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, tom.cunningham@metr.org

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.

11 I NTRODUCTION

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).

2Table 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 3abilities, 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-4ities 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).

2 M ODELS OF RECURSIVE SELF -I MPROVEMENT

We present a progression of models to understand the economics of recursive self-improvement. The models are presented graphically, where each directed edge indicates that one variable is an input to the production function of the other, and with a strength that is an elasticity. The condition for self-sustaining acceleration can be read off from the graph: as we describe below, it is related to the partial elasticities represented by the strength of the edges. In technical details boxes, for interested readers only, we make precise how to translate our graphs into equations.

2.1 Basic Model of Algorithmic Progress (Jones, 1995)

Figure 1: Jones Model of Innovation R&D labor ( L)algorithmic efficiency ( A)algorithmic improvements ( ˙ A)

▼

We start by applying the Jones (1995) model of innovation to AI progress. We let A denote algorithmic efficiency, de-fined as the inverse of the training com-pute required to reach a given level of ca-pabilities. 3

Improvements to algorithmic efficiency

( ˙A) are determined by two factors: 1. The quantity of R&D labor (L).2. The current level of algorithmic effi-ciency ( A). Higher achievements could either make improvements harder (dimin-ishing returns) or easier (increasing returns). The second effect implies a feedback loop between the stock of technology ( A) and new technological improvements ( •

A). Its strength is characterized by the elasticity of •

A to A,which is denoted ε •

A,A

.

3One simple operationalization is the training time required to reach the GPT-2 level pretraining loss. Algorithmic progress has caused this to fall by a factor of 700 over 2019-2026, implying A2026 A2019 =700. A fuller accounting of algorithmic progress would also account for downstream capabilities, and scale-dependence. We discuss these further below.

5Self-sustaining acceleration. We say there is self-sustaining acceleration in A if, holding exogenous inputs fixed, the growth rate of technology ( ˙ A/A) is higher when the level of technology ( A) is higher. In this model, the exogenous input held fixed is R&D labor ( L). In this model, a self-sustaining acceleration occurs when the elasticity ε •

A,A

1, meaning that a 1% increase in the stock of ideas ( A) causes an increase in the discovery of new ideas ( •

A) of more than 1%, holding labor ( L) constant. Empirically, in traditional indus-tries ranging from agriculture to semiconductors, the elasticity is well below 1, implying stable growth of A requires an ever-increasing quantity of R&D effort (Bloom et al., 2020). Studies examining historical elasticities of software and AI algorithmic progress also es-timate that this condition does not hold without additional feedback loops (Erdil et al., 2024; Eth and Davidson, 2025), which we discuss next.

Definition: Elasticity

An elasticity measures responsiveness, in proportional terms: the percentage change in an output caused by a one-percent change in an input, holding other inputs fixed. For an output variable Y = f (X1, . . . , Xn), the elasticity of Y with respect to one of its inputs Xj is

εY,Xj ≡ ∂ log Y

∂ log Xj

= ∂ f

∂Xj

Xj

Y .Equivalently, it is the local slope of Y against Xj on logarithmic axes. For a power function Y = Xa, the elasticity is constant and equal to the exponent a.

Technical Details: Graphs & self-sustaining acceleration in technology

What do graph edges mean? Graph edges ( −→ ) indicate that one variable is an input to the production function of another. The diagram for the Jones model im-plies there exists some function ˙A = f (A, L).The strength of a graph edge is determined by the elasticity of a variable with re-spect to its parents. Denote the two elasticities in the Jones model as:

ε •

A,A

= ∂ log f (A, L)

∂ log A and ε •

A,L

= ∂ log f (A, L)

∂ log L

where ε •

A,A

is the rate of diminishing returns to R&D and ε •

A,L

is the returns to scale in contemporaneous research effort. The Jones model is often written assuming that these two elasticities are constant ( •

A = Lλ A1−β with constant λ and β), but we do not make that assumption.

Accumulation. Our directed graphs distinguish stock variables from flow vari-ables to ensure that the diagrams map one-to-one to a system of equations without ambiguity (Richardson, 1986). We use solid arrows ( −→ ) to represent how variables relate to each other at each point in time, and use triangles ( ▶) to denote how the rate of change of a stock variable, which is a flow (e.g. ˙A), accumulates into itself 6(e.g. into A) over time.

Feedback loops and their strength. In the Jones model, there is only one feedback loop, between technological improvements ˙A and the level of technology A. Below we will consider models with many feedback loops, and ones where each feedback loop may traverse many edges ( A −→ B −→ C −→ · · · ). Formally, each feedback loop is an ordered sequence of directed edges eee = ( e1, . . . ei, . . . ), whose strength is governed by the partial elasticities that we denote εei .The strength of any individual feedback loop eee is determined by the product of the elasticities along the edges , Πiεei .The strength of all feedback loops is determined by the total elasticity of ˙A with respect to A, which sums over all individual feedback loops:

E •

A,A

≡ d log ˙ A

d log A = ∑

paths eee from Ato ˙A

∏

i

εei

!

In Jones, with a single edge, the total elasticity is the partial elasticity: E •

A,A

= ε •

A,A

.

Self-sustaining acceleration in technological growth. If all exogenous inputs are held constant, the total elasticity determines how the growth rate of technology

gA = ˙A/A changes as A grows, yielding three regimes:



E •

A,A

< 1: gA falls as A grows ⇒ sub-exponential growth (fizzling out),

E •

A,A

= 1: gA constant ⇒ exponential growth (knife-edge),

E •

A,A

1: gA rises as A grows ⇒ self-sustaining acceleration. That is, A shows self-sustaining acceleration when

E •

A,A

= d log ˙ A

d log A > 1. (1) In the Jones model, since there is a single feedback path A → ˙A with a single edge, growth shows self-sustaining acceleration when ε •

A,A

1.

Non-constant elasticities and growth spurts. Self-sustaining acceleration at one point in time does not imply self-sustaining acceleration forever, because the elas-ticities are not necessarily constant. In the bottlenecks section below we discuss this likely case. Even locally self-sustaining acceleration would be notable.

72.2 Baseline Model of RSI

Figure 2: Baseline model of RSI R&D labor ( L)algorithmic efficiency ( A)algorithmic improvements ( ˙ A)capabilities (C)training compute ( T)

▼

Our baseline model of RSI adds a few ele-ments. 1. We introduce AI capabilities (C), which are determined by algorithmic efficiency ( A) as well as training com-pute (T). Compute is held fixed, for now. Measuring AI capabilities is notoriously difficult, but two com-mon metrics are METR’s time hori-zon measure (Kwa et al. (2025)) and the Epoch Capabilities Index (ECI, Ho et al. (2025)), though both metrics have flaws. 2. Algorithms are improved ( •

A) not just by human R&D labor ( L) but also with AI capabilities. Critically, the fact that AI capabilities now feed into algorithmic improvements creates a new feedback loop: the core feedback loop (A → C → •

A). This loop is in addition to a self-feedback loop ( A → •

A) that appeared in the Jones model. The strength of a multi-step feedback loop like the core loop is determined by the strength of all edges along it. In particular, the strength is the product of all elasticities along the loop, ε •

A,C

εC,A.

