TrajMamba: An Efficient and Semantic-rich Vehicle Trajectory Pre-training Model

We sincerely appreciate your recognition of our work—this means a great deal to us. Below, we address your doubts as follows.

[W1] For the DP task, we believe our paper already employs path-aware metrics for performance evaluation. In Section 5.1, beyond computing the MAE/RMSE for the last coordinate, we also predict trajectory destinations at the road segment level to assess model performance. This road segment prediction is treated as a multi-classification task, optimized via cross-entropy loss, with evaluation metrics including Accuracy@N (Acc@1, Acc@5) and macro-Recall. We consider these metrics as 'path-aware metrics' because road segments are intrinsic components of the path itself. Predicting road segments and evaluating via these indicators directly reflects our model's ability to learn and predict path-related information. Compared to relying solely on MAE/RMSE for final coordinates, this approach enables a more comprehensive evaluation of the model's capability in the DP task across multiple dimensions. Detailed results are presented in Tables 1, 7, and 8. If our understanding of "path-aware metrics" differs from your expectation, we sincerely apologize and look forward to your clarification in the second round of review.

[W2/Q1] For the without fine-tune setting used in our experiments, we clarify that all models under this setting fix their parameters after the pre-training stage and only update the predictors' parameters. In other words, the other methods in Table 7 also have a pre-training stage, and all models simply do not participate in fine-tuning with task supervision (only predictors are trained). To assess the intrinsic value of the pre-training stage, the variants "w/o Purpose" and "w/o KD" in our ablation study remove the two training stages proposed in the paper (for DP and ATE tasks under the fine-tune setting), and their worse performance compared to our complete model demonstrates that both pre-training procedures contribute to TrajMamba's performance. Moreover, we supplement the performance of these variants under the w/o ft setting on the Chengdu dataset to further demonstrate the effectiveness of the two training stages.

We sincerely hope that the above content has adequately addressed your questions and concerns. Your positive feedback has been highly encouraging, and we look forward to further enhancing the work with your continued guidance.

We sincerely appreciate your detailed and insightful comments, which are highly valuable for improving our work. We have carefully addressed each point below.

[W1] Here is our clarification of external data quality's influence on performance, based on the actual design and implementation:

• Our model does rely on city road networks and POI data, which are independent of trajectory data. However, these can be easily obtained through the following means: (1) Road networks from OpenStreetMap, a widely used open-source platform with stable data quality. (2) POI information from reliable map APIs like AMap and Google Maps. Such sources are widely available and effective, ensuring stable and high-quality data that is less prone to noise or missing information. For our experimental datasets, we directly obtained these external data through the above channels.

• Regarding the accuracy of map-matching algorithms, it is common practice to use such algorithms (e.g., FMM[1], LMM[2]) to map GPS trajectories to urban road networks. Most recent map-matching algorithms have strong capabilities to handle noisy data and complex road networks.

  [1] Can Yang and Gyozo Gidofalvi. 2018. Fast map matching, an algorithm integrating hidden Markov model with precomputation. International Journal of Geographical Information Science 32, 3 (2018), 547–570.

  [2] Wannes Meert and Mathias Verbeke. 2018. HMM with non-emitting states for Map Matching. In ECDA.

[W2] This design is rooted in the teacher-student framework of knowledge distillation, where a well-trained teacher model transfers knowledge to a student model. Specifically:

• The travel purpose-aware pre-trained teacher model first learns semantically-rich embeddings from complete trajectories, capturing both movement patterns and travel purposes. This aligns with the principle that a knowledgeable teacher is essential for effective knowledge transfer.
• In knowledge distillation pre-training stage, the student model then learns to generate compressed trajectory representations guided by the teacher's output embeddings. This avoids the instability of training two uninformed student models to learn from each other. They may fall into the local optimal solution during training, unable to obtain an effective learning direction, which will lead to training collapse.

Moreover, we designed an ablation variant "w/o KD" in our ablation study, which removes the knowledge distillation pre-training and directly trains compressed representations through travel purpose-aware pre-training. Its worse performance compared to our complete model demonstrates that the two-stage pre-training procedure is necessary and effective for TrajMamba's performance.

