Updated Paper Club

economics of RSI

The Economics of Recursive Self-Improvement by Tom Cunningham and co-authors

Click here to open and read The Economics of Recursive Self-Improvement ↗

The paper abstract with its central claims underlined

The paper's core argument about measuring how much one generation of models improves the next

This paper and the ideas are all about elasticities. Elasticity is a measure of responsiveness: how much one thing changes when another changes. In RSI, the elasticities along the loop - better AI → better R&D → better algorithms → better AI - multiply together.

A microphone moving closer to a speaker, illustrating a self-reinforcing feedback loop

If one round of improvement produces at least one equally large next round, the loop can sustain itself; if not, progress still requires more people, compute or data.

Definition · Elasticity

∂ log Y∂ log X∂Y∂XXY

An elasticity measures the percentage change in Y caused by a 1% change in X, holding other inputs fixed.

1 × ???? × 6.5 ≈ 11 × 15% × 6.5 ≈ 1

Redefining RSI: self-sustaining acceleration

Click here to open and watch the full Dwarkesh Patel conversation on YouTube ↗

“Whether or not this turns out to be the case, I think is the most important question in the world right now.”— Dwarkesh Patel, conversation with Ryan Greenblatt ↗

In 1965, mathematician I. J. Good proposed that an ultraintelligent machine could design superior successors, causing an unstoppable intelligence explosion.

Portrait of mathematician I. J. Good in 1966

“An ultraintelligent machine could design even better machines; there would then unquestionably be an ‘intelligence explosion.’”— I. J. Good, 1965 ↗

The term “recursive self-improvement” (RSI) has been used in several ways, often inconsistently.

Broad definitions

Technology aids its own improvement. This is too broad to be useful—many technologies already do this.

A wheel leads to a cart that carries better materials used to make a better wheel

Narrow definitions

AI systems independently choose research goals, run experiments, implement changes, and deploy successors. This assumes full agency.

A sequence of increasingly capable robots acting autonomously to improve their successors

The paper redefines RSI as

Self-sustaining accelerationAI capabilities accelerate technological progress without growth in exogenous inputs such as human labour, training compute or data.

How do you compare model improvements across different benchmarks, over time?

To measure RSI, we need to compare model capability - between models, over time over different and quickly saturated benchmarks. This is hard.

Title and abstract of A Rosetta Stone for AI Benchmarks

179 models, 38 benchmarks, and 1,324 scores. The current public ECI has expanded to 50+ benchmarks.

Animated scroll through Epoch AI's catalogue of benchmarks and the models evaluated on each

Different overlapping AI benchmarks unified into a single quantitative capability scale

ECI is the public index built from that paper.

The Epoch Capabilities Index (ECI) estimates:

Each model’s capability
Each benchmark’s difficulty
How quickly each benchmark saturates

The Epoch Capabilities Index showing model scores across releases

Animated comparison of Epoch's Software Engineering, Math and Cyber domain-specific ECI views

Models have a latent capability level, and the tests have a latent difficulty.

General ECI progress across OpenAI and Anthropic model releases

We’ll come back to this.

How to model self-sustaining RSI?

The paper builds a bunch of different models of RSI. In the interests of time, we’re focusing on one.

The paper introduces a progression of graphical models of recursive self-improvement

Figure 1: Jones Model of Innovation — Figure 1Open the Jones model in the paper ↗

Figure 2: Baseline model of recursive self-improvement — Figure 2Open the baseline RSI model in the paper ↗

Figure 3: Model with human, compute and data bottlenecks—the model this explainer focuses on — Figure 3 · Focus modelOpen the focus model ↗

Figure 4: Narrow capabilities feed back while broad capabilities dangle — Figure 4Open the narrow and broad capabilities model ↗

Figure 5: AI helps one subalgorithm — Figure 5Open the subalgorithm model in the paper ↗

Figure 6: Model with economic feedback loops — Figure 6Open the economic feedback model in the paper ↗

Simple intuition builder

To increase model capability: compute, data and better algorithms—and some humans.

Compute, data and algorithmic improvements flowing into model capability and back through AI-assisted R&D

Hold the exogenous stuff fixed, measure the core loop.

R&D → Better Algorithms → Better AI → Better R&D

The detailed core AI R&D feedback loop with compute and data held fixed

Under the models (very rough) assumptions - if you hold the external inputs fixed, a one-ECI-point improvement must make total AI R&D about 15% more productive.

Three links from total R&D to algorithmic progress to AI capability and back to R&D

This is the chain

How much does total R&D contribute to algorithmic progress?
How much do better algorithms improve AI capability?
How much does better AI contribute back to total R&D?

