Definitions of Recursive Self-Improvement | Tom Cunningham

This page surveys definitions related to recursive self-improvement.: Most of the content was put together by LLM agents, there are validation checks but it’s possible this contains errors. Any corrections or additions would be very welcome, send me an email!

Inclusion criteria (source of truth)

Coined (red diamond) — the publication is the earliest in this reference to use the term in its modern sense. Each term is coined exactly once.
Later use (open circle) — the publication defines the term, or uses it in a way that is load-bearing for its argument.
Concept anticipated (dashed grey square) — the publication anticipates the idea but predates, or does not use, the term.
Excluded (no marker) if the term appears only as an offhand or passing mention; a reference-list citation; an organisation or event name (e.g. “Singularity Institute”, “Singularity Summit”); an explicit disavowal (“this is not the same as X”); or — for “singularity” — the purely economic “growth-to-infinity” sense (which is tracked separately under the growth-explosion terms).

Coverage. For the shared-vocabulary terms — “intelligence explosion”, “singularity”, “seed AI”, “recursive self-improvement”, “artificial superintelligence (ASI)”, and “software intelligence explosion” — every qualifying use is marked. For all other terms, only coinages and notable (re)definitions are shown.

Scope. In scope: terms for the dynamics of AI improving AI — the feedback/explosion conditions, the milestones or capability thresholds said to trigger them, and the superintelligence or economic-explosion outcomes they imply. Out of scope: general technological-acceleration framings not specific to AI-improving-AI (e.g. Kurzweil’s “Law of Accelerating Returns” and The Singularity Is Near, deliberately omitted); broad AGI / AI-capability taxonomies and alignment vocabulary; and any work that merely mentions these ideas in passing. “Artificial superintelligence (ASI)” is tracked only where it bears on the self-improvement loop. Within scope, only reasonably prominent works are catalogued — those that coined a term, are widely cited, or are otherwise notable in the debate — rather than every paper that uses these terms.

Validation Checks

Overall: ⚠️ Warning

✅ [54/54] Cited sources exist in posts/ai.bib (programmatic)
⚠️ [48/54] Cited sources have a quote field in posts/ai.bib (programmatic)
✅ [54/54] Chart publications have a literature-review section (programmatic)
✅ [81/81] Chart markers reference defined terms & publications (programmatic)
✅ [31/31] Each term is coined exactly once (programmatic)
⚠️ [30/48] Bib quotes present in local fulltext version (programmatic)

Last checked: 2026-06-25

Each row is a publication (in chronological order); each column is a term. Hover over a marker to see the definition. Most terms are coined once and never reused; a handful—“intelligence explosion”, “singularity”, “seed AI”, “recursive self-improvement”, “artificial superintelligence (ASI)”, and the recent “software intelligence explosion”/“ASARA”/“SAR” cluster—become shared vocabulary. See the inclusion criteria box above for exactly when a marker is placed.

Taxonomy and observations

A useful taxonomy

Suppose we define \(A_t\) as the level of technology (e.g. on some scale of AI capabilities), \(L_t\) as human research labor, and \(\dot A(L,A)\) as the increase in technology given those two inputs. The conditions below are properties of this function, which may hold locally (at a particular \((L,A)\)) or globally (for all values):

Feedback effects	\(\frac{\partial}{\partial A}\dot A(L,A) > 0\)	Technology helps its own growth. Having a bigger stock of discoveries today causes you to make more discoveries tomorrow, holding fixed human inputs.
Super-linear feedback effects	\(\frac{\partial}{\partial A}\dot A(L,A) > 1\)	Feedback effects are sufficiently strong that each additional discovery causes more than one additional discovery. However note this depends on the time-scaling.
Super-exponential feedback effects	\(\frac{\partial}{\partial \ln A} \ln \dot A(L,A) > 1\)	The elasticity of new discoveries with respect to the stock exceeds one. If the elasticity is bounded above one (i.e. \(\ge 1+\varepsilon\) as \(A\to\infty\)) then \(A\) reaches infinity in finite time.
Autonomous progress	\(\dot A(0,A) > 0\)	Discoveries accumulate even without human inputs.

Some observations using this taxonomy.

