Abstract
<title>Abstract</title> <p>Educational item banks can be globally diverse while locally coupling particular language realizations with particular problem types. We investigated how such local allocation affects structured parsing and whether a plausible graph-theoretic property explains the effect. The task required a character-level Transformer trained from random initialization to output an operation label and START, CHANGE, and RESULT roles for synthetic addition and subtraction word problems; it did not require computing the unknown quantity. Experiment 1 used a 2 × 2 fixed-marginal design that concentrated or distributed lexical families and syntax/discourse-family bundles across six operation-by-unknown-role cells. Global family counts, cell budgets, fact families, and total characters were fixed, while local coverage, pair count, repetition, duplication, entropy, and graph structure changed as allocation packages. Across 384 held-out-seed runs, distributing lexical families increased lexical-reassignment exact accuracy by .484, 95% crossed-seed CI [.414, .560], and distributing syntax/discourse bundles increased the corresponding reassignment accuracy by .929, [.901, .951], without reducing matched performance. Within the fully distributed condition, exact pairs withheld from the target cell were parsed at .923 accuracy. Experiment 2 then matched within-cell component exposure, vertex degree, edge count, repetitions, characters, and the exact common withheld pairs while changing only whether the lexical-by-discourse graph was one connected 8-cycle or two disconnected K2,2 components. Across 256 new runs, connectivity produced no advantage: the 2.67M-model difference was −.007, [−.041, .025], while both graph structures exceeded .90 accuracy on the common composition test. The smaller 0.80M model showed the same pattern. Together, the experiments show that fixed global marginals do not prevent severe local-allocation effects, but global graph connectivity is unnecessary once every component has within-cell multi-partner exposure under the tested design. The result supports auditing and designing educational data at the problem-type-by-language level rather than relying on corpus-wide diversity counts alone.</p>