AI Sovereignty as National Learning Capacity: A Human-Centered Learning Mechanics Viewpoint on France, the United States, and China

Technical Summary: AI Sovereignty as National Learning Capacity

Problem Statement
Current debates regarding Artificial Intelligence (AI) sovereignty in France (and globally) often treat critical dimensions—compute capacity, regulation, education, industrial deployment, and energy—as isolated policy silos. This fragmentation leads to a conceptual gap where national strategy is viewed merely as the sum of hardware investments and legal constraints, rather than as a cohesive system. The paper argues that this separation fails to address the core challenge: AI sovereignty is not solely a function of scale (e.g., number of GPUs), but a function of a nation's capacity to regulate its own information dynamics. Without a unified framework, countries risk "instability, inequality, waste, or dependency" if information injection outpaces institutional absorption, or stagnation if institutional entropy (friction, complexity, uncertainty) outpaces innovation.

Methodology: Human-Centered Learning Mechanics (HCLM)
The paper proposes a unified theoretical framework called Human-Centered Learning Mechanics (HCLM), extending a dynamical framework originally formulated for entropy-regulated representation learning in machine learning to the macro-policy level.

1. Theoretical Analogy: The authors model a national AI ecosystem as a learning system analogous to a neural network.

   • Information Injection ($IFR$): Corresponds to the input of useful knowledge, talent, capital, compute, data, and industrial experimentation.
   • Entropy Dissipation ($DFR$): Corresponds to the loss of potential value due to organizational complexity, coordination frictions, energy constraints, regulatory uncertainty, and talent mobility pressures.
   • Learning Dynamics: The evolution of national AI capability ($H_{FR}$) is governed by the differential equation:
     $$\frac{dH_{FR}}{dt} = IFR(t) - DFR(t)$$
   • The Learning Ratio: The core metric is the ratio $R_{FR} = \frac{IFR}{DFR + \epsilon}$. Sustainable sovereignty requires $IFR$ to grow faster than $DFR$ (specifically, the scaling exponent of injection $\alpha$ must exceed that of dissipation $\gamma$).

2. Economic and Game-Theoretic Integration:

   • The framework integrates Endogenous Growth Theory (Romer) and Creative Destruction (Aghion & Howitt), interpreting innovation as the reorganization of entropy where new information must be absorbed by institutions.
   • It incorporates Game Theory to model the national ecosystem as a set of strategic agents (state, universities, firms, investors). The paper demonstrates that without mechanism design, decentralized agents will under-invest in public goods (like shared compute or data) and fall into coordination failures (Prisoner's Dilemma), leading to suboptimal national learning ratios.

3. Empirical and Simulation Approach:

   • The paper constructs normalized diagnostic proxies for the US, China, and France/Europe using documented empirical anchors (Stanford AI Index, French Commission reports). These are not econometric estimates but transparent, Python-generated scenarios to illustrate the HCLM mechanism.
   • Numerical Simulations: The authors simulate three regimes (Balanced, Excessive Dissipation, Insufficient Dissipation) and coordination scenarios to demonstrate how different policy mixes affect the "residual policy-learning risk."

Key Contributions

• Unified Conceptual Framework: The paper reframes AI sovereignty from a resource-acquisition problem to a governance of information flow problem. It posits that sovereignty equals "information flow + entropy control + incentive alignment."
• Mathematical Formalization of Policy: It provides a mathematical condition for successful scaling: $\alpha > \gamma$. If the scaling exponent of institutional entropy ($\gamma$) equals or exceeds that of information injection ($\alpha$), scaling alone yields no asymptotic improvement in capability.
• "No-Free-Lunch" Lemma for Compute: The paper proves that compute-only investment strategies are insufficient. If talent, industrial absorption, and institutional reform remain bounded while compute scales, the effective information ratio remains bounded, preventing unbounded capability growth.
• Game-Theoretic Diagnosis: It identifies specific coordination challenges (e.g., university-industry gaps, data sharing) as equilibrium outcomes of rational local incentives. It argues that policy must shift from "investment races" to mechanism design that aligns private incentives with national learning dynamics.
• Measurable Policy Dashboard: The paper proposes a set of operational Key Performance Indicators (KPIs) for both injection (e.g., AI graduates, GPU-hours, adoption rates) and dissipation (e.g., grant cycle times, regulatory uncertainty, talent retention) to diagnose national AI health.

Results and Comparative Diagnosis
Using the HCLM diagnostic proxies, the paper offers a comparative analysis:

• United States: Characterized by a high information injection ($I$) driven by venture capital, frontier firms, and rapid commercialization. The primary challenge is managing the resulting entropy (energy, social risk, concentration).
• China: Characterized by a coordinated scaling regime with strong industrial policy and state-led deployment, resulting in intermediate information ratios but constraints in openness and global compute access.
• France/Europe: Possesses strong scientific and engineering assets (high potential $I$) but suffers from high institutional dissipation ($D$) due to coordination frictions and administrative complexity.
  • Simulation Outcome: The paper's "France HCLM reform scenario" suggests that by streamlining administration ($D_{admin}$), consolidating coordination ($D_{coord}$), and strengthening industrial absorption, France could nearly double its learning ratio ($R$) without needing to replicate the US or Chinese models.
  • Regime Analysis: Simulations show that "Balanced HCLM" (coordinated growth of injection and controlled dissipation) yields stable improvement (65% loss reduction), whereas "Insufficient Dissipation" leads to instability and "Excessive Dissipation" suppresses innovation.

Significance and Claims
The paper claims its significance lies in shifting the policy discourse from a binary opposition between "techno-optimism" and "regulation-first caution" to a controlled, non-equilibrium learning regime.

• Reframing Sovereignty: It argues that AI sovereignty is not about owning the most GPUs, but about the capacity to regulate information dynamics. A country competes because it "learns better with the information it already has."
• Policy Implication: The central claim is that France (and similar economies) must move beyond simply increasing investment. The strategic objective is to increase the learning ratio ($R_{FR}$) by simultaneously increasing useful information injection and constructively managing institutional entropy through mechanism design.
• Modesty and Falsifiability: The authors explicitly state that the numerical indicators are diagnostic proxies for hypothesis generation, not definitive national rankings. The framework is presented as a "viewpoint" intended to discipline policy reasoning, with a roadmap for future empirical validation using country-year data to test the scaling laws and learning ratios proposed.

In conclusion, the paper asserts that a competitive, human-centered AI strategy requires a regime where information injection grows faster than institutional dissipation, governed by incentive-aligned mechanisms that prevent instability while maximizing the absorption of knowledge into national capability.