A Unified Federated Framework for Trajectory Data Preparation via LLMs
Authors: Zhihao Zeng
Ziquan Fang
Wei Shao
Lu Chen
Yunjun Gao
Venue: ICLR 2026 Poster (2026)
Keywords: Trajectory Data Preparation
Federated Learning
Large Language Model
Trajectory Preprocessing
Primary area: foundation or frontier models, including LLMs

Abstract: Trajectory data records the spatio-temporal movements of people and vehicles. However, raw trajectories are often noisy, incomplete, or inconsistent due to sensor errors and transmission failures. To ensure reliable downstream analytics, Trajectory Data Preparation (TDP) has emerged as a critical preprocessing stage, encompassing various tasks such as imputation, map matching, anomaly detection, trajectory recovery, compression, etc. However, existing TDP methods face two major limitations: (i) they assume centralized access to data, which is unrealistic under strict privacy regulations and data silo situations, and (ii) they train task-specific models that lack generalization across diverse or unseen TDP tasks. To this end, we propose FedTDP for Federated Trajectory Data Preparation (F-TDP), where trajectories are vertically partitioned across regions and cannot be directly shared. FedTDP introduces three innovations: (i) lightweight Trajectory Privacy AutoEncoder (TPA) with secret-sharing aggregation, providing formal privacy guarantees; (ii) Trajectory Knowledge Enhancer (TKE) that adapts LLMs to spatio-temporal patterns via trajectory-aware prompts, offsite-tuning, sparse-tuning, and bidirectional knowledge distillation; and (iii) Federated Parallel Optimization (FPO), which reduces communication overhead and accelerates federated training. We conduct experiments on 6 real-world datasets and 10 representative TDP tasks, showing that FedTDP surpasses 13 state-of-the-art baselines in accuracy, efficiency, and scalability, while also generalizing effectively across diverse TDP tasks.

Published as a conference paper at ICLR 2026
A UNIFIED FEDERATED FRAMEWORK FOR TRAJECTORY DATA PREPARATION VIA LLMs
Zhihao Zeng'. Ziquan Fang', Wei Shao', Lu Chen', Yunjun Gao
1 School of Software Technology, Zhejiang University
2 Coolleee of Computer Science and Technology. Zhejiang University sengzhihao, zæfang, wei.. shao, luchen,
ABSTRACT
Trajectory data records the spatio-temporal movements of people and vehicles. However, raw trajectories are often noisy, incomplete, inconsistent due sensor errors and transmission failures. To ensure reliable downstream analytics, Trajectory Data Preparation (TDP) has emerged encompassing various tasks such as imputation, map matching, anomaly detection, trajectory recovery, compression, etc. However, existing TDP methods face two major limitations: (i) they assume centralized access to data, which is unrealistic under strict privacy regulations and data silo situations, and (ii) they train task- specific models that lack generalization across diverse or unseen TDP tasks. To this end, we propose FedTDP for Federated Trajectory Data Preparation (F-TDP), where trajectories are vertically partitioned across regions and cannot be directly shared. FedTDP introduces three innovations: (i) lightweight Trajectory Privacy AutoEncoder (TPA) with secret-sharing aggregation, providing formal privacy guarantees; (ii) Trajectory Knowledge Enhancer (TKE) that adapts LLMs to spatio- temporal patterns via trajectory-awars prompts, offsite-tuning, sparse-tuning, and bidirectional knowledge distillation; and (iii) Federated Parallel Optimization (FPO), which reduces communication overhead and accelerates federated training. We conduct experiments on 6 real-world datasets and 10 representative TDP tasks, showing that FedTDP surpasses 13 state-of-the-an -he- baselines in accuracy, efficiency, and scalability, while also generalizing effectively across diverse TDP tasks.
critical preprocessing stage,
INTRODUCTION
Trajectory data, which records the movement of people (Chen al.) 2024a) and vehicles (Miao) et al., 2024b) in space and time, plays critical role in traffic optimization and urban planning. However, raw trajectory data often contains inconsistencies (Liu et al., 2024b), noise (Fan et al.. 2023), and missing values (Chib & Singh 2024) due to sensor errors and communication failures. To improve data quality, Trajectory Data Preparation (TDP) has emerged as a crucial preprocessing stage, covering tasks such data imputation (Musleh & Mokbel 2023), map matching (Liu et al.) 2024b), trajectory- linking (Chen et al.) (024b), anomaly detection (Gao et al., 2023). trajectory recovery (Liu et al., (2024c), data compression (Fang al. (023), etc. These tasks are indispensable for enabling robust downstream analytics, such as traffic forecasting, trajectory clustering, and anomaly explanation. Note that, each of these TDP tasks has attracted considerable attention in the teatio-temppral community (Liu et al. 2024b Miao et al. 2024a Hu et al. (2024)). Despite their considerable efforts, existing TDP methods have two limitations in the following.
L1: Decentralized requirement. Trajectory data is highly sensitive, as it encodes individuals' movements. To safeguard such data, strict privacy regulations have been enacted worldwide. For example, the Federal Geographic Data Committee (FGDC) 2015) and China's 's Personal Information Protection Law (PIPL, 2021) explicitly restrict the sharing of raw mobility data across areas. In practice, platforms (e.g., Uber Movement) split trips along administrative boundaries to comply with privacy rules (UMP) 2022). This leads to vertical partitioning, where each region only observes partial trajectories. Models trained only partial trajectories suffer from boundary discontinuities and biased spatio-tempores patterns, which severely impact TDP tasks such as imputation or anomaly detection near administrative borders (Musleh & Mokbel| 2023 Fang et al. 2023). Fig. shows an

---

Published as a conference paper at ICLR 2026
example using the GeoLife dataset (Zheng et al. 2010), where trajectories crossing administrative regions (depicted in different colors) are split into disjoint sub- trbjtrrjccooisss each managed by a local data silo. However, existing federated learning studies mostly focus on horizontal partitioning, where different users' data reside at different institutions. In contrast, the vertical partitioning of trajectories across regions has not been systematically studied.
L2: Lack of a general TDP framework. Existing TDP methods are typically designed for a single, narrowly defined task, which makes them hard generalize. For example, map-matching methods (e.g., HMM-based alignment or deep neural map-matching) are effective only for projecting GPS points onto road networks; trajectory imputation models (e.g.. RNN- or GAN-based sequence completion) are restricted to handling missing points; and trajectory denoising or anomaly detection algorithms often rely on handcrafted spatio-temporal features tailored to specific datasets. Fach of these TDP methods must be retrained or redesigned when applied to a different or unseen TDP task, As a result, the overall pipeline remains fragmented, with high computational cost and limited scalability, Moreover, the diversity of TDP tasks makes it infeasible to adapt single-task task models; thus, a unified approach is required.
These two limitations motivate us to study a new problem, iee, Federated Trajectory Data Preparation (F-TDP). Given vertically partitioned trajectories stored in different regional silos, we aim to collaboratively perform multiple TDP tasks without sharing raw data across silos,
Filcring
Soy Paint
Server
LLM
Maaching
Tudl
Cilon
Clisrt
Glies
Gleer
Cliont
Clivnt
Hoidise
Design Motivation. To address privacy concerns in this setting, we build on Federated Learning (FL), a distributed paradigm that enables clients to train mod- els collaboratively while keeping data lo- cal (Liu et al., 2024a, MMao al., (025). Specifically, we treat each region as client that stores partial trajectories and contributes to federated server for model training, thus preserving privacy in F-TDP. As shown in Fig. FL enables multiple Clients (i.e., regions) to collaboratively train a model on a Server while keeping trajectory data decentralized, thereby preserving the data privacy of each client. Meanwhile, Large Language Models (LLMMs) have demonstrated strong multi-task generalization in diverse domains, including mobility applications (Fang et al. (026) and trajectory analysis (Du et al. (022). This suggests the potential of developing ToP-orietted LLM to unify different TDP tasks within a unified framework, avoiding repeated training of task-specific models across silos.
Suza JELAO
Shaineshaa
Dangikmng
Xichena
$20
Pengui
Cheoning
Figure 1: Federated trajectory data preparation
However, directly combining FL and LLMs to perform TDP tasks is insufficient, as F-TDP raises three unique challenges that existing methods fail to address.
C1: Privacy. TDP tasks often necessitate considering the data context Gao et al. (2023) Muslch & Mokbel (2023): Liu al. (2024b). which involves the exchange and sharing of data and demands collaborative processing across clients (i.e., cross-client TDP), raising privacy concerns. Such data sharing may reveal highly sensitive information, including: home/work locations, fine-grained movement patterns, lifestyle routines, and cross-border movements of individuals. As shown in Fig. 1, if the data p is missing, the Fengtai region needs to utilize the context of the missing data (i.e., and P2) for data imputation. However, due to data privacy constraints, the Fengtai region cannot access p1 from the Dongcheng region. Consequently, ensuring the privacy of trajectory data thus constitutes the challenge the FedTDP framework must address.
C2: Trajectory Knowledge Learning. Existing LLMs are primarily designed for textual cor- pora (Fan al. [0244] Lee et al. (022), , and thus fail to capture the unique spatio-temporal properties of trajectories MMusleh & Mokbel] 2022) Fang et al. 2023), such as temporal regularity and spatial dependency, Moreover, their pre-training relies on large-scale unsupervised text corpora (Eltabakh ct al. 2024; Gu et al. 2023). which lack the intricate mobility patterns required by TDP tasks (Liu al. 2024b |uu et al.] 2024b). As a result, directly applying LLMs to trajectory data preparation leads to suboptimal performance. A key challenge is therefore to develop a TDP -rieented LLM that can effectively bridge this gap and generalize across diverse preparation tasks.
2

---

Published as a conference paper at ICLR 2026
C3: Efficiency. Deploying and training LLMs locally on clients is infeasible due to limited computa- tional resources and storage capacities (Sun et al. 2024; Zhang et al., 2222a] Hou et al. 2024). As a result, LLMs often hosted on servers, which introduces both communication overhead and storage burdens (Liu et al.
2025), while wasting computational resources on the client side. Furthermore, LLMs contain hundreds of millions of parameters, and even parameter-efficient fine-tuning (PEFT) techniques (Hu et al. 2022) remain highly time- and resource-intensive under federated settings, as proved by Appendix 5.4 The challenge thus design scalable optimization strategies that reduce communication cost and accelerate training while maintaining high accuracy.
Contributions. To the best of our knowledge, no existing studies (Related Work in Appendix A address the above challenges. In this paper, we propose FedTDP, a unified federated framework for trajectory data preparation via L.MMs. Our main contributions are as follows:
Problem formulation of F-TDP. We formally define Federated Trajectory Data Prepa- ration (F-TDP) and provide a unified framework addressing vertical partitioning and multi-task challenges, which to our knowledge, has not been systematically studied before.
Trajectory-specffic privacy mechanism. We design a lightweight Trajectory Pri- vacy AutoEncoder (TPA). Unlike generic embedding encoders, TPA is explicitly de- continuity while protecting privacy. To resist embed-
signed to preserve ding/gradient inversion, TPA integrates decentralized secret-sharing aggregation protocol, with formal privacy guarantees provided in Appendix C.2
TDP-oriented LLM with trajectory knowledge enhancement. We develop Trajectory Knowledge Enhancer (TKE) to bridge the gap between text-oriented LLMSs and trajectory data. TKE incorporates trajectory-awanl prompt engineering, offsite-tuning, and bidirec- tional knowledge distillation between server-side LLMs and client-side SLMs, enabling effective cross-task generalization for 10 TDP tasks.
Federated parallel optimization for efficiency. We propose Federated Parallel Optimiza- tion (FPO), which coordinates the training of TPA, SLMs, and LLMS under vertical FI. constraints. By combining split learning, alternating optimization, and parallel execution, FPO reduces communication overhead and significantly accelerates convergence.
PRELIMINARY
The frequently used notations and deseriptions in this paper shown in Appendix B
Point). A teatioltemporal point is represented as p == (I,t), where I = (Ion, lat) is a tuple of longitude and latitude location coordinates, and refers to the observed time associated with this apatio-tempord point.
Definition 1 "Spatio-Temport
Definition (Trajectory). A trajectory comprises chronological spatio-temporal points, denoted as T = (21.P2.... P2....,, which rypically represents the movement of user. In addition, trajectory can be segmented into multiple sub-trajectories. denoted as = ())T)))).....
Definition 3 (Data Silo). A data silo S has its own collected trajectory datasel D. In federated learning, data silo S represented as a client C. typically a regional data storage platform or institution. responsible for the collection and management of trajectory data within that region. Specifically, a trajectory = (P1, .2....}
...). is segmented into sub-trajectories based on the geographic locations, denoted as = (ST(C1) (T((C),....) where sub-trajae uub-trajectory (T( is stored in client Ct.
Problem Formulation (F-TDP). Given the server's LLM OLLM and the trajectory dataset D [Di, D2....) + (T,. . J of all clients C = {C1, C2....). where client C, holds dataset D; and T, is the i-th complete trajectory, F-TDP is to employ OLLM on D for performing various trajectory data preparation tasks, where collected trajectories D, of client C2 cannot be shared and exchanged to the server and other clients, i.e., F-TDP(D) = (T.) where T, (S7(C1) ,ST(CC), ...) and (TI) is the result of fLMM the trajectory T,, with different forms of output depending the TDP task, such as the cleaned trajectory, points, or classification result.
TRAJECTORY DATA PREPARATION TASK
We demonstrate all major types of TDP tasks, with the illustration examples shown in Appendix
3