Feedback effects do not imply an explosion. Many of the definitions below, read literally, define RSI as feedback effects. Yet the authors often go on to say that RSI would have explosive implications. I think this is a mistake: many technologies have feedback effects, e.g. if I’m writing a code editor, each generation of editor makes the next editor somewhat better (because it helps me write better code), but this won’t cause an explosion in editor quality.
Autonomous progress doesn’t imply an explosion. Many of the definitions below, read literally, define RSI as autonomous progress. But it’s easy to see that you could have autonomous progress without an explosion, e.g. LLMs in 2025 could already do some basic fine-tuning of their own weights, so they could be set to autonomously improve themselves, but they would also very likely hit a ceiling.
An explosion requires a cardinal scale. To define super-exponential feedback effects we need a ratio scale, i.e. some cardinal measure of AI capabilities with a meaningful zero. Most definitions quoted below typically just say “intelligence,” without offering a scale, and it’s notoriously difficult to give a cardinal scale of machine intelligence. (An alternative route would be to say that the growth is “unbounded”, but then you still need some definition of levels of capability).
Many definitions don’t distinguish local and global properties. The definitions above can be read either locally (for specific values of \(L\) and \(A\)) or globally (for all values). Implicitly most of the definitions below are meant to apply above a threshold: (a) often feedback effects are expected to get stronger with stronger \(A\); (b) people often draw conclusions from RSI that assume a global interpretation, e.g. “infinite \(A\) in finite time,” meaning they expect local explosions cause global explosions.

Definitions

Earlier, vaguer precursors (not recursive self-improvement per se): an 1847 anticipation of self-improving machines (Thornton 1847), Samuel Butler’s 1863 “Darwin among the Machines” (Butler 1863), Turing’s 1951 warning that “we should have to expect the machines to take control” (Turing 1951), and Teilhard de Chardin’s “Omega Point” (Teilhard de Chardin 1955), later reworked by Tipler (1994). See also Nikola Danaylov’s survey, 17 Definitions of the Technological Singularity (Danaylov 2012).

Thornton (1847), The Expounder of Primitive Christianity (on a calculating machine)

(no term coined — an early anticipation of self-improving machines): “…such machines, by which the scholar may, by turning a crank, grind out the solution of a problem without the fatigue of mental application, would by its introduction into schools, do incalculable injury. But who knows that such machines when brought to greater perfection, may not think of a plan to remedy all their own defects and then grind out ideas beyond the ken of mortal mind!” (Quoted secondhand via Danaylov’s singularity survey; I have not verified the wording or title against an original scan of the 1847 Expounder item.)

Butler (1863), Darwin among the Machines (letter to The Press)

(no term coined — the standard companion to Thornton): “We are ourselves creating our own successors… we are daily giving them greater power… In the course of ages we shall find ourselves the inferior race… the time will come when the machines will hold the real supremacy over the world and its inhabitants is what no person of a truly philosophic mind can for a moment question.” (Published under the pseudonym “Cellarius”; later expanded into the “Book of the Machines” chapters of Erewhon.)

Turing (1951), Intelligent Machinery, A Heretical Theory

(no term coined — a direct anticipation of the intelligence-explosion idea): “It seems probable that once the machine thinking method had started, it would not take long to outstrip our feeble powers… they would be able to converse with each other to sharpen their wits. At some stage therefore we should have to expect the machines to take control, in the way that is mentioned in Samuel Butler’s Erewhon.” (Lecture to the ’51 Society, Manchester, c. 1951.)

Teilhard de Chardin (1955), The Phenomenon of Man

“Omega Point”: “…the zoological group of mankind…is turning…towards…a point through which we can prognosticate the contact between thought…and that transcendent focus we call Omega, the principle which…makes this involution irreversible and moves and gathers it in.” (Written in the 1930s and published posthumously as Le Phénomène humain, Paris, 1955; English translation The Phenomenon of Man, 1959.)

Tipler (1994), The Physics of Immortality

“Omega Point”: “Life must eventually engulf the entire universe and control it…the amount of information processed between now and the final state is infinite…the future c-boundary is a point — the Omega Point.” (Tipler’s physicalized reworking of Teilhard’s concept.)

