Optimal Allocation of Embedding Dimensions under Finite-Sample Constraints

What the math gives to ML

The paper turns categorical embedding-size selection into a finite-budget resource-allocation problem rather than tuning every dimension independently. Its transferable asset is the explicit approximation–estimation tradeoff: representation quality is summarized by a singular-value-based approximation value, while estimation cost grows with the number of embedding parameters. This suggests allocating embedding dimensions nonuniformly across tables, with larger dimensions going to predictors whose latent category structure has both high spectral complexity and low parameter cost. The most practical adaptation is to use a short pilot model to estimate each table's spectral value, compute a square-root allocation under a global parameter budget, and then integer-round and locally refine the result.