Are AI Capabilities Increasing Exponentially? A Competing Hypothesis

TL;DR

This note challenges the claim that AI capabilities grow exponentially by re-analyzing METR's 50% model horizon data and proposing a multiplicative model that separates base capabilities from reasoning. By fitting sigmoid-based link functions to a base and a reasoning component, the authors show an inflection point occurring in the past for base capabilities and project a near-term inflection for reasoning, implying potential plateauing rather than unbounded exponential growth. The approach uses Bayesian/Stan estimation and compares against METR's exponential fit, highlighting how model structure and decomposition can dramatically alter forecasts. The work argues for more domain-grounded forecasting and robust evaluation to avoid fragile exponential projections that may not generalize as technology evolves.

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.

Figures (4)

• Figure 1: Sigmoid Curve. This sigmoid curve is fit by minimizing the mean-squared error (MSE) of the curve $h_{\text{model}}=\gamma\cdot\sigma(\delta_1\cdot d_{\text{model}}+\delta_2)$ to the METR dataset, where $h_{\text{model}}$ is METR's "50% model horizon time" for the given model, $d_{\text{model}}$ is the model release date, and $\gamma,\delta_1,\delta_2$ are parameters. We use gradient descent in PyTorch for parameter estimation. While it is not clear that progress will plateau, recent progress clearly fits in the linear part of the sigmoid and the inflection point (2025-06-06) is in the past.
• Figure 2: Sigmoid link inflection points. The curves are as in Figure \ref{['fig:projection']}; we show inflection points of the orange and green curves as dashed vertical lines of the corresponding color.
• Figure 3: Projections under Different Link Functions. The orange curves project base model capabilities, the green curve projects reasoning capabilities assuming the best base model (i.e., gpt-5.1-codex-max), and the blue curve shows the overall capabilities. The black points denote the 50% model horizon estimated by METR.
• Figure 4: Comparison of Sigmoid Link and METR Projection.

Theorems & Definitions (1)

• Theorem 3.1