Self-sustaining acceleration. Self-sustaining acceleration in algorithmic efficiency now depends on the combined strength of these two feedback loops. The condition is that the

total elasticity of ˙A with respect to A, denoted E •

A,A

, exceeds one:

E •

A,A

= ε •

A,A

|{z}

self-feedback loop

• ε •

A,C

εC,A

| {z }

core feedback loop

1 (2)

Self-sustaining acceleration in AI capabilities. It is possible for algorithmic efficiency (A) to accelerate while capabilities ( C) do not, if the elasticity from A to C is falling, for example if there was a hard ceiling on model capabilities. We discuss the issue further in Section 2.4. 82.3 Bottlenecks: Human, Compute, or Data

Figure 3: Model with bottlenecks human R&D labor ( L)algorithmic efficiency ( A)algorithmic improvements ( ˙ A)capabilities (C)experimental compute ( E)inference compute ( K)training compute ( T)data ( D)

▼

The elasticities in our baseline model may fall over time: the feedback loops could become bottlenecked by critical inputs. Whether or not one input may bottleneck an output depends on how complementary

different inputs are. To emphasize the possibility of bottle-necks, we modify the baseline model to al-low for three more inputs in the system. Experimental compute ( E) and inference compute ( K) are both used to make algo-rithmic improvements. Data ( D), mean-while, is used to produce AI capabilities. Because the two feedback loops remain the same ( A → ˙A and A → C → ˙A), the total elasticity remains the same as above, and thus the self-sustaining condition also remains the same as (2). However these additional terms give us additional reasons why the core elasticity, ε •

A,C

, may fall: the arrow from

C → ˙A may weaken. We discuss these bottlenecks in turn: • Labor. Algorithmic improvements could become bottlenecked by a shortage of hu-man labor if AI agents can only help with some but not all parts of the research pro-cess (e.g. due to “lack of taste”). If inference compute increases disproportionately relative to human labor, bottlenecks reduce the marginal value of such compute in research (Jones, 2025). • Experimental compute. AI labs often allocate a large part of their compute to ex-perimentation. If model capabilities and experimental compute are strong comple-ments, then this could be a bottleneck (Whitfill and Wu, 2025; Ho and Whitfill, 2025). • Inference compute. There is clearly a strong interaction between model capabilities and inference compute in producing algorithmic improvements. If they are strong complements then slow growth in inference compute could serve as a bottleneck, diminishing the effect of capabilities on algorithmic improvements. • Data. A lack of high-quality data could bottleneck the advance of capabilities (Far-boodi et al., 2025; Erdil et al., 2025; Millidge, 2025). On the other hand, Ho et al. (2024) argue that most algorithmic progress is “data-augmenting”, implying that data will not become a bottleneck. • Training compute. A shortage of compute for training could also bottleneck the advance of AI capabilities (Gundlach et al., 2025). 9Technical Details: The C −→ ˙A arrow

Aside on AI capabilities → algorithmic improvements Note that human re-searchers ( L), AI capabilities ( C) and experimental compute, E, combine to produce algorithmic progress. Previous literature, such as Eth and Davidson (2025) and Whitfill and Wu (2025), has tried to parametrize this function. But our view is that it is not obvious what this function looks like because it depends on “the returns to intelligence” and how humans and AI systems differ, both of which we have a poor understanding of. Luckily the only thing we need to know is the elasticity noted above and it may be possible to measure this elasticity without fully understanding AI capabilities. We discuss this further in the data section.

2.4 Narrow and Broad Capabilities

Figure 4: Narrow capabilities feed back; broad capabilities dangle. R&D labor ( L)algorithmic efficiency ( A)algorithmic improvements ( ˙ A)narrow capabilities (C1)broad capabilities (C2)economic output ( Y)

▼

Our baseline model treats AI capabilities as a scalar C, which could be interpreted as the capability to both (1) contribute to algorithmic improvements ( •

A) and (2) con-tribute to producing economic output ( Y). However, the core feedback loop only re-quires the C → ˙A arrow, not any arrow from C → Y.Here, we make explicit the possibility of a

narrow acceleration, where algorithmic ef-ficiency accelerates but economic output does not. (For simplicity, this subsection suppresses training compute T.) The fig-ure illustrates the model: we distinguish between a ‘narrow’ capability ( C1) that is useful for contributing to algorithmic im-provements, and a ‘broad’ capability ( C2)that affects economic output ( Y). The clean cut we draw between capabilities useful for algorithmic improvements and all other capabilities is a strong simplification. In reality, it is plausible that a “narrow” ac-celeration occurs across easier-to-verify tasks which includes optimizing algorithms but also many parts of mathematics, coding writ large, and more. Such progress would have impacts on the real economy but would be exceptionally jagged. It is also of course pos-sible for progress in narrow tasks to eventually spill over into harder-to-verify tasks that matter for the broader economy. 10 Self-sustaining acceleration. The condition for a self-sustaining acceleration in algo-rithmic efficiency remains as before, but with narrow capabilities C1 substituted for C:

E •

A,A

= ε •

A,A

|{z}

self-feedback loop

• ε •

A,C1

εC1,A

| {z }

narrow capability loop

Broad capabilities C2 do not appear in this expression. Such an acceleration in algorithmic efficiency A need not imply a self-sustaining accel-eration in broad capabilities C2, and therefore need not imply such an acceleration in economic growth ( Y). The condition for broad capabilities depends additionally on a su-perelasticity : how the passthrough from algorithmic efficiency A into broad capabilities C2

changes as A rises: 4

ε •

A,A

• ε •

A,C1

εC1,A + d log εC2,A

d log A

| {z }

superelasticity

1 (3) Intuitively, the elasticity εC2,A could fall – the superelasticity could be negative – if tradi-tional scaling was sufficient to surpass human abilities at algorithmic optimization ( C1), but not to surpass human abilities in other practical areas ( C2) due to unmodeled data bottlenecks on the latter. 5

4A corresponding condition for acceleration in output depends on an additional superelasticity from C2 to Y; but for practical purposes we could define broad capabilities by their economic value, so Y∝C2. 5This seems plausible because computers already outperform humans at many well-defined optimiza-tion tasks.