Ulam (1958), Tribute to John von Neumann

“singularity”: “One conversation centered on the ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue.” (Ulam recounting a conversation with John von Neumann; the earliest prominent related use of “singularity” for accelerating technological change — not yet the superhuman-AI sense later made central by Vinge, who explicitly distinguished his usage from this “normal progress” one.)

Good (1965), Speculations Concerning the First Ultraintelligent Machine

“intelligence explosion”: “an ultraintelligent machine could design even better machines; there would then unquestionably be an ‘intelligence explosion’, and the intelligence of man would be left far behind. Thus the first ultraintelligent machine is the last invention that man need ever make.”

Vinge (1983), First Word (Omni)

“singularity”: “We will soon create intelligences greater than our own. When this happens, human history will have reached a kind of singularity, an intellectual transition as impenetrable as the knotted space-time at the center of a black hole, and the world will pass far beyond our understanding.” (Vinge’s first use of “singularity” for superhuman intelligence, a decade before his better-known 1993 essay.)

Solomonoff (1985), The Time Scale of Artificial Intelligence

“infinity point”: “This equation has the property that for any positive value of R, the value of c will at some finite time t = T, approach infinity. […] Usually, when infinities like this one occur in science, they indicate a breakdown of the validity of the equations as we approach the infinity point.” (A related speed-explosion / infinity-point model — faster AI researchers shorten each design cycle, driving a finite-time limit — rather than the Good/Vinge/Yudkowsky-style intelligence explosion per se. Chalmers (2010) treats it specifically as a speed-explosion argument.)

Vinge (1993), The Coming Technological Singularity

“the Singularity”: “Within thirty years, we will have the technological means to create superhuman intelligence. Shortly after, the human era will be ended. […] I think it’s fair to call this event a singularity (‘the Singularity’ for the purposes of this paper). It is a point where our old models must be discarded and a new reality rules.”

Yudkowsky (2001), General Intelligence and Seed AI

“seed AI”: “A seed AI is an AI capable of self-understanding, self-modification, and recursive self-enhancement. […] the goal is to build a mind capable of enhancing itself, and then re-enhancing itself with that higher intelligence, until the goal point is reached.” (The first precise published definition of “seed AI”; Yudkowsky’s companion Creating Friendly AI (2001) defines the term alongside “Friendly AI”. The exact phrase “recursive self-improvement” appears the following year in LOGI.)

Yudkowsky (2002), Levels of Organization in General Intelligence

“recursive self-improvement” (“seed AI”): “A seed AI is an AI designed for self-understanding, self-modification, and recursive self-improvement. […] The later consequences of seed AI (such as true recursive self-improvement) only show up after the AI has achieved significant holonic understanding and general intelligence.” (Circulated as a draft in 2002 for the Goertzel–Pennachin AGI volume; formally published by Springer in 2007. Dated here to the 2002 draft, since the chart tracks first use.)

Schmidhuber (2007), Gödel Machines: Fully Self-referential Optimal Universal Self-improvers

“recursive self-improvement” (formal model): “We present the first class of mathematically rigorous, general, fully self-referential, self-improving, optimally efficient problem solvers. […] such a problem solver rewrites any part of its own code as soon as it has found a proof that the rewrite is useful.” (The rigorous formal model of recursive self-improvement; circulated as a draft from 2003, arXiv:cs/0309048, and published in the same AGI volume as LOGI.)

Omohundro (2007), The Nature of Self-Improving Artificial Intelligence

“self-improving AI”: “A self-improving AI is a system that understands its own behavior and is able to make changes to itself in order to improve itself. […] any system which acts in a rational way will want to self-improve itself, so this discussion actually applies to all AIs.”

Hall (2007), Self-improving AI: An Analysis (Minds and Machines)

“self-improving AI”: “the contention that an AI system could be built to learn and improve itself indefinitely has acquired the label of the bootstrap fallacy. […] Technological optimists […] have maintained that such a system is possible, producing, if implemented, a feedback loop that would lead to a rapid exponential increase in intelligence.”

