GINIO: A Geometric SO(3)-Equivariant Interface for Neural Inertial Odometry

Chankyo Kim¹ · Minghan Zhu¹ · Tzu-Yuan Lin¹ · Avantika Rattan¹ · Maani Ghaffari¹

¹University of Michigan, CURLY Lab

Conference on Robot Learning (CoRL) 2026 · Austin, TX

[Paper & reviews] [Model zoo] [Data] [Reproduce Table 2] [Known issues] [BibTeX]

TL;DR. GINIO is an SO(3)-equivariant interface between an IMU window and the filter that consumes it. Given a calibrated window, the network predicts a motion measurement whose mean transforms as a vector and whose covariance transforms congruently (Σ ↦ RΣRᵀ) under any rotation of the IMU measurement frame, by construction rather than by augmentation. The same interface is instantiated on three backbones, Lie-Neuron ResNets, a Vector-Neuron version of the AirIO recurrent model, and a full-SO(3) canonicalised EqNIO-style model, and evaluated on TLIO, RIDI, NanoBench and a Fetch remounting set. Every released checkpoint ships with its SHA-256, parameter count and the paper value it reproduces (Model zoo).

Formerly imu-equivariant-learning. This repository started in 2023 as a yaw-equivariant network-coupled inertial odometry code base. GINIO is the same project matured to full SO(3) equivariance with a covariance interface, now named after the CoRL 2026 paper. Old links redirect here; the last pre-GINIO snapshot is tagged imu-equivariant-learning-final.

News

• 2026-10-18 — Code release: all three instantiations, the paper's evaluation scripts (scripts/paper/), 16 checkpoints with SHA-256 (every surviving Table 1 and Table 2 model and baseline) across TLIO / RIDI / NanoBench (release v1.0-corl2026), and the exact split lists (splits/). Repository renamed from imu-equivariant-learning to GINIO.
• 2026-10 — Camera-ready and OpenReview page (reviews included) are public. GINIO is a poster at CoRL 2026 (Nov 9–11, Austin).
• Planned — processed NanoBench split and the Fetch remounting set as a data release (pending the redistribution terms); the Fetch models and the AquaticVision evaluation could not be recovered from the original machines, see docs/KNOWN_ISSUES.md.

What is in the box

Suffix	Benchmark	What it is	Code	Released checkpoint
GINIO-W / GINIO-S	TLIO, RIDI (filter-connected)	world-frame / sensor-frame Lie-Neuron ResNet (ln_resnet) + SCEKF / InEKF	src/	W: yes · S: no
GINIO-RD / GINIO-RS	NanoBench	ln_resnet with a diagonal / spectral covariance head	src/	yes / yes
GINIO-R	Fetch remounting	ln_resnet	src/	no (lost)
GINIO-A	NanoBench	Vector-Neuron AirIO recurrent model (VN-CNN + VN-GRU), with or without an attitude channel	airio/	yes
GINIO-E	NanoBench	full-SO(3) canonicalised EqNIO-style model	eqnio/	yes

Last-Frame Alignment (LFA) expresses a window in the frame of its last IMU sample; for an SO(3)-equivariant predictor it is provably equivalent to world-frame training (Appendix D). It is implemented in src/dataloader/sequences_dataset.py and switched by the dataset path (bodyframe selects the sensor-frame branch, nolfa turns LFA off). The standalone reference implementation is scripts/lfa_preprocessing.py.

Installation

git clone https://github.com/chankyo123/GINIO.git && cd GINIO
conda env create -f environment.yml && conda activate ginio
pip install torch torchvision --index-url https://download.pytorch.org/whl/cu124   # pick the wheel for your CUDA driver

Known-good versions, optional extras and gotchas: docs/INSTALL.md.

