The Economics of Recursive Self-Improvement [pdf]

The Economics of Recursive Self-Improvement Tom Cunningham* Lukas Althoff† Basil Halperin† Brian Jabarian† Andrew Koh† Arjun Ramani† Phil Trammell† Parker Whitfill† Cheryl Wu† July 13, 2026 Abstract We model the economics of recursive self-improvement (RSI) and assess its plausibility and impacts. First, we build a sequence of increasingly rich mod- els of AI progress to highlight the feedback loops behind RSI. We represent our models as directed graphs and show that net acceleration in AI capabilities depends on the product of elasticities across each feedback loop. Second, we distinguish between “narrow” and “broad” AI capabilities, capturing the pos- sibility that AI systems improve narrowly at optimizing AI R&D benchmarks without improving at broader economically valuable tasks. Third, we docu- ment existing estimates of key parameters, and provide a wish list of empiri- cal objects that AI companies can measure and feasibly share publicly. Finally, we calibrate the model with existing data. A back-of-the-envelope calculation suggests that feedback loops are not currently strong enough to generate a self- sustaining acceleration, though they appear to be strengthening. We conclude by assessing the plausibility and implications of such an acceleration. Contributions: *Lead author. †Listed in alphabetical order; these authors contributed equally. Corresponding author: Tom Cunningham, [email protected] Latest version of the paper: https://github.com/elasticity-ai/elasticity/raw/main/paper/elasti city-rsi-paper.pdf Acknowledgements: Thanks for comments from Anson Ho, Thomas Houlden, Shrey Jain, Whitney Zhang, Alan Chan, Thomas Kwa, Anton Korinek, Jason Abaluck. Affiliations: Tom Cunningham (METR); Lukas Althoff (Stanford University); Basil Halperin (University of Virginia); Brian Jabarian (Carnegie Mellon University and Google AI); Andrew Koh (Columbia University); Arjun Ramani (MIT); Phil Trammell (Stanford DEL and Epoch AI); Parker Whitfill (METR); Cheryl Wu (Yale University). All authors are affiliated with the Elasticity Institute (https://elasticity.institute). Support: We gratefully acknowledge administrative and financial support from METR, and hosting from Constellation.

1 1 INTRODUCTION Motivation. Over the past year many signs have emerged of a feedback loop in which AI is accelerating AI research (Favaro and Clark, 2026), implying we could expect an acceleration in the already rapid growth of AI capabilities.1 If the feedback loops are as strong as some expect, the transformation in productivity could have consequences comparable in scale to historical shifts such as the Enlightenment, reshaping economic, social, and political life (Mokyr, 2002). Core argument. The degree of acceleration depends on what we call the core feedback loop: for a one-unit increase in model capabilities, how much do the capabilities of the next generation of models increase? Estimating the strength of this relationship is challenging because it is governed by many inputs and possible bottlenecks. This note presents a series of theoretical models to clarify the forces behind the core feedback loop. We draw a tight connection to empirical data needed to measure the strength of the feedback loop, which can help assess the degree of current and future acceleration. Defining RSI. The term “recursive self-improvement” (RSI) has been used in several ways, often inconsistently.2 Some define RSI as a technology contributing to its own improvement, which could apply to almost any technology since the dawn of humanity. Favaro and Clark (2026) recently defined the term more narrowly as a technology that has fully automated the process of its own improvement. Other definitions highlight the importance of acceleration or feedback loops, even if full automation is not realized. To avoid confusion, we instead focus on the possibility of a self-sustaining acceleration in AI capabilities and derive the conditions under which it arises. We begin by defining self-sustaining acceleration and related terms in Table 1. Table 1: Definitions Term Definition Feedback loops When outputs of a system today are routed back as in- puts to the system tomorrow. Arguably most technolo- gies exhibit feedback effects f are part of feedback loops when embedded in the economy), and AI has certainly exhibited feedback loops for a long time. 1Measured, for example, via the Epoch Capabilities Index or the METR time horizon metric, though measuring capabilities remains difficult.