Hanson (2008), Economics of the Singularity

“singularity”: “Its arrival could produce a singularity—an overwhelming departure from prior trends, with uneven and dizzyingly rapid change thereafter […]. The world economy, which now doubles in 15 years or so, would soon double in somewhere from a week to a month.”
“intelligence explosion”: “Others envision an ‘intelligence explosion’ via a series of powerful design innovations, beginning with one that would make machines smart enough to help us quickly find a second innovation, allowing even smarter machines, and so on.”

Yudkowsky (2008), Recursive Self-Improvement

“recursive self-improvement”: “Recursion is the sort of thing that happens when you hand the AI the object-level problem of ‘redesign your own cognitive algorithms.’ […] Eventually the AI becomes sophisticated enough to start improving itself, not just small improvements, but improvements large enough to cascade into other improvements. And then you get what I. J. Good called an ‘intelligence explosion’. […] When you fold a complicated, choppy, cascade-y chain of differential equations in on itself via recursion, it should either flatline or blow up.”

Hanson and Yudkowsky (2008), The Hanson–Yudkowsky AI-Foom Debate

“hard takeoff” / “FOOM”: “I think that at some point in the development of Artificial Intelligence, we are likely to see a fast, local increase in capability — ‘AI go FOOM.’ Just to be clear on the claim, ‘fast’ means on a timescale of weeks or hours rather than years or decades; and ‘FOOM’ means way the hell smarter than anything else around.” (The 2008 Hanson–Yudkowsky debate; “FOOM” and “hard takeoff” function as synonyms, predating Christiano’s “fast/slow takeoff” framing by a decade.)

Legg (2008), Machine Super Intelligence

“machine super intelligence” (≈ artificial superintelligence): “if there is ever to be something approaching absolute power, a super intelligent machine would come close. By definition, it would be capable of achieving a vast range of goals in a wide range of environments.” (PhD thesis whose title and concept of a “super intelligent machine” predate, and share the meaning of, the later acronym ASI.)

Bostrom (2009), Superintelligence (Edge.org / Forbes)

“intelligence explosion” (“seed AI”): “some sufficiently advanced and easily modifiable machine intelligence (a ‘seed AI’) applies its wits to create a smarter version of itself. This smarter version uses its greater intelligence to improve itself even further. The process is iterative, and each cycle is faster than its predecessor. The result is an intelligence explosion.” (This passage — usually attributed to Superintelligence (2014) — was already published verbatim in Bostrom’s 2009 Edge.org essay, reprinted in Forbes.)

Shulman and Sandberg (2010), Implications of a Software-Limited Singularity

“software-limited singularity”: “human-level AI would likely be capable of developing still more sophisticated AIs soon thereafter, resulting in an ‘intelligence explosion’ or ‘technological singularity’ with potentially enormous impact.” (The coined term “software-limited singularity” appears in their title rather than in this sentence — the body argues that an intelligence explosion bottlenecked by software rather than hardware would, when it finally arrives, be sharper because of accumulated hardware overhang. This is the direct precursor of the idea later termed “software-only singularity” by Davidson (2023), which is why it sits under that column in the chart above.)

Chalmers (2010), The Singularity: A Philosophical Analysis

“intelligence explosion” (“AI+”, “AI++”): “we can put the argument for an intelligence explosion as follows […]. AI+ is artificial intelligence of greater than human level […]. AI++ (or superintelligence) is AI of far greater than human level (say, at least as far beyond the most intelligent human as the most intelligent human is beyond a mouse). […] There will be AI+. […] If there is AI+, there will be AI++. […] There will be AI++.”
“proportionality thesis”: “a proportionality thesis: it holds that increases in intelligence (or increases of a certain sort) always lead to proportionate increases in the capacity to design intelligent systems.”
“singularity”: “This intelligence explosion is now often known as the ‘singularity’.”
“recursive self-improvement”: “Perhaps the core sense of the term, though, is a moderate sense in which it refers to an intelligence explosion through the recursive mechanism set out by I. J. Good.” (Chalmers uses “recursive mechanism” / “recursive path to AI++”; cited, with Yudkowsky, as a standard source for recursive self-improvement.)
“artificial superintelligence (ASI)”: “AI++ (or superintelligence) is AI of far greater than human level (say, at least as far beyond the most intelligent human as the most intelligent human is beyond a mouse).”