Quick start

# 1. checkpoints (SHA-256 verified) — one benchmark or everything (~0.7 GB)
bash scripts/download_checkpoints.sh nanobench

# 2. data: TLIO golden / RIDI / NanoBench in the TLIO layout under local_data/  -> docs/DATA.md
#    (NanoBench: world-frame .npy + `python scripts/derive_body_npy.py` for the sensor-frame copy)

# 3. reproduce a Table-2 row with the released weights (NN-only, Umeyama ATE = `ate_um`)
python src/main_net.py --mode test --arch ln_resnet --body_frame True \
  --root_dir local_data/nanobench_bodyframe_nolfa_2nd_version --out_dir test_outputs/ginio_rd \
  --model_path checkpoints/nanobench_ginio_rd_t119/checkpoint_best.pt \
  --imu_freq 200 --imu_base_freq 1000 --window_time 0.775 --sample_freq 50 --batch_size 1024
#    GINIO-A rows + ID/SO(3) + equivariance / covariance-law errors:
cd airio && python -m evaluation.eval_idso3 --config configs/Nanobench/motion_body_noatt_vn_small.conf --n_rot 3

# 4. train one configuration (GINIO-RD recipe)
python src/main_net.py --mode train --arch ln_resnet --body_frame True \
  --root_dir local_data/nanobench_bodyframe_nolfa_2nd_version --out_dir models/ginio_rd \
  --epochs 170 --batch_size 256 --lr 5.44e-4 --weight_decay 2.41e-4 \
  --imu_freq 200 --imu_base_freq 1000 --window_time 0.775 --sample_freq 50 \
  --do_bias_shift --accel_bias_range 0.3878 --gyro_bias_range 0.0189 --nll_weight 1.0

Full command sheets for the three families, the filter chains (SCEKF / InEKF), the attitude-error sweep and the frozen-mean covariance study: docs/TRAIN_EVAL.md. Scripts that regenerate the paper's tables and figures: scripts/paper/README.md. A one-minute CPU self-check of the equivariance machinery: cd airio && python -m model.test_a2_spectral_equivariance (24 checks).

Model zoo

Checkpoints are assets of the v1.0-corl2026 release, one archive per benchmark plus paper_results.tar.gz (the stored outputs behind every "reproduced" value) and a SHA256SUMS file; bash scripts/download_checkpoints.sh fetches and verifies them. The table lists the 16 released folders and the paper rows they back; checkpoints/MANIFEST.md is the source of truth for hashes, parameter counts, loader notes, the 18 traps you should read before loading anything, and the 16 further surviving models that are documented but not part of this release. Table numbers follow the camera-ready PDF.

Paper row	Folder	Family / registry key	Params	Paper → reproduced	Status
Table 1 TLIO GINIO-W	tlio_ginio_w_ln189	src/ · ln_resnet (two weight sets, see MANIFEST)	0.57M	1.615 → 1.615 (ID/ID)	PINNED / ID-SO(3) CKPT_ONLY
Table 1 TLIO EqNIO	tlio_eqnio_o2	eqnio/ · eq_o2_frame_fullCov_2vec_2deep	6.02M	1.554 → 1.554 · 76.389 → 76.39	PINNED
Table 1 TLIO ResNet+SCEKF+aug.	tlio_resnet_so3aug	src/ · resnet	5.42M	1.844 → 1.842	CKPT_ONLY
Table 1 TLIO ResNet-S+InEKF	tlio_resnet_s_lfa_candidate	src/ · resnet, LFA	5.42M	2.814 → 2.876	CKPT_ONLY
Table 1 RIDI GINIO-W, Sec. 4.2 NN-only	ridi_ginio_w	src/ · ln_resnet_slope1_nobias	0.57M	0.927 → 0.927 (NN); filter cells not reproduced	PINNED / CKPT_ONLY
Table 1 RIDI "EqNIO" (SO(3)-aug.)	ridi_eqnio_o2_so3aug	eqnio/ · eq_o2_frame_fullCov_2vec_2deep	6.02M	2.408 → 2.408	PINNED / ID-SO(3) CKPT_ONLY
Table 1 RIDI ResNet+SCEKF+aug.	ridi_resnet_so3aug	src/ · resnet	5.42M	1.401 → no stored output	CKPT_ONLY
Table 2 AirIO (no-att. / with-att.)	nanobench_airio_noatt, nanobench_airio_withatt	airio/ · codenetmotion, codewithrot	0.33M / 0.39M	5.579 → 5.5785 · 1.205 → 1.2049	PINNED
Table 2 GINIO-A (no-att. / with-att.)	nanobench_ginio_a_noatt, nanobench_ginio_a_withatt	airio/ · vn_codenetmotion_small, vn_codewithrot_small	0.045M	1.430 → 1.4302 · 1.045 → 1.0453	PINNED
Table 2 ResNet1D	nanobench_resnet1d	src/ · resnet	5.43M	0.645 → 0.6455	PINNED
Table 2 EqNIO O(2)	nanobench_eqnio_o2	eqnio/ · eq_o2_frame_fullCov_2vec_2deep (NanoBench-trained)	6.03M	0.828 → 0.8282	PINNED
Table 2 GINIO-E	nanobench_ginio_e_so3aug_tlio	eqnio/ · eq_so3_frame_fullCov_2vec_2deep (TLIO-trained, zero-shot)	6.03M	0.785 → 0.7854	PINNED
Table 2 GINIO-RD	nanobench_ginio_rd_t119	src/ · ln_resnet (0.775 s window, no LFA)	0.54M	0.581 → 0.5805	PINNED
Table 2 GINIO-RS	nanobench_ginio_rs_chol_mse	src/ · ln_resnet_chol (trained without LFA)	0.80M	0.789 → 0.7887	PINNED (label caveat)

