Long-horizon stability in neural systems

Establish training and architectural mechanisms that ensure stable behavior of neural systems over long temporal horizons, with particular relevance to neural computer instances that aim for consistent, reproducible execution across extended tasks.

Background

The paper introduces Neural Computers (NCs) as systems that unify computation, memory, and I/O in a learned runtime state, and outlines requirements for their mature form, Completely Neural Computers (CNCs).

Achieving reliable, behavior-consistent operation over long time horizons is identified as critical for acceptance and governance of NCs. The authors note that despite theoretical results on computational power, maintaining stability over extended execution remains unresolved in practice, citing challenges such as drift and catastrophic forgetting.

References

Furthermore, ensuring stable behavior over long temporal horizons remains an open problem in neural systems.

— Neural Computers  (2604.06425 - Zhuge et al., 7 Apr 2026) in Section 4 (Position: Toward Completely Neural Computers) — From Neural Computers to Completely Neural Computers

In strongly amplifying regimes such as the Gray--Scott system, transport amplification dominates long-horizon state drift, requiring explicit trajectory regularization. Incorporating manifold-aware regularization to constrain off-manifold latent solver trajectories remains a topic for future work.

— Analysis of Error Propagation in Autoencoder-Based Reduced-Order Neural Ordinary Differential Equations  (2608.13132 - Zhang et al., 13 Aug 2026) in Section 5, Conclusion

The closed-loop result we do not prove ---the field, its host, and the interoception/modulation path considered as one system--- is exactly what CON proves for its setting. What is genuinely unoccupied in this literature is the conjunction of second order, instance-gated (time-varying) coefficients, and closed loop: REN has the loop without the first two, CON has the first and third without gating, LinOSS has only the first. We do not fill that gap here; we mark it.

— Can a Dynamic Internal Field Govern a Transformer's Cognition? Certifiability, not Superiority, in Homeostatic Compute Control  (2608.24319 - Arrabal-Campos et al., 25 Aug 2026) in Section 3, paragraph “Certified learned dynamics, and where our certificate sits” (Related work)