Are AI Capabilities Increasing Exponentially? A Competing Hypothesis

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.

💡 Research Summary

The paper critically examines the claim made by the Model Evaluation & Threat Research (METR) report that AI capabilities have been growing exponentially since 2019, a claim that has attracted considerable attention due to its implications for safety, labor markets, and policy. METR introduced a novel metric called the “50 % model horizon,” which measures the difficulty of tasks that a model can solve correctly half of the time. By regressing the logarithm of this horizon against model release dates, METR reported an R² of 0.98 and concluded that capabilities double roughly every six months, supporting an exponential growth narrative.

The authors of this note argue that the data do not substantiate such a strong exponential trend, even over short horizons. First, they re‑fit a logistic (sigmoid) curve to the same METR dataset using mean‑squared‑error minimization. Their fitted curve places the inflection point on 2025‑06‑06, i.e., in the past. This suggests that the recent rapid gains correspond to the linear region of a sigmoid, and that the growth rate is already flattening. In contrast, METR’s own analysis treated the sigmoid’s inflection as far in the future, a conclusion the authors show to be inconsistent with the data.

To explain why a period of apparent exponential growth can coexist with an underlying plateau, the authors propose a multiplicative two‑component model. They decompose overall capability (h_model) into a base component (h_base) reflecting pre‑training scale, data, and non‑reasoning fine‑tuning, and a reasoning component (h_reason) reflecting chain‑of‑thought and other post‑training reasoning techniques. The model is formalized as:

 h_model = γ₁ · h_base · (1 + γ₂ · h_reason),

with h_base and h_reason each modeled by sigmoid functions of release date (d). The reasoning term is activated only for models that explicitly incorporate reasoning (e.g., OpenAI’s o1 series). This multiplicative structure captures the intuition that reasoning improvements can only amplify a sufficiently strong base model, and that each component follows its own growth‑then‑plateau trajectory.

The paper provides a theoretical analysis (Theorem 3.1) showing that a product of k sigmoids with evenly spaced inflection points yields three distinct phases: (i) early exponential growth (≈ e^{k x}), (ii) a middle phase of “squared‑exponential” growth (≈ e^{c x²}) as successive components plateau, and (iii) a final plateau once all components have saturated. This mathematical result aligns with the empirical pattern observed in the METR data: an early exponential rise driven by scaling, a second surge coinciding with the introduction of reasoning capabilities, and an emerging flattening.

Empirically, the authors compare three link‑function families for the base and reasoning components: sigmoid, pure exponential, and B‑spline. Using mean‑squared‑error on the 50 % horizon values, the sigmoid link achieves the lowest error (27.37), far outperforming the exponential (2 874.67) and B‑spline (511.80) alternatives, and also beating METR’s own exponential fit (339.93). Visualizations (Figures 1‑3) illustrate that the sigmoid fit places the inflection point in mid‑2025, that the reasoning component’s inflection occurs later, and that the combined model reproduces the observed data points while predicting an imminent slowdown.

In conclusion, the authors argue that the apparent exponential trend reported by METR can be explained as a transient effect of introducing reasoning capabilities on top of a plateauing base model. Without further breakthroughs, the multiplicative model predicts that overall AI capability growth will soon decelerate and eventually plateau. This challenges forecasts that assume continued exponential improvement and underscores the fragility of such predictions for policy‑making, investment, and workforce planning. The paper does not claim to provide a definitive forecast but highlights the need for more nuanced modeling and careful interpretation of early‑stage capability data.