---

Published as a conference paper at ICLR 2026
Data Flow
Data Communication CP
Seoret Sharing
* Frozzn Data
Emnbodinn Data
2 Trajectory Data
Trajectory Knowledge Enhancer
Trijetory Knnslellee
Federated Par Paralle Optimizzation
SE-tragetey Xpo
L.M
SLM
Trijectory Privacy AutoEncoder
4
Fedlerated Parallel Optimization
Client
Server
Figure 2: The overview of our framework
T-1: Anomaly Detection (AD). It aims to detect trajectories that deviate significantly from typical movement patterns. These anomalies may arise from unusual user behavior or data collection errors. T-2: Trajectory Imputation (77). It aims to reconstruct a complete trajectory by estimating the missing points based on available spatio-temporal points. This often occurs when GPS signals are lost or data collection is interrupted.
T-3: Noise Filtering (NF). It aims identify and remove irrelevant
points that deviate from the trajectory. These noisy points often arise from GPS inaccuracies or sensor malfunctions. T-4: Stay Point Detection (SPD). aims to identify locations where a moving object stays an area for a certain duration. A stay point usually represents point of interest, such as residence, office. T-5: Map Matching (MM). It aims to map the spatio-temporal point to the most probable segment in the road network. This is often the case when there is a deviation in the collected GPS position.
T-6: Trajectory-User Link (TUL). It aims to link an anonymous trajectory with its corresponding user. These trajectories are often collected without any user-identifying information.
T-7: Travel Mode Identification (TMI). It aims to identify the travel mode based on the moving pattern of trajectory, which is walking, biking, taking the bus, or driving car.
T-8: Trajectory Simplification (TSim). It aims to reduce the number of spatio-temporal points in trajectory while preserving essential shape and features.
T-9: Trajectory Segmentation (TSeg). It aims to divide trajectory into meaningful segments based on specific criteria such as stay points or travel modes.
T-10: Trajectory Recovery (TR). It aims to reconstruct complete trajectory from partially observed spatio-temporal points. This often occurs when some parts of the trajectory are missing or unobserved.
OUR APPROACH
Fig. provides an overview of the Fe framework, which involves a central server and multiple regional clients. FedTDD consists of three core modules-the Trujectory Privacy AutoEncoder (TPA), the Trajectory Knowledge Enhancer (TKE), and the Federated Parallel Optimization (FPO) (FPO)-cac) cach designed to address one of the key challenges in the F-TDP problem.
To enable distributed computation, we introduce the notion of a Small Language Model (SLM), a lightweight counterpart of the server-side LLM,, which is deployed each client. The SL.M is used whenever client can process its local sub-trajectory ST(C) independently, thereby reducing server workload and leveraging local computational resources. If (T) requires cross-client collaboration (e.g., when trajectories span multiple regions). the encoded representations are transmitted to the server, where the I.LM is used for global TDP. The overall workflow as follows.
Local TDP. For local tasks, TKE generates a trajectory-specifie prompt and feeds to the client's SLM (Q-2) The SLM produces preliminary results, which are further refined by TKE @).
Cross-client TDP. For tasks requiring collaboration across silos, TPA first encodes local trajectories into secure embeddings hefore transmission (Q-2) FPO then freezes the transmitted data to reduce
communication overhead (Ø). On the server side, TKE generates prompts for the LLM (Ø-5), ), and
TPA subsequently decodes the LLM outputs back into trajectory representations (0 (0-7), Finally, FPO manages the return flow (8), and TKE refines the results at the client level @ (0+)).
4.1 TRAJECTORY PRIVACY AUTOENCODER (TPA)
Design Motivation. As aforementioned, F-TDP involves the joint processing of data from multiple clients, ie., cross-client TDP, necessitating data exchange and sharing. Consequently, safeguarding the privacy of trajectory data becomes essential. Although differential privacy (Dwork al. 2006)
4

---

Published as a conference paper at ICLR 2026
can be applied to ensure data privacy, it requires adding noise to the data, which diminishes its utility and reduces model accuracy. In contrast, FedTDP proposes lightweight Trajectory Privacy AutoEncoder (TPA) to protect trajectory data privacy while maintaining spatio-temporal correlations. Specificallyy, the TPA module employs an encoder-decoder architecture that encodes trajectory data T = (pi, P2, into embeddings E- {ei, e2,...), where each spatio-temporal point p; is inde- pendently encoded as = (p:)) Then, these clients' embeddings are transmitted to the server for aggregation and alignment via the anonymized user identifier, i.e., - U E,, preserving both intra- and inter-client spatio-temporal dependencies (e.g.. speed, direction), which helps the LLM to capture spatio-temports relationships the trajectory data. Next, the server splits and distributes results& & = {Ei, ... outputted by the LLM clients, where the decoder reconstructs the esti- mated trajectory T = {pi. Pe..... through p. Dec(é.). Here, TPA implemented as lightweight three-layer MLP (Rosenblati 1958) with GELU (Hendrycks & (ampee)(201) activation, 256 hidden dimensions, and 32 embedding dimensions, which does not introduce significant computational overhead, as also proved in the ablation study (see Section 5.2)
However, merely using embeddings for transmission cannot safeguard data privacy completely in FL, attackers and gradient (Zhu et al. 2019 2023) inversion attacks during TPA model aggregation. Specifically, traditional FI. model aggregation, which exchanges client gradients and aggregated parameters, vulnerable to these attacks. While homomorphic encryption (Rivest et al. 1978) and differential privacy offer solutions, they introduce computational overhead or degrade model accuracy. In contrast, we propose decentralized aggregation approach based on secret sharing (Shamir 1979). achieving secure TPA aggregation without compromising training efficiency or model accuracy.
recover the raw data by embedding (Chen et al. 2024c Huang et al. 2024)
Initially, each client pair (C,, C₁) generates shared secret key skaj = sk3, stored locally, respectively, Then, the TPA parameters are partitioned into C| parameter blocks (p())_p(2) p(2))..)))..... For aggregation, the client C2 masks its parameter block using secret keys {skço, sk,,;-... determined with the other clients to mask parameter blocks, adding sks, if >>> j or subtracting it if < j. shown below:
ICI
p(A)
(k)
Σ J=1
aij * skij
Ooj 1-, i 1-,
1, i i<j
where client C2 holds the parameter block p(()) and p(()) is the mask parameter block.
from Theorem 1. Given the mask parameter blocks (p(1) ,P22) ,.... from all clients, the result of aggre- gating them is equal to the result of aggregating raw parameter blocks {p(A) p(k) .....
) for all clients:
C
C
(k)
Proof. The detailed proofs of Theorem are provided in Appendix C.1
According to Theorem the client Ck can obtain the aggregation result (()) of the parameter block p(k) by aggregating the mask parameter blocks transmitted from clients, formally shown below:
(k)
(k)
Finally, the aggregated parameter block is broadcast to clients for the TPA model updates.
Approach Analysis. Note that TPA fundamentally different from differential privacy (DP), not only in whether noise is added but also in its underlying privacy paradigm. DP achieves privacy by injecting random noise into data, which inevitably distorts spatio-temporal correlations that are essential for TDP tasks. In contrast, TPA is deterministic, learning- based transformation that removes privacy-sensitive details while preserving useful patterns. Unlike DP, which requires careful calibration of noise scales and suffers from a utility-privacy tradeoff, TPA avoids this tension by design. Moreover, while De-perrurbed trajectories can still leak probabilistic information about the original locations time ranges within privacy budget (Yao al.] [022; Zhang al.) (024b), TPA provides a different but strong guarantee: as long as the encoder and decoder remain private, reconstructing the raw trajectory is computationally infeasible (see Appendix C.2
5

---

Published as a conference paper at ICLR 2026
4.2 TRAJECTORY KNOWLEDGE ENHANCER (TKE)
Design Motivation. Since existing LLMs are designed for text data and contain only general textual knowledge (Fan et al. to trajectory data and TDP tasks. Although a few
2024 Lee al. 2022 Eltabakh et al. 2024). they cannot be directly applied
LLMs (Li et al. 2024c Zhang al. 2023b Li et al., 2023) have been proposed, none of them have considered TDP. In contrast, to
develop a ToP-oriented LLM, FedTDP designs Trajectory Knowledge Enhancer (TKE) that consists of trajectory prompt engineering. trajectory offsite-tuning, LoRA sparse-tuning, and bidirectional knowledge learning, to enhance the model learning abilities on TDP knowledge.
i) Trajectory Prompt Engineering To help the SLM and L.LM understand trajectory data and learn TDP knowledge, TKE designs trajectory instruction paradigm generate the TDP prompt. defined as (Task, Data, Information, Format). Specifically, Task is the textual instruction consisting of the task name and the task description, listed in Section 3 Data is the input trajectory data, either as trajectory data T = {PI. ipt.P..... .2....} to the SLM for local TDP or embeddings E fei.ee..... to the LLM for cross-client TDP. Information is the optional trajectory context (e. g.. road network, weather) from public sources such as (OpenStreetMap (2025) and OpennWetherMan (2025), to enhance the model's ability perform TDP tasks, which is manually configured and task-specific rather than determined automatically by the model. Format is task-specific output format, such as classification results for TDP tasks including AD, TUL, and TMI, trajectories for TDP tasks including TI, NE, TSim, TSeg. MM, and TR, and spatio-temporal points for the SPD task. A few representative TDP tasks constructed via trajectory prompt engineering are provided in Appendix C.3 to illustrate the flexibility and applicability of our framework.
ii) Trajectory Offsite-Tuning. To enhance the learning capabilities of the SLM in clients, TKE employs the LLM to assist it in learning trajectory knowledge by trajectory off-site tuning. Specifically, inspired by the dffsite-tuniing (Xiao et al. 2023), we divide the LLM into two components, denoted as BLLM F]. Here, the adapter A is the last few layers of the LLM to specialize general features for specific tasks, enabling task-specific feature mapping and decision making. Besides, the foundation F is the remaining layers excluding A, extract general data features, transforming raw inputs into meaningful representations. Initially, it dispatches the server's adapter AA to the client as the final few layers to be integrated into the client's SLM. Consequently, the SLM is composed of two components, denoted as 0SLM = [A, where F' is the foundation of the SLM. Subsequently, the SLM employs LoRA to reduce the number of parameters in the adapter and then transmits the fine-tuning adapter to the server for aggregation and updates.
Note that FedTTD does not simply transfer the trained LLM adapter to the SLM. Instead, the adapter A is leveraged to augment the SLM's 's learning capacity during training. Specifically, during tuning, A is dispatched to the client and attached to the tail of the local SLM. The client fine-tunes only A on its local data, and the updated adapters are then returned to the server for aggregation. To ensure compatibility across different model families, the only requirement is hidden dimension aligument: the output dimension of the SLM's final layer must match the input dimension of the adapter A.
iii) LoRA Searse-Tuning. To duce the number of training param- eters, TKE proposes LoRA sparse- tuning, as shown in Fig. [3] Accord- ing to works on sparsity (Alistarh
Clange reto
Seloied
Randumly select
S Traning
SLM Aggregate
SLM
Pichulsiity
X
Not selcced
* Frosm
N
L
LoRA
W
ct al. 2018 Dai et al. 22022 ZZhag ltt al.) 2023a). more significantly varying parameters have a greater contribution to model convergence. Therefore, we only choose the layer in the SLM where the LoRA param- eter change rate is the top for training. Specifically, the client calculates the ratio of the LoRA parameters change rate of each layer to the global LoRA parameters change rate of all N layers ("ratio" for short), as shown below:
Troatommn 2y
Ja
Tanatomen Joer
L
LatIA
Client
We
Server
Figure 3: LoRA sparse-tuning
CR())
(L)) = ΣST (L.)
where (RR))(Ta) is the LoRA parameters change rate of layer Ta at round r, as shown below:
6

---

Published as a conference paper at ICLR 2026
L (
L (r-
CR (T:;)
L 1(-1)
Then, randomly select M = m. NJ layers to participate in the next round of the SLM training.
Theorem 2. Given the ratio (()) of layer Li and the number of layers M to be trained, the probability P(Ls, M) of layer Lg to train is shown:
M), = R(L.) + R(L,) Σ R(L))
N
+...
1 R(L5,)
Ji
(6)
N Σ Ja Sethi Ja Aio
R(L,)).. ... (.(Ij))..RLLjM--))
R(L.)
(1 (--R() ... (1- R(L)))
Proof. The detailed proofs of Theorem 2 are provided in Appendix C.4
According Theorem 2, chooses the training layers based their probability at each training round. Finally, the client uploads the LoRA parameters of the trained layers to the server for aggregation, and the server assigns different weights the parameters based on the number of clients involved training on these layers, as formally shown below:
(IC) - (C')) Σ/= w
W (r-1)
I,
CC|
where W is the LoRA parameters layer I, sent by client C, at training round r, (r(r) the Laj aggregated LoRA parameters, and CC' is the number of clients that have trained layer T.- iv) Bidirectional Knowledge Learning. To improve the model learning capabilities, TKE develops bidirectional knowledge learning to enhance their TDP knowledge. Specifically, in order for the SLM to learn useful TDP knowledge in the complex output space of the LLM, it aligns the SLM's output with LLM's high frequency output using the inverse KL divergence (Kullback & Leibler 1951):
Poun (T)
min DKL (Pénsul | OSIM
Σ T
Pesus (T) log(
8
PeLu (T)
where Pasus and PoLEs are the output distribution of the SLM and LLM, respectively. Besides, since the SLM can access raw trajectory data, aligns the LLM'' output with the SLM's output using forward KL divergence, which enables the LLM to learn the trajectory knowledge of the SLM:
Poun
min DEL (Pessxl (Peux) = Σ OLLM
Peax (T) log(
Pe
T
4.3 FEDERATED PARALLEL OPTIMIZATION (FPO)
Design Motivation. To improve training efficiency, FedTDP in- troduces Federated Parallel Op- timization (FPO), which utilizes split learning, alternating opti- mization, and parallel training reduce data transmission and enhance the training parallelism. The overall process of the FPO module is shown in Fig. 4
SLM
LLM Training FoFeaz Data
JOED Enkedding
Trajectory
....> Encoding
Encoder
Decoder
JDP Locks
Client
Server
First, to enable the simultaneous training of the client and server, it employs split learning to decompose the federated training process into client and server training. Specifically, the client is responsible for the training of the TPA model (i.e., the encoder and decoder) and SLM, while the server manages the training of the LLM. Besides, to reduce data transmission, utilizes alternating optimization to freeze the data required by the client and server, respectively. During training, the server freezes the embeddings uploaded by the
Figure 4: Federated parallel optimization
7

