the same  strategy as baseline method TopoNet, i.e., predict 2D bounding box of traffic elements using DETR, and reason topology between them with lane utilizing vanilla MLP. Since our work focused on lane topology, we rarely mentioned traffic elements, which will be added in the final version.\n\n----\n\n**Q10:** Typos.\n\n**A10:** Thank you for carefully pointing out these typos. We will diligently correct these issues.\n\n\n\n**We hope this response could help address your concerns, and wish to receive your further feedback soon.**", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
We sincerely thank all reviewers for their valuable time and comments. In order to better response for the questions, we have attached a Rebuttal PDF that includes some figures related to Reviewer 8GTK's questions. We hope that following responses could address reviewers’ concerns.

Meta-review: The paper proposes TopoLogic, an interpretable framework for topology reasoning in autonomous driving. It introduces several modifications to mitigate several issues in existing approaches. e.g. explicit similarity calculation. It brings significant improvement over previous SOTA on OpenLane-v2 benchmark.

Authors have carefully addressed reviewers comments and provide more details. There are two positive reviews and two negative ones. The negative comments are mainly focused on the lack of implementaion details / explaination on the experimental settings / typos / etc. Since it falls into the category of borderline paper, AC steps in, read the paper carefully and rebuttal feedbacks. 

There are concerns on the technical contribution as pointed out by reviewers. In AC's view, the field of lane detection is **slowly** evolving over the years. There are not too many research on topology reasoning, which is a critical issue for the next-level of lane detection. Given the importance of the topic, great improvement over previous SOTA and detailed feedback on the rebuttal, AC would champion this work for this time. Please incorporate all the concerns, release the code and contribute to the community.
Decision: Accept (poster)