DriveCode:
Domain Specific Numerical Encoding
for LLM-Based Autonomous Driving

Zhiye Wang^2*, Yanbo Jiang^1*, Rui Zhou², Bo Zhang^3,4, Fang Zhang^5†,
Zhenhua Xu^1†, Yaqin Zhang³, Jianqiang Wang^1,5

¹The School of Vehicle and Mobility, Tsinghua University,
²School of Information Science and Engineering, Lanzhou University,
³The Institute for AI Industry Research (AIR), Tsinghua University, ⁴DiDi, ⁵State Key Laboratory of Intelligent Green Vehicle and Mobility, Tsinghua University

* Equal contribution, † Corresponding author

Paper arXiv Code Data

Abstract

Large language models (LLMs) have shown great promise for autonomous driving, yet their discrete tokenization of numbers not only limits precise numerical reasoning but also introduces redundant decoding steps for each value, posing challenges for vehicle control. These limitations affect both the processing of sensor measurements and the generation of precise control commands, creating a fundamental barrier for deploying LLM-based autonomous driving systems. In this paper, we introduce DriveCode, a novel numerical encoding method that represents continuous values as dedicated embeddings rather than discrete text tokens. DriveCode employs a number projector to map scalars into the language model's hidden space, enabling seamless integration with visual and textual features in a unified multimodal sequence. Evaluated on OmniDrive, DriveGPT4, and DriveGPT4-V2 datasets, DriveCode demonstrates superior performance in trajectory prediction and control signal generation, confirming its effectiveness for LLM-based autonomous driving systems.

Overview

Samples

We provide some data examples here.

Results

DriveCode consistently outperforms baselines across multiple datasets in both trajectory prediction and control signal generation tasks.

Trajectory Prediction on OmniDrive

Method	L2 Error (m) ↓
Text	3.0797
DriveCode (Ours)	2.8274

Control Signals Prediction on DriveGPT4

Method	Speed (m/s)					Turning Angle (degree)
Method	RMSE ↓	A_0.1 ↑	A_0.5 ↑	A_1.0 ↑	A_5.0 ↑	RMSE ↓	A_0.1 ↑	A_0.5 ↑	A_1.0 ↑	A_5.0 ↑
ADAPT	3.02	9.56	24.77	37.07	90.39	11.98	27.93	66.83	75.13	89.45
DriveGPT4	1.30	30.09	60.88	79.92	98.44	8.98	59.23	72.89	79.59	95.32
xVal	1.13	26.58	63.46	82.53	99.10	8.78	56.99	72.89	80.08	93.20
DriveCode (Ours)	1.08	27.50	64.60	82.99	99.10	7.71	57.18	72.54	80.25	93.71

Control Signals Prediction on DriveGPT4-V2

Method	Theta Error (degree) ↓	Point Error (L2, m) ↓	Speed Error (m/s) ↓
xVal	0.07409	0.01166	0.02162
DriveCode (Ours)	0.07377	0.01137	0.02131

Supplementary Results

Robustness Experiments

We conduct robustness experiments on normalization strategies, unit variation, numerical magnitude, and sign changes. Decimal variants such as "3", "3.0", "3.00", and "3e0" are parsed into the same floating-point value before numerical encoding.

Normalization Strategies

Comparison of normalization strategies on control signal prediction across DriveGPT4 and DriveGPT4-V2 datasets. DriveGPT4 does not include point error evaluation (marked as —).

Dataset	Method	Theta Error (deg) ↓	Point Error (L2, m) ↓	Speed Error (m/s) ↓
DriveGPT4	Raw value (DriveCode)	7.71	—	1.08
	Per-type z-score	8.90	—	1.14
	Per-type min-max	8.88	—	1.11
DriveGPT4-V2	Raw value (DriveCode)	0.07377	0.01137	0.02131
	Per-type z-score	0.07276	0.01131	0.02164
	Per-type min-max	0.07066	0.01261	0.02229

Unit Variation Robustness

Speed uses m/s, km/h, mph; angle uses degree and radian (DriveGPT4 dataset).

Setting	Speed RMSE ↓	Angle RMSE ↓
Original DriveCode	1.08	7.71
Mixed units	1.34	8.89

Numerical Magnitude Robustness

Samples are grouped by the magnitude of ground-truth values using the 33.3%, 66.7%, and 95% quantiles (DriveGPT4 dataset).