11 2.5 Specific Optimization Ability and Growth Spurts

Figure 5: AI helps one subalgorithm human R&D labor ( L1)human R&D labor ( L2)algorithm 1 efficiency (A1)improvements to algorithm 1 ( ˙ A1)algorithm 2 efficiency (A2)improvements to algorithm 2 ( ˙ A2)overall efficiency (A)capabilities (C)

▼▼

It seems very likely that AI will be rela-tively better at contributing to some parts of model training than others. This in turn is likely to cause “growth spurts” in AI progress. The model at right assumes overall effi-ciency ( A) depends on the efficiency of two sub-algorithms ( A1 and A2), but AI di-rectly helps improve only the second one,

C → •

A2. To isolate this AI-assisted chan-nel, hold A1 fixed. The relevant feedback loop is then A2 → A → C → •

A2. Because

gA = ε A,A2 gA2 , self-sustaining acceleration in overall efficiency requires:

ε •

A2,A2

• ε •

A2,C

εC,Aε A,A2

| {z }

d log ˙ A2/d log A2

• d log ε A,A2

d log A2

| {z }

changing passthrough into overall efficiency

1. If these elasticities were constant then the second term would be zero, and self-sustaining acceleration today would imply self-sustaining acceleration forever. However there are two reasons why the condition may cease to hold, producing only a temporary “growth spurt”: 1. Parallel algorithms. Overall algorithmic efficiency could be bottlenecked by type-1 algorithmic efficiency, which is not improved by AI capabilities. As type-2 algo-rithms become abundant, the arrow from A2 → A weakens: ε A,A2 falls and its log derivative is negative. For example, if the compute costs of two necessary processes add, so that 1/ A = 1/ A1 + 1/ A2, then as A2/A1 → ∞,

ε A,A2 → 0 and d log ε A,A2

d log A2

→ − 1. Thus a spurt driven by progress on the easy component stalls unless AI also starts accelerating progress on the bottleneck component. 2. Low ceilings. If one of the algorithms is already close to a natural ceiling then its elasticity must necessarily fall. Some algorithms are naturally limited, e.g. if kernel efficiency is currently 50%, it can only increase by a factor of two; while the efficiency of other algorithms has improved by orders of magnitude, and may continue to improve by large factors. Empirically, it will be useful to document which types of algorithms are receiving the 12 biggest boost from AI-assisted research. On first principles, we might expect bigger boosts where there are low costs of verification (e.g., optimizing inference, optimizing elicitation) than where there are high costs of verification (optimizing architectures). Ad-ditionally, it is plausible that improvements to type-1 algorithms do advance capabilities, but only ‘narrowly’ in the spirit of the model in Section 2.4. We leave combining the two models for future work.

2.6 Economic Feedback Loops

Figure 6: Model with Economic Feedback Loops human R&D labor ( L)algorithmic efficiency ( A)algorithmic improvements ( ˙ A)capabilities (C)economic output ( Y)experimental compute ( E)inference compute ( K)training compute ( T)data ( D)˙E

˙K ˙T ˙D ▼ ▶ ▶ ▶ ▶

The previous models held constant the level of compute (for training, inference, or experiments) and held constant the quan-tity of data. This isolated the role of feed-back loops driven by algorithmic improve-ments. There are also economic feedback loops (Davidson et al., 2026): 1. Increased AI capabilities (C) drive higher economic output (Y).2. Higher economic output in turn fi-nances further investment in com-pute (for experiments E, for inference

K, and for training T), which feeds back into AI capabilities. AI-induced economic growth also gener-ates more data, likewise increasing AI ca-pabilities, and further increasing economic growth (Farboodi et al., 2025). We emphasize that economic output ( Y) – and the model as a whole – can be interpreted macroeconomically, where Y is GDP, or microeconomically, where Y is the revenue of a single AI firm. In the latter case, as AI capabilities progress and the firm grows, more chips or data are affordable (without substantially altering factor prices). Such microeconomic effects are self-evidently already occurring, and the resulting loops may drive capability acceleration even without substantial macroeconomic impacts.

Feedback loops and self-sustaining acceleration. Aside from the two feedback loops discussed above ( A → •

A and A → C → •

A), self-sustaining acceleration in algorith-mic efficiency now depends on the strength of additional economic feedback loops that run through AI capabilities. For instance, capabilities might drive the accumulation of 13 high-quality data, which in turn drives capabilities ( C → Y → •

D → D → C), or the accu-mulation of training compute, which in turn drives capabilities ( C → Y → •

T → T → C). The condition for a self-sustaining acceleration is now substantially more complicated and requires taking into account these more complicated feedback loops. The technical details box below states the condition; Davidson et al. (2026) offers a general framework and solution.

Technical Details: Self-sustaining acceleration with economic feedback loops

The prior boxes on technical details apply only when there is a single accumulating state: before, this was merely A. Now, instead, there is an entire state vector:

X ≡ (A, T, D, E, K)′

Define the reduced-form elasticity matrix M, with Mij ≡ d log ˙ Xi

d log Xj

. Each entry of

M measures how strongly one accumulable input increases the accumulation of another, after tracing through the contemporaneous graph. Davidson et al. (2026) show that there is self-sustaining acceleration in algorithmic efficiency when ρ(M) > 1, where ρ(M) is the dominant eigenvalue of the feedback matrix M.After some math, it can be shown that the eigenvalue condition holds when the sum of three feedback channels exceeds one: the core feedback loop ( A → C → •

A); the indirect loop between economic output and capabilities through training com-pute and data; and the direct economic loop through experimental and inference compute for algorithmic improvements. In math:

ε ˙A,CεC,A

1 − ε ˙A,A

| {z }

core feedback loop

• εY,C (εC,T + εC,D)

| {z }

indirect economic loops

• εC,AεY,C

1 − ε ˙A,A

(ε ˙A,E + ε ˙A,K)

| {z }

direct economic loops through experimental and inference compute

1. (4) Note that this condition assumes that the direct algorithmic efficiency self-loop does not on its own power a self-sustaining acceleration ( ε •

A,A

< 1). a It also imposes the Solow-like assumption that capital-like variables accumulate one-for-one with out-put: ε •

T,Y

= ε •

D,Y

= ε •

E,Y

= ε •

K,Y

= 1. If there are no economic impacts of AI capa-bilities ( εY,C = 0), the condition collapses to the earlier condition without economic feedback loops. 14 A subtlety is that the second loop does not run through algorithmic efficiency A and is self-contained: higher capabilities produce more output, financing more training compute and raising capabilities ( C → Y → •

T → T → C), or producing more data and raising capabilities ( C → Y → •

D → D → C). In either of these loops, the economy achieves a self-sustaining acceleration in algorithmic efficiency A ‘merely’ by raising GDP, which produces more compute or data (Davidson et al., 2026). An additional takeaway is that the condition with economic feedback loops, (4), requires estimating five new elasticities: the elasticity of economic output to AI ca-pabilities εY,C; the elasticity of capabilities to training compute εC,T; the elasticity of capabilities to data εC,D; the elasticity of algorithmic improvements to experimental compute ε •

A,E

; and the elasticity of algorithmic improvements to inference compute

ε •

A,K

.

a

Analogously, the rearrangement into this three-term form assumes the indirect economic loop is not self-sustaining on its own, εY,C (εC,T + εC,D ) < 1; if it were, acceleration would occur through that loop alone.

