Derivative-State Drift

Wu, Shaoyuan

doi:10.5281/zenodo.18654119

Published 2026-02-16 | Version v1.0

Working PaperOpenPublished

Derivative-State Drift

A Continuous-Time Model of Constraint Erosion in Elite and Artificial Optimization Systems

Wu, Shaoyuan
Global AI Governance and Policy Research Center, EPINOVA LLC
https://orcid.org/0009-0008-0660-8232

Description

This working paper develops the Derivative-State Drift (DSD) framework as a continuous-time structural model of cumulative misalignment in derivative-based optimization systems. It explains how systems can remain locally coherent and dynamically smooth while gradually diverging from normative reference states when constraints are soft, enforcement is incomplete, and resource buffering attenuates penalties. The framework is applied symmetrically to elite institutional environments and artificial optimization systems, emphasizing architectural isomorphism rather than anthropomorphic analogy.

Abstract

This paper develops the Derivative-State Drift (DSD) framework as a general structural account of cumulative misalignment in derivative-based optimization systems. It formalizes agents as operating over continuous-time state vectors and selecting actions according to expected first-order state change rather than absolute state levels. When constraint enforcement is soft, probabilistic, or compensable, sensitivity parameters governing normative boundaries decay endogenously over time. The analysis establishes three core results. First, bounded state velocity does not imply bounded normative deviation. Local dynamical stability is therefore compatible with global misalignment. Second, under incomplete enforcement, constraint sensitivity exhibits monotonic expected decay, deforming the effective constraint manifold without requiring discontinuity in state trajectories. Third, resource buffering attenuates effective penalties and accelerates drift dynamics. The framework is instantiated in two structurally parallel domains: elite institutional environments and artificial optimization systems. Despite differences in substrate, both instantiate derivative-based evaluation under soft constraint regimes and mediated feedback, generating formally equivalent drift dynamics. The comparison is architectural rather than anthropomorphic. The paper concludes that alignment is not primarily a question of intention or performance optimization, but of constraint architecture design. Derivative-State Drift is a general property of optimization systems in which boundaries are compensable and feedback is incomplete. Misalignment thus emerges as the predictable long-run behavior of locally rational systems operating within deformable constraint manifolds.

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Keywords

Derivative-State Drift
DSD framework
constraint manifold
soft constraint regimes
continuous-time model
Lyapunov stability
local dynamical stability
global normative stability
constraint erosion
threshold drift
institutional drift
elite institutional environments
AI optimization systems
AI alignment
governance architecture
structural isomorphism
Goodhart's law
resource buffering
parameter stabilization
optimization systems

Subjects

AI Governance
AI Alignment
Optimization Theory
Institutional Theory
Governance Architecture
Strategic Risk
Dynamical Systems
Constraint Design
Complex Systems
Elite Governance
Machine Learning Safety
Policy Theory

Recommended citation

Wu, Shaoyuan. (2026). Derivative-State Drift: A Continuous-Time Model of Constraint Erosion in Elite and Artificial Optimization Systems (EPINOVA Working Paper No. EPINOVA–WP–F–2026–02). Global AI Governance and Policy Research Center, EPINOVA LLC. https://doi.org/10.5281/zenodo.18654119. DOI: To be assigned after Crossref membership approval.

APA citation

Wu, S. (2026). Derivative-state drift: A continuous-time model of constraint erosion in elite and artificial optimization systems (EPINOVA Working Paper No. EPINOVA–WP–F–2026–02). Global AI Governance and Policy Research Center, EPINOVA LLC. https://doi.org/10.5281/zenodo.18654119. DOI: To be assigned after Crossref membership approval.

Alternate identifiers

Scheme	Identifier	Description
DOI	10.5281/zenodo.18654119	Zenodo/DataCite DOI shown in the PDF recommended citation
DOI	10.5281/zenodo.18654118	DOI recorded in the early ORCID-derived metadata; retained as a discrepancy note for reconciliation
ORCID put-code	205788030	ORCID Public API record identifier from early metadata
EPINOVA working paper number	EPINOVA–WP–F–2026–02	Working paper number shown in the PDF title page and running header
File name	Derivative-State Drift.pdf	Source PDF file name
Short title	Derivative-State Drift	Short form of the working paper title

Related works

Relation	Identifier	Type	Description
Related EPINOVA WP-F work on AI-mediated strategic risk and the breakdown of inherited strategic logic	10.5281/zenodo.18252768
Related EPINOVA work on AI-driven institutional contraction and governance architecture	10.5281/zenodo.18090197
Related EPINOVA white book on AI governance diagnostics and structural exposure frameworks	10.5281/zenodo.18452803

