Equation 3 · Multimodal AI in 2035: Scenarios and Falsifiers
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol C
C is part of the quantity the equation computes from the expression on the right.
Symbol t
t is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Symbol U
U is one factor in the product that computes the quantity on the left.
Symbol u^*
is one factor in the product that computes the quantity on the left.
Symbol R
R is one factor in the product that computes the quantity on the left.
Symbol r^*
is one factor in the product that computes the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →superscript
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
See an illustrated explanation →How to interpret it
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What the article says around this equation
Whether the multimodal AI market consolidates around a small number of vertically integrated any-to-any platforms, or remains a supply chain of composed specialist vendors the way it mostly is today, is not a third axis; it is what the other two jointly produce. Write U(t) for the share of new production multimodal deployments built on a single native any-to-any model rather than a composed pipeline — Axis A’s own proxy — and R(t) for the share of multimodal deployments operating in open, uncurated conditions that meet a reliability bar without a human fallback — Axis B’s own proxy. A platform bet on one any-to-any vendor only pays off if that vendor’s model is both the one everyone is…
Read the full surrounding passage
Whether the multimodal AI market consolidates around a small number of vertically integrated any-to-any platforms, or remains a supply chain of composed specialist vendors the way it mostly is today, is not a third axis; it is what the other two jointly produce. Write U(t) for the share of new production multimodal deployments built on a single native any-to-any model rather than a composed pipeline — Axis A’s own proxy — and R(t) for the share of multimodal deployments operating in open, uncurated conditions that meet a reliability bar without a human fallback — Axis B’s own proxy. A platform bet on one any-to-any vendor only pays off if that vendor’s model is both the one everyone is building on and reliable enough to run without a safety net; a highly reliable system stitched together from several vendors’ best components does not consolidate the market around any one of them. Consolidation is therefore better modelled as a conjunction than an average: . C(t) stays at zero however high either term climbs alone. Axis A determines whether U(t) can plausibly clear within this article’s horizon; Axis B determines whether R(t) can. Neither can be inferred from the other, which is why they are kept as two axes rather than folded into one.
Sources cited in the article section
- [1] Hello GPT-4o ↗
- [3] Gemini: A Family of Highly Capable Multimodal Models ↗
- [4] Chameleon: Mixed-Modal Early-Fusion Foundation Models ↗
- [6] Efficient Multimodal Large Language Models: A Survey ↗
- [5] Scaling Native Multimodal Pre-Training From Scratch ↗
These citations give research context. Read each source to check which claims it supports.
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