3 D ATA RELEVANT TO RSI

We primarily focus this section on calibrating the basic bottlenecks model. This is moti-vated primarily by simplicity and because larger economic feedback loops will be slower. To get empirical traction, we modify the bottlenecks model by assuming the existence of an “R&D effort aggregator ( R)” which combines human researchers ( L), automated AI researchers (running on inference compute, K), and experimental compute ( E) into a single scalar. R&D effort is then the sole input to algorithmic improvements ( •

A). This essentially assumes that all R&D inputs interact with the existing stock of algorithmic progress in the same way. This will let us use historical data on human inputs to calibrate what will happen with AI inputs. Once we make this assumption, we can expand and re-arrange the condition for self-sustaining acceleration in algorithmic efficiency, (2): 6

ε •

A,R

1 − ε •

A,A

| {z }

return to R&D

· εR,C

|{z}

research effort’s elasticity to AI capabilities

· εC,A

|{z}

capabilities’ elasticity to algorithmic efficiency

1 (5)

6

The condition (2) delineates a self-sustaining acceleration in algorithmic efficiency. In this section, we are most interested in a self-sustaining acceleration in AI capabilities . The condition for capabilities is the same as the condition for efficiency, augmented with a fourth, ‘superelasticity’ term, 11−ε •

A,A d log εC,A d log A

. This measures the change in the capabilities elasticity εC,A as algorithmic efficiency A grows. If εC,A is constant, the superelasticity term is zero and the condition reduces to the three terms shown here. In Section 3.4, which we put in a technical box, we argue the evidence indeed points to a superelasticity near zero.

15 Technical details: rearranging the self-sustaining acceleration condition

The condition for a self-sustaining acceleration in algorithmic efficiency, under the assumption of an R&D effort aggregator R, is

ε •

A,A

• ε •

A,R

εR,C εC,A > 1. This is the same as the core feedback loop condition used in the bottlenecks section, (2), except that now AI capabilities C pass through the R aggregator to affect •

A.Subtracting the direct-spillover term and dividing both sides by 1 − ε •

A,A

isolates the capability loop: ε •

A,R

εR,C εC,A

1 − ε •

A,A

1. Note that the denominator is positive whenever the direct spillover alone is not already self-sustaining, ε •

A,A

< 1. Then, grouping the first factor of the first term gives the form above,

ε •

A,R

1 − ε •

A,A

| {z }

return to R&D

· εR,C

|{z}

research effort’s elasticity to AI capabilities

· εC,A

|{z}

capabilities’ elasticity to algorithmic efficiency

1.

In our view, estimating this quantity, tracking it over time, and extrapolating when it might cross 1 is arguably the most important empirical exercise for assessing whether a self-sustaining acceleration will occur. The rest of this section maps each term in the condition to the data needed to estimate it: Section 3.1 covers the return to research, Sec-tion 3.2 covers the elasticity of research effort with respect to AI capabilities, and Sec-tion 3.3 covers the response of capabilities to algorithmic progress. We then collect de-tailed supplementary evidence on model-training inputs and model economics to build a broader picture of AI R&D automation.

3.1 Return to Research

It turns out – derived in the technical details box below – that the first term, the “returns to research”, can be measured from two growth rates: the growth rate of algorithmic efficiency ( gA ≡ ˙A/A) and the growth rate of R&D effort ( gR ≡ ˙R/R). On a balanced growth path: ε •

A,R

1 − ε •

A,A

| {z }

return to R&D

= gA

gR

We therefore need to estimate the growth rate of algorithmic efficiency, gA, and the growth rate of research effort, gR:16 1. We can measure growth in algorithmic efficiency gA directly from model-training data. 2. We derive in a technical box below that one can measure R&D effort as the spend-weighted average of growth rates in inputs : human researchers L, experimental com-pute E, and inference compute used for research K. Using S to denote spend shares,

gR = ∑

input

Sinput ginput

Alternatively, we can measure gR directly from spending. Total R&D spend is the sum across inputs of price times quantity, and log-differentiating shows its growth splits into a price component and a quantity component:

gspend = ∑

input

Sinput gprice of input

| {z }

≡gprices , input price inflation

• ∑

input

Sinput ginput

| {z }

=gR, by the result above

so gR = gspend − gprices : growth in total R&D spend, deflated by an index of R&D input prices.

Model primitive Existing data Data ask Growth in algorithmic efficiency ( gA)

Ho et al. (2024) estimate pretraining algorithmic progress of 3x a year (i.e. compute needed to achieve a given level of capability is 1/3 as much each year). Whitfill et al. (2025) estimate 3.5x/year for the entire stack. Ho (2026) estimates 10x/year for the entire stack. Gundlach et al. (2025) argue that algorithmic progress has grown at different rates across scales: 1.5x/year at small scale, and 2.5x/year at frontier scale, for pretraining.

Current data weakness :Compute estimates for models since 2024 are uncertain.

Ideal new data : model training compute after 2024 to estimate gA.17 Model primitive Existing data Data ask Share of human researchers ( L) of R&D spend, and its growth gL

Its share SL and growth gL enter

gR =

∑input Sinput ginput .Epoch AI (2026) estimates growth rates of around 2–3x/year in total staff for frontier labs over 2023–2025. Whitfill and Wu (2025) estimate headcount growth rates of 2–3X/year for Anthropic and OpenAI over 2022–2024. Cottier et al. (2024) estimates that around 1/3 of the cost of training models was spent on researcher salaries.

Current data weakness :Employee headcount does not necessarily map to the researcher headcount.

Ideal new data : Granular lab data on staff, split by seniority and by researchers vs. engineers, would let us treat these as separate inputs rather than an aggregate L.

Share of experimental compute ( E) of R&D spend, and its growth gE

Its share SE and growth gE enter

gR =

∑input Sinput ginput .You (2025) estimates that in 2024 only 10% of OpenAI’s R&D compute was on final training runs, while 90% was on experimental compute (i.e. training which did not directly affect weights used in a public product). Denain and Wu (2026) estimate similar ratios for Chinese companies. Morrison et al. (2026) estimate similar ratios for OLMo 3 family. You et al. (2026) finds that the total growth rate of chips is about 3.3 x ayear (doubling every 7 months).

Current data weakness :Experimental compute share in total compute is not the same as the experimental compute share of total R&D spending. The composition of experimental compute is also not clear.

