Recursive Self-Improvement: Intelligence Takeoff Simulator

Recursive Self-Improvement

Regime: —

Improvement rate r 0.35

How fast each unit of capability compounds into more capability per second.

Returns exponent p 1.6

p<1 diminishing returns (soft takeoff) · p=1 exponential · p>1 accelerating returns (hard takeoff).

Compute ceiling K 150

Hardware / data / energy limit the system cannot self-improve past.

Live Readouts

Capability I(t)

1.0

Growth rate dI/dt

0.02 /s

% of ceiling

0.7%

Elapsed time

0.0 s

How it works

Model a system's capability I(t) growing through recursive self-improvement: each increment of intelligence is spent partly on making the next increment easier to find. Following Bostrom's optimization-power / recalcitrance framing, normalise capability as x = I/K ∈ [0,1] against a hardware/data/energy ceiling K, and integrate:

dx/dt = r · x^p · (1 − x)
I(t) = x(t) · K

r — optimization power: how effectively the system converts its current capability into research output.
p — returns to intelligence. p<1: each doubling helps less (recalcitrance rising faster than capability — a soft takeoff). p≈1: capability compounds at a roughly constant rate. p>1: capability accelerates its own growth (recalcitrance falling) — a slow start followed by a runaway hard takeoff.
(1 − x) — the ceiling term: no matter how sharp the takeoff, growth must saturate once the system exhausts the compute/data/energy available to it.
Breakthrough — a one-off jump in x, modelling an external algorithmic insight (e.g. a new training method) rather than the system's own recursive gains.

The network on the right visualises I(t) directly: each node is one unit of capability, wired to the earlier capability it was built on (a literal recursion tree), so the graph's own growth rate is the plotted curve.

ceiling K = 150

Capability nodes (recursion tree) Core / singularity threshold

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