Documented in the MANIFEST but not part of v1.0-corl2026 (available on request; planned as a later asset): the Fig. 5(b) frozen-mean covariance arms, the Table 8 covariance-ablation models other than the Table 2 GINIO-RS, the Table 9 SO(3)-augmented NanoBench baselines, the 2026 ResNet+SCEKF retrain (the TLIO authors' own pretrained ResNet is the reference for that row) and eight non-paper controls. Not released because nothing survives: the Fetch models (Tables 10–12), AquaticVision (Table 13), GINIO-S on TLIO/RIDI, the RIDI ResNet+SCEKF model, the Table 2 ID/SO(3) generator for the non-equivariant rows, and the 0.273M GINIO-A originals of Table 4 (they no longer load strictly). Details and evidence: checkpoints/MANIFEST.md, docs/PAPER_ARTIFACT_MAP.md, docs/KNOWN_ISSUES.md.

Data

All loaders read the TLIO layout (one folder per sequence with imu0_resampled.npy, calibration.json, description JSON; split lists at the dataset root) under local_data/. The exact train / val / test lists are committed in splits/. Sources, conversions and caveats (including that the processed NanoBench accelerometer has gravity removed): docs/DATA.md.

Dataset	Used in	Source
TLIO golden (CC BY-NC)	Table 1, Tables 5–7, Fig. 5 / 11 / 12	CathIAS/TLIO release
RIDI	Table 1, Table 9	RIDI data_publish_v2 + scripts/ridi/ converters
NanoBench (Crazyflie 2.1, Vicon)	Table 2, Tables 4 / 8 / 9, Figs. 8–11	NanoBench; our 100 Hz world-frame conversion + scripts/derive_body_npy.py
Fetch remounting (ours)	Tables 10–12, Figs. 13–14	fetch_dataset.zip in the CoRL supplement (69 sequences)

Reproducibility notes

Three things to know before comparing numbers; everything else is in docs/EVAL_PROTOCOL.md and the MANIFEST traps.