Ideal new data : Labs could publish detailed data on experimental compute spend across domains and over time, which would help estimate how much experimental compute bottlenecks automated research.

Share of inference compute ( K) of R&D spend, and its growth gK

Its share SK and growth gK enter

gR =

∑input Sinput ginput .No data available. Ideal new data : Labs could publish detailed data on inference compute spend across domains and over time. 18 Model primitive Existing data Data ask Total R&D spend in dollars, and its growth

Deflated by an index of input prices, this is an alternative way to measure gR.Denain and Wu (2026) estimate R&D compute spending for several labs from public filings.

Current data weakness : No spending over time yet. Even given spend, no off-the-shelf deflator fits AI R&D, since compute prices fall rapidly while wages do not.

Ideal new data : Labs could publish total annual R&D expenditure alongside a self-constructed deflator.

Substitutability of labor and experimental compute

How substitutable labor and compute are controls how fast

εR,C falls as research becomes bottlenecked by experimental compute. Whitfill and Wu (2025) try to estimate the substitutability between labor and experimental compute in AI R&D, using variation in relative prices, but their findings are inconclusive.

Current data weakness :Aside from data quality, it is unclear whether the need for experimental compute increases with higher training compute.

Ideal new data : labs could conduct experiments that would give teams randomized amounts of R&D labor and experimental compute, but this is expensive. One cheaper substitute is using AI labor in place of human labor in the experiment. Cheaper still is to survey managers how much more progress they would make with (A) twice the researchers (compute fixed); (B) twice the compute (researchers fixed); (C) both doubled. 19 Technical details: cost minimization and elasticities

Throughout this section we use the correspondence that, under cost-minimizing input choice, the elasticity of an output with respect to an input equals that input’s share of expenditure.

Setup. Let output R = R(X1, . . . , Xn) be produced from inputs Xi with prices pi.A firm minimizing the cost ∑i pi Xi of attaining a target ¯ R has first-order conditions

pi = μ ∂ R/∂Xi for a common multiplier μ. The cost share of input i is then

Si ≡ pi Xi

∑j pj Xj

= (∂R/∂Xi) Xi

∑j(∂R/∂Xj) Xj

.

Constant returns to scale. We take R to have constant returns to scale. This is without loss of generality: R is a latent index, and its returns to scale are absorbed by the elasticity ε •

A,R

in the return-to-research term. Under constant returns, Euler’s theorem gives ∑j(∂R/∂Xj) Xj = R, so

Si = ∂R

∂Xi

Xi

R = εR,Xi .Cost shares equal elasticities.

When firms do not optimize. If input choices are not fully cost-minimizing, the equality becomes a revealed-preference bound: observed cost shares reflect the firm’s own belief about marginal products, so they remain informative about the elasticities.

Technical details: return to research

The return to research as gA/gR. Write the discovery rate as ˙A = f (R, A), so

gA ≡ ˙A/A = f (R, A)/A. Log-differentiating with respect to time, d log gA

dt = ε ˙A,R gR − 1 − ε ˙A,A

gA.On a balanced growth path gA is constant, so the left-hand side is zero and

gA

gR

= ε ˙A,R

1 − ε ˙A,A

,which is exactly the return-to-research term. This holds exactly on a balanced growth path and approximately when gA is approximately constant. The smooth, steady historical rate of algorithmic progress makes this a reasonable benchmark, though not one we expect to hold if RSI pushes us off the balanced-growth path.

20 Decomposing gR. The growth rate of research effort follows the growth-rate chain rule across its inputs,

gR = ∑

input i

εR,i gi.Using the cost-share correspondence above, εR,i = Si, so

gR = ∑

input i

Si gi,a spend-weighted average of input growth rates over human labor L, experimental compute E, and inference compute K.

3.2 Research Effort to Capabilities

The second term measures how strongly effective research effort responds to more capa-ble AIs. This is the hardest of the three to measure, since it captures how AI capabilities translate into real-world research effort. This requires scientifically understanding AI ca-pabilities and how they feed into research. The science of AI capabilities is in its infancy. One possible route is to measure it directly, through studies of how much AI acceler-ates end-to-end research. A second route uses a cost-share argument. If we model “effective AI labor” as a Cobb–Douglas function of AI capabilities and the quantity of AI researchers (inference compute), e.g. CγK, then this term equals γSK, where γ is the returns to capabilities rela-tive to scaling the quantity of AI labor and SK is the inference-compute cost share (derived in the technical details below).

Model primitive Existing data Data ask Share of AI R&D inference compute ( K) of total R&D spend ( SK)

The inference spend share SK,one of the two components of

εR,C = γSK.As aforementioned in the last subsection, we have almost no data on lab expenditure on inference or its share relative to other R&D inputs.

Ideal new data : Labs could publish detailed data on inference compute spend across domains and over time. 21 Model primitive Existing data Data ask Tradeoff between training and inference compute ( γ)

The quality–quantity exponent

γ, the other component of

εR,C = γSK.The parameter γ governs the returns to scaling capabilities C versus scaling inference compute

K, since we model effective AI labor as CγK.Estimates from Villalobos and Atkinson (2023) imply

γ ≈ 0.15–0.3 under the ECI normalization of capabilities ( C = eECI ). 7

Current data weakness :The estimation is not up to date, and the implied γ

divides estimates from two separate studies with different tasks and model generations.

Ideal new data : More extensive study on public benchmarks/with ECI.

The effect of AI use on researcher productivity

A direct (if loose) measure of

εR,C: how much capability raises effective R&D. We have self-reported productivity gains from surveys: 1.4–2X in METR’s survey of technical workers (Becker, 2026), and roughly 4X in the Claude Mythos Preview system card (Anthropic, 2026). The magnitudes are hard to interpret, but the upward trend is clear. Favaro and Clark (2026) report lines of code merged per engineer per day rose roughly 8X between 2024 and Q2 2026.

Current data weakness :Note that this is the productivity effect of AI, but εR,C is the total research effort added due to one extra unit of capability.

Ideal new data : An RCT that measures productivity benefits from extra capabilities. 22 Model primitive Existing data Data ask The strength of autonomous R&D

A direct measure of εR,C (and the discovery-rate response

ε ˙A,C): AI’s standalone contribution to discovery. AI agents have recently advanced the frontier in some optimization problems; however, it is difficult to find a metric to measure their overall ability. 8

Recent system cards report mixed results on benchmarks of AI R&D. Models generally outperform humans on optimization problems when the humans are given between 8 and 40 hours, but show low pass rates on complex debugging problems (Claude Mythos Preview system card, Anthropic, 2026, Table 2.3.3.A; GPT-5.5 system card, section 9.1.3). These results are difficult to place on a common scale.