Task	GT Value Range	DriveCode	Variant	Text-only
Turning Angle	[0, 0.26)	1.1416 95% CI: 0.7626–1.4807; N=1404	1.4035 95% CI: 0.9880–1.7955; N=1403	1.5338 95% CI: 1.1637–1.8924; N=1401
	[0.26, 6.98)	2.1996 95% CI: 1.9950–2.4145; N=608	2.7438 95% CI: 2.1821–3.3726; N=608	2.7683 95% CI: 2.4180–3.1255; N=607
	[6.98, ∞)	34.1333 95% CI: 23.0185–44.7093; N=104	37.6696 95% CI: 25.9657–48.5228; N=106	38.7174 95% CI: 26.9667–50.4053; N=107
Speed	[0, 1.44)	0.6544 95% CI: 0.4411–0.8653; N=705	0.7037 95% CI: 0.4835–0.9238; N=705	0.8359 95% CI: 0.5740–1.0823; N=705
	[1.44, 7.54)	1.1763 95% CI: 1.0438–1.3050; N=705	1.2319 95% CI: 1.0848–1.3835; N=706	1.3251 95% CI: 1.1534–1.4963; N=706
	[7.54, 15.70)	1.3535 95% CI: 1.1455–1.5731; N=600	1.3422 95% CI: 1.1592–1.5386; N=600	1.4156 95% CI: 1.2430–1.6002; N=598
	[15.70, ∞)	1.0292 95% CI: 0.7689–1.3121; N=106	1.1536 95% CI: 0.8704–1.4487; N=106	1.3385 95% CI: 0.9583–1.6979; N=106

Sign Robustness

Samples are grouped into negative, near-zero, and positive intervals by the sign of ground-truth values (DriveGPT4 dataset).

Task	GT Value Range	DriveCode	Variant	Text-only
Theta	(-∞, -0.05)	9.3818 95% CI: 6.4341–12.2534; N=421	9.2308 95% CI: 6.2741–12.1288; N=421	9.8490 95% CI: 6.6775–12.6932; N=422
	[-0.05, 0.05]	1.1889 95% CI: 0.7754–1.5594; N=1251	1.4857 95% CI: 1.0493–1.9053; N=1250	1.6188 95% CI: 1.2121–1.9940; N=1249
	(0.05, ∞)	14.0074 95% CI: 7.0870–19.6879; N=444	16.3430 95% CI: 9.2816–22.5797; N=446	16.7208 95% CI: 9.4964–22.9874; N=444
Speed	(-∞, -0.05)	3.5897 95% CI: 1.6277–5.1443; N=13	3.6364 95% CI: 1.5787–5.2521; N=13	3.6722 95% CI: 1.4158–5.3855; N=13
	[-0.05, 0.05]	0.1735 95% CI: 0.1107–0.2385; N=366	0.2152 95% CI: 0.1223–0.3109; N=366	0.3085 95% CI: 0.1404–0.4671; N=366
	(0.05, ∞)	1.1533 95% CI: 1.0518–1.2607; N=1737	1.1882 95% CI: 1.0862–1.2877; N=1738	1.2948 95% CI: 1.1820–1.4103; N=1736

Ablation Studies

Variant vs. DriveCode on DriveGPT4

Method	Theta Error (deg) ↓	Speed Error (m/s) ↓
Variant	8.63	1.11
DriveCode (Ours)	7.71	1.08

Encoding Variants on DriveGPT4-V2

Method	Theta Error (deg) ↓	Point Error (L2, m) ↓	Speed Error (m/s) ↓
Text	0.07950	0.01363	0.02231
Variant	0.07078	0.01140	0.02139
Variant2	0.08877	0.01391	0.02264
DriveCode (Ours)	0.07377	0.01137	0.02131

Efficiency Analysis

Efficiency comparison between baseline models and DriveCode. Tested on DriveGPT4 dataset.

Method	Latency (s) ↓	Avg Time / Sample (s) ↓
xVal	6776.41	3.1979
Text	7152.36	3.3769
Variant	6763.79	3.1920
DriveCode (Ours)	6737.91	3.1798

Lane Change Visualization

Examples of lane changing with DriveCode: successful lane change, no collision.

Contact

For any questions, please send email to wzhiye2023 at lzu dot edu dot cn.

Citation

@misc{wang2026drivecodedomainspecificnumerical,
      title={DriveCode: Domain Specific Numerical Encoding for LLM-Based Autonomous Driving}, 
      author={Zhiye Wang and Yanbo Jiang and Rui Zhou and Bo Zhang and Fang Zhang and Zhenhua Xu and Yaqin Zhang and Jianqiang Wang},
      year={2026},
      eprint={2603.00919},
      archivePrefix={arXiv},
      primaryClass={cs.CV},
      url={https://arxiv.org/abs/2603.00919}, 
}