---

Published as a conference paper at ICLR 2026
Table I:
The evaluated trajectory data preparation (TDP) tasks
Type
Category
Task
Dataset
Anomaly Detection (AD)
Data Cleaning
Trajectory Impulation (TT)
Map Matching (MM)
Seen
Data Matching
Trajectory User Linking (TUL)
Geolife
(seen in training)
Data Annotation
Travel Mode Identiiication (TMI)
Data Reduction
Trajeclory Simpliicaaiin (TSim)
Data Augmentation
Trajectory Recovery (TR)
Trajectory Impotation
Anomaly Detection
Purto
Cleaning
Noise Fitering (NF)
Stay Point Detection (SPD)
T-Drive
Unseen
Data Matching
Map Matching
Tencent
(unseen training)
Trajectory User Linking
Gowalla
Data Annolation
Travel Mode Ilenttication
SHL
Trajectoy Segmentation (TSeg)
Data Reduction
Trajectory Simplification
T-Drive
Data Angmentation
Trajectory Recovery
client for the LLM training, while the client freezes the results outputted by the server's LLM for the TPA model and SLM training. Finally, to enhance the training parallelism, uses parallel training to optimize several objectives in parallel. Specifically, the client has three optimization objectives: (i) minimizing the reconstruction loss L1 of the TPA model, (ii) reducing the inverse KL loss C2 between SLM and LLM outputs, and (iii) minimizing the loss L3 between SLM outputs and labels. On the other hand, the server has two optimization objectives: (i) minimizing the forward KL loss C between L.M and SLM outputs, and (ii) reducing the loss L2 between L.M outputs and labels.
The multi-task training and few qualitative examples LLM/SLM outputs on different TDP tasks are shown in Appendix C.5 and Appendix C.6. respectively.
5 EXPERIMENT
Datasets. We evaluate the framework on the 10 mainstream TDP tasks in Table 1 which are widely studied in the communities (Liu et al., 2024b; Musleh Mokbel 2023 Hu et al. 2024a). For seen tasks, train FedTDP via unified multi-task learning objective using 10% of GeoLife (Zheng) ctt al. 2010) dataset. contains various quality issues such as positional inaccuracies, data noise, and lower precision, which makes it suitable for various tasks. For the unseen tasks, the following datasets are used: (i) Porto (2015), (ii) T-Drive (Yuan et al. 2010), (iii) Tencent (Liu et al. 2024b
(iv) Gowalla (Cho al. 2011), and (v) SHL (017) Dataset details provided in Appendix D.I
Baselines. As FedTDP is the first framework for LLM-based general trajectory data preparation, we compare FedTDP against three categories of representative baselines: (i) Single-Tass -ask methods (referred to as S-TDP). We include ATROM (Gao et al.] (023) (anomaly detection), Kamel (Musleh &
Mokbel 2023) (trajectory imputation), GraphMM (Liu et al. (2224b) (map matching). AttTUL (Chen
et al.] 2024b) (trajectory-user link), Estimator (Hu et al. (024a) (travel mode identification), S3 (Fang
al. 2023) (trajectory simplification). and LightTR (Liu et al.] (024c) (trajectory recovery). These methods are recognized as leading task-specific approaches in their respective domains and serve as strong single-task baselines. (ii) LLM--basd general data preparation methods.
Since FedTDP is the first proposal for general trajectory data preparation settings, we compare FedTDP with three state-of-the- art approaches that leverage LLMs for general table data preparation, namely FM4DP (Narayan al. 2022). MELD Yaan et al.) 2024). and TableGPT (Li et al. 2024a). (iii) LLM-based spatio-tempor poral data analysis methods. Finally, we consider three recent state- of-the-art methods that employ LLMs for spatio-temporal modeling, including PromptGAT (Da et al.)
2024). UniST (Yuan et al. 2024), and UrbanGPT (Li et al. 20024b) For LLM-based baselines, they directly input raw trajectory data into LLMs perform TDP tasks.
To ensure fairness, all -asedd baselines are applied under identical data preprocessing as FedTDP, ensuring that performance differences primarily reflect the contribution of our framework rather than implementation bias. More implementation details and evaluation metries are provided in Appendix and Appendix(D.3 D.3] respectively.
5.1 OVERALL PERFORMANCE
Table reports the overall performance of FedTDP compared with all baselines across different datasets and tasks, under both few-shot and zero-shot scenarios ("-" denotes unsupported tasks). First, FedTIP consistently outperforms single-task TDP methods, achieving at least 18.38 % improvement.
8

---

Published as a conference paper at ICLR 2026
Table 2: The overall performance on various trajectory data preparation tasks (few-shot/zero-shho)
Dataset
Task
Metric'
S-TDF=
FM4DP
MELD
TableGT
PrompiGAT
UniST
UrbanGPT
FedTDP
Fi
60.36/57.75
52.0947.84
21.5248.21
31.5849444
66. 66.24/66.12 12
70.26/70.14
74.39/70.31
81.20/9004
Ace
7387/71.24
64.5053345
65.48/54.80
560383.71
73.1870422
77.85/74.65
79. 79.38778.25
87.45/87_38
II
Fi
69.4865.92
62 621125610 10
62.67/58.29
6115666.77
73.14/10.73
76 76.86/70.75 76,28/1667
82.89/81.66
Acc
T8 08.2866.66 61
69.7960.59
69.45667.55 599
70.9661 32
75. 15/2.90
8088/777.21
81 81.29475.76 78
94.99/92.07
Fi
39.75/36.23
28996255755
54.59131.58
30.11/26.15
47.40/4134
13.777
56.91751.51
65.32764.85
Ace
40,05/39.37
29 5K/28.45
33.75/38.88 80
33 67
48. 19/46. 14
48. 48.44/22,82
55,17/51.15
76.48/74.25
GeoLife (Seen)
TUL
Ace
Fi
22,06/21.27
29.85/28.78
23 00/26/1111 20
18 11/11/71.1
23.29/21.28
17.75/15.08
79
17.35/15.43
24.00/23.79 79
36. 36.75/34
37. 37.88/35.31
41. 53
38.42/37.47
46. 46.56/45.17
29.86246.8 69
54.79/54.44
64. 44.84/88.4 SS
69,05162.82
57.01/5194
66.98/62.26
69:22168
69,45766.20
82 82.69/80.48
TMI
Acc
79.98/77.82
82
692 20222064338 28
70.1664.07
66
66-4865 38
70.0064885
76.72/68.57
75.13967.79
89.6693166
TSim
SRD
0.590.70
188/1995
082/100
229/2:33
1.9922:01
L9922.29
0.800.99
L33/199
0,600080
1.57/1.71
01550.71
16991889
04399.3
1.39/135
TR
Acc
Fi
57.1655.16
59 59.00555 89
44
4.4842000
15.56700.55
S3.7344.57
22
48 20445 41
58.15666.99
60 60.40/58.0 99
64. 64.23/57.23
60.13/56.7 73
62.
02.9755735
62.72/62.51 51
54
70.03/67.12
35.37/35.03
1699000199 19
37.76256.39
48. 12445.84
33.54996 26
ST.9388755
68, 78/62.9
Porto
11
Ace
Acc
Fi
39,59/37.98
17.36/5.99
19.5789.7
4684443 65
35.23/2005
99447/966
45, 47.73741
49,47/41122
40.1427 80 860428612 12
53 5344542 58
45 $5,229 56
42 694404449
53.8949.55 57
46
54/42 35
-2.77AKES
48 WWNS
58 8210050011
55,98500
45.1392.19 19
4884445-70 70
55.9820.99 79
41/56.6
63.90/77.11
69.59/68.46
Fi
S4. 82
52 00000001 64
1000 07
61.90/5.11
Ace
25 40/1995
22 26/15335
58. 070
77
46 49005.00 000
64.63/56.33
T-Drive
SPD
Ace
Fi
384991685
11,76/20.99
38.5221
24 2411110000
26 72/2000
39 50/20/2235
$3.09/51.8 11.09/1181
46 177774111
38 88.00090
51
ST.28477
96
6.65/99
63.84/%6.44 04
TSim
DAD
SED
98
$773331
0.68/882
0.910198
0.618881
0.77008
0.250 84
2 1/2XX
0.569.72
TR
Ace
Fi
21.22/5.82
19,342.65 65
27 275991366
7166926.71
35.73/21.77
35 14
69
42.05/41.0
46. 18.1883.77
52.
4R 85
Tencent
MM
Fi
15,39/1440
3011118711
82.06223.06
44.61/11339
46.08/4883
48,
8686699114 14
61.33/50.2 29
Acc
23.62/18.91
33.73/66 12
58.18/77994 94
39 94/46/622 24
46 46.82/4405 05
49.0547.82
49 58441.61
66/46/50
Gowalla
TUL
Ace
Fi
16.18/5.38
6.36/1
23.28/11.45
19.3176.15 28
24.16/26.00
09
29.28/28.15
29.71/20:3
31.42/20.75
36.092199
37, 37,92/26.94
36.7113360
37,58/33.44 48
49 60
38.76
SHL
TMI
Ace
Fi
44 44.23/40.24
15,92/51.15
40,91/38 66
20.24/99.0 69
47,47/36.50 50
54.0644..6
$3.21/45. 14
46 4633/33650 50
59. 70/5.88
52 12.88/499.23 23
56, 31
16558888.88
65.72/56.97 97
59.83511 59
74.34/68.0
71.54/6367
TSeg
Acc
F1
23.77/18.14
30.2014.39
29.1 1/211/2
21V1833
30.36/28.69
36 46.4233010
39.98/33.00
42.28832.83
43.21/37.51
45.42/36.95
42,76:52.45
53.75/51.17
47.13/46.17
The percent sign of the F. score and accuracy results is omitted.
S-TDP refers to various SOTA methods siugle trajectory data preparation task.
This demonstrates that simply training separate models for individual tasks cannot capture the shared spatio-temporal knowledge needed for generalized trajectory reasoning. Second, although LLM- based tabular data preparation methods exhibit moderate zero-shot performance due to the base LLM's inherent generalization ability, they still fall short. In contrast, FedTDP improves performance by at least 32.26 %. The gap stems from the fact that generic tabular LLMs treat trajectory data as unordered rows, overlooking the sequential, temporal. and spatial dependencies essential for mobility modeling. Third, compared with SOTA I.MM spatio-temporal analysis methods, FedTDP achieves improvements ranging from 4.84% to 45.22%. These methods do not incorporate TDP-specific knowledge and cannot adapt to the diverse semantics required by 10 heterogencous TDP tasks. In contrast, FedTDP leverages the Trajectory Knowledge Enhancer (TKE) to inject trajectory-aware priors and unify task instructions, enabling both the SLM and LLM to perform robust reasoning across unseen tasks and unseen domains. Overall, the results confirm that the base LLM alone provides limited benefits, and the substantial performance gains arise from FedTDP's trajectory- aware knowledge enhancement and federated trajectory learning design.
5.2 ABLATION STUDY
We evaluate the effectiveness of cach module by systematically removing one at a time, yielding FedTDP without TPA (w/o TPA), without TKE (w/o TKE), and without FPO (w/ FPO). The results are shown in Fig. 5 First, the performance of FedTDP is slightly degraded compared to w/o TPA, as TPA can not fully capture the spatio-temporaa information of the trajectory data, leading to a marginal performance decline when using TPA. Besides, FedTDP has a little in runtime and communication costs with approximately 5GB additional communication over 10 rounds, because TPA transmits higher-dimensional embedding data instead of three-dimennional spatio-temporal points. However, to safeguard data privacy, the use of TPA in the FedTDP framework is essential. Second, removing TKE causes a dramatic performance drop with at least 27.52% degradation, highlighting that the base LLM'' s inherent generalization ability insufficient for TDP reasoning. TKE introduces trajectory-aware prompting, off offsite-tuning, sparse-tuning, and bidirectional knowledge distillation, all of which guide the LLM/SLM to acquire TDP-specific semantics. Notably, models without TKE also incur higher training costs because they must update more parameters. These results confirm that TKE is the primary source of FedTDP's strong cross-task task and cross-datased generalization. Finally, the performance does not change significantly compared to w/o FPT. but its training runtime and communication overhead are significantly reduced by almost 4 times less. This reduction is because FPO can reduce data transmission and improve training efficiency.
9

---

Published as a conference paper at ICLR 2026
FaITDP
wio TPA
wio TKE
wio FRO
197
Time Deom
Size (C
1R.
Task
Task
Efficincyy Teiinggg efficincyy
Efficieccy
(a) Training performance
Testing performance
(0) Testing efficincc
Figure 5: The ablation study
5.3 MODEL GENERALIZATION STUDY
To evaluate the proposed FedTDP framework generalization different numbers of training tasks, we system- atically remove the training task from back to front based their order in Table As illustrated Fig. 6 the results indicate that the performance of FedTDP across various tasks de- clines as the number of training tasks decreases. This decline is primarily attributed the reduced acquisition of TDP knowledge, which adversely affects generalization. Notably, when the number of tasks is reduced to one (i.e., training Fe solely on the anomaly detection task using Geol.ife), the performance also falls below that of S-TDP in Table ?
AD
TI MM V
TUI
G
NF
SPD TR
TSim
80%
60%
F: searre
40%
2.1
Seen Tasks
# Seen Tasks
(a) Training performance
(b) Testing performance
Figure 6: Generalization study
5.4 EFFICIENCY STUDY
Fig. 7 shows the communication costs (in GB) and running times (in hours) of various methods across all TDP tasks. During the training process, the proposed framework incurs the largest communication size because it must transfer embeddings and model pa- rameters, whereas L.M-based meth- ods transmit all perturbed data, gen- erated through differential privacy, to
||]
PromptGAT
UnIT
LirbanaaP
640
Tine (bours)
Time (bours)
3000
ann CBB)
(GB))
Commanicaion
Ruitans
Cummannaaron
Efficiency
Effielency (b) Testing
Training
Figure Efficiency study
the server in the first round training and do not require data transmission the following rounds
of training. Furthermore, the runtime of FedTDD is reduced by factor of 11.3 to 14.2 compared to other --aseded methods, effectively mitigating the high computational costs typically incurred by LLMs due to their massive parameter sizes. In the testing phase, the communication size of FedTDP is nearly identical to that of S-TDP and 1.4 to 1.8 times less than that of other LLM-based methods, which require transferring all data the server, whereas FedTDP only transmits the data necessary for cross-client TDP. Additionally, the runtime of FedTDP is 2.6 to 4.8 times lower than that of other LLM-based methods, further underscoring efficiency.
5.5 ADDITIONAL EXPERIMENTS
We further evaluate FedTDP across the following aspects. We evaluate the performance of different LLMs and SLMs to examine the influence of backbone choice in Appendix (.4 We aim to study the robustness under hyperparameter settings in Appendix D.5
CONCLUSION
This paper presented FedTDP, unified federated framework for trajectory data preparation (TDP). FedTDP integrates three key components: (1) a trajectory privacy autoencoder designed to protect sensitive data while preserving spatio-temporal correlations; (2) trajectory knowledge enhancer that develops TDP-oriented large language models (LLMs); and (3) a parallel optimization mechanism six datasets across ten TDP tasks demonstrated the framework's 's superior effectiveness, efficiency, and robustness compared to state-of- the-art methods. Limitations and future directions of this paper discussed in Appendix
to boost computational efficiency. Extensive experiments
10