Current data weakness :Benchmark questions are not the same as real-life LLM training problems.

Ideal new data : How autonomous AI systems perform on real LLM training problems would be especially informative. The ideal data would characterize the returns to expenditure on agentic, human, and hybrid labor. 23 Model primitive Existing data Data ask Capabilities of AI R&D

A direct, qualitative read on

εR,C — which parts of research AI substitutes for, and where it remains weak. Si et al. (2025) find that AI-generated AI research ideas are rated highly relative to human-generated ones. Trehan and Chopra (2026) find a range of weaknesses, including both taste and execution. The Claude Mythos Preview system card has an extended discussion of the model’s qualitative strengths and weaknesses in AI R&D (Anthropic, 2026).

Current data weakness :It remains unclear how to describe AI’s weaknesses in AI R&D relative to human researchers. A common split is between idea generation (taste) and idea execution.

Ideal new data :Unstructured interviews with lab staff with well-designed questions eliciting AI R&D weaknesses.

Technical details: research effort to capabilities

Suppose AI enters research effort through a capability-adjusted count of effective researchers, N = K C γ, where K is the quantity of inference compute and Cγ is a quality adjustment, so that R = R(. . . , N, . . . ). By the chain rule,

εR,C = ∂ log R

∂ log C = ∂ log R

∂ log N

∂ log N

∂ log C = εR,N · γ,since ∂ log N/∂ log C = γ. Effective researchers are purchased through inference compute, so the expenditure on this input is the inference-compute spend and its cost share is SK. Applying the cost-share correspondence (see the technical details on cost minimization above), εR,N = SK, giving

εR,C = γ SK.

3.3 Capabilities Response to Algorithmic Efficiency

The third term is the elasticity of capabilities with respect to algorithmic progress. Sup-pose that algorithmic efficiency and training compute enter C symmetrically (both through effective compute, C = C(A × T)). This implies that the elasticity of capabilities to algo-rithmic progress equals the elasticity of capability to training compute i.e. εC,A = εC,T.Note that εC,T is precisely the object estimated by scaling-law studies. Epoch’s work on the capabilities–compute relationship (Ho et al., 2025; Epoch AI, 2025) estimates values 24 of εC,T around 6.5 when C is defined as the exponential of the Epoch Capabilities Index,

eECI .9

One qualification is needed: the symmetry εC,A = εC,T relies on algorithmic progress being scale-free, so that it enters capability only through the product A × T. Gundlach et al. (2025) present evidence that algorithmic progress is instead scale-biased (faster at frontier scale than at small scale for pretraining), in which case εC,A and εC,T can diverge and scaling-law estimates identify only the latter. Nonetheless, we treat this term as the best-measured of the four; the supporting model-training data is collected in the supple-mentary material (Section 3.5).

Model primitive Existing data Data ask Capabilities’ elasticity to algorithmic progress ( εC,A)

Ho et al. (2025) and Epoch AI (2025) estimate the capability–compute relationship, implying εC,A ≈ 6.5 when C = eECI .

Current data weakness :Estimates assume scale-free algorithmic progress; Gundlach et al. (2025) suggest it is scale-biased.

Ideal new data : Algorithmic efficiency estimates at multiple scales, to separate

εC,A from εC,T.

Technical details: Measuring the superelasticity term

3.4 The Superelasticity Term

As described in footnote 6, the condition for a self-sustaining acceleration in ca-pabilities (5) technically has a fourth term. The fourth term asks whether the ca-pabilities elasticity εC,A itself changes as algorithmic efficiency grows, i.e. whether d log εC,A/d log A̸ = 0. Our best guess is that it is close to zero. As we showed in the previous subsection, εC,A = εC,T under certain conditions. Thus the superelasticity measures the proportional change in εC,T as effective compute grows, which de-pends on the curvature of the capability–compute relationship rather than its slope. That relationship has looked close to log-linear across many orders of magnitude of training compute (Ho et al., 2025; Epoch AI, 2025), so εC,T appears approximately constant and therefore the superelasticity near zero. The caveat is the same scale-free assumption as in the previous subsection: if algo-rithmic progress is scale-biased (Gundlach et al., 2025), the symmetry breaks, and constancy of εC,T need not imply constancy of εC,A.

9The magnitude depends on this normalization of capabilities; the loop gain εR,CεC,Athat enters the condition is invariant to it.

25 Model primitive Existing data Data ask Superelasticity of capabilities (d log εC,A

d log A

)

No direct estimates, but the capability–compute relationship appears close to log-linear across many orders of magnitude of compute (Ho et al., 2025; Epoch AI, 2025), which suggests εC,T,and by symmetry εC,A, is approximately constant.

Current data weakness :Scale-biased algorithmic progress would break the symmetry with εC,T.

Ideal new data :Capability–compute estimates spanning a wide range of effective compute, updated past 2024, to estimate curvature and not just slope.

3.5 Supplementary Data

The data below do not measure the three terms in (5) directly but fill out the broader picture of AI R&D automation, including economic feedback loops. For example, the model-training laws row helps pin down the third term, the capability–compute scaling relationship (Section 3.3). The same data also help identify historical growth in algorith-mic efficiency and predict the effects of future growth in training compute and data. The final row covers the economic feedback loop, through which capability funds further in-puts.

Model primitive Existing data Data ask Model training laws

Calibrates the capability map

C(AT ); pins down εC,A = εC,T.The basic model remains Chinchilla (Hoffmann et al., 2022), which maps data and compute to pretraining loss.

Current data weakness :Scaling laws for RL remain largely unpublished.

Ideal new data :post-training compute usage of models.

Growth in training compute

gT; since effective compute is

AT , it drives capability growth. Training compute has grown 4–5X per year since 2010 (Rahman and Owen, 2024). Whitfill et al. (2025) discusses possible GDP constraints on continued compute scaling.

Current data weakness :There is scarce data on model training compute since 2024.

Ideal new data : training compute of new models. 26 Model primitive Existing data Data ask Growth in data

Data D, an input to capability beyond effective compute AT .There are minimal existing estimates of data spend by labs. 10

Ideal new data : Labs could publish data spend, or partial estimates could be constructed from third-party data providers such as Surge AI or Scale AI.

Share of AI’s economic value creation captured by AI labs

Economic output Y, the channel through which capability funds further inputs (the economic feedback loop). We can use firm revenue estimates, but these are likely to represent only a small share of the value created. Brynjolfsson et al. (2026) use online choice experiments to elicit willingness-to-accept for giving up generative AI chatbots, estimating that consumer surplus substantially exceeds firms’ revenues.

Current data weakness :More estimation needed, with time variation.

Ideal new data : AI firms’ revenue over time.

