Are AI Capabilities Increasing Exponentially? A Competing Hypothesis

Abstract: Rapidly increasing AI capabilities have substantial real-world consequences, ranging from AI safety concerns to labor market consequences. The Model Evaluation & Threat Research (METR) report argues that AI capabilities have exhibited exponential growth since 2019. In this note, we argue that the data does not support exponential growth, even in shorter-term horizons. Whereas the METR study claims that fitting sigmoid/logistic curves results in inflection points far in the future, we fit a sigmoid curve to their current data and find that the inflection point has already passed. In addition, we propose a more complex model that decomposes AI capabilities into base and reasoning capabilities, exhibiting individual rates of improvement. We prove that this model supports our hypothesis that AI capabilities will exhibit an inflection point in the near future. Our goal is not to establish a rigorous forecast of our own, but to highlight the fragility of existing forecasts of exponential growth.

• The paper challenges the exponential growth narrative by showing that a sigmoid model (MSE ≈ 27.4) fits AI progress data better than an exponential curve.
• It introduces a multiplicative framework that decomposes AI progress into distinct 'base' and 'reasoning' capabilities with separate sigmoid growth dynamics.
• The study implies that near-term AI capabilities may plateau, urging a reassessment of long-term forecasting and policy planning in AI development.

Plateauing AI Capabilities: A Competing Hypothesis to Exponential Growth

Introduction and Motivation

The prevailing narrative in AI forecasting literature posits exponential increases in AI capabilities, particularly in state-of-the-art LLMs post-2019, with widely cited claims including those by the Model Evaluation Threat Research (METR) study attributing observed accelerations to unconstrained, ongoing exponential trends. This paper interrogates the adequacy of the exponential growth hypothesis, offering an alternative interpretation grounded in both empirical model fitting and theoretical analysis: recent capability improvements can be better explained by a plateauing sigmoid dynamic, not a continuing exponential increase. Furthermore, the authors introduce a decomposition of AI progress into "base" and "reasoning" capabilities, modeled as interacting but distinct sub-technologies with potentially disparate scaling behaviors, and analyze the implications of this for long-term AI forecasting.

Empirical Reassessment of Growth Trends

The METR analysis, which underpins much current discourse about rapid AI progress, hinges on the "50% model horizon" metric—a regression-derived measure of the maximum task difficulty (in terms of human time investment) that a given model can solve with at least 50% probability. Fitting an exponential model to this metric over the release dates of frontier LLMs yields an impressive coefficient of determination ($R^2 = 0.98$), which METR and others interpret as strong evidence of sustained exponential capability increase.

The present paper challenges this interpretation by fitting several alternative functional forms to the same data, prominently the sigmoid (logistic) function. The sigmoid fit demonstrates an inflection point—where growth transitions from acceleration to deceleration—that is already in the past (2025-06-06), directly contradicting METR's claim that the inflection remains far in the future. The results from this fit are visually and quantitatively demonstrated (see below).

Figure 1: Sigmoid curve fit to METR’s 50% model horizon data, indicating the inflection point occurred in the past.

These findings suggest the plausibility of near-term plateauing in aggregate AI capabilities. The authors emphasize that in-sample goodness-of-fit for the sigmoid is superior (MSE ≈ 27.4) to the exponential model (MSE ≈ 339.9) as well as to more flexible alternatives such as splines, under their probabilistic modeling approach.

Multiplicative Model of Base and Reasoning Capabilities

A key insight of the paper is the decomposition of AI progress into a multiplicative model with two core drivers:

• Base Capability: Underpinned by scale (data, model parameters), architectural, and data curation improvements, historically responsible for pre-2023 capability growth.
• Reasoning Capability: Associated with targeted post-training for chain-of-thought and manipulation of reasoning skills, with a marked recent impact since models like OpenAI’s o1-preview.

Each component is modeled via a sigmoid progression, and their product forms the composite model horizon capability:

$$h_{\text{model}} = \gamma_1 \cdot h_{\text{base}} \cdot (1 + \gamma_2 h_{\text{reasoning}})$$

where $h_{\text{base}}$, $h_{\text{reasoning}}$ are modeled as separate, time-dependent sigmoid or exponential functions.

This framework captures the intuition that apparent recent exponential progress may simply reflect sequential, staggered introduction and maturation of distinct underlying technologies (base, then reasoning), each growing rapidly before saturating. The theoretical analysis under this multiplicative, multi-sigmoid construction shows three phases: initial exponential growth, a period of super-exponential (squared-exponential) growth as secondary technologies come online, then eventual plateauing. This explains observed historical dynamics and undermines the inevitability of indefinite exponential scaling in the future.

Figure 2: Inflection points of base and reasoning sigmoid curves, with plateauing initiated as each saturates.

Figure 3: Separate contributions of base and reasoning sigmoid links and their aggregate effect.

Implications for Long-Term Forecasting

The longer-term implications of these modeling choices are striking. The comparison of the multiplicative sigmoid model with the standard exponential forecast, over a 10-year horizon, reveals only minor short-term divergence but starkly different long-run outcomes:

• The exponential model predicts continually accelerating capabilities, with transformative impacts implied by mid-to-late 2020s.
• The sigmoid-based model projects that aggregate capability will plateau in the near future unless driven by fundamentally new breakthroughs.

Figure 4: Long-term projection comparing exponential and sigmoid growth models, with the sigmoid-based forecast predicting imminent plateauing.

This divergence highlights the critical importance of model selection and functional form in AI forecasting: near-term data may insufficiently discriminate between models, but long-term outcomes diverge dramatically.

Limitations and Modeling Assumptions

Several caveats are acknowledged:

• All regressions are in-sample due to limited available data; model selection may be affected by overfitting.
• The compositional (multiplicative) structure, while theoretically motivated, is a modeling choice that may not reflect all technological interactions.
• The base/reasoning dichotomy is a simplification; further disaggregation into more granular drivers (e.g., algorithmic advances, data type expansion) is limited by lack of transparency in proprietary models.
• Differences in objective functions between this paper and METR complicate direct comparison.

Nevertheless, the modeling highlights epistemic fragility in current exponential projections and the necessity for more granular, mechanistic models that can accommodate technological regime shifts.

Implications and Future Directions

Practically, the paper’s results suggest that near-term capability forecasting should treat exponential growth as a contingent, not inevitable, reference case, and that policy or safety planning should account for possible deceleration—even plateauing—of frontier model improvements. Theoretically, the proposed decomposition encourages further work toward modular, mechanistic forecasting frameworks able to identify, model, and anticipate the maturation of component technologies—possibly extending beyond base and reasoning to domains such as planning, memory retrieval, or embodied cognition.

In the absence of new transformative breakthroughs (comparable to the introduction of explicit reasoning), the model forecasts limited further growth—a prediction with major implications for AI safety, economic impact, and research prioritization.

Conclusion

This paper mounts a methodologically rigorous and theoretically grounded challenge to the now-standard exponential growth hypothesis for AI capabilities, offering a concrete alternative with both empirical and analytic support. By introducing a decompositional, multiplicative model distinguishing base from reasoning contributions, and by establishing—via statistical fit and inflection analysis—the plausibility of imminent plateauing, the authors urge caution in making strong claims of relentless exponential progress. Future forecasting work, and indeed policy and safety analysis, should critically evaluate underlying model assumptions and incorporate the possibility that current rapid rates of improvement are neither universal nor guaranteed to persist in the absence of new technological breakthroughs.