---

Published as a conference paper at ICLR 2026
7 ACKNOWLEDGMENT
This work was supported in part by the NSFC under Grants No. (62402422, 62025206, U23A20296, and 62472377). Yongjiang Talent Introduction Programme (2024A-162-G) Zhejiang Provincial Natural Science Foundation of China under Grant No. LZ25F020001, and Zhejiang Province's "Lingyan" R&D Project under Grant No. 2024C01259. Ziquan Fang is the corresponding author.
ETHICS STATEMENT
We affirm that this work fully adheres to the ICLR Code of Ethics. We do not collect, use, or release any new human subject data. All experiments are conducted on established and publicly available datasets, which have been widely used in prior academic research.
REPRODUCIBILITY STATEMENT
We are committed ensuring the full reproducibility of our work. All source code, datasets, and detailed experimental configurations are publicly available at ltttps://qithbb. com/ Section 5 provides comprehensive overview of the evaluation setup, including the specific datasets and baseline methods. For theoretical claims, complete proofs for Theorems 1 and 2, along with the theoretical privacy analysis, are provided in Appendices C. C.4 and C.2 Detailed descriptions of all datasets, including their statistics and the specific quality issues they exhibit, are found in Appendix [.I] Detailed descriptions of all baselines are found in Ap- pendix D.2 Details of evaluation metrics and hardware environment are provided in Appendix D.3
EJU-DAALY/FedIIi
REFERENCES
Dan Alistarh, Torsten Hoefler, Mikael Johansson, Nikola Konstantinov, Sarit Khirirat, and Cédric Renggli. The convergence of sparsified gradient methods. In NeurIPS, pp. 5977-5987, 2018.
Jinze Bai, Shuai Bai, Yunfei Chu, Zeyu Cui, Kai Dang, Xiaodong Deng, Yang Fan, Wenbin Ge, Yu Han, Fei Huang, Binyuan Hui, Luo Ji, Mei Li, Junyang Lin, Runji Lin, Dayiheng Liu, Gao Liu, Chengqiang Lu, Keming Lu, Jianxin Ma, Rui Men, Xingzhang Ren, Xuancheng Ren, Chuanqi Tan, Sinan Tan, Jianhong Tu, Peng Wang. Shijie Wang, Wei Wang, Shengguang Wu, Benfeng Xu, Jin Xu, An Yang. Hao Yang, Jian Yang. Shusheng Yang. Yang Yao, Bowen Yu, Hongyi Yuan, Zheng Yuan, Jianwei Zhang, Xingxuan Zhang, Yichang Zhang, Zhenru Zhang, Chang Zhou, Jingren Zhou, Xiaohuan Zhou, and Tianhang Zhu. Qwen technical report. CoRR, abs/2309, 16699, 2023.
Thomas Bayes. An essay towards solving problem in the doctrine of chances. Biometrika, 45(3-4): 296-38 315, 1958.
Tom B. Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel M. Ziegler, Jeffrey Wu, Clemens Winter, Christopher Hesse, Mark Chen, Eric Sigler, Mateusz Litwin, Scott Gray, Benjamin Chess, Jack Clark, Christopher Berner, Sam McCandlish, Alec Radford, Ilya Sutskever, and Dario Amodei. Language models are few-shot learners. NeurlPS, 2020.
Jiahe Chen, Jinkun Cao, Dahua Lin, Kris Kitani, and Jiangmiao Pang. MGF: mixed gaussian flow for diverse trajectory prediction. In Advances in Neural Information Processing Systems 38: Annual Conference on Neural Information Processing Systems 2024, NeurlPS 2024, Vancouver, BC, Canada, December 10 15, 2024, 2024a.
Wei Chen, Chao Huang. Yanwei Yu, Yongguo Jiang, and Junyu Dong. Trajectory-use linking via hierarchical spatio-temporal attention networks. ACM Trans. Knowl. Discov. Data, 18(4): 85:1-85:22. 2024b.
Yiyi Chen, Heather C. Lent, and Johannes Bjerva. Text embedding inversion security for multilingual language models. In ACI, pp. 7808-7827, 2024c.
11

---

Published as a conference paper at ICLR 2026
Pranav Singh Chib and Pravendra Singh. Pedestrian trajectory prediction with missing data: Datasets, imputation, and benchmarking. In NeurlPS, 2024.
Eunjoon Cho, Seth A. Myers, and Jure Leskovec. Friendship and mobility: user movement in location-based social networks. KDD, pp. 1082-1090, 2011.
Longchao Da, Minquan Gao, Hao Mei, and Hua Wei. Prompt to transfer: Sim-to-real transfer for traffic signal control with prompt learning. In AAAI, pp. 82-90, 2024.
Rong Dai, Li Shen, Fengxiang He, Xinmei Tian, and Dacheng Tao. Dispfi: Towards communication- efficient personalized federated learning via decentralized sparse training. In ICMI., volume 162, pp. 4587-4604, 2022.
Yuwei Du, Jie Feng, Jie Zhao, Jian Yuan, and Yong Li. Trajagent: An Ilm- llm-based agent framework for automated trajectory modeling via collaboration of large and small models. arXiv preprint arXiv:2410.2044. 2024.
Cynthia Dwork, Frank McSherry, Kobbi Nissim, and Adam Smith. Calibrating noise sensitivity in private data analysis. In TCC, pp. 265-284, 2006.
Mohamed Y. Eltabakh, Zan Ahmad Naeem, Mohammad Shahmeer Ahmad, Mourad Ouzzani, and Nan Tang. Retclean: Retrieval-bar based tabular data cleaning using Ilms and data lakes. Proc. VLDB Endow. 17(12):441144424 2024.
Ju Fan, Zihui Gu, Songyue Zhang, Yuxin Zhang. Zui Chen, Lei Cao, Guoliang Li, Samuel Madden, Xiaoyong Du, and Nan Tang. Combining small language models and large language models for zero-shot NL2SQL. Proc. VLDB Endow., 17(1 (1:21)))22766666 2024.
Yangxin Fan, Xuanji Yu, Raymond Wieser, David Meakin, Avishai Shaton, Jean-Nicolas Jaubert, Robert Flottemesch, Michael Howell, Jennifer Braid, Laura S. Bruckman, Roger H. French, and Yinghui Wu. Spatio-temporal denoising graph autoencoders with data augmentation for photovoltaic data imputation. Proc. ACM Manag. Data, (1l):50:1-50:15 2023.
Yuchen Fang, Hao Miao, Yuxuan Liang, Liwei Deng, Yue Cui, Ximu Zeng. Yuyang Xia, Yan Zhao, Torben Bach Pedersen, Christian S. Jensen, Xiaofang Zhou, and Kai Zheng. Unraveling spatio- temporal foundation models via the pipeline lens: A comprehensive review. IEEE Transactions Knowledge and Data Engineering, pp. 1-24, 2026.
Ziquan Fang, Changhao He, Lu Chen, Danlei Hu, Qichen Sun, Linsen Li, and Yunjun Gao. A lightweight framework for fast trajectory simplification. In ICDE, pp. 2386-2399, 2023.
Robert M Fano and David Hawkins. Transmission of information: A statistical theory of communica- tions. American Journal of Physics, 29(11):793-794 1961.
FGDC. Geospatial otg. http://wwww..oooooo/oooooo/ooaaa 2015.
https: //tp:://wwww.. www
Qiang Gao, Xiaohan Wang, Chaoran Liu, Goce Trajcevski, Li Huang, and Fan Zhou, Open anomalous trajectory recognition via probabilistic metric learning. In IJCAI, pp. 2095-2103, 2023.
Zihui Gu, Ju Fan, Nan Tang, Lei Cao, Bowen Jia, Sam Madden, and Xiaoyong Du. Few-shot text-to-sql translation using structure and content prompt learning. Proc. ACM Manag. Data, 1(2): 147:1-147:28. 2023.
Dan Hendrycks and Kevin Gimpel. Gaussian error
linear units (gelus). arXiv preprint
0rXiv:1606.08415, 2016.
Charlie Hou, Akshat Shrivastava, Hongyuan Zhan, Rylan Conway, Trang Le, Adithya Sagar, Giulia Fanti, and Daniel I Lazar. Pre-text: Training language models on private federated data in the age of 1lms. In ICML, 2024.
Danlei Hu, Ziquan Fang, Hanxi Fang, Tianyi Li, Chunhui Shen, Lu Chen, and Yunjun Gao. Estimator: An effective and scalable framework for transportation mode classification over trajectories. IEEE Trans. Intell. Transp. Syst., pp. 1-12, 2024a.
12

---

Published as a conference paper at ICLR 2026
Edward J. Hu, Yelong Shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang. Lu Wang, and Weizhu Chen. Lora: Low-rank adaptation of large language models. In ICLR, 2022.
Yujia Hu, Yuntao Du, Zhikun Zhang, Ziquan Fang. Lu Chen, Kai Zheng, and Yunjun Gao. Real-time trajectory synthesis with local differential privacy. In ICDE, pp. 1685-1698, 2024b.
Yu-Hsiang Huang, Yu-Che Tsai, Hsiang Hsiao, Hong-Yi Yi Lin, and Shou-De Lin. Transferable embedding inversion attack: Uncovering privacy risks in text embeddings without model queries. In ACL, pp. 4193-4205, 2024.
G. Kreer. question of terminology. IRE Trans. Inf. Theory, 3(3):208, 1957.
Solomon Kullback and Richard A Leibler. On information and sufficiency. The annals of mathemati- cal statistics, 22(1):9--8, 1951.
Nayeon Lee, Wei Ping, Peng Xu, Mostofa Patwary, Pascale Fung, Mohammad Shoeybi, and Bryan Catanzaro. Factuality enhanced language models for open-ended text generation. In NeurIPS, 2022.
Peng Li, Yeye He. Dror Yashar, Weiwei Cui, Song Ge, Haidong Zhang, Danielle Rifinski Fainman, Dongmei Zhang, and Surajit Chaudhuri. Table-gpt: Table fine-tuned GPT for diverse table tasks. Proc. ACM Manag. Data, 2(3):176, 2024a.
Zhonghang Li, Lianghao Xia, Yong Xu, and Chao Huang. GPT-ST: generative pre-training of spatio-temporal graph neural networks. In NeurlPS, 2023.
Zhonghang Li, Lianghao Xia, Jiabin Tang, Yong Xu, Lei Shi, Long Xia, Dawei Yin, and Chao Huang. Urbangpt: Spatio-temporal large language models. In KDD, pp. 5351-5362, 2024b.
Zhonghang Li, Lianghao Xia, Yong Xu, and Chao Huang. Flashst: A simple and universal prompt- tuning framework for traffic prediction. In ICML, 2024c.
Chenxi Liu, Qianxiong Xu, Hao Miao, Sun Yang, Lingzheng Zhang, Cheng Long, Ziyue Li, and Rui Zhao. Timecma: Towards llm-empowered multivariate time series forecasting via cross-modality alignment. In AAAI, pp. 18780-18785 2025.
Qingxiang Liu, Xu Liu, Chenghao Liu, Qingsong Wen, and Yuxuan Liang. Time-ffm: Towards Im-empowered federated foundation model for time series forecasting. In NewrlPS, 2024a.
Yu Liu, Qian Ge, Wei Luo, Qiang Huang, Lei Zou, Haixu Wang, Xin Li, and Chang Liu. Graphmm: Graph-based vehicular map matching by leveraging trajectory and road correlations. IEEE Trans. Knowl. Data Eng.. 36(1):184-199) 2024b.
Ziqiao Liu, Hao Miao, Yan Zhao, Chenxi Liu, Kai Zheng, and Huan Li. Lighttr: A lightweight framework for federated trajectory recovery. In ICDE, pp. 4422 4434, 2024c.
Hao Miao, Ziqiao Liu, Yan Zhao, Chenjuan Guo, Bin Yang. Kai Zheng, and Christian S. Jensen. Less more: Efficient time series dataset condensation via two-fold modal matching. Proc. VLDB Endow. 18(2):226-23)) 2024a.
Hao Miao, Yan Zhao, Chenjuan Guo, Bin Yang, Kai Zheng, Feiteng Huang, Jiandong Xie, and Christian S. Jensen. A unified replay- continuous learning framework for spatio-temporal prediction on streaming data. In ICDE, pp. 1050-1062, 2024b.
Hao Miao, Yan Zhao, Chenjuan Guo, Bin Yang, Kai Zheng, and Christian S. Jensen. Spatio-temporal prediction on streaming data: A unified federated continuous learning framework. IEEE Trans. Knowl. Data Eng.. :7(4):211 26-21400 2025.
Mashaal Musleh and Mohamed F. Mokbel. KAMEL: A scalable bert-based system for trajectory imputation. Proc. VLDB Endow., 17(3):525-$55 538, 2023.
Avanika Narayan, Ines Chami, Laurel Orr, and Christopher Ré. Can foundation models wrangle your data? Proc. VLDB Endow,, 16(4):738 746,738-746,. 2022.
OpenStreetMap. Openstreetmap. httta://www..gensstreetmmgg org 2025.
http://wwwwc..
13