Sotala (2012), Advantages of Artificial Intelligences, Uploads, and Digital Minds

“recursive self-improvement”: “Recursive self-improvement (Yudkowsky 2008a; Chalmers 2010) is a situation in which a mind modifies itself, which then makes it capable of further improving itself. For instance, an AGI might improve its pattern-recognition capabilities, which would then allow it to notice inefficiencies in itself. Correcting these inefficiencies would free up processing time and allow the AGI to notice more things that could be improved.”

Muehlhauser and Salamon (2012), Intelligence Explosion: Evidence and Import

“intelligence explosion”: “If human-level AI is created, there is a good chance vastly superhuman AI will follow via an ‘intelligence explosion’ […]. An uncontrolled intelligence explosion could destroy everything we value, but a controlled intelligence explosion would benefit humanity enormously if we can achieve it.” (A widely-cited adoption of Good’s term in the existential-risk literature.)
“artificial superintelligence (ASI)”: “But if AI is likely to lead to machine superintelligence, as we argue next, the implications could be even greater.”

Hutter (2012), Can Intelligence Explode?

“intelligence explosion”: “The most popular scenarios are an ‘intelligence explosion’ [Good 1965] or a speed explosion [Yudkowsky 1996] or a combination of both [Chalmers 2010].” (A peer-reviewed augmentation of Chalmers (2010) that uses “intelligence explosion” more than twenty times — in both software and hardware senses — and carefully separates a speed explosion from an intelligence explosion. Pointed out by Marcus Hutter; he notes it may be among the first papers to pose the question in its title, though not the first to discuss the idea.)

Yudkowsky (2013), Intelligence Explosion Microeconomics

“intelligence explosion”: “I. J. Good’s thesis of the ‘intelligence explosion’ states that a sufficiently advanced machine intelligence could build a smarter version of itself, which could in turn build an even smarter version, and that this process could continue to the point of vastly exceeding human intelligence.”
“returns on cognitive reinvestment”: “returns on cognitive reinvestment—the ability to invest more computing power, faster computers, or improved cognitive algorithms to yield cognitive labor which produces larger brains, faster brains, or better mind designs.”
“recursive self-improvement”: “The Intelligence Explosion Thesis says that, due to recursive self-improvement, an AI can potentially grow in capability on a timescale that seems fast relative to human experience.”

Bostrom (2014), Superintelligence

“recursive self-improvement”: “an early version of the AI could design an improved version of itself […] such a process of recursive self-improvement might continue long enough to result in an intelligence explosion […] to radical superintelligence.” (The book’s well-known “seed AI”/intelligence-explosion passage is older — see the 2009 entry above — so it is credited there rather than to the 2014 book.)
“artificial superintelligence (ASI)”: “We can tentatively define a superintelligence as any intellect that greatly exceeds the cognitive performance of humans in virtually all domains of interest.”

Yampolskiy (2015), On the Limits of Recursively Self-Improving AGI

“recursive self-improvement” (taxonomy): “In this work we analyze limits on computation which might restrict recursive self-improvement. We also introduce Convergence Theory which aims to predict general behavior of RSI systems.” (A companion AGI-2015 paper, Analysis of Types of Self-Improving Software, gives an explicit taxonomy distinguishing modification, weak (improvement), and strong (recursive) self-improvement.)

Christiano (2018), Takeoff Speeds

“slow takeoff” / “fast takeoff”: “whether the development of AGI will look more like a breakthrough within a small group (‘fast takeoff’), or a continuous acceleration distributed across the broader economy or a large firm (‘slow takeoff’). […] [operationalized:] There will be a complete 4 year interval in which world output doubles, before the first 1 year interval in which world output doubles […] fast takeoff is the negation of the above statement.” (The takeoff vocabulary is older — “hard”/“soft” takeoff and “FOOM” go back to the 2008 Hanson–Yudkowsky debate; Christiano’s contribution is the specific continuous-but-fast “slow takeoff” framing and its economic operationalization.)
“recursive self-improvement”: “The most common argument for recursive self-improvement introducing a new discontinuity seems be: some systems ‘fizzle out’ when they try to design a better AI, generating a few improvements before running out of steam, while others are able to autonomously generate more and more improvements.”

