Neural Spectral Capacity with Residual Context for Heterogeneous Resource Allocation within Transformers

Chenyu Zhu, Ruoyu Zhao, Zhichao Lu

Predicting relative trained performance from architectural specifications can guide design when training costs limit experimentation. Neural Spectral Capacity (NSC) provides such a heuristic, but scores projections independently and assigns identical scores to compatible reorderings of the same layer configurations. We introduce Residual-Aware Neural Spectral Capacity (ResNSC) for Transformers, using a specification-derived statistical reference for accumulated residual updates to determine the input and residual-state statistics in each projection's capacity calculation, while retaining additive evaluation without data or instantiated weights. When residual widths vary, earlier choices affect later scores, so we augment NSC's allocator (NSC-DP) with residual history beyond its layer-and-budget state. ResNSC-DP jointly allocates residual and feed