imagining syntax

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scaling → vocabulary-scale

vocabulary-scale

investigation

Intent

Intent: How the result scales with vocabulary size and holdout \@{vocabulary-scale-intent}

This investigation asks how the paper's agreement result scales along the vocabulary axis. The grammar makes vocabulary a free parameter, and two things change with it at once: how many tokens the fixed model must represent, and how much seen pairing evidence training provides. The member experiments hold the model at the paper's architecture and pull those apart: a six-size sweep from vocabulary 20 to 160 at a fixed quarter holdout, and two matched sweeps at a one-third holdout, at vocabulary 60 and 120, that vary the evidence fraction with the vocabulary held still.

Referenced by (1 direct)

Direct references:

Conclusions

The intermediate peak is not an artifact of the paper's vocabulary: it appears at every size from 20 to 160 (peak universal). Its height is set by model capacity rather than by evidence: the peak rises to vocabulary 60 and falls back (the capacity ceiling), the decline carries the signature of capacity binding, with the otherwise easy conditions off their ceilings (capacity binding), and the same 256-dimensional embedding limit the model-scale work reaches by shrinking the model is reached here by growing the token inventory (the embedding ceiling).

The holdout fraction turned out to be a second-order axis that matters only where capacity is already strained. At vocabulary 60, raising the holdout from a quarter to a third changes nothing: the peak keeps its location and height (the peak holds). At vocabulary 120 the same change costs the peak about three points and pushes it toward more concentrated distributions (drops and moves right), and it drives the cohort's seed bimodality deeper into the grid (the split approach), extending the deepening the quarter series already shows (deepening splits); the seed-level mechanics of those splits belong to the bimodality thread (bimodality).

What would change this reading. The one-third-holdout sweeps carry five seeds against the series' ten, so their spread estimates are coarse. Everything here sits at the paper's 1200-step budget and single architecture, and the series' own named follow-up, a wider model at the largest vocabulary, is the direct test of the capacity reading.

Referenced by (1 direct)

Experiments

Referenced by

vocabulary-scale-conclusion: A robust peak whose location is set by the budget
vocabulary-scale-intent: How the result scales