Aghion, Jones, and Jones (2019), Artificial Intelligence and Economic Growth

“singularities”: “A.I. can become rapidly self-improving, leading to ‘singularities’ that feature unbounded machine intelligence and/or unbounded economic growth in finite time.”
“Type I” / “Type II” growth explosion: “a ‘Type I’ growth explosion, where growth rates increase without bound but remain finite at any point in time; and a ‘Type II’ growth explosion, where infinite output is achieved in finite time.”

Roodman (2020), Modeling the Human Trajectory

“superexponential” growth: “A univariate stochastic model is introduced that is mathematical kin with the neoclassical economic model […] when projected forward, the superexponential equation sends [GWP] to infinity in finite time. […] if the patterns of history continue, then some sort of economic explosion will take place again, the most plausible channel being AI. It wouldn’t reach infinity, but it could be big.”

Davidson (2021), Could Advanced AI Drive Explosive Economic Growth?

“explosive growth”: “‘explosive growth’, meaning > 30% annual growth of gross world product (GWP)”.

Nordhaus (2021), Are We Approaching an Economic Singularity?

“Singularity”: “rapid growth in information technology and artificial intelligence will cross some boundary, after which economic growth will rise rapidly […]. I define Singularity as a time when the economic growth rate crosses 20 percent per year.”

Karnofsky (2021), Forecasting Transformative AI: What Kind of AI?

“Process for Automating Scientific and Technological Advancement (PASTA)”: “AI systems that can essentially automate all of the human activities needed to speed up scientific and technological advancement. I will call this sort of technology Process for Automating Scientific and Technological Advancement, or PASTA. (I mean PASTA to refer to either a single system or a collection of systems that can collectively do this sort of automation.)”

Davidson (2023), What a Compute-Centric Framework Says About Takeoff Speeds

“software-only singularity”: “There’s a ~65% chance of a temporary ‘software-only singularity’, where AGIs improve software increasingly quickly while being run on a ~fixed hardware base.” (The first use of the exact term “software-only singularity”; the scenario is later reused by Erdil and Barnett (2025). Epoch credits the related “software singularity” to Davidson.)
“artificial superintelligence (ASI)”: “we go from AGI […] to superintelligence (AI that very significantly surpasses humans at ~100% of cognitive tasks) in less than a year.”

Erdil and Besiroglu (2023), Explosive Growth from AI Automation

“explosive growth”: “we will refer to ‘explosive growth’ as growth an order of magnitude greater than what is typical in today’s frontier economies. Specifically, we define this as annual real gross world product (GWP) exceeding 130% of its maximum value over all previous years.” (First posted as arXiv:2309.11690 in September 2023; the “2024” sometimes cited reflects a later revision.)

Trammell and Korinek (2023), Economic Growth under Transformative AI

“self-replicate” / “self-improve”: “fully automating production alone (so that machines can self-replicate) would dramatically raise the growth rate […]. Automating R&D (so that machines can self-improve) would accelerate the transformation, but may not produce it in isolation.” (NBER WP 31815, issued October 2023; revised April 2026.)

Zelikman et al. (2023), Self-Taught Optimizer (STOP): Recursively Self-Improving Code Generation

“recursively self-improving code generation” (a boundary case): “We refer to this problem as recursively self-improving code generation, which is inspired by but not completely a Recursively Self-Improving (RSI) system, as the underlying language model remains unchanged. […] Since the language models themselves are not altered, this is not full recursive self-improvement.” (A useful definitional boundary case: a language model improves the scaffold that calls it, but not its own weights.)

Hutter, Quarel, and Catt (2024), An Introduction to Universal Artificial Intelligence

“artificial superintelligence (ASI)”: “We use the term Artificial Super-Intelligence (ASI) to describe an agent that is on par or beyond human geniuses exceeding the cognitive performance of most humans in a reasonably broad domain. It could compose music like Mozart, or derive new insights in mathematics to rival that of Gauss.” (A recent UAI/AIXI-theory definition of ASI. Note this is not an early origin of the acronym — explicit uses of “artificial superintelligence (ASI)” appear earlier, e.g. Pohl 2015 and Barrett & Baum 2016.)

Eth and Davidson (2025), Will AI R&D Automation Cause a Software Intelligence Explosion?

