# Position: Certifiable State Integrity Should Be Built from Local Validity, Not Global Scale

arXiv: https://arxiv.org/abs/2601.21249 · HTML: https://mlsanity.com/paper/2601.21249/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 43 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 18 of 18)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [Learning under Concept Drift: A Review](https://mlsanity.com/paper/2004.05785/) (2020)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [Overview frequency principle/spectral bias in deep learning](https://mlsanity.com/paper/2201.07395/) (2022)
- [A Survey for Foundation Models in Autonomous Driving](https://mlsanity.com/paper/2402.01105/) (2024)
- [Battling the Non-stationarity in Time Series Forecasting via Test-time Adaptation](https://mlsanity.com/paper/2501.04970/) (2025)
- [Mixture of Experts Made Intrinsically Interpretable](https://mlsanity.com/paper/2503.07639/) (2025)
- [GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEs](https://mlsanity.com/paper/2303.14878/) (2023)
- [State estimation with the Interacting Multiple Model (IMM) method](https://mlsanity.com/paper/2207.04875/) (2022)
- [S2GPT-PINNs: Sparse and Small models for PDEs](https://mlsanity.com/paper/2506.15687/) (2025)
- [Foundation vs. Specialized Models: Evaluating Catastrophic Forgetting in Continual Time Series Forecasting](https://mlsanity.com/paper/2510.00809/) (2025)

## Built on by (most cited first, 1 of 1)

- [White-Box Neural Ensemble for Vehicular Plasticity: Quantifying the Efficiency Cost of Symbolic Auditability in Adaptive NMPC](https://mlsanity.com/paper/2602.01516/) (2026)

## Abstract (arXiv)

Breakthroughs in language and vision have motivated increasingly general foundation models for time series and physical dynamics, where evidence is promising but less mature. In safety-critical Cyber-Physical Systems (CPS), globally parameterized dynamics models must remain valid through regime shifts, degradation, and lifecycle updates while supporting traceable assurance evidence. We argue that shared global parameters couple adaptation, frequency-sensitive fault representation, and verification evidence in ways that obstruct retained regime knowledge and bounded analysis. For systems whose operating conditions can be covered by a finite set of locally valid models, assurance evidence should be organized around those bounded models and their explicit composition, not around a single globally adapted model; increasing scale cannot supply explicit validity boundaries. HYDRA is a reference architecture for this position: frozen local specialists, runtime arbitration, and explicit coverage-gap monitoring. It illustrates how modular auditability and formal analysis of bounded components support Certifiable State Integrity, while whole-system certification, switching guarantees, and empirical validation remain separate obligations.