Figure from Frank (2024) "Bridging the Data Gap"

scale.R

library(xkcd)
library(tidyverse)

d <- tibble(age = 1:20) |>
  mutate(upper = 1e6 * age * 12 + ifelse(age > 5, 2.5e5 * 52 * (age - 5), 0), 
         lower = 1e5 * age * 12) |>
  pivot_longer(upper:lower, names_to = "bound", values_to = "vocabulary")

pdf("~/Projects/AI commentaries/scale.pdf", width = 5, height = 4)
ggplot(d, aes(x = age, y = vocabulary, col = bound)) + 
  annotate(geom = "text", y = 9e8, x = 19.5, label = "human upper bound", 
           hjust = 1, col = "#dc322f") + 
  annotate(geom = "text", y = 5e7, x = 19.5, label = "human lower bound", 
           hjust = 1, col = "#268bd2") +  
  geom_point() + 
  geom_line() + 
  geom_hline(yintercept = 5e11 * .75, lty = 2, col = "darkgray") + 
  geom_hline(yintercept = 1e12 * .75, lty = 2, col = "black") + 
  annotate(geom = "text", y = 1.4e12, x = 1, label = "Chinchilla", hjust = 0) + 
  annotate(geom = "text", y = 2e11, x = 1, label = "GPT-3", hjust = 0, col = "darkgray") +  
  geom_vline(xintercept = 5, lty = 3) + 
  geom_vline(xintercept = 20, lty = 3) +
  scale_y_log10(breaks = c(1e6, 1e9, 1e12), 
                minor_breaks = c(1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12),
                limits = c(1e5, 1e13))+ 
  ggthemes::theme_few() +
  ggthemes::scale_color_solarized(guide = "none") + 
  xlab("Age (years)") + 
  ylab("Words of language input")
dev.off()