[W3] Our efficiency focus is explicitly on downstream inference—the phase critical for real-world applications (e.g., real-time trajectory encoding), rather than pre-training.

The two-stage training, along with additional modules and information collection, are part of the offline pre-training process. Pre-training involves more flexible resource allocation, so their computational costs are acceptable. Importantly, these components do not participate in downstream tasks: they are only used during model training, leaving no additional overhead in real-world applications.

This design ensures that the efficiency metrics we highlight—final embedding computation time—accurately reflect the performance users will experience in deployment, avoiding the persistent downstream costs that would arise from alternative designs.

[W4] To address this, we conducted supplementary experiments on a new real-world trajectory dataset: Porto. Hosted on Kaggle for a taxi trajectory prediction contest, this dataset is widely used in TRL studies and contains GPS trajectories of taxis in Porto, Portugal. We obtained POI information from the Azure Maps API and road networks from OpenStreetMap.

We re-evaluated our model and several best-performing baselines from the Chengdu and Xi'an datasets, including START, MMTEC, and JGRM, on the Porto dataset across all downstream tasks. The results demonstrate that our model maintains consistent performance advantages over baselines on the Porto dataset, aligning with its behavior on the Chengdu and Xi'an datasets. These experimental results verify our model's generalization ability across trajectories from different geographical regions and data sources.

[Q1] Yes, our mask generator primarily identifies key trajectory points and removes redundant ones. We conducted supplementary experiments to compare its effect with directly downsampling trajectories by a certain ratio (sampling ratio=60%) across all downstream tasks on the Chengdu dataset. These results verify our mask generator's ability to identify key trajectory points for effective compression, which is superior to direct downsampling.

Additionally, we designed an ablation variant "w/o MG" in our ablation study, which replaces the mask generator with the Douglas-Peucker algorithm to generate compressed trajectories. Its worse performance compared to our complete model in the DP task also indicates the advantages of our mask generator for various downstream tasks.

[Q2] In our experimental datasets (Chengdu and Xi'an), trajectory points do not have strictly uniform sampling intervals—unlike the Porto dataset, which has a fixed 15-second interval. While most trajectories have sampling intervals of at least 6 seconds, there is significant variability:

Moreover, our ATE task is designed to predict the end time of trajectories still in movement. This setting aligns with practical scenarios such as ride-hailing arrival time estimation and traffic management, where real-time estimation of remaining travel time for ongoing trips holds substantial application value. These variations and task design choices reflect real-world trajectory data characteristics and practical needs, enhancing the model's adaptability to real-world scenarios.

Thank you again for your earnest efforts in identifying weaknesses and raising relevant questions. We hope these supplements meet your expectations and look forward to further suggestions for improvement.

We sincerely appreciate your detailed and insightful comments, which are highly valuable for improving our work. We have carefully addressed each point below.

[W1] We clarify the motivation as follows:

(1) Our focus is eliminating additional downstream overhead, which is more critical for real-world applications (e.g., real-time trajectory encoding), rather than pre-training costs. As noted, pre-training is offline with flexible resources, so its computational costs are acceptable if enabling effective downstream inference. Addressing your concerns:

• The initial textual embeddings are obtained using OpenAI's text-embedding-3-large model (See Appendix H). We apologize for omitting this.
• Regarding lightweight text encoders, we acknowledge their effectiveness but emphasize they conflict with our downstream efficiency goal: (i) Their sizes (e.g., 45.8, 83.8, and 251.7MB) are 8–47× larger than our downstream module (5.407/5.182MB), increasing deployment memory. (ii) They typically require 1024+ hidden dimensions to encode complex textual information, while our model (and most standard trajectory learning models) uses approximately 256. Integrating them into downstream tasks would inevitably add non-negligible overhead.
• The dual-text encoder is exclusive to offline pre-training and does not participate in downstream tasks. Therefore, it introduces no additional overhead in downstream inference, avoiding persistent computational costs.

(2) The variant "w/o Compress" without compression in our ablation study shows consistent performance degradation across all downstream tasks, directly verifying that redundant GPS points harm effectiveness.

