TAIN: Time-Aware Inertial Normalization

Code and paper source for:

Time-Aware Inertial Normalization for Irregularly-Sampled Tabular Streams Tuhan Agay, Segmora AI, 2026 [arXiv preprint (coming soon)]

What is TAIN?

The running-statistics update inside normalization layers (BatchNorm-style EMA) applies a fixed coefficient alpha regardless of the time gap between observations. TAIN is a time-aware update rule for those running statistics: it replaces alpha with alpha^(dt), where dt is the real elapsed time between consecutive observations.

# Standard EMA (time-blind)
mu_t = (1 - alpha) * x_t + alpha * mu_{t-1}

# TAIN (time-aware)
mu_t = (1 - alpha^dt) * x_t + alpha^dt * mu_{t-1}

(In the BatchNorm setting the per-step input is the batch mean mu_batch; for the single-stream tracker setting used in this paper it is simply x_t.)

This is the natural discretization of the Ornstein-Uhlenbeck process. A 30-day gap resets statistics toward current conditions; a 1-hour gap preserves accumulated inertia.

Scope of this paper. TAIN is validated as a running-statistics tracker across five real-world domain settings. Integration as a drop-in BatchNorm replacement in end-to-end tabular neural network training (TabNet, FT-Transformer, NODE) is future work.

Results

Validated on five settings drawn from four real-world data sources (5,409 entities, 659,325 observations):

Domain	Entities	RMSE Improvement	p-value	Win Rate
Retail (Rossmann)	50	+1.05%	< 0.001	40/50 (80%)
Sensor (Beijing AQ, all 12 stations)	12	+0.62%	0.0002	12/12 (100%)
Finance (US Equities, Mag-7 subset)	5	+17.32%	0.031	5/5 (100%)
ICU-Temp (PhysioNet 2012)	1,787	+3.04%	< 0.001	1,088/1,787 (60.9%)
ICU-Urine (PhysioNet 2012)	3,555	+3.78%	< 0.001	2,539/3,555 (71.4%)

ICU-Temp and ICU-Urine share the PhysioNet 2012 cohort and recording infrastructure; the two should not be regarded as fully independent corroborating domains.

Post-gap recovery increases with gap size in the largest stratum of four of five domains. The Sensor domain shows a clean monotonic relationship (7.6% to 67.6%) consistent with the Ornstein-Uhlenbeck discretization; the other domains exhibit within-domain non-monotonicities at intermediate strata. The negative ICU-Temp entity-level correlation (rho = -0.139) is verified to be a patient-acuity confound (mean gap correlates with SAPS-I at rho = -0.281 and SOFA at rho = -0.375; see verify_icu_acuity_confound.py).

Repository Structure

tain-validation/
  tain_empirical_validation.ipynb       # Source of truth for all paper results (5 domains)
  tain_empirical_validation_executed.ipynb  # Executed copy with cached outputs
  tain_validation.py                    # Older 3-domain demo script (paper uses the notebook)
  regenerate_figures.py                 # Regenerates Table 4 and Table 5 figures
  verify_icu_acuity_confound.py         # Verifies ICU-Temp SAPS-I/SOFA correlations
  paper-source/
    segmora_arxiv.tex                   # LaTeX source
    segmora_arxiv.pdf                   # Compiled paper (20 pages)
    fig_*.png                           # Paper figures
  retail/ sensor/ finance/ physionet/   # Data folders (not tracked; see Data below)
  requirements.txt

Data

Datasets are not included due to size. Download instructions:

1. Retail: Rossmann Store Sales -> extract to retail/
2. Sensor: Beijing Multi-Site Air Quality -> extract to sensor/
3. Finance: Run the notebook cell that downloads via yfinance, or place stocks_all.csv in finance/
4. ICU-Temp: PhysioNet 2012 Challenge -> extract set-a/ and Outcomes-a.txt to physionet/
5. ICU-Urine: Same PhysioNet 2012 source as above (different variable, same physionet/ folder)

Usage

pip install -r requirements.txt

# Full validation (5 domains, all tables and figures from the paper)
jupyter notebook tain_empirical_validation.ipynb

# Reproduce the figures from cached results
python regenerate_figures.py

# Reproduce the ICU-Temp acuity-confound verification (SAPS-I, SOFA correlations)
python verify_icu_acuity_confound.py

# Optional: older 3-domain demo (Retail, Sensor, Finance only)
python tain_validation.py

Citation

@article{agay2026tain,
  title={Time-Aware Inertial Normalization for Irregularly-Sampled Tabular Streams},
  author={Agay, Tuhan},
  journal={arXiv preprint},
  year={2026}
}

License

MIT License. See LICENSE for details.