• Metrics. Table 2 reports the Umeyama-aligned (rotation + translation, no scale) position RMSE after integrating the predicted body velocity through ground-truth attitude (ate_um); the TLIO-style ate in metrics.json is an unaligned mean error and not comparable. Table 1 mixes two filter metric codes (TLIO-metric vs EqNIO-metric); the MANIFEST says which one each value used.
• ID/SO(3). Rotate IMU channels and vector targets by the same R, transform covariance targets by RΣRᵀ, un-rotate predictions. airio/evaluation/eval_idso3.py and --test_perturb_type so3 implement this; both equivariant families are unchanged under any rotation by construction (≤ 5e-9 relative for the attitude-free GINIO-A). The with-attitude GINIO-A is equivariant only when its attitude channel is rotated like the other vectors.
• Checkpoint selection. airio/train_motion.py (upstream AirIO behaviour) selects best_model.ckpt on the config's test block, which for NanoBench is the reported 17-sequence test split, for AirIO baselines and GINIO-A alike; the RIDI val_list equals its test_list. No rotation augmentation is used for any paper model.

Discrepancies between the camera-ready and the surviving evidence (for example the Table 8 Spectral/NLL NLL and NEES cells, and the GINIO-RS "body+LFA" label) are listed with file-level evidence in docs/KNOWN_ISSUES.md; we will keep that page and the OpenReview thread in sync.

Repository layout

GINIO/
├── src/                    Lie-Neuron family (GINIO-W/S/RD/RS/R): training, test, SCEKF / InEKF trackers   [TLIO-derived]
├── airio/                  Vector-Neuron AirIO family (GINIO-A) and the AirIO baselines; run from inside   [Air-IO-derived]
├── eqnio/TLIO-master/      canonicalised family (GINIO-E) and the EqNIO O(2) baseline                        [EqNIO-derived]
├── scripts/
│   ├── download_checkpoints.sh   release assets + SHA-256 verification
│   ├── paper/                    scripts behind the paper's tables and figures (see its README)
│   ├── export/  ridi/            TorchScript exports with full covariance; RIDI -> TLIO-layout converters
│   ├── derive_body_npy.py  lfa_preprocessing.py  run_test_all.sh  run_sweep*.sh  run_finetune.sh
│   └── provenance/               diffs of the forks behind the ledger-only Table 1 / 6 / 7 numbers
├── checkpoints/MANIFEST.md        model zoo: every released checkpoint, hash, loader note, status, traps
├── docs/                   INSTALL · DATA · TRAIN_EVAL · EVAL_PROTOCOL · FILTER_EVALUATION · KNOWN_ISSUES · PAPER_ARTIFACT_MAP · RELEASE_LAYOUT
├── splits/                 exact train / val / test lists (TLIO, RIDI, NanoBench)
├── assets/                 figures used in this README
├── CITATION.cff · LICENSE · THIRD_PARTY_NOTICES.md · CONTRIBUTING.md · environment.yml · requirements.txt

The three families are modified copies of three upstreams with their own config systems, so they live in three subfolders (the way EqNIO ships TLIO-master/ and RONIN/).

License

Code written for GINIO is released under the MIT License. The repository contains modified copies of TLIO (BSD), AirIO (BSD-3-Clause), Vector Neurons (MIT), Lie Neurons (BSD-3-Clause) and EqNIO (no license file upstream; redistributed for research reproduction, see THIRD_PARTY_NOTICES.md); their terms apply to the corresponding files. Datasets are not redistributed. The checkpoints inherit the license of the data they were trained on (TLIO golden is CC BY-NC).

Acknowledgements

GINIO grew out of the public TLIO code base and would not exist without the groups who released theirs: TLIO, EqNIO, AirIO, Vector Neurons and Lie Neurons (same lab). If we have missed an attribution, please open an issue and we will fix it. Related repositories from our group: LieNeurons.

Citation

If the code or the checkpoints helped your work, please cite the paper.

@inproceedings{kim2026ginio,
  title     = {{GINIO}: A Geometric {SO(3)}-Equivariant Interface for Neural Inertial Odometry},
  author    = {Kim, Chankyo and Zhu, Minghan and Lin, Tzu-Yuan and Rattan, Avantika and Ghaffari, Maani},
  booktitle = {Proceedings of The 10th Conference on Robot Learning (CoRL)},
  year      = {2026},
  url       = {https://openreview.net/forum?id=nl8iBTm3Mt}
}

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