[W2] We appreciate your attention to the novelty of the Traj-Mamba Encoder. The referenced Trajectory Mamba[1] and our TrajMamba differ fundamentally in their core goals and technical designs, which we clarify as follows:

1. Trajectory Mamba is tailored for real-time autonomous driving decision-making, where the focus lies in short-term (seconds) behavior prediction at intersections. Its data is often high-frequency (10-20Hz) and captures precise, rule-bound maneuvers (e.g., lane changes, turns). In contrast, our work targets vehicle GPS trajectories from ITS (e.g., taxi, logistics), which is low-frequency (seconds level), sparse, and reflects long-term (minutes/hours) human mobility patterns. Moreover, our work aim to encode trajectories into semantically-rich embedding vectors, which can then be adapted to multiple downstream tasks. This pre-training paradigm represents a different technical direction from task-specific prediction models.

2. Trajectory Mamba optimizes SSM for recursive forecasting efficiency in dynamic scenes. Our Traj-Mamba Encoder, however, targets capturing long-term movement patterns of trajectories by jointly modeling and fusing GPS and road perspectives with linear time complexity: (1) Unlike directly input-dependent parameterization, it uses high-order movement behavior features to parameterize GPS-SSM, enabling precise control over how trajectory movement behavior changes affect the input selection. (2) Instead of parallel dual-view modeling followed by independent fusion module, it adopts bidirectional interaction between GPS and road views. Road-SSM parameters are extended to trajectory geographical space (rather than road network space), selecting input embeddings based on changes in trajectory movement details, while GPS intermediate embeddings are also selected via a dot-product gate at road level.

[W3] To address the potential confounding effect of preprocessing on the soft masking mechanism, we conducted experiments without rule-based preprocessing. The results show that removing preprocessing yields comparable performance to the full model across all downstream tasks, directly validating the efficacy of the proposed soft masking mechanism.

Regarding the case study, due to the fact that this rebuttal can only provide textual information and is unable to offer any additional content in any form, we kindly ask for your understanding regarding our inability to present it to you here. We promise to include this experiment in subsequent versions.

[W4] We have reproduced UniTR[3] and included it in our experiments. The results show that TrajMamba outperforms UniTR across all downstream tasks with high encoding efficiency, supporting our SOTA claim.

Regarding the other two works: (1) MRGRP[2] is dedicated to courier route prediction in food delivery services. It takes a set of discrete pick-up and delivery tasks as inputs and focuses on optimizing task scheduling with strict order constraints (e.g., delivery must follow pick-up for the same order). This differs fundamentally from our scenario: we process vehicle GPS trajectories and aim to learn semantically-rich embeddings for diverse downstream tasks, rather than task scheduling. (2) Path-LLM[4] studies path representation learning, where "path" refers to a theoretically navigable route on the road network, not the actual GPS trajectory generated by vehicle movement (which records real spatio-temporal behaviors). Its focus is on aligning path semantics with language models for navigation-related tasks, which does not overlap with our multi-downstream scenario. Due to these fundamental differences in input data, core objectives, and application scenarios, MRGRP and Path-LLM are not suitable as baselines for our work.

[W5] Below we provide a detailed complexity analysis of TrajMamba's downstream components (Mask Generator + Traj-Mamba Encoder), compared with typical baselines JGRM and START.

Inference Time Complexity of TrajMamba:

1. Symbols Definition: $d$ is the number of trajectory point features for the input mask generator, $E$ is the embedding dimension, $L$ is the number of Traj-Mamba blocks, and $n, n'$ are the lengths of the input trajectory and the compressed trajectory after processing by the Mask Generator, respectively.
2. In the mask generator, the time complexity is $O(nd^2)$.
3. For the Traj-Mamba Encoder, the time complexity is $O(n'dE)$ and $O(Ln'E^2)$ for embedding initial latent vector and $L$ stacked Traj-Mamba blocks, respectively.
4. The combined time complexity of TrajMamba is $O(nd^2+n'd E+Ln'E^2)$

Complexity of Typical Baselines:

• JGRM: $O(mE^2+L_rm^2E+L_f(2m)^2E)$, where $m$ is the number of unique road segments in trajectories, and $L_r, L_f$ are the numbers of route encoder layers and model interaction layers, respectively.
• START: $O(L_gH|\mathcal{V}|E^2+L_en^2E)$, where $|\mathcal{V}|$ is the number of road segments in the road network, $H$ is the number of attention heads used by TPE-GAT, and $L_g, L_e$ are the numbers of TPE-GAT layers and TAT-Enc layers, respectively.