2The origin of the term is not clear, but it was popularized by (and plausibly originated with) Yudkowsky (2001, 2008), extending an argument by Good (1965). 2 Table 1: Definitions Term Definition R&D automatability When AI is able to autonomously make technological im- provements at least equivalent to those made by human researchers, at an equal cost. Automatability does not im- ply automation: humans could still be employed in R&D due to slow diffusion or regulation. Self-sustaining acceleration When AI systems are sufficient for accelerating progress in AI capabilities without any growth in ex- ogenous inputs (human labor, training compute, etc.). Intelligence explosion When AI capabilities go to infinity in finite time. Relevant references: Davidson et al. (2026), Chan et al. (2026), Eth and Davidson (2025), Davidson and Houlden (2025), Davidson (2023), Good (1965), Hanson (2008), Christiano (2018), Ho and Whitfill (2025), Aghion et al. (2017). These concepts are often conflated with each other and the term “RSI.” Some have treated full automation of AI R&D as sufficient for self-sustaining acceleration. For ex- ample, I.J. Good in 1965 states: “an ultraintelligent machine could design even better machines; there would then unquestionably be an intelligence explosion.” But our mod- els make it clear that such an explosion may not follow if there are diminishing returns (“ideas become harder to find”) or if feedback loops become bottlenecked. Modeling RSI. We construct a sequence of progressively richer models of RSI. We pre- sent the models in diagrams for readability. Our basic model distinguishes two production functions that combine to form the core feedback loop: improvements to algorithmic efficiency are produced with human labor and AI capabilities; in turn, algorithmic efficiency, along with training compute, raises AI capabilities. A third production function, for economic output, determines how AI capabilities impact the wider economy.

We extend the model to emphasize the possibil- ity of bottlenecks, where the feedback loop may be broken by the necessity of humans, compute, or data; and for economic feedback loops, where higher output finances further compute investment and data collection, potentially alleviating bottlenecks. We derive a condition under which each model features a self-sustaining acceleration. We also discuss the possibility that there would be an acceleration only in “narrow” capabilities. The core feedback loop requires a strong connection between algorithmic efficiency and the capabilities required to find new algorithmic optimizations. This con- nection could be strong without necessarily accelerating real-world impacts because such impacts depend on “broad” capabilities less sensitive to algorithmic efficiency. Finally, we discuss the possibility that AI capabilities may rapidly advance for specific optimization 3 abilities, but not for all types of algorithmic improvements, bottlenecking RSI. Our key technical contribution is to introduce a simple graphical framework to rep- resent an otherwise complicated system of variables and feedback loops. Nodes of the graph represent outputs of a production function; the strengths of edges in the graph represent elasticities of an output with respect to inputs. There is a self-sustaining accel- eration under a condition which can be derived simply using these elasticities and the graph. Details of this framework are outlined in technical boxes. Existing empirical evidence & requests for data. Our models depend on a set of critical measurable parameters. We review existing empirical estimates of these parameters. We also put forward a list of measures that would be useful for AI companies to pro- vide while remaining feasible to share publicly. The biggest unknowns to be informed by additional data are (i) the growth rate of algorithmic efficiency in labs, (ii) the fraction of lab R&D expenditures going to each input (humans, data, experimental compute, infer- ence for R&D), and (iii) direct measures of how much models contribute to research, like the share of technical advances produced by AI. Plausibility and implications. We make a tentative calibration of the self-sustaining ac- celeration condition using the existing data that is available, measuring AI capabilities using the Epoch Capabilities Index (Ho et al., 2025). We find that the condition is met if a one-unit increase in AI model capabilities results in at least 15% higher AI R&D pro- ductivity.

A rough back-of-the-envelope calculation based on reported AI engineer uplift suggests this return has been around 9% since the launch of coding agents. This number is below the model-implied threshold, suggesting we are not experiencing a self-sustaining acceleration. Nonetheless, there is ample evidence that this return is not constant and has been increasing of late. Our model therefore does not rule out the possibility of self- sustaining acceleration in the near future. Given the vast uncertainty in both the data and model behind our calibration, we also discuss other qualitative evidence for and against a self-sustaining acceleration. Exist- ing survey and benchmark evidence suggests that AI systems are increasingly useful in discovering new algorithmic improvements. On the other hand, algorithmic progress has historically depended on continued compute scaling, and future compute growth may be- come constrained by power, capital, or broader economic growth. Moreover, even if the technical conditions identified by our calibration are eventually met, deployment could be substantially slowed by political and regulatory constraints. Position in the literature. The economics literature on RSI is founded on Aghion et al. (2017), who derived conditions under which AI-driven automation could generate ac- celerating or even explosive economic growth, and Davidson (2023), whose compute- centric framework offered an early formal model of AI takeoff dynamics. We comple- ment an emerging literature on the economics of RSI in three ways. First, our networked models build on Davidson et al. (2026), who formally develop a general theory of semi- endogenous growth models with innovation networks plus economic feedback loops and apply it to AI. Second, we emphasize the distinction between narrow and broad capabil- 4 ities in both theory and the discussion of economic impact. This distinction is largely set aside in the review articles of Trammell and Korinek (2025) and Jones (2026). Third, we provide a wish list of empirical objects that AI companies can both measure and feasibly share openly that would be informative for the public conversation on RSI. This supple- ments the existing empirical efforts that we review (e.g., Whitfill and Wu 2025, Gundlach et al. 2025, Epoch 2026).