Fluidity Index: Next-Generation Super-intelligence Benchmarks (2510.20636v1)

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.

• The paper introduces the Fluidity Index as a novel metric that assesses AI adaptability through real-time context switching and prediction error normalization.
• It demonstrates that emergent efficiency in LLMs leads to dramatic cost reductions and scalability improvements as model size increases.
• The framework formalizes orders of adaptability via closed-loop evaluation, providing actionable insights for developing autonomous, self-sustained AI systems.

Fluidity Index: A Benchmark for Super-Intelligent Adaptability

Motivation and Context

The Fluidity Index (FI) is introduced as a next-generation benchmark for evaluating super-intelligent systems, with a focus on adaptability in dynamic, scaling environments. Traditional intelligence metrics, such as static accuracy or closed-ended task performance, are insufficient for capturing the real-time context switching and continuity required for advanced AI systems. The FI framework emphasizes the measurement of a model’s accuracy in response to deviations in environment states, thereby quantifying its ability to adapt, predict, and optimize behavior in evolving scenarios. This approach is motivated by the observed emergence of qualitative changes in model behavior as quantitative parameters (e.g., model size, compute) scale, a phenomenon well-documented in recent LLM research.

Emergence and Efficiency in LLMs

The paper situates FI within the context of emergent abilities in LLMs, where increased model size correlates with non-linear improvements in performance and efficiency. As shown in the literature, larger models not only achieve higher accuracy on intelligence benchmarks but also enable more efficient inference and quantization strategies, reducing the cost per token and facilitating scalable deployment.

(Figure 1)

Figure 1: Model size and model performance, illustrating the non-linear emergence of capabilities as LLMs scale.

This emergent efficiency is further evidenced by dramatic reductions in inference costs over time, as models surpass key intelligence thresholds. For example, the cost per million tokens has dropped by orders of magnitude as models have become more capable, with the cheapest models achieving high MMLU scores at exponentially lower prices.

Figure 2: Estimated price for processing one million input/output tokens across AI models, highlighting the rapid decrease in cost with increased model capability.

Figure 3: Cost of the cheapest model achieving a minimum MMLU score (log scale), demonstrating the economic impact of emergent intelligence.

Formalization of the Fluidity Index

The FI is mathematically defined to capture the accuracy of a model’s predictions relative to changes in the environment:

$$\text{FI}(t) = \frac{\sum_{i=1}^{n} \text{AA}_i}{\text{NC}}$$

where $\text{AA}_i$ (Accuracy Adaptation) for agent $i$ is:

$$\text{AA}_i = 1 - \frac{|\text{New Prediction}_i - \text{Old Prediction}_i|}{\text{Change in Initial Environment State}_i}$$

This formulation normalizes the prediction error against the magnitude of environmental change, penalizing both under- and over-reactions. The FI aggregates these adaptation scores across all actions and environment changes, providing a robust metric for model fluidity.

The framework further distinguishes between orders of adaptability:

• First Order: Model adapts inference tokens to current environment state.
• Second Order: Model self-replenishes compute, sustaining adaptation over time.
• Third Order: Model autonomously manages infrastructure and long-horizon tasks, achieving full self-sustained operation.

These orders are formalized via integrals over the relevant dimensions (tokens, current, time), with optimality conditions defined by throughput constraints.

Benchmarking Methodology

The FI benchmark is designed as a closed-loop, open-ended evaluation, where the environment is treated as ground truth and the model must predict and adapt to state changes without prior knowledge. Success is measured by the model’s ability to maintain high accuracy adaptation scores across iterative environment shifts, reflecting both context switching and continuity.

The simulation setup involves:

• Iterative changes in environment state.
• Measurement of prediction accuracy post-context shift.
• Assessment of intelligent allocation of resources (tokens, compute) to meet current and future needs.

This methodology addresses the limitations of closed-ended benchmarks, which become increasingly inadequate as models approach super-intelligent capabilities.

Experimental Results and Implications

Empirical results demonstrate that models with high FI scores exhibit superior context understanding and adaptability, aligning with theoretical expectations of super-intelligence. Notably, the paper highlights:

• Strong numerical results: At an MMLU threshold of 42, a 1000x reduction in price per million tokens was observed; at a threshold of 83, a further 62x reduction was achieved.
• Contradictory claim: The paper asserts that closed-ended benchmarks will always become less expensive as model size increases, due to emergent phenomena, challenging the notion that intelligence evaluation must be static.

These findings have significant implications for both the practical deployment and theoretical understanding of advanced AI systems. The FI provides a scalable, future-proof metric for benchmarking adaptability, supporting the development of models capable of autonomous, self-sustained operation in complex environments.

Advanced Research Directions

The FI framework opens avenues for research into self-interested models, where fluidity is leveraged to align agent behavior with long-term self-sustenance and optimization. This has potential applications in autonomous agents, reinforcement learning, and real-world systems requiring continual adaptation.

Conclusion

The Fluidity Index establishes a rigorous, mathematically grounded benchmark for evaluating super-intelligent adaptability in AI systems. By focusing on accuracy relative to environmental deviations and formalizing orders of adaptability, FI addresses the shortcomings of traditional metrics and sets a new standard for intelligence evaluation. The framework’s emphasis on closed-loop, open-ended benchmarking is well-suited to the demands of future AI systems, with strong empirical support for its efficacy and scalability. Future work will refine the technical specifications and platform architecture for FI-based evaluation, further advancing the field of adaptive intelligence.