“AI Systems for AI R&D Automation (ASARA)”: “systems, which we call AI Systems for AI R&D Automation (ASARA), would represent a critical threshold in AI development. The hypothesis is that ASARA would trigger a runaway feedback loop: ASARA would quickly develop more advanced AI, which would itself develop even more advanced AI, resulting in extremely fast AI progress – an ‘intelligence explosion.’ […] [ASARA] can be thought of as being able to substitute for any remote R&D workers at companies advancing the state of the art for AI.”
“software intelligence explosion (SIE)”: “AI systems could become dramatically more capable just by finding software improvements […]. We call this scenario a software intelligence explosion (SIE).”
“intelligence explosion”: “ASARA would trigger a runaway feedback loop: ASARA would quickly develop more advanced AI, which would itself develop even more advanced AI, resulting in extremely fast AI progress – an ‘intelligence explosion.’”

Davidson and Houlden (2025), How Quick and Big Would a Software Intelligence Explosion Be?

“AI Systems for AI R&D Automation (ASARA)”: “we define ASARA as AI that can replace every human researcher at an AI company with 30 equally capable AI systems each thinking 30X human speed.”
“software intelligence explosion”: “this could precipitate a software intelligence explosion – a period of rapid AI progress due to AI improving AI software.”

Ho and Whitfill (2025), The Software Intelligence Explosion Debate Needs Experiments

“software intelligence explosion”: “These AIs are smart enough to find new algorithms to make smarter AIs, which make even smarter AIs, and so on […] multiple years of AI progress compressed into a single year just through software advances — a ‘software intelligence explosion’.”

Erdil and Barnett (2025), Most AI Value Will Come from Broad Automation, Not from R&D

“software-only singularity” (reusing Davidson (2023)): “If AI systems were able to automate the process of their own software R&D, a software-only singularity might become possible: on a fixed stock of compute, we could run AI researchers who search for ways to improve their own algorithms, which would allow us to run even more virtual researchers to make yet more software progress, et cetera.”

Clark (2025), Import AI 455: AI Systems Are About to Start Building Themselves

“no-human-involved AI R&D”: “no-human-involved AI R&D - an AI system powerful enough that it could plausibly autonomously build its own successor”.

Zhang et al. (2025), Darwin Gödel Machine: Open-Ended Evolution of Self-Improving Agents

“self-improving coding agent”: “The Darwin Gödel Machine is a self-improving coding agent that rewrites its own code to improve performance on programming tasks. […] the DGM hints at a future in which such ingenuity is automated, evolving through self-referential cycles of continuous self-improvements.” (An empirical, evolutionary relaxation of Schmidhuber’s Gödel machine: instead of proving a rewrite is beneficial, it validates each self-modification against coding benchmarks such as SWE-bench.)

Kokotajlo, Alexander, et al. (2025), AI 2027 (Takeoff Forecast)

“superhuman coder (SC)”: “an AI system that can do any coding tasks that the best AGI company engineer does, while being much faster and cheaper.”
“superhuman AI researcher (SAR)”: “An AI system that can do the job of the best human AI researcher but faster, and cheaply enough to run lots of copies.”
“superintelligent AI researcher (SIAR)”: “An AI system that is vastly better than the best human AI researchers. The gap between SAR and SIAR is 2x the gap between an automated median AGI company researcher and a SAR.”
“artificial superintelligence (ASI)”: “An AI system that is much better than the best human at every cognitive task.”

Kokotajlo, Lifland, et al. (2025), AI Futures Model: Dec 2025 Update

“superhuman AI researcher (SAR)”: “An AI system that can do the job of the best human AI researcher but 30x faster and with 30x more agents […]. It must have enough diversity of expertise to on average do the same for other top researchers with complementary skills.”
“software intelligence explosion”: “Models of the software intelligence explosion (SIE), i.e. AIs getting faster at improving its own capabilities without additional compute.”

Chan et al. (2026), Measuring AI R&D Automation

“AI R&D automation (AIRDA)”: “We use AI R&D automation (AIRDA) to refer to the use of AI to carry out parts of [the activities involved in developing and improving AI systems]. Automation can be implemented to differing degrees, from simply using AI as a hypothesis generator, to deploying teams of artificial researchers that carry out all parts of the pipeline. […] increasing involvement of AI in the R&D pipeline could shift human involvement towards verifying that experiments have been designed and run correctly.”