1 × ???? × 6.5 ≈ 11 × 15% × 6.5 ≈ 1

Hypothetical Claude example

Imagine the following hypothetical: Claude 8, Claude 9, Claude 10, and so on—holding exogenous inputs fixed.

Line graph comparing hypothetical Claude capability progress under 10%, 15%, and 20% AI R&D uplift scenarios with exogenous inputs fixed

Scenario 1: 10%

Claude 9 is one ECI point more capable than Claude 8.

Suppose this makes total AI R&D 10% more productive.

10% more productive R&D produces roughly 10% better algorithms.
10% better algorithms produces roughly 0.65 ECI points.

1 × 10% × 6.5 = 0.65

The feedback gets smaller rather than reproducing itself, so it is not self-sustaining. Progress can still continue through additional compute, people, data and other outside inputs.

Scenario 1 graph showing the 10 percent R&D uplift trajectory flattening from Claude 8 through Claude 16

Scenario 2: 15%

Claude 9 is one ECI point more capable than Claude 8.

Suppose this makes total AI R&D 15% more productive.

15% more productive R&D produces roughly 15% better algorithms.
15% better algorithms produces roughly one additional ECI point.

1 × 15% × 6.5 ≈ 1

In this simplified hypothetical, the feedback loop becomes self-sustaining without further growth in outside inputs such as compute, people or data.

Scenario 2 graph showing the 15 percent R&D uplift trajectory rising steadily from Claude 8 through Claude 16

Scenario 3: 20%

Claude 9 is one ECI point more capable than Claude 8.

Suppose this makes total AI R&D 20% more productive.

20% more productive R&D produces roughly 20% better algorithms.
20% better algorithms produces roughly 1.3 additional ECI points.

1 × 20% × 6.5 = 1.3

Each AI-generated gain is roughly 30% larger than the one before it. In this simplified hypothetical, the feedback loop does more than sustain itself—it accelerates.

Scenario 3 graph showing the 20 percent R&D uplift trajectory accelerating from Claude 8 through Claude 16

Hypothetical Claude trajectories with a reaction image appearing when the loop crosses the self-sustaining threshold

Obviously, none of these scenarios will play out exactly like this. They provide intuition for the possible trajectories.

1How much does total R&D contribute to algorithmic progress?1-to-1Locked

2How much do better algorithms improve AI capability?6.5Locked

3How much does better AI contribute back to total R&D?9%Adjustable

The loop does not close

1 × 6.5 × 9.0% = 0.585. One unit of progress feeds back as 0.585 units of new progress.

Loop gain0.585

Loop fades

FadesThreshold = 1Amplifies

Better AI → total R&D9.0%

Break-even better AI → R&D: 15.4%

A threshold test, not a forecast.

Self-sustaining RSI may require 15% per ECI point

So how much are the models currently contributing back to the R&D process which creates them?

We don’t know.

The paper constructs a very rough estimate using Anthropic engineers’ self-reported 4× productivity improvement.

Click here to open Anthropic’s full “When AI Builds Itself” research note ↗

“I started leaning hard into Claudifying about a year ago. That’s been a crazy adventure and it’s now been ~5 months since I last wrote any code myself.”Anthropic Institute ↗

If you spread that 4× uplift across approximately 16 ECI points:

ln(4) ÷ 16 ≈ 9% per ECI point

The reported 4× uplift is probably an overestimate.

15%

Estimated self-sustaining threshold per ECI point.

9.1%

Crude historical estimate per ECI point.

Actual current value: unknown.

There are many other variables

What if additional compute lets labs exploit AI-generated research much faster—or compute becomes the bottleneck?
Figure 3 · Open the model with bottlenecks in the paper ↗
What if humans and AI strongly complement each other—or essential human work becomes the bottleneck?
Figure 3 · Open the model with bottlenecks in the paper ↗
What if AI becomes exceptionally good at AI research even while remaining weak at other tasks?
Figure 4 · Open the narrow and broad capabilities model ↗
What if AI rapidly optimises the current bottleneck before progress shifts to a different bottleneck?
Figure 5 · Open the one-subalgorithm model in the paper ↗
What if better AI generates additional economic resources that can be reinvested in compute, data and research?
Figure 6 · Open the economic feedback model in the paper ↗

If we had better data, we could make better predictions about RSI.

Run the full model

Paradigm’s simulator adds resource allocation, time paths and the paper’s extended models.

Play the RSI game ↗