How rising and falling topics are screened AI

Combining a year-score test, endpoint effect size and rank consistency to identify directional topic histories.

A topic can become more common in a sample without increasing every single year. The rise and fall screen combines the direction of the whole history with the size of the difference between its early and late years.

Compare rates before comparing histories

Let $c_y$ be a topic’s paper count in year $y$, and $n_y$ the number of papers sampled that year. Its annual rate is $c_y/n_y$. Using that denominator prevents a larger annual sample from looking like topic growth by itself. The sample timeline note explains what these rates can and cannot say about the broader literature.

The trend score compares the observed distribution across years with a constant-share reference. Years are centered using the annual sample sizes as weights. A positive score places more topic papers toward later years; a negative score places more toward earlier years. The conditional variance fixes the total topic count, and a normal approximation gives a two-sided p-value.

Require a change large enough to inspect

The effect size compares the pooled last three years with the pooled first three:

$$F=\frac{(C_{\mathrm{late}}+0.5)/N_{\mathrm{late}}}{(C_{\mathrm{early}}+0.5)/N_{\mathrm{early}}}.$$

The half-count keeps the ratio finite when an endpoint has no papers; the statistical test uses the observed counts. A rise requires $F\geq1.5$, and a fall requires $F\leq1/1.5$.

The screen also requires an absolute Spearman rank correlation of at least 0.6 between year and annual rate, plus an adjusted p-value no greater than 0.05. Rank correlation describes directional consistency; it does not require a straight line or uninterrupted growth.

Ranking is separate from screening

The ordering score multiplies the absolute standardized trend score, the absolute log-base-two fold-change capped at four, and the absolute rank correlation. This favors pronounced, consistent histories while limiting the influence of extreme ratios from near-zero endpoints.

A large endpoint jump can therefore rank highly without meeting the consistency threshold. “Screened only” applies all criteria; the broader list remains useful for inspecting abrupt or irregular changes. Multiple-testing adjustment addresses the number of histories inspected, rather than the magnitude of a change.