---

Published as a conference paper at ICLR 2026
OpenWeatherMage Openweathermap.
2025.
PIPL. Personal information protectioon law of the people's republic of china. httt::/en.npo.
gov. -n cddrrdlll....... 2ttiaaocccc/22211////_660333300
htm 2021. Chapter I1, Section 2, Article
28; Section 3, Article 36.
Porto. Ecml/pkdd 15: Taxi trajectory prediction.
https: www www.kaggle.ccm//cccc
pkde-15-predict- taxlecttttai--ei
2015.
Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, Ilya Sutskever, et al. Language models are unsupervised multitask learners. OpenAl blog, 1(8):9, 2019.
Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter J. Liu. Exploring the limits of transfer learning with a unified text-to-text transformer. J. Mach. Learn. Res., 21: 11:14011140:67 2020.
Ronald L Rivest, Adi Shamir, and Leonard Adleman. A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM, 21 1978.
Frank Rosenblatt. The perceptron: probabilistic model for information storage and organization in the brain. Psychological review, 65(6))386, 1958.
Adi Shamir. How to share secret. Commun. ACM, 22(11))612661111, 1979.
SHI.. Sussex-huawei locomotion dataset.
wtw.:/sshlddttsst.orrr 2017.
Congzheng Song and Ananth Raghunathan. Information leakage in embedding models. In CCS, pp. 377-390, 2020.
Jingwei Sun, Ziyue Xu, Hongxu Yin, Dong Yang. Daguang Xu, Yudong Liu, Zhixu Du, Yiran Chen, and Holger R. Roth. Fedbpt: Efficient federated black-box prompt tuning for large language models. In ICML, 2024.
Yongxin Tong, Yuxiang Zeng, Yang Song, Xuchen Pan, Zeheng Fan, Chunbo Xue, Zimu Zhou, Xiaofei Zhang, Lei Chen, Yi Xu, Ke Xu, and Weifeng Lv. Hu-fu: efficient and secure spatial queries over data federation. VLDB J. 34(2):19, 2025.
Hugo Touvron, Thibaut Lavril, Gautier Izacard, Xavier Martinet, Marie-Anne Lachaux, Timothéc Lacroix, Baptiste Rozière, Naman Goyal, Eric Hambro, Faisal Azhar, Aurélien Rodriguez, Armand Joulin, Edouard Grave, and Guillaume Lample. Llama: Open and efficient foundation language models. CoRR, abs/2302.13971, 2023.
UMP.
Uber movement platform.
https://cionews: co. in/ ubberr 2022.
da data- aetta-governance-Fraeeee
Yanbo Wang. Jian Liang, and Ran He. Towards eliminating hard label constraints in gradient inversion attacks. In ICLR, 2024.
Guangxuan Xiao, Lin, and Song Han. Offsite-tuning: Transfer learning without full model. CoRR, abs/2302.04870,, 2023.
Mengyi Yan, Yaoshu Wang, Kehan Pang, Min Xie, and Jianxin Li. Efficient mixture of experts based on large language models for low-resource data preprocessing. In KDD, pp- 3690-377,7,, 2024.
Lin Yao, Zhenyu Chen, Haibo Hu, Guowei Wu, and Bin Wu. Privacy preservation for trajectory publication based on differential privacy. ACM Trans. Intell. Syst. Technol., 13(3):42:1-42:21, 2022.
Jing Yuan, Yu Zheng, Chengyang Zhang, Wenlei Xie, Xing Xie, Guangzhong Sun, and Yan Huang. T-drive: driving directions based on taxi trajectories. SIGSPATIAL, pp. 99-108, 2010.
Yuan Yuan, Jingtao Ding, Jie Feng, Depeng Jin, and Yong Li. Unist: A prompt-empowered universal model for urban spatio-temporal prediction. In KDD, pp. 4095-4106, 2024.
14

---

Published as a conference paper at ICLR 2026
Jianyi Zhang, Saeed Vahidian, Martin Kuo, Chunyuan Li, Ruiyi Zhang, Tong Yu, Guoyin Wang, and Yiran Chen. Towards building the federatedgpt: Federated instruction tuning. In ICASSP, pp. 6915-6919, 2024a.
Qiong Zhang, Taochun Wang, Yuan Tao, Fulong Chen, Dong Xie, and Chuanxin Zhao. Trajectory privacy protection method based on differential privacy in crowdsensing. IEEE Trans. Serv. Comput., 17(6):4423-445 2024b.
Wenhao Zhang. Zimu Zhou, Yansheng Wang, and Yongxin Tong. DM-PFL: hitchhiking generic federated learning for efficient shift-robust personalization. In KDD, pp. 3396-3408, 2023a.
Xinyi Zhang, Qichen Wang, Cheng Xu, Yun Peng, and Jianliang Xu. Fedknn: Secure federated k-nearest neighbor search. Proc. ACM Manag. Data,
2024c.
Zijian Zhang, Xiangyu Zhao, Qidong Liu, Chunxu Zhang, Qian Ma, Wanyu Wang, Hongwei Zhao, Yigi Wang, and Zitao Liu. Promptst: Prompt-enhanced spatio-temporal multi-attribute prediction. In CIKM, pp. 3195-3205, 2023b.
Joshua C. Zhao, Atul Sharma, Ahmed Roushdy Elkordy, Yahya H. Ezzeldin, Salman Avestimehr, and Saurabh Bagchi. Loki: I Large-scale data reconstruction attack against federated learning through model manipulation. In SP. pp. 1287-1305, 2024.
Lele Zheng, Yang Cao, Renhe Jiang, Kenjiro Taura, Yulong Shen, Sheng Li, and Masatoshi Yoshikawa. Enhancing privacy of spatiotemporal federated learning against gradient inversion attacks. In DASFAA, volume 14850, pp. 457-473 2024.
Yu Zheng, Xing Xie, and Wei- Ying Ma. Geolife: A collaborative social networking service among user, location and trajectory. IEEE Data Eng. Bull., 33(2):32-39) 2010.
Junyi Zhu, Ruicong Yao, and Matthew B. Blaschko. Surrogate model extension (SME): A fast and accurate weight update attack on federated learning. ICML, volume 202, pp. 43228-43257, 2023.
Ligeng Zhu, Zhijian Liu, and Song Han. Deep leakage from gradients. In NeurlPS, volume 32, 2019.
15

---

Published as a conference paper at ICLR 2026
APPENDIX
Appendix A
Related Work
Trajectory Data Preparation
A.2
Large Language Models for Other Data Preparation
A.3
Large Language Models for Spatio-Temporal Data Analysis
Appendix B
Notation and Trajectory Data Preparation Task
18
Appendix C
Additional Methodology Details
Proof of Theorem 1
19
Theoretical Privacy Analysis
20
Examples of Trajectory Prompt Engineering
20
Proof of Theorem 2
Multi Task Training
C.6
Examples of LLM/SLM on TDP Task
Appendix D Experimental Details
26
D.I
Dataset
26
D.2
Baseline
26
D.3
Evaluation Metrics and Implementations
D.4
Model Base Study
28
D.5
Parameter Sensitivity Study
Appendix E
Limitation and Future Study
28
Appendix F
LLM Usage Statement
29
16

---

Published as a conference paper at ICLR 2026
APPENDIX
In the subsequent sections, present supplementary materials to provide more details of this paper, offering deeper insights and additional technical details for readers seeking further clarification. The appendix is organized follows.
In Section A, we present a systematic review of related work to help readers understand the key development areas relevant this paper, including (i) the latest trajectory data preparation methods, (ii) applications of large language models in other data preparation, and (iii) recent ad advancements in large language models for
data analysis.
In Section B, we summarize the preliminary of notations and trajectory data preparation tasks for better understanding our work, including (i) the frequently used notations and (ii) detailed description of trajectory data preparation tasks.
In Section C, we provide the additional methodology details to support the analysis shown in the main body of this paper, including (i) complete theoretical proofs of Theorems and 2, (ii) practical examples of trajectory data preparation tasks using the trajectory prompt engineering of the proposed trajectory knowledge enhancer, and (iii) the training process of FedTDP.
In Section D, we describe the extensive experimental details to provide more information about experimental settings and further demonstrate the superior performance of the proposed FedTDD framework, including (i) datasets description, (ii) compared baselines introduction, (iii) evaluation metrics and implementations details, and (iv) the detailed experimental results of model base and parameter sensitivity studies.
In Section E, we discuss several limitations of the proposed FedTDP framework that warrant further exploration.
In Section F, provide transparent account of the role Large Language Models (LLMs) played in the preparation of this manuscript, in accordance with ethical research practices and ICLR's commitment to research integrity.
A RELATED WORK
A.1 TRAJECTORY DATA PREPARATION
Numerous Trajectory Data Preparation (TDP) methods have been proposed to improve the quality of trajectory data for trajectory data preparation tasks. For the anomaly detection task, ATROM (Gao al., (023) addresses the critical challenge of anomaly recognition in open-world scenarios through the development of probabilistic metric learning model, which significantly improves the accuracy of anomaly detection in complex environments. For the trajectory imputation task, Kamel (Musleh) & Mokbel 2023) proposes scalable architecture that incorporates additional real trajectory points to predict the missing trajectory data, improving the accuracy of trajectory imputation. For the map matching task, GraphMM (Liu et al. 2024b) leverages the graphical structure using graph neural network to effectively model the topology of road network and trajectory features, improving the accuracy of map matching. For the trajectory-user link task, AttnTUL (Chen et al. (024b) introduces a hierarchical spatio-temporal attention neural network, which co-encodes local trajectory transition patterns and global spatial dependencies to establish links between trajectories and users more accurately. For the travel mode identification task, Estimator (Hu et al. (2224a) proposes an effective and scalable framework that partitions the traffic space into disjoint spatial regions based on traffic conditions, improving the accuracy of travel mode identification. For the trajectory simplification task, S3 (Fang et al. 2023) presents lightweight framework consisting of two chained to-euueec--e modules, which is integrated within graph neural architecture. improving the accuracy and efficiency of trajectory simplification. For the trajectory recovery task, LightTR (Liu) et al. 2024c) presents an efficient framework using local trajectory embedding module, robust feature extraction capabilities while significantly reducing computational overhead.
However, none of these studies have considered data privacy constraints. They typically assume that the trajectory data collection is centralized, which introduces a significant risk of privacy leakage, especially in federated learning environments. In addition, all of them are single-task methods. When
17

---

Published as a conference paper at ICLR 2026
Table 3: Notation and description
Notation
Description
P
spatio-temporal point consisting of location and time (1, A trajectory consisting of multiple spatio-temporal points {p1, (2,,22... P2....}
T
ST
A sub-tran sub-trajectory of the trajectory T
S
data silo that represents a region A client that represents a region The trajectory database in a client C A set of clients {C1, C2....)
C
D
C
D
A set of trajectory datasets {D1, D2....}
OLLM,OSLM
The large language model and small language model
handling multiple TDP tasks, different models need to be trained for each specific task. It not only demands substantial time and computational resources but also results in poor model generalization ability. In contrast, we aim to propose a unified federated framework to support various trajectory data preparation tasks while safeguarding trajectory data privacy.
A.2 LARGE LANGUAGE MODELS FOR OTHER DATA PREPARATION
A few works on table data preparation using Large Language Models (LLMs) have been proposed recently. For instance, MELD (Yan et al. 2024) introduces a general solver for low-resource table data preparation, leveraging domain-specifer experts trained on limited annotated examples. Besides, TableGPT (Li et al.. 2024a) presents table-tunin teneettningg paradigm, where LLMs are fine-tuned using various table tasks synthesized from real tables to enhance the model's ability to understand and process table-related tasks. Moreover, Narayan al. (2022) explores the performance of LLMS for table data preparation tasks, which evaluates their performance on five data cleaning and integration tasks through prompt-based methods.
offexre-of-experts architecture to support merging and augmentation of
However, these works specifically tailored for table data preparation and to trajectory data preparation tasks. They lack the necessary understanding of trajectory data and do not account for the spatio-temporal characteristics and complexity of trajectory data preparation tasks, making them unsuitable for such applications. In contrast, we aim to develop TDP-oriented LLM to effectively support various trajectory data preparation tasks.
directly applicable
A.3 LARGE LANGUAGE MODELS FOR OPATIO-TEMPORE DATA ANALYSIS
There are few spatio-temporal LLMs proposed (Li et al. 2024c Zhang et al. 2023b Li et al. 2023), which have achieved superior performance in spatio- spatio-tempora downstream applications. For example, UrbanGPT (Li al.) 2024b) integrates spatio-tempord dependency encoder with command adjustment paradigm to enhance the LLMS' understanding of complex temporal and spatial interdependencies. Besides, UniST (Yuan al., 2024) develops general-purpose model for urban spatio-temporal prediction through diverse data utilization, effective pre-training, and knowledge- guided prompts. In addition, PromptGAT (Da et al. 2024) employs prompt-based grounded action transformations to analyze system dynamics by leveraging reasoning capabilities of large language models to understand environmental impacts on traffic patterns.
However, none of them have considered trajectory data quality. If the quality of trajectory data is extremely poor, the performance of spatio-temporal large language models in downstream tasks will not be satisfactory either. In contrast, we aim to explore the powerful capabilities of large language models for trajectory data preparation to enhance the quality of trajectory data.
B NOTATION AND TRAJECTORY DATA PREPARATION TASK
Notation and Description. We first present the frequently used notations and descriptions in this paper, listed in Table
18

