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Fluidity Index: Next-Generation Super-intelligence Benchmarks

Eric Ngoiya, Tianshu Bao

TL;DR

The Fluidity Index (FI) addresses a gap in evaluating true intelligence by measuring a model's adaptability to dynamic, scaling environments, focusing on accuracy relative to changes in initial, current, and future states. The approach distinguishes closed-loop from open-ended benchmarks and emphasizes closed-loop open-ended scenarios to capture real-world adaptability, including self-replenishment and higher-order token dynamics. The paper formalizes FI with mathematical definitions, defines adaptability orders, and introduces throughput-based index conditions to classify performance, supported by a simulation framework of iterative environment changes. If validated, FI could set a new standard for assessing super-intelligence by emphasizing context-switching, prediction continuity, and resourceful self-sustaining computation in evolving environments.

Abstract

This paper introduces the Fluidity Index (FI) to quantify model adaptability in dynamic, scaling environments. The benchmark evaluates response accuracy based on deviations in initial, current, and future environment states, assessing context switching and continuity. We distinguish between closed-ended and open-ended benchmarks, prioritizing closed-loop open-ended real-world benchmarks to test adaptability. The approach measures a model's ability to understand, predict, and adjust to state changes in scaling environments. A truly super-intelligent model should exhibit at least second-order adaptability, enabling self-sustained computation through digital replenishment for optimal fluidity.

Fluidity Index: Next-Generation Super-intelligence Benchmarks

TL;DR

The Fluidity Index (FI) addresses a gap in evaluating true intelligence by measuring a model's adaptability to dynamic, scaling environments, focusing on accuracy relative to changes in initial, current, and future states. The approach distinguishes closed-loop from open-ended benchmarks and emphasizes closed-loop open-ended scenarios to capture real-world adaptability, including self-replenishment and higher-order token dynamics. The paper formalizes FI with mathematical definitions, defines adaptability orders, and introduces throughput-based index conditions to classify performance, supported by a simulation framework of iterative environment changes. If validated, FI could set a new standard for assessing super-intelligence by emphasizing context-switching, prediction continuity, and resourceful self-sustaining computation in evolving environments.

Abstract

This paper introduces the Fluidity Index (FI) to quantify model adaptability in dynamic, scaling environments. The benchmark evaluates response accuracy based on deviations in initial, current, and future environment states, assessing context switching and continuity. We distinguish between closed-ended and open-ended benchmarks, prioritizing closed-loop open-ended real-world benchmarks to test adaptability. The approach measures a model's ability to understand, predict, and adjust to state changes in scaling environments. A truly super-intelligent model should exhibit at least second-order adaptability, enabling self-sustained computation through digital replenishment for optimal fluidity.
Paper Structure (14 sections, 18 equations, 7 figures)

This paper contains 14 sections, 18 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Intelligence and Adaptability Experiments
  3. Theoretical Framework
  4. Formalization of the Fluidity Index
  5. Order of Fluidity Formalization
  6. Scaling environment in Fluidity index
  7. Mathematical Formalization
  8. Adaptability Orders
  9. Throughput and Index Conditions
  10. Simulation Setup
  11. Results and Discussion
  12. Accuracy and Intelligence
  13. Advanced research
  14. Conclusion

Figures (7)

  • Figure 1: Fluidity Index Author2025.
  • Figure 2: Model size and model performance jason2022emergence.
  • Figure 3: Estimated price for processing one million input/output tokens across AI models a16z2024llmflation
  • Figure 4: Cost of the cheapest nodel achieving a minimum mmlu score (log scale) a16z2024llmflation.
  • Figure 5: 1D Region representing $\int_{\text{tokens}}^{\text{current}} \text{FI}(t) \, dt$ for Sub Optimal fluidity
  • ...and 2 more figures