Cotra (2026a), Self-Sufficient AI

“self-sufficient AI”: “Let me take a stab at defining a different milestone that’s hopefully more concrete and less debatable: a completely self-sufficient AI population. By this I mean a set of AI systems along with enabling physical infrastructure (e.g. the chips those AIs run on and the industrial stack that produces and powers those chips and robots that can build and maintain that stack) such that if every human being suddenly dropped dead, the AIs could keep making more copies of themselves indefinitely.”

Cotra (2026b), Six Milestones for AI Automation

“Adequacy”: “the very first time the hit from removing humans is smaller than 100% in a given sector — the first time that machines can just barely produce output in that sector, painstakingly limping along by themselves without any humans to operate them. Let’s call this milestone adequacy.”
“Parity”: “The next interesting milestone is parity — the first point when getting rid of the AIs slows down progress in the sector more than getting rid of all the humans.”
“Supremacy”: “Beyond parity, we can talk about supremacy — the first point when productivity in a given sector would actually increase from removing humans.”

Davidson et al. (2026), When Does Automating AI Research Produce Explosive Growth?

“recursive self-improvement”: “recursive self-improvement—where AI systems become increasingly capable of designing and improving themselves—creates a feedback loop leading to an ‘intelligence explosion’ and rapid economic growth.”
“technological feedback loop”: “technological feedback loops across the innovation network […] a network of heterogeneous research sectors, where innovations in one sector spill over to increase the rate of innovation in other sectors.”
“economic feedback loop”: “an economic feedback loop, in which higher output generates more resources that can be deployed to drive further economic growth. The classic example is capital accumulation: higher output leads to more investment, which produces yet more output.”
“explosive growth”: “growth becomes superexponential (‘explosive’) […] if the combined strength of technological and economic feedback loops overcomes diminishing returns.”
“mathematical singularity”: “if β < 0, so that there are increasing returns, then there is a literal mathematical singularity: \(S_t\) approaches infinity in finite time.”
“intelligence explosion”: “AI labs are increasingly using AI itself to accelerate AI research, creating a feedback loop that could lead to an intelligence explosion.”

Favaro and Clark (2026), When AI Builds Itself

“recursive self-improvement”: “Taken far enough, and given enough compute, that trend points to an AI system capable of fully autonomously designing and developing its own successor. This is called recursive self-improvement. We are not there yet, and recursive self-improvement is not inevitable. But it could come sooner than most institutions are prepared for.”

Clark (2026), Import AI 460

“maximalist” RSI: “a maximalist version where an AI system is smart enough to autonomously design its own successor”.
“prosaic” RSI: “a more prosaic version where we begin to see a compounding speedup of the productivity of the AI labs themselves.”

Google DeepMind (2026), From AGI to ASI (post-publication addition)

“recursive improvement” / “artificial superintelligence”: “the report discusses four potential pathways from AGI to ASI: scaling AGI, AI paradigm shifts, recursive improvement, and ASI emerging from large-scale multi-agent collectives.” (Published 12 June 2026 — after this post’s original 5 June date but before its last-checked date. Notable for treating recursive self-improvement as one of several routes to superintelligence, alongside multi-agent collectives.)

Acknowledgements

Thanks to Marcus Hutter for pointing out several earlier attributions that my first version missed.

Solomonoff’s “infinity point” (1985) — pointed out by Hutter — has now been checked against the original paper (raysolomonoff.com) and the wording is confirmed. One residual caveat: the 2026 arXiv identifiers for very recent preprints may not be fully stable.

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Citation

BibTeX citation:

@online{cunningham2026,
  author = {Cunningham, Tom},
  title = {Definitions of {Recursive} {Self-Improvement}},
  date = {2026-06-05},
  url = {tecunningham.github.io/posts/2026-06-05-rsi-definitions.html},
  langid = {en}
}

For attribution, please cite this work as:

Cunningham, Tom. 2026. “Definitions of Recursive Self-Improvement.” June 5, 2026. tecunningham.github.io/posts/2026-06-05-rsi-definitions.html.