---

Published as a conference paper at ICLR 2026
Table 4: Trajectory data preparation task
Task Category
Task
Description
Anomaly Detection (AD)
Detect anomalous trajectory
Trajectory Imputation (TT)
Predict missing points
Data Cleaning
Noise Filtering (NF)
Filter point noise
Stay Point Detection (SPD)
Identify stationary points
Map Matching (MM)
Align trajetory road network
Data Matching
Trajectory-Usee Linking (TUL)
Associate trajectories
users
Data Annotation
Travel Mode Identification (TMI)
Identity transportation mode
Trajectory Simplification (TSim)
Remove number of points
Data Reduction
Trajectory Segmentation (TSeg)
Divide a trajectory segments
Data Augmentation
Trajectory Recovery (TR)
Recovery complete trajectory
Detnct
Prodict
Filter out
Detect
Map
oi
Aboorral armomsa
A munally detectiun
(bl Trijectory impulation
Noise filering
detection
(o) Mipp matching
Tink
Tdenilly
Simpliy
Segment
Recover
Erajectory
Pejjecory simplificaiion
Trjactory segmentation
(1 Tijoctory menney
Figure 8: The supported trajectory data preparation tasks
Trajectory Data Preparation Task. Besides, we summarize the supported trajectory data preparation tasks of the proposed FedTDP in this paper, as shown in Table E with the rough processing of each task shown Fig.
C ADDITIONAL METHODOLOGY DETAILS
C.I PROOF OF THEOREM
We provide the complete theoretical proof of Theorem proposed in this paper that provides the correctness of the trajectory privacy autoencoder model aggregation, as detailed below.
Proof. According to Eq. we can get the result aggregating masked parameter blocks {p(k) ((A) p(0) for all clients, as formally shown below:
IC
IC
Σ
ag
ski
(10)
i=1
i=1
Here, sk,, = sky, and au
=
oga
thus we can get the result formally shown below:
jC|
c
Σ
Σ
aiy # skij
Σ
(ais ski, + +g, * sky,)
(11)
i=jt1j=1
The aggregation ((k) of the masked parameter block is formally shown below:
|c|
ci
|c|
(kk
p
(k)
ay
skij
p (k)
(12)
1&
19

---

preserving Published as a conference paper at ICLR 2026
C.2 THEORETICAL PRIVACY ANALYSIS
The privacy protection mechanism of the proposed FedTDP framework is built upon the Trajec- tory Privacy Autoencoder (TPA), which protects trajectory data privacy while maintaining spatio- temporal correlations. Besides, it develops a decentralized aggregation approach based on secret sharing (Shamir 1979) that ensures the parameters of the TPA model remain confidential against trajectory data recovery or inference through embedding (Song & Raghunathan, 2henn Chen ct al. 2024c. Huang et al. 2024) and gradient (Wang et al., 2024; Zheng et al., 2024 Zhu et al. 2023) inversion attacks. Specifically, the privacy of our framework is rigorously protected through two safeguards to defend against advanced embedding and gradient inversion attacks:
To prevent embedding inversion attacks, we ensure that the TPA model is kept private and never ex- posed to the server. The server only receives encoded embeddings without access to the embedding model parameters, thereby breaking the necessary precondition for embedding inversion. Without knowledge of the embedding model, reconstructing raw trajectories from embeddings is infeasible.
To prevent gradient inversion attacks during TPA model aggregation, secret-sharing protocol for secure model aggregation. Instead of exchanging raw gradients, the TPA model is split into several parameter blocks that are then masked using pairwise secret keys before transmission. Then, each client is responsible for aggregating one block without access to other clients' model updates, ensuring that no client can reconstruct another client's data from the gradients. The correctness of this aggregation scheme is formally proven in Appendix C.I.
design decentralized
Overall, our privacy guarantee stems from isolating the TPA model from the server and protecting the TPA model during the federated optimization process. To rigorously analyze the capability of TPA, we first define the threat model as follows.
Threat Model. Following prior works (Zhag et al. 2024c| Tong et al., 2025 Zhao et al. 2024) in federated learning, we assume the server acts as semi-honest adversary who will honestly execute required operations (e.g., aggregation) but also remains curious about the private client data. In the F-TDP problem, the server seeks to reconstruct clients' raw trajectory data using adversary's 's knowledge, which includes the client model architecture, including the client model architecture, the privacy-preserving mechanism, and the encoded embeddings uploaded by clients.
Based on this, leakage, i.e., [TT E), which measures the information about original trajectory data T that can be inferred from encoded embeddings E transmitted the server, as shown below:
mutual information (Kreer 1957) to quantify the upper bound of privacy
I(T; H(T) H
(13)
where H(-) denotes the entropy. Since derived from T through the encoder O the conditional entropy H(T E)) can be decomposed as:
(T) = Eeg. Pe [H (nc))] (0 E),
(14)
where Ogne is drawn from prior distribution Pe and θ is the parameter space. Besides, both (T]F,, (fnc) and H Ff E)) are large because Opw is private and inaccessible to the server. Conse- quently, the conditional entropy H(T remains high, leading minimal privacy leakage T(T; E). Furthermore, leveraging Bayes' theorem (Bayes) 1958) and Fano's inequality (Fano & Hawkins 1961), the probability P. of the attacker recovering T incorrectly satisfies:
H(P.) + Palog T 2 (T))E),
(15)
where T denotes the trajectory data space. The large HTT)E) results in a correspondingly high Pa. indicating a low likelihood of successful reconstruction of the original trajectory data, which further underscores the effectiveness of TPA in protecting trajectory privacy.
C.3 EXAMPLES OF TRAJECTORY PROMPT ENGINEERING
For better understanding the trajectory prompt engineering of the proposed trajectory knowledge enhancer, we show practical examples of noise filtering and travel mode identification tasks using the trajectory prompt engineering in the small language model of the client.
As shown in Fig. 9 uses the raw trajectory data in clients, consisting of spatio-temporal points i.e., 7 (pi, ......).
Task shows the task name with its description listed in Section 3
Besides, Data
20

---

Published as a conference paper at ICLR 2026
T-3: Noise Filtering
T-7: Travel Mode Identification
Task: noise filtering task. It turgets identifying and removing irrelevant spalio-temporal puints that deviale from a Inieecooyy These noisy points can result from GPS inacouracics, signal interference, or sensor malfunctions.
Task: is travel mode identification task. aims to identify the travel mode trajectory based on the moving paltern data. The iravel mode is usually the walk, bike, bus, or car.
Data: the trajectory data consisting of spatio- temporal points is (lon,, lat, f)). (lon lat, (2), ...
Data: the trajectory data consisting of spatio- temporal points is {llo,, lat, ft), (lons, lat,, fs), ...--
Information: is sunny with an average temperature of 15. The road network of the map is {ids, sturt-lon, start-lat;, stop-lon, stop-lats), (idy sturt-lony, start-lat,, stup-lony stop-latz), wd..
Information: the weather is sunny with an average temperature of 15.
Format: the output should be the trajectory data.
Format: the output should the travel mode.
Model response: the result of noise filtering is {lonn lat, time,), (long, laly, time:).....
Model response: the travel mode is car.
Figure The example of trajectory prompt engineering in clients
Additionally, Information includes optional road network and weather data. Specifically. sunny and 15 represent the weather tokens during the trajectory, id denotes the segment ID, start-lon and start-lat indicate the segment's longitude and latitude at the starting point, and stop-lon and stop-lat denote the segment's longitude and latitude at the stopping point. Specifically, we utilize the weather data for these tasks and the road network for the travel mode identification task. Moreover, Format refers to the expected output data of the task. We anticipate the outputs of noise filtering and travel mode identification to be the trajectory data and travel mode, respectively. Finally, the model's response should return the expected results in Format. Note that, in the server Data uses embeddings uploaded by clients, consisting of encoded
points i.c., E = {ei, .
Note that the inclusion of the "Information" field in the Trajectory Knowledge Enhancer (TKE) is task-specific and manually configured based on domain knowledge, rather than automatically determined by the model. For instance, road network information is indispensable for the Map Matching task, as understanding road topology is crucial. In contrast, weather information is optional and only incorporated when external conditions are expected affect mobility behavior. For example, in the Travel Mode Identification task, weather can influence the choice of transportation mode. This design ensures flexibility, enabling the integration of the most relevant contextual factors for each TDP task while avoiding unnecessary noise.
C.4 PROOF OF THEOREM 2
We provide the complete proof for Theorem 2, which gives the probability that layer L,; is selected during LoRA sparse-tuning when M layers are sampled without replacement according to their normalized change ratios R(L;).
Proof. We consider the standard weighted sampling without replacement procedure. Let R(L,) denote the probability of selecting layer L, at the first draw. After each draw, the selected layer is removed and the remaining probabilities are renormalized.
Step 1: Probability of selecting L; at the first draw. Since the first draw is directly sampled according to R(L;), we have
Pi(L)) = R(L.)
(16)
Step 2: Probability of selecting I.; at the second draw. For L, be selected at the second draw, some layer I.j, (ii # i) must be drawn first, after which L, is sampled from the remaining layers. The probability of this event is
R(La))
R(I,g,) 1- -R((5)))
(17)
21

---

Published as a conference paper at ICLR 2026
Summing over all possible ja we obtain
R(Ln) R(1,))
Pa(L.) - R(L.) Σ
(18)
fi
Step 3: Probability of selecting L, at the third draw. For Lg to be selected at the third draw, two distinct layers Lnj, and Lja (J1 * j2 7 i) must be drawn first, in any order. The probability of specific sequence (21,22 followed by is
R( R(L)) 1 R(L,)) 1 R(L,)) R(L
R(L,)
(19)
Thus,
R(L,)) (1 -1- R(L,))) - R(TT))) R((
Pa(L,) = R(L.)
E
(20)
fud2 $1#12
Recursive step: Probability selecting L, at the M-th draw. Extending the above pattern, L to be selected exactly at draw M, the first M - draws must be any sequence of distinct layers
(J......M jM-1),
je x i, Ju # jo.
(21)
and the M-th draw selects L, from the remaining probability mass. Thus, the probability of one such sequence is
M-1
R(L,.)
R(L.)
R(
II
(22)
1-
R(L;.)
1 IA
M- R(L5.)
t=2
Therefore, the probability of selecting L, at draw M is
N
R(Ln) ... R(Li 1)
(m)L))= = R(L))
(23)
(1 R(L,))) ... (1-
M-1 R(L,))
D jeHt Ja
Final Expression. The probability that L, is selected in any of the M draws thus
M
N
R(L,))
P(Li, M) Σ
P,( P((L))=((L,) R(L.) + R(L))
Σ
+...
R((x5.)
j=1
f1
3171
(24)
N Σ j jeHt, JaHjs
R(L.)) ...h)....((.))
+R(L))
(1- R(L,)) ... (1-EN M-1 R(L,)))
Correctness Veritication. We finally verify that the derived probabilities satisfy Ed PLL, M) M, i.e., the expected number of selected layers is exactly M.
Recall that (b4 denotes the probability that layer Lg is selected at the k-th draw. By definition,
M
P(L, = Σ Pa(L.),
and thus
N
N M
M N
M) = ΣΣ Pa(L))
= ΣΣ Pa(L.).
=
k=
It therefore suffices to show that for each draw k EN and consider any concrete sequence of previously selected layers sequence, the probability of selecting layer L, at step is
- (L.) = 1. Fix particular draw index A
Conditional on this
R(L))
Pa(L.)
I R(L
22

---

Published as a conference paper at ICLR 2026
Algorithm 1: The training on the server Input: the number of training rounds 7R for round = 0,-.., - TR 1 do
f- IsFrozen(r) // Get the frozen status of this round;
if f False then
- (C) // Get the embeddings data from clients;
E Connect(E) // Connect into complete embeddings;
else
+ GedFrozenData(rr 1) // Get the frozen data;
prompt - TKE(E) // Construct the prompt the embeddings:
- OLM (prompt) // Input the prompt data to the LLM; o (p)it(o) Split the output of the LLM;
10
a1
if f == False then
for client number = 0, ... |C] do
12
Send(o; 0z, Ct) // Send split results to respective clients;
for any i that has not been selected in the first k -1 draws. Summing over all remaining layers, obtain
R(L))
Je-1 R(L,) Eieth Σk=1 R(Tg))
1 1 R(T.je) 1 E R(T.g.)
Σ # 1e.J....ee-111
1 1- EE R(T,))
In other words, for any fixed history (fi,..,, Ja.....,J--ll jk-1), the denominator 1 1-E R(L;) is exactly canceled by the sum of the remaining R(La). Averaging all possible histories of the first k: draws does not change this fact, and we still have M,V Ps (Li) 1. Therefore,
k-1
N
M N
M
Σ
-I=M,
k=
which shows that the expected number of selected layers is indeed M, as desired.
C.5 MULTI-TASK TRAINING
Due to the diverse range of trajectory data preparation tasks that need to be addressed, we propose multi-task training strategy to enhance the model's 's learning and generalization capabilities. Specifi- cally, prepare trajectory dataset applicable to most trajectory data preparation tasks and construct labels for each task. During the training phase, we exccute multiple trajectory data preparation tasks on the same trajectory data input, calculate the loss for each task, and jointly optimize the model formulaically shown below:
L= Lr2
LT-10
(25)
where Lyz is the loss of trajectory data preparation task T-i listed in the Section 3 Note that the proposed FedTDP framework can be easily extended to support other trajectory data preparation tasks benefiting from its modular architecture, decoupled data processing pipeline, and variable model base
Training Algorithm. For convenient method reproduction, we provide detailed training process of the entire FedTDP framework, which can be divided into the server and client, as shown in Algorithms I and 2.
In the server (i.e., Algorithm 1), the input is the number training rounds (line 1). For each training round it begins get the frozen state (lines 2-3). If is not frozen, the server gets the trajectory embeddings E from clients and connects them, or it gets local frozen in the last training round (lines 4-9). Then, the server uses TKE construct the TDP prompt for the LLM and get the output (lines 10-11). Finally, the server splits it into several parts and sends them to respective clients if is not frozen (lines 12-18).
23

