Limits RegistryPUBLIC RECORDLimits RegistryResearch Console →Fully connected ReLU networks no wider than the input dimension fail universal approximation.
The question, scope, and sources behind this Registry record.
Under the recorded neural network theory model, establish width <= d_in is not universal.
Current frontiers derived from accepted Claims.
Assertions tied to evidence, attribution, and review.
The frontier as it changed over time.
Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.
No accepted machine-checked reproductions are recorded for this Limit.
Limits Registry. LR-003616. ReLU width-d universal-approximation impossibility. 2026.