Direction A · Reveal the bigger picture
How much curve is left?
One 10× gain is useful. Six independent 10× gains multiply to a million. Explore what changes when the paths improve together.
Six paths. A much bigger curve.
Choose which paths improve. Set how far each one goes.
1 order of magnitude (OOM) = 10×. Two = 100×. Six = 1,000,000×.
Paths that improve together
Endpoint gain for each path: 1× to 1,000×.
Try a limit
This example treats gains as independent. Real gains can overlap, depend on one another, or meet limits.
What this model assumes
Each path follows an assumed exponential curve: fᵢ(p) = 10^(gᵢ × p). Progress p runs from 0 to 1. The endpoint gain gᵢ runs from 0 to 3 orders of magnitude. For example, gᵢ = 1 means a path reaches 10× at the endpoint.
Combined output = ∏ fᵢ. Added output = 1 + Σ(fᵢ − 1), so the starting output is counted once. The gap in orders of magnitude = log₁₀(combined / added). Six 10× gains give 1,000,000× combined versus 55× added: a 4.26-OOM gap. Six 100× gains give one trillion× combined versus 595× added: a 9.23-OOM gap.
The optional limit freezes the first selected path at 40% progress. All curves use the same visible horizontal range. The vertical scale adjusts when you change paths, gains, or range; it stays fixed when you move the progress marker.
The six paths follow the themes discussed in the source video. The names do not make them independent, measured factors in one equation. In particular, hardware, training, and AI-assisted research can affect the same underlying resources. Their real gains may overlap. Test-time training changes model parameters during use; test-time compute can increase without such changes.
This is a model of a possible mechanism, not measured intelligence, a forecast, or a claim that all six gains will multiply. The horizontal axis is illustrative progress, not elapsed time or compute. Classic neural scaling laws describe empirical power laws for prediction loss; they do not establish these six exponential curves. Original scaling research ↗
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