---

Published as a conference paper at ICLR 2026
Algorithm 2: The training on the client
Input: the number of training rounds 7R and server s for round r O...., 7R do
D GetData() Get the local trajectory data; f IsFrozen(r) // Get the frozen status of this round; f = False then
E Enc D) // Encode the trajectory into embeddings;
Send(E, E, s) // Send the embeddings data to the server;
prompt - D) Construct the prompt of the data; o' 4 (stm(prompt) // Input the prompt data to the SLM;
f False then
Ger(s) // Get the result from the server;
11
0 Dec(o) // Decode the server's ' result;
12
else
GelFrozenDatt(r- // Get the frozen data; result t TKE(d', o) // Compute the distillation result; 14
In the client (i.e., Algorithm 2), the input are the number of training rounds and the server (line 1). For each training round r, it begins to get the trajectory data D and frozen state f (lines 2-4). If f is not frozen, clients encode D into embeddings and send them the server (lines 5-8). Then, clients TKE construct the TDP prompt for the SLM and get the output (lines 9-10). If f is not frozen, clients get the LLM's output o from the server and decode it, or it gets local o frozen in the last round 1 (lines 11 11-16). Finally, clients use TKE to compute the final result between o and (lines 17-18).
Complexity Analyses. We also give complexity analyses for Algorithms 1 and 2. Specifically, given the number of trajectory embeddings data [E] from all clients, the complexity of Algorithm is O( * 7R MC), where MC is the model complexity of the LLM. Given the number of trajectories [D] in the client, the complexity of Algorithm O(D) complexity of the SLM.
TR MC'), where MC' is the model
C.6 EXAMPLES OF LLM/SLM ON TRAJECTORY DATA PREPARATION TASK
To better explain what the LLM/SLMM actually learns, we provide qualitative examples of LLM/SLM outputs on local trajectory simplification task and cross-client trajectory imputation tasks.
Local Trajectory Simplification Task. For local trajectory simplification task, the client's SLM processes a sub-trajectory, as shown in Fig. I0 Specifically, (i) the raw data is first normalized using MinMax scaling, (ii) the client uses the Trajectory Knowledge Enhancer (TKE) construct a structured prompt, and (iii) the client's SLM processes this prompt and output the simplification result, where shows that it removed the second and last points.
Cross-Client Trajectory Imputation Task. For cross-client trajectory imputation task, two clients hold sequential -rajetrjjessoiis of the same user, as shown in Fig. Specifically, (i) these two clients first normalized their local raw data, respectively. (ii) each client uses the TPA to encode its sub-trajectory into embeddings sent to the server (For brevity, we denote these embeddings as [pl, p2, p3, ()] for the first client and [p5, p6] for the second client.), (iii) the server aligns the embeddings and use TKE to construct a prompt, (iv) the server's 's LLM processes this prompt and output the imputation result, (v) the result is split and sent back to clients, and (vi) the first client uses TPA to decode the server's output for p4: (0.2021, 0.707531, 0.612032), with the original format: (120195 957233, 1 116.66446. 39.91442).
24

---

Published as a conference paper at ICLR 2026
Local Trajectory Simplification
Processing
Raw Data: [(299163833, 116,61667. 39.85 (33851 (74), (1201964432, 167. 19.85175), (1201965032. 116,69 167. 39.8577)) (1201965622, 116.69172. 39,85208), (1201965632. 116.69172, 39.85208), (1201966232, 116.69172, 39 85199, (120196632, 116.69171.
39.85196), (1291967432, 16.69171, 39.85182)
Normalized Data: (59,616, 0.772114, 0,576568) (0.2561, 013561,0,777 0.772114, 0,576674), (0.2606,
0.772114, 0.576679), (0. (, 0.7721,4, (..7724400 (9.2651, 0.772140, 0.576860), (0.2696, 0,772110 0.576809), (0.2711 0.57679))) (0.2786, 0.772135, 0.576713)
Prompt
Tusk: it is a Injeclory simplification lask. aims to reduce the number of spulic-lemporal
points in Injectory while preserving essential shape and features.
Data: the trajectory datu consisting of sputio-temporal points is {[(0 2516, 0.772114, 0. 0.666,8),
(11.2611, 0.772114, 0.576674), (0 2606, 1.772114, 0.576679). (0.2651, 0.772140, 0.576850). (0.2651. 0,772140, 0.576860), (0.2696, 140, 0,576809). (0.2741, 0.772135. 0.576792). (0.2786,, 0,772135, 0.576713)]3
Information: nonc.
Format: the output should the trajectory data.
Output
Model response: the result of trajectory simplification (022166, 0,7721 0.576568), (0.2606. 0.772114. 0,576679), (0.2651, 0.772140, 0.576860), (0.2651, 0.77244, 0.576800), (0 2696 0.772140, 0.576809), (0.2741, 0. 072135., 0.576792)
Figure 10: The example of local trajectory simplification
Cruss-Clicnt Trajectory Imputation
Processing
Raw Data I: [(1201955434, 116.49625, 39.9146), (1201956033, 116.5096,, 39.91071). (120 1956633, 16.52231, 58.91588). (1
Normalized Data 1886, 0.672904, 0,612130), 1931, 0.679691, 0.609936), 19.6. 0.686134, 0.612852), O]
Raw Data 2: [(1201957833, 116.59512. 39.90798). (1201958433, 116.61153. 39.88277). 1950033,3 65522, 39.8622)]
Normalized Data [(0.2066, 0.723098, 0. 0.608396), (0.2111, 0.731429, 0.594173), (0.2156, 0.753610, 0.582569)]
Prompt
Task: is a trajectory imputation task. It aims to rocon a complete trajectory by predicting or estimating the missing points basod on available spatio-tomporal data, This often oceurs when GPS signals are lost or data collection is intercupted.
Data: the traj enjorry duta consisting of spatio-lemporal points is [pl, p2, O. p4, p6).
Information: none.
Format: the output should be the trajectory data.
Output Model response: the result trajectory imputation [pl, pl. p5,
Figure 11: The example of cross-client trajectory imputation
25

---

Published as a conference paper at ICLR 2026
Table 5:
The statistics of dataset
Dataset
trajectories
# points
Quality Issue
Task
Positional inaccuracies,
ADS, 11, MM, TUI,
GeaLife
182
24,876,978
noise, lower precision
TMI. TSim,
Porto
442
83,409,386
Anomalies and missing data
AD and
NF, TR.
T-Drive
10,336
17.662,984
Noisy and incomplete points
SPD, and TSim
Tencent
40,966
1,610,216
Inuocurate points
MM
Gowalla
107,092
6,442,890
Sp Sparse and non-contimuoss data
TUL
SHT.
109,390
Duplicate records
TSeg TMI
D EXPERIMENTAL DETAILS
D. DATASETS
We evaluate the proposed FedTDP framework using datasets, including Geolife (Zheng al.
2010), Porto 2015). T-Drive (Yuan et al. 2010), Tencent (Liu et al. 2024b), Gowalla (Cho et al.
2011 and SHL (2117). with their statistics shown in Table as detailed below.
GeoLife. It collected 182 trajectories with 24,876,978 spatio-temporal points, used for the training tasks, including Anomaly Detection (AD), Trajectory Imputation (TT), Map Matching (MM), Trajectory-User Link (TUL), Travel Mode Identification (TMI), Trajectory Simplification (TSim), and Trajectory Recovery (TR) tasks. It contains various quality issues such as positional inaceu- racies, data noise, and lower precision due to irregular sampling intervals and sensor limitations, which make suitable for various trajectory data preparation tasks.
Porto. collected 442 trajectories with 83,409,3386 spatio-temporal points, which contains quality issues such as anomalies and missing data, used for AD and TI testing tasks.
T-Drive. It collected 10,336 trajectories with 17, 77,662,984 pemporl points, which contains quality issues such as noisy and incomplete points, used for NF, TR, SPD, and TSim testing tasks.
Tencent. It collected 40,966 trajectories with 1,610,216 spatio-temporal points, which contains quality issues such as inaccurate points due to the low sampling rate, used for the MM testing task.
Gowalla. It collected 107,092 trajectories with 6,442,890 spatio-temporal points, which contains quality issues such as sparse and non-continuous data, used for the TUL testing task.
SHI. It collected 3 trajectories with 109,390 spatio-temporal points, which contain quality issues such as duplicate records, used for TSeg and TMI testing tasks.
D.2 BASELINES
We compare the proposed FedTDP framework with state-of-the-art baselines, as shown in Table 6
First, we compare FedTDP with various Trajectory Data Preparation (TDP) methods in single TDP task (referred to S- S-TDP), including ATROM (Gao et al. 2023) for the AD task, Kamel (Muslch & Mokbel, 2023) for the TI task, GraphMM (Liu et al. 2024b) for the MM task. AttnTUL (Chen et al.
2024b) for the TUL task, Estimator (Hu et al. (024a) for the TMI task, S3 (Fang et al. 2023) for the TSeg task, and LightTR (Liu et al. 2024c for the TR task, as detailed below.
ATROM. It solves the anomaly detection task in open-world scenarios and introduces a new probabilistic metric learning model.
Kamel. It proposes scalable system that inserts additional real trajectory points to improve the accuracy of the trajectory imputation task.
GraphMM. It develops the graphical nature of the map matching task to exploit the road network and trajectory graphical topology.
AttnTUL. It proposes hierarchical trajectory attention neural network for co-encoding local trajectory transition patterns and global spatial dependencies to solve the trajectory-user link task.
Estimator: It partitions the entire traffic space into disjoint spatial regions based on the traffic conditions for the travel mode identification task.
26

---

Published as a conference paper at ICLR 2026
Table 6: The compared baselines
Category
Method
ATROM
Anomaly Detection
2023
Kamel
Trajectory Imputation
2023
GraphMM
Map Matching
2024
S-TDP
AttoTUr
Trajectory-Usee Linking
2024
Estimator
Travel Mode Identilication
2024
Trajectory Simplilication
2023
LightTR
Trajectory Recovery
2024
FM4DP
2022
Large Language Models for Table Data Preparation
MI
2024
TableGPT
2024
All tasks for evalustion
PrompicAT
Large Language Models for Spatio-Temporyy Data Analysis
UmiST
2024
UrbanGiT
2024
$3. It presents a lightweight trajectory segmentation task framework augment the trajectory representation paradigm with geo-semantics.
LightTR. It develops local trajectory embedding module that provides higher computational efficiency for the trajectory recovery task.
Besides, we compare FedTDP with three methods using Large Language Models (LLMs) for
table data preparation, including FM4DP (Narayan et al. 2022). MELD Yan et al. 2024), and TableGPT (Li et al. 2024a), as detailed below.
FM4DP. It helps LLMs understand table DP tasks, which uses data cleaning and integration table DP tasks prompt tasks and evaluates the performance of LLMs on these tasks.
MELD. It employs the vixture-of-expertt architecture support the merging and augmentation of experts trained on the domain-spectt
experts trained on limited annotated examples.
TableGPT. It proposes a table-tuning paradigm using various table tasks synthesized from real tables as the training data to help LLMs understand the table data and perform table tasks.
Moreover, we compare FedTDP with three LLM-based models for spatio-temporal data analysis, including PromptGAT (Da et al. 2024), UniST Yuan et al. 2024), and UrbanGPT (Li et al. 2024b), as detailed below.
PromptGAT. uses the LLM to analyze system dynamics, leveraging the context and spatio- temporal data to understand how weather, traffic, and road conditions affect traffic dynamics.
UniST. It proposes general-purpose model, which is designed for urban spatio-temporal prediction in various urban scenarios to capture the complex spatio-tempora relationship.
UrbanGPT. It integrates spatio-temporal dependency encoder with a command adjustment paradigm, which enables LLMs to understand complex spatio-temporal interdependencies.
D.3 EVALUATION METRICS AND IMPLEMENTATIONS
For evaluation, we use Synchronized Euclidean Distance (SED) for the trajectory simplification task and F, scores for other tasks, where lower SED and higher F, indicate better performance. Model efficiency is further assessed by runtime and communication size.
All baselines are run under their optimal settings. To ensure fairness in F-TDP, we extend baselines with differential privacy (Dwork et al. 2006). where clients perturb local trajectory data before transmitting to the server, since FedTDP inherently preserves privacy through TPA module. All experiments are conducted in federation of 9 nodes (1 server and 8 clients), each equipped with two Intel Xeon CPU E5-2650 12-core processors, two GeForce RTX 3090 GPUs, and 100 MB/s internet bandwidth. To simulate the real-world F-TDP scenario, we partition each dataset according to geographic regions. Specifically, we divide the geographic area covered by a dataset into non- overlapping regions, each assigned distinct client. A complete trajectory that traverses multiple regions is segmented at the region boundaries, and each resulting bbb-rrajectory is stored locally by the corresponding client.
27

---

Published as a conference paper at ICLR 2026
Liore
GPT3
Quenn
S--alll
GPT7-Smal
TSSmoll
90%
9075
6075
60%
4209
+075
407
30%
40%
2095
11
0%
5113
1H1
0%
52113
Tack
Task
Task
Task
(a) Training performance of LLMs
(b) Testing performance of LLMs
(c) Training perforannce of SLMs
(d) Testing performance of SLMs
Figure 12: Large language model and small language model base study
D.4 MODEL BASE STUDY
To evaluate the impact of various model bases on the proposed FedTDP framework. we choose widely used model bases for the LLM (Llama-8B (Touvron et al., 2023), GPT3-7B (Brown et al. 2020), and Qwen-7B (Bai et al. 2023) and SLM (GPT3-Smail- 125M (Brown et. 2020), GPT2- Small-137M, (Radford et al. 2019), and T5- 155-Smal-600 (Raffel et al. 2020)). Besides, to evaluate the impact of different LLMs on FedTDP, we use GPT3-Small as the client's SLM while we use Llama as the server's s LLM to evaluate the impact of different SLMs on FedTDP. The results are shown in Fig. 12 As observed, Llama achieves optimal performance in most TPD tasks for the server's 's LLM, followed by GPT3 and then Qwen. In contrast, GPT3-Small demonstrates the best performance for the client's s SLM, succeeded by T5-Small and then GPT2-Small. Consequently, we adopt Llama and GPT3-Small as the default server's LLM and client's SLM in other experiments, respectively.
D.5 PARAMETER SENSITIVITY STUDY
We evaluate the effects of hyperparam- eters of the proposed FedTDP frame- work (i.e., the training layers ratio m of LoRA pparse-tuning in the TKE module), as shown in Fig. 13 where change the m from 25% 100%. We can observe that as m increases, the performance of FedTDP improves slightly. However, this improvement comes the cost of increased training time and communication size, as the number parameters that need be trained and transmitted also rises when m is increased. Therefore, the suggested value of m is 25% or less, as long as the model performance with the value of acceptable.
AD O-10 A 7 TUL
4- SPD
TR
TSm
Runtine
Communiction
80%
Stze (GBb)
1.9
60%
Time
50%
50% Layers
Layers
(n) Performance
(b) Training efficiency
Figure 13: Parameter sensitive study
E LIMITATION AND FUTURE STUDY
Despite its promising results, this work has certain limitations.
First, while FedTDD excels at preparing trajectory data for downstream tasks, it is not designed as direct analysis engine for tasks like clustering, pattern mining, or long-term forecasting. Specifically, many downstream analysis tasks are highly sensitive to the quality of input data. FedTDP's strength in noise filtering and imputation directly enhances the signal-to-noiss. ratio for these tasks. However, a model trained on Fed FedTDP-processeed data may still fail if the semantic structure of the data (c.g.. complex movement patterns, high-level behavioral semantics) inherently beyond the representation capacity of the underlying LLM/SLM. For instance, while FedTDP can perfectly map GPS point to a road segment, it does not inherently learn the motivation behind a detour or the cultural context of stay point. Extending FedTDP to support these tasks would require fundamentally rethinking its objective: shifting from a data preprocessor to a semantic interpreter. This would necessitate integrating task-specific knowledge graphs. incorporating higher-order temporal dependencies, and potentially moving away from the pure prompt-based paradigm to a more end-to mo--to-end generative architecture, which would dramatically increase complexity and computational cost. We view this as
28