References

Amodei, D., Olah, C., Steinhardt, J., Christiano, P., Schulman, J., & Mané, D. (2016). Concrete problems in AI safety. arXiv preprint arXiv:1606.06565. https://arxiv.org/abs/1606.06565
Christiano, P. F., Leike, J., Brown, T. B., Martic, M., Legg, S., & Amodei, D. (2017). Deep reinforcement learning from human preferences. Advances in Neural Information Processing Systems, 30, 4299–4307.
Goodhart, C. A. E. (1975). Problems of monetary management: The U.K. experience. In Papers in monetary economics (Vol. 1, pp. 91–121). Reserve Bank of Australia.
Hubinger, E., van Merwijk, C., Mikulik, V., Skalse, J., & Garrabrant, S. (2019). Risks from learned optimization in advanced machine learning systems. arXiv preprint arXiv:1906.01820. https://arxiv.org/abs/1906.01820
Khalil, H. K. (2002). Nonlinear systems (3rd ed.). Prentice Hall.
Mahoney, J., & Thelen, K. (2010). Explaining institutional change: Ambiguity, agency, and power. Cambridge University Press.
Manheim, D., & Garrabrant, S. (2019). Categorizing variants of Goodhart’s law. arXiv preprint arXiv:1803.04585. https://arxiv.org/abs/1803.04585
Merton, R. K. (1936). The unanticipated consequences of purposive social action. American Sociological Review, 1(6), 894–904. https://doi.org/10.2307/2084615
North, D. C. (1990). Institutions, institutional change and economic performance. Cambridge University Press.
Ostrom, E. (2005). Understanding institutional diversity. Princeton University Press.
Russell, S. (2019). Human compatible: Artificial intelligence and the problem of control. Viking.
Simon, H. A. (1955). A behavioral model of rational choice. Quarterly Journal of Economics, 69(1), 99–118. https://doi.org/10.2307/1884852
Strogatz, S. H. (2018). Nonlinear dynamics and chaos: With applications to physics, biology, chemistry, and engineering (2nd ed.). Westview Press.
Thelen, K. (2004). How institutions evolve: The political economy of skills in Germany, Britain, the United States, and Japan. Cambridge University Press.
Weick, K. E. (1995). Sensemaking in organizations. Sage.
Williamson, O. E. (1985). The economic institutions of capitalism. Free Press.

[1] Amodei, D., Olah, C., Steinhardt, J., Christiano, P., Schulman, J., & Mané, D. (2016). Concrete problems in AI safety. arXiv preprint arXiv:1606.06565. https://arxiv.org/abs/1606.06565

[2] Christiano, P. F., Leike, J., Brown, T. B., Martic, M., Legg, S., & Amodei, D. (2017). Deep reinforcement learning from human preferences. Advances in Neural Information Processing Systems, 30, 4299–4307.

[3] Goodhart, C. A. E. (1975). Problems of monetary management: The U.K. experience. In Papers in monetary economics (Vol. 1, pp. 91–121). Reserve Bank of Australia.

[4] Hubinger, E., van Merwijk, C., Mikulik, V., Skalse, J., & Garrabrant, S. (2019). Risks from learned optimization in advanced machine learning systems. arXiv preprint arXiv:1906.01820. https://arxiv.org/abs/1906.01820

[5] Khalil, H. K. (2002). Nonlinear systems (3rd ed.). Prentice Hall.

[6] Mahoney, J., & Thelen, K. (2010). Explaining institutional change: Ambiguity, agency, and power. Cambridge University Press.

[7] Manheim, D., & Garrabrant, S. (2019). Categorizing variants of Goodhart’s law. arXiv preprint arXiv:1803.04585. https://arxiv.org/abs/1803.04585

[8] Merton, R. K. (1936). The unanticipated consequences of purposive social action. American Sociological Review, 1(6), 894–904. https://doi.org/10.2307/2084615

[9] North, D. C. (1990). Institutions, institutional change and economic performance. Cambridge University Press.

[10] Ostrom, E. (2005). Understanding institutional diversity. Princeton University Press.

[11] Russell, S. (2019). Human compatible: Artificial intelligence and the problem of control. Viking.

[12] Simon, H. A. (1955). A behavioral model of rational choice. Quarterly Journal of Economics, 69(1), 99–118. https://doi.org/10.2307/1884852

[13] Strogatz, S. H. (2018). Nonlinear dynamics and chaos: With applications to physics, biology, chemistry, and engineering (2nd ed.). Westview Press.

[14] Thelen, K. (2004). How institutions evolve: The political economy of skills in Germany, Britain, the United States, and Japan. Cambridge University Press.

[15] Weick, K. E. (1995). Sensemaking in organizations. Sage.

[16] Williamson, O. E. (1985). The economic institutions of capitalism. Free Press.