Conclusion: TrajMamba achieves linear inference time complexity with respect to trajectory length $n$ by avoiding the quadratic terms present in baselines: JGRM introduces $O(m^2)$ from Transformer-based modules, while START relies on $O(n^2)$. This design ensures encoding efficiency for long or large-batch trajectories in real-world scenarios, which is crucial for real-time applications.

[Q1] In Fig.4(b), the performance at E=256 shows significant improvement compared to E=128, but the improvement at E=512 is limited. Considering the increase in model size and encoding time resulting from changing E from 256 to 512 (which affects downstream inference efficiency and contradicts our goal of efficient inference), we chose E=256 to balance performance and efficiency.

[Q2] We concur F1-score is a widely recognized metric for multi-class DP tasks. Our DP task involves predicting trajectory destinations at both road segment and GPS levels. For the latter, RMSE and MAE are necessary to measure prediction errors. Due to table width constraints, we selected metrics for road segment prediction following [5], and reasoned that these metrics provide complementary perspectives. To address your question, we provide supplementary F1-score results as follows, which are consistent with our Accuracy/Recall performance:

[5] "TrajCogn: Leveraging LLMs for Cognizing Movement Patterns and Travel Purposes from Trajectories." Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI). 2025

Thank you again for your earnest efforts in identifying weaknesses and raising relevant questions. We hope these supplements meet your expectations and look forward to further suggestions for improvement.

We sincerely appreciate your recognition of our work—this means a great deal to us. Below, we address your doubts as follows.

[W1] We provide the following supplementary analysis:

• The average compression ratio of trajectories (=compressed length/raw length) on Chengdu and Xian is shown below. This result proves that our model successfully identifies and removes a considerable part of the implicit redundancy contained in trajectories, retaining key points that benefit trajectory embedding representation.

  Dataset	ratio after preprocessing	ratio after soft masking mechanism
  Chengdu	67.189%	42.159%
  Xian	70.419%	35.094%

• We set the weights for the loss functions $L^{MEC}$ and $L^{mask}$ to 1/2 to balance these two objectives. A larger weight for $L^{MEC}$ results in compressed representations containing more information from the full-trajectory embedding; a larger weight for $L^{mask}$ produces shorter compressed trajectories from the mask generator, achieving greater compression. We conducted supplementary experiments on the Chengdu dataset to explore the impact of different weights on downstream tasks and compression performance. The results demonstrate that when the weights for ($L^{MEC}$, $L^{mask}$) are (0.5, 0.5), our model achieves the best overall performance across all downstream tasks and encoding time.

  Task		Destination	Prediction			Arrival	Time	Estimation	Similar	Trajectory	Search	Embed Time
  Metric	RMSE	MAE	Acc@1	Acc@5	Recall	RMSE	MAE	MAPE	Mean Rank	ACC@1	ACC@5	seconds
  (1.0, 0.0)	125.619	86.543	56.277%	83.854%	26.363%	51.766	19.657	5.335%	1.662	95.800%	98.300%	1.944
  (0.7, 0.3)	135.447	91.966	58.130%	86.362%	30.075%	54.509	17.940	4.802%	1.155	96.600%	98.900%	1.731
  (0.3, 0.7)	134.870	90.072	58.145%	86.546%	30.031%	50.978	18.556	5.053%	1.204	95.800%	98.800%	1.692
  (0.5, 0.5) (Ours)	129.474	85.947	58.205%	86.813%	30.446%	50.166	17.727	4.772%	1.148	96.525%	99.125%	1.721

[W2] We evaluated two additional pre-trained textual embedding modules from HuggingFace: hfl/chinese-lert-large and BAAI/bge-large-zh-noinstruct. We explored how different textual embedding modules affect our model's performance. The results show that using alternative models has limited impact on performance, demonstrating that our pre-training process enables the model to learn robust representations.

We sincerely hope that the above content has adequately addressed your questions and concerns. Your positive feedback has been highly encouraging, and we look forward to further enhancing the work with your continued guidance.