---

Published as a conference paper at ICLR 2026
critical, non-trivial research direction, and current work establishes necessary, high-qualit data foundation upon which such advanced analysis models can be built.
The of LLMs the reasoning engine for TDP tasks introduces a significant black box challenge. While our TKE module provides a structured prompt, the internal decision-making process within the LLM/SLM remains opaque. The current framework outputs cleaned trajectory classification result, but it provides no explanation for why point was flagged as an anomaly, how a missing segment inferred, or which spatio-temporal features were decisive in a map-matching decision. This lack of interpretability has three critical implications:
Domain experts (e.g., urban planners, traffic engineers) are unlikely trust deploy system whose reasoning they cannot audit. A black box TDP system is unusable in safety-critical applications.
Trust and Adoption:
Debugging and Error Analysis: When the system makes an error (e.g., misclassifying a noisy point as valid stay point), it is currently impossible to diagnose whether the fault lies in the TPA encoding, the prompt design, the LLM's internal knowledge, or the distillation process.
Bias and Fairness: LLMs can inadvertently encode biases present in their pre-training data (e.g.. favoring car travel over walking in dense urban areas). Without interpretability, we cannot detect or mitigate such biases in the TDP output.
Future work must integrate techniques like attention visualization, counterfactual explanations, LLM-as-a-judge frameworks to provide post-hoc justifications for FedTDP's decisions, transforming from purely functional tool into transparent, accountable system.
F LLM USAGE STATEMENT
In the preparation of this manuscript, Large Language Models (LLMs) were used solely a general- purpose writing assistance tool to improve the clarity, grammar, and fluency of the text. The core research ideas, experimental design, data analysis, and all technical content were conceived and developed entirely by the human authors. No LLM was involved in generating novel ideas, interpreting results, or producing scientific claims. The authors take full responsibility for the accuracy and integrity of all content presented in this paper.
29


Reviews:
[{"review_id": "5fzjAsRzAK", "reviewer": "Reviewer_2n9U", "summary": "This paper proposes FedTDP, a unified federated framework to address Trajectory Data Preparation (TDP). The authors identify two major limitations in existing methods: (L1) they require centralized data, which is unrealistic due to privacy laws, leading to \"vertically partitioned\" data silos (e.g., by region); and (L2) they are task-specific (e.g., one model for imputation, another for map matching) and lack generalization. To solve this, FedTDP proposes a complex server-client architecture with a central LLM and on-device SLMs. Its core innovations are three-fold, designed to solve three new challenges: The framework is evaluated on 10 TDP tasks and 6 real-world datasets, where it reportedly outperforms 13 state-of-the-art baselines.", "questions": "Q1: Critical Privacy Question: Your privacy analysis relies on the server not being able to reverse the embedding because the encoder is private. The paper's threat model assumes that the server is “semi-honest”, but that the server receives the client's data embedding when performing cross-client tasks. Why is this approach (sending data embeddings) inherently more privacy-secure than “sending gradients” (vulnerable to gradient reversal attacks), which the paper criticizes?\nQ2: TKE Complexity: The TKE module is key to the model's high performance but is extremely complex, with four sub-components (prompts, offsite-tuning, sparse-tuning, KD) . Have you conducted an ablation within TKE to identify which of these components are essential? Is it possible the performance gain comes from just one or two (e.g., only offsite-tuning and prompting)?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.\tNovel Problem Formulation: The paper clearly defines F-TDP (Federated Trajectory Data Preparation) as a novel problem. It accurately targets two real-world challenges: (L1) vertical data partitioning due to privacy silos and (L2) the need for a general-purpose framework to replace 10+ single-task models.\n2.\tStrong Experimental Results: This is the paper's greatest strength. As shown in Table 2, FedTDP consistently and significantly outperforms 13 baselines across 10 TDP tasks and 6 datasets.\n3.\tExcellent System Design and Ablation: The ablation study in Figure 5 is highly effective. It clearly demonstrates the performance.", "weaknesses": "1.\tMisleading Privacy Guarantees: The paper's central privacy claim is unsound. It rejects Differential Privacy (DP) for degrading utility and claims its TPA + Secret Sharing mechanism provides \"formal privacy guarantees\". The paper's entire privacy for data-in-transit relies on \"computational infeasibility\", which is a (weaker) \"encryption-like\" guarantee, not the \"formal\" (mathematical, statistical) guarantee that DP provides. This core contradiction undermines the C1 contribution.   \n2.\tOverly Complex System: The FedTDP framework is a massive, complex system integrating numerous distinct technologies (TPA, Secret Sharing, SLMs, LLMs, Offsite-tuning, Sparse-tuning, KD, Split Learning, etc.). This \"kitchen sink\" approach makes the system extremely difficult to reproduce and analyze.\n3.\tQuestionable Theoretical Analysis: The mathematical derivation for Theorem 2 (LoRA sparse-tuning probability) in Appendix C.4 is overly complex and its correctness is not immediately obvious.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "QNnGZR4htW", "reviewer": "Reviewer_Dh2g", "summary": "The paper proposes \"FedTDP,\" a unified federated learning framework for Trajectory Data Preparation (TDP). It incorporates three key components: a Trajectory Privacy AutoEncoder (TPA) with secret-sharing for privacy, a Trajectory Knowledge Enhancer (TKE) to adapt LLMs to spatio-temporal data, and a Federated Parallel Optimization (FPO) method for efficiency. The authors claim superior performance over 13 baselines across 10 TDP tasks on 6 real-world datasets. Overall, the paper is well-written.", "questions": "1.\tThe TPA structure is a lightweight MLP. How does the reconstruction error of the autoencoder impact the accuracy of downstream tasks that require high spatial precision, such as Map Matching? \n\n2.\tThe privacy guarantee assumes the TPA model is private. In the federated setting, how is the secrecy of the aggregated TPA model's architecture and parameters maintained against the semi-honest server?\n\n3.\tHow much of the model's generalization to unseen tasks is due to the inherent few-shot ability of the base LLM versus the specific design of the TKE? Could a centrally fine-tuned LLM with good prompts achieve similar results without the federated complexity? These questions could be more emphasized.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1.\tThe paper does a great job of identifying and clearly describing the challenges of vertical partitioning and multi-task generalization in trajectory data preparation.\n\n2.\tThis paper conducts comprehensive experiments with enough baseline models and datasets, covering both seen and unseen tasks.\n\n3.\tThe overall quality of this paper is good, with a clear structure and well-defined modules.", "weaknesses": "1.\tThe authors advocate for three key challenges, but the solutions feel like a patchwork of existing LLM-related techniques (secret-sharing, LoRA, prompting) rather than a fundamental innovation. The core methodology remains a conventional federated learning setup augmented with off-the-shelf LLM adaptation methods, although it may be suitable for ICLR.\n\n2.\tThe motivation for the strong privacy threat model is kind of weak. The paper lacks a compelling reason for why trajectory data preparation requires such stringent protection against a semi-honest server. It should be more illustrated.\n\n3.\tThe claimed \"unified\" and \"generalized\" framework relies on manually configured, task-specific prompts and external information. This suggests the generalization is not autonomous but is significantly enabled by human-in-the-loop engineering for each task, limiting the claimed novelty.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "pGX3hB1vg9", "reviewer": "Reviewer_i8Ui", "summary": "The paper proposes FedTDP, a unified federated framework for trajectory data preparation (TDP) that addresses two key limitations of existing methods: the assumption of centralized data access and the lack of generalization across diverse TDP tasks. FedTDP enables privacy-preserving and multi-task TDP without raw data sharing with its core innovations including a lightweight Trajectory Privacy AutoEncoder (TPA) with secret-sharing aggregation, a Trajectory Knowledge Enhancer (TKE) that adapts LLMs to TDP tasks, and a Federated Parallel Optimization (FPO) strategy to reduce communication overhead and accelerate training. Evaluated on six real-world datasets across ten representative TDP tasks, FedTDP consistently outperforms 13 state-of-the-art baselines in accuracy, efficiency, and generalization.", "questions": "See Weakness.", "limitations": "", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "S1. The paper introduces a novel and well-motivated problem formulation: Federated Trajectory Data Preparation (F-TDP), a new and practical setting that addresses the realistic challenges of vertically partitioned trajectory data under strict privacy regulations.\n\nS2. FedTDP is the first LLM-based framework capable of handling 10 diverse TDP tasks within a single architecture, demonstrating impressive generalization across seen and unseen tasks and datasets.\n\nS3. FedTDP introduces novel technical contributions with three purpose-built modules: (i) TPA that enable secure aggregation while preserving spatio-temporal structure, (ii) TKE that adapts generic LLMs to trajectory semantics and TDP tasks, and (iii) FPO that improves training efficiency.\n\nS4. The paper provides rigorous theoretical privacy analysis to quantify the upper bound of information leakage, showing that the probability of successful trajectory reconstruction is low.", "weaknesses": "W1. It would be beneficial to include key experiments such as model efficiency and generalization study in the main paper rather than appendix.\n\nW2. For clarity, the caption of Figure 10 in Appendix D.4 should be revised to “Generalization Study.”\n\nW3. While Appendix E outlines the limitations of FedTDP, a more in-depth discussion of each limitation would strengthen the paper.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "xWSnpnroa1", "reviewer": "Reviewer_Lr1C", "summary": "This paper proposes FedTDP, a unified federated framework for Trajectory Data Preparation (TDP) leveraging Large Language Models (LLMs) to address limitations of existing TDP methods. Raw trajectory data often suffers from noise, incompleteness, and inconsistency, while traditional TDP approaches rely on centralized data access (conflicting with privacy regulations like PIPL) and task-specific models (lacking generalization). FedTDP, designed for vertically partitioned trajectory data across regional silos, integrates three core modules, i.e., TPA, TKE, and FPO. Experiments on 6 real-world datasets (e.g., GeoLife, Porto) and 10 TDP tasks (e.g., anomaly detection, map matching) show FedTDP outperforms 13 state-of-the-art baselines in accuracy, efficiency, and scalability, with strong cross-task generalization.", "questions": "Comments:\n\n1. Inadequate Formal Privacy Analysis: The claimed privacy guarantee of TPA relies on secret-sharing aggregation but lacks quantitative leakage bounds or empirical resistance tests against reconstruction attacks.\n\n2. Ambiguous Vertical Partition Setting: The paper assumes vertical partitioning across regions but does not clarify how overlapping or boundary trajectories are handled during training and aggregation.\n\n3. Unclear Contribution of Submodules: Although ablation studies exist, they fail to isolate interactions between TKE and FPO; improvements may overlap rather than reflect independent effects.\n\n4. Questionable Scalability: The model introduces heavy communication (≈5 GB per 10 rounds), which may be infeasible in real federated environments with limited bandwidth.\n\n5. Limited Explainability of LLM Adaptation: The proposed trajectory-aware prompt design and knowledge distillation process are heuristic and lack ablation or visualization of learned representations.\n\n6. Inconsistent Evaluation Metrics: The results mix F1, accuracy, and distance-based metrics without discussing normalization or the statistical significance of performance gains.\n\n7. Underexplored Generalization Factors: The zero-shot and few-shot evaluations lack control experiments on domain shifts, leaving it unclear whether improvements arise from pre-training, task similarity, or federated effects.\n\n8. The recommended LoRA layer ratio (m ≤ 25%) is arbitrary; no systematic method is proposed to balance accuracy and efficiency for different TDP tasks.\n\n9. FedTDP’s performance on extremely sparse trajectory data (e.g., low-sampling-rate GPS) is unevaluated, limiting its utility for real-world scenarios with poor sensor quality.", "limitations": "", "rating": 4, "confidence": 5, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- New Problem Formulation: First to formally define Federated Trajectory Data Preparation (F-TDP) for vertically partitioned trajectory data, filling the gap of federated learning research focused on horizontal partitioning.\n\n- Privacy-Preserving Design: TPA with secret-sharing aggregation provides formal privacy guarantees without sacrificing data utility (unlike differential privacy, which distorts spatio-temporal correlations via noise injection).\n\n- Strong Generalization & Efficiency: TKE enables LLMs/SLMs to generalize across 10 diverse TDP tasks, while FPO reduces communication overhead and training time, addressing the inefficiency of LLM deployment in federated settings.", "weaknesses": "- **The conclusion section of this paper is missing from the main text:** ICLR 2026 submission policy requires authors to organize the main text reasonably, which means that reviewers are not obliged to read the appendix provided by the authors.\n\n- Limited Theoretical Grounding of Privacy Guarantees: While the paper claims formal privacy protection through secret sharing, the analysis lacks rigorous proof of robustness against advanced gradient or embedding inversion attacks.\n\n- Overstated Generalization Claims: The generalization across unseen TDP tasks is not convincingly demonstrated, as performance differences might stem from dataset similarity rather than true cross-task transfer.\n\n- High System Complexity: The integration of TPA, TKE, and FPO introduces substantial architectural and computational complexity, making real-world deployment questionable.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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:

Decision: Accept (Poster)