Elasticity of GDP to capabilities ( εY,C)

How much a given capability improvement raises aggregate output. Little direct evidence: AI’s measured contribution to GDP remains small relative to its measured capabilities. Yotzov et al. (2026) survey over 5000 executives: 9/10 report no impact of AI on their firm’s productivity or employment over the past three years, but on average they expect AI to raise firm productivity by 1.4% and output by 0.8% over the next three years.

Current data weakness :Adoption and usage data are not tightly linked to impact on output.

Ideal new data :Task-level adoption and usage data linked to firm or sector output, tracking how output effects grow as capabilities improve. 27 Model primitive Existing data Data ask Elasticity of AI firm budget to capabilities ( εY,C)

We might instead interpret Y

as the budget AI firms have to spend on data, compute, and researchers. Then, εY,C is how much additional budget a given capability improvement generates (via fundraising or revenues). Frontier-lab revenues have grown around 3x/year (Epoch AI, 2026) with notable outliers, e.g. Anthropic. But lab expenditure is largely financed by external investment rather than revenue so the loop runs through expectations.

Current data weakness :Revenue is observed but at low frequency. Lab budgets are largely financed by investor expectations rather than current revenue.

Ideal new data : Credible estimates for how lab financing costs (through equity or debt) respond to changes in capabilities progress.

4 D ISCUSSION

To assess the plausibility of self-sustaining acceleration, we provide a very rough cali-bration of our analytical condition with the available estimates from Section 3. Certain parameters are unknown, especially the elasticity of R&D to AI capabilities. Thus, we derive a condition on the range of values for this elasticity that implies self-sustaining acceleration. We have a high degree of uncertainty in many of these empirical estimates, and also acknowledge the possibility of model misspecification. Thus we additionally provide a general discussion of the most important points of evidence for and against self-sustaining acceleration.

4.1 Model calibration

We now use the estimates we have from Section 3 to calibrate the self-sustaining acceler-ation condition (5):

ε •

A,R

1 − ε •

A,A

| {z }

return to R&D

· εR,C

|{z}

research effort’s elasticity to AI capabilities

· εC,A

|{z}

capabilities’ elasticity to algorithmic efficiency

1. We plug in the following values: • ε ˙A,R

1−ε˙A,A

= gA

gR

≈ ln (3)

ln (3)

= 1. We take gA = ln (3) as the annual growth rate in al-gorithmic progress per Ho et al. (2024), meaning A triples each year. Next recall

gR = SL gL + SE gE + SK gK. We take gL ≈ ln 3 from Epoch AI (2026); Whitfill and 28 Wu (2025) and gE ≈ ln (3) from You et al. (2026). gK was probably small until the rise of coding agents but has since increased. Indeed OpenAI reported in the GPT-5.6 launch post in July 2026 that “over the past six months, the share of research com-pute devoted to internal coding inference grew 100-fold,” implying a much larger

gR at present. But since we do not know the spend shares on these factors, and

SK is likely still low relative to SL and SE, we assume gR = ln (3) for now. This assumption is further justified by the fact that gA was estimated in 2024. • εR,C. We have almost no evidence for this parameter because AI uplift studies do not report capability improvements in a form that maps cleanly to this elasticity. • εC,A ≈ 6.5. Define capabilities as the exponential of the Epoch Capabilities Index, exp (ECI ). Also recall the assumption that C = C(A × T) which implies εC,A = εC,T.Thus we can get the elasticity of capabilities to algorithmic efficiency from the slope of a regression of ECI on log (compute ) across models using data from Epoch AI which yields an estimate of roughly 6.5. 11

Plugging in these values tells us that self-sustaining acceleration is achieved if εR,C >

0.15. This is the increase in R&D effort per additional unit of ECI. For comparison, Claude Opus 4.8 scores one ECI unit more than Claude Opus 4.7. Thus under our model, An-thropic would meet the self-sustaining acceleration condition if adopting Claude Opus 4.8 led to 15% higher research productivity than Opus 4.7. Note that the increase in re-search output per unit of AI capabilities tends to be smaller than the uplift for human tasks from AI use, because labor only accounts for a fraction of all research tasks. It is hard to say whether one unit of the ECI is worth 15% more research effort, but a rough calculation based on the last two years of AI progress reassuringly suggests that the returns to capabilities are currently lower than this threshold. Claude Opus 4.8 scores 16 ECI points more than Claude 3.7 Sonnet, which was released in February 2025 alongside Claude Code. At the time, estimates for AI uplift on engineering tasks varied but were not conclusively larger than 0. 12 More recently, Anthropic engineers surveyed in the Claude Mythos Preview system card reported a 4X uplift from Claude use (Anthropic, 2026). The 4X uplift is very likely to be an overestimate, but even if it were true it would imply a 9% increase in productivity per unit of ECI, below the threshold for self-sustaining accelera-tion over this period. Of course, these elasticities are likely increasing – the move from GPT-4 to GPT-5 led to a much larger increase in research productivity than the move from GPT-1 to GPT-2. The continual measurement of those elasticities is necessary for understanding the current state of RSI. Understanding how and why εR,C changes over time is therefore an important research priority. 13

11 Setting aside the scale-bias in algorithmic progress, discussed below. 12 For example, an influential study from Becker et al. (2025) found a negative impact of AI on engineering productivity. 13 One promising direction here is to model automation as endogenous: as AI capabilities improve, which research tasks do labs choose to automate, and how do those choices affect the aggregate responsiveness of research effort to capabilities?

29 4.2 Arguments for and against acceleration

Given the uncertainty in the above calibration, we now turn to general qualitative argu-ments for and against acceleration, informed by our models and data.

Best evidence in favor of acceleration:

• AI systems are meaningfully contributing to AI progress. The Claude Mythos Pre-view system card reported a self-assessed productivity uplift of roughly 4X among Anthropic researchers (although there are reasons to think this is likely overstated), and a 40-hour time horizon at which Claude Mythos Preview beat human researchers (Anthropic, 2026). Favaro and Clark (2026) assess the performance of human re-searchers versus Claude Code in making AI research decisions. In April 2026, Mythos Preview beat humans 64% of the time, up from 50% for Claude models released in 2025. OpenAI reported in July 2026 that internal coding inference’s share of research compute grew 100-fold in the prior six months, suggesting that the value of AI in R&D has dramatically increased. • In August 2025, experts and superforecasters (METR, 2025) 14 predicted an 8–20% chance that the growth rate of effective compute would triple by 2029. In May 2026, Jack Clark predicted a 60% chance that by the end of 2028, there will be “an AI sys-tem powerful enough that it could autonomously build its own successor” (Clark, 2026).

Best evidence against acceleration:

• Compute bottlenecks could bind for multiple reasons. Algorithmic improvements may require increases in training compute (Gundlach et al., 2025). Cognitive labor increases may require increases in experimental compute (Whitfill and Wu, 2025). Productivity growth may not be fast enough to support continued AI R&D invest-ments, that is, we “run out of GDP” (Halperin, forthcoming). • Autonomous contributions to algorithm optimization may quickly hit diminishing returns. This has been widely observed informally and formalized in the apple-picking model of AI R&D developed by Cunningham and Shetty (2026). • Capabilities may depend on data. Millidge (2025) argues that “most algorithmic progress is data progress”. This includes everything from better filtering of pre-training data to the substantial resources spent on post-training data. Pre-training filtering seems to be a one-time boost, whereas post-training data might be supplied more elastically and be amenable to automation. We are only beginning to learn how to build better reinforcement learning environments, and AI systems could help design future ones.

14 “Experts and superforecasters both find a three-fold acceleration of effective compute scale-up by 2029 plausible but unlikely, with experts giving it a median 20% chance and superforecasters 8%.”

30 Narrow capabilities acceleration before broad capabilities acceleration. It seems plau-sible that AI R&D agents, while effective at making concrete algorithmic progress as cap-tured by benchmarks, might remain less effective at developing major breakthroughs that enable models to learn efficiently in new environments, or develop more amorphous ca-pabilities like ‘vision’ or ‘taste’. This idea would be captured by combining our models in Sections 2.4 and 2.5 so that the feedback loop from narrow capabilities is helpful for generating narrow algorithmic progress but not broad progress. Nonetheless, spillovers from narrow to broad progress remain possible. For example, an advanced narrow sys-tem, in pursuit of benchmark optimization, may discover new capabilities, such as highly sample-efficient algorithms able to update their weights during deployment, that quickly turn narrow progress into broader progress.

Political and social barriers. Even if a self-sustaining acceleration is technically plau-sible, political and social barriers could stop it in its tracks. In America, at least 20 data center projects were canceled in the first three months of 2026 due to local pushback; $85 billion worth of projects have been canceled in the last three years (The Economist, 2026). Recent policy reactions to Mythos by the Trump administration, despite an ear-lier laissez-faire stance, also suggest placing greater weight on these barriers. If compute scaling remains important, even minor frictions in model deployment will slow revenue growth and further scaling.

4.3 Impacts of a capabilities acceleration on the world

A self-sustaining acceleration in AI progress differs from generic AI progress in speed :it could compress generations of progress into short periods of time. Indeed, if self-sustaining progress were feasible, it is likely that the returns to increasing investment in inputs like compute and data would be high, further increasing investment and the pace of progress. We highlight several aspects of rapid progress that distinguish it from gradual AI progress, and that may be especially important for understanding its social, economic, and political consequences. • Transition costs: It seems plausible that transition costs increase with the speed of technological change. Labor markets are one such case: the costs of structural transformation may rise with its speed, as some economists argue was the case with the China Shock. • Institutional inertia: In a world of rapidly accelerating capabilities growth, insti-tutions broadly defined — regulatory capacity, democratic procedures, legal frame-works, infrastructure, and so on — might lag behind (Bostrom, 2014; Ord, 2020). Rapid technological change might also grant political elites a temporary spike in de facto power, which they could use to capture institutions. • Asymmetric progress across domains: As noted, we see self-sustaining acceleration in narrow capabilities as more likely in the near term than an acceleration in broad capabilities. The former would likely be concentrated in tasks that are easy to verify 31 in closed loops, such as software development, games, mathematics, and related ar-eas. This could create acute asymmetries in progress across domains. For example, we may find solutions to long-standing puzzles in mathematics and breakthroughs in computational chemistry that enable new materials, alongside sluggish progress in less self-contained or messier domains. • Power imbalances across firms and nation-states: Even model providers with rela-tively small gaps in technical skill could see large gaps open up in effective capabil-ities and power over the world. Imagine Anthropic or the US government having access to capabilities that are vastly superior to those of any other actor. • Greater misalignment risk: Misaligned AI might also create bigger risks under a capabilities acceleration. Sudden increases in model capabilities would provide less time for technical and social safeguards to be put in place.

4.4 Future Steps

There are several directions for future work that build off this note, some of which we are actively pursuing: • Empirically estimating the self-sustaining acceleration condition for the model with economic feedback loops. • Measuring the return to research off the balanced growth path. • Combining models with multiple types of AI algorithms and capabilities (Sections 2.4 and 2.5). • Distinguishing quality from quantity improvements in data and compute. • Extending the model to multiple research sectors (software, hardware, data). • Modeling research taste and vision in AI R&D. • Endogenizing the decision to automate AI R&D. • Incorporating directed technical change. • Surveys and field experiments within AI frontier labs to improve estimates of the key parameters in the model. • Developing new ways to incentivize participation in prediction markets to produce better forecasts of AI progress (Fradkin et al. (2026)). 32 REFERENCES

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35 APPENDIX

A S CALE -D EPENDENT ALGORITHMIC PROGRESS

Since algorithmic progress is usually not directly observable, it is typically estimated as the increase in capabilities not explained by increases in training compute, just as TFP is estimated by the Solow residual. That is, if we know (from a “scaling law”) that in the absence of algorithmic progress some index of AI capabilities C would track training compute T, it is conventional to propose the model

C = A · T (6) and calculate A as C/T. Using a model like our “baseline model” in Section 2.2, the resulting time series for A, in combination with a time series for research inputs R and the semi-endogenous AI R&D function, can then be used to generate a prediction for how fast algorithms would advance after the automation of AI R&D. Gundlach et al. (2025) show conclusively that model (6) is misspecified because algo-rithmic progress in AI development to date has been largely biased toward large scales. For an extreme case of large-scale-biased algorithmic progress, consider instead the model

C = min (A, T) · T. (7) Here, algorithmic improvements proportionally advance AI capabilities as long as there is the training compute to leverage them (i.e., here, as long as T > A). If we stopped scaling the compute, however, capabilities would ultimately stagnate (here, at T2). Like-wise, even if automating AI R&D yields a leap in the quality of the algorithms available, under (7) this will not deliver arbitrarily large advances in AI capabilities until we have accumulated the training compute to leverage these algorithms. Another potential explanation for Gundlach et al.’s finding, however, is that we have been developing large-scale-biased algorithms precisely because we have been scaling compute. Indeed, we might imagine living in a somewhat different world in which we knew exactly what architectures would take us to superintelligence but were simply too compute-constrained to make efficient use of them. Why don’t we live in that world? One answer is that we have no incentive to discover such algorithms—and would not be able to validate them if we did—in a world in which we are compute-constrained. This also suggests that if we faced a long-term compute constraint, or if an AI model were tasked with recursively self-improving on fixed compute, we might develop algorithms that made ever better use of “small” training runs—as academic labs do to some extent to-day. That is, rapid RSI may still be feasible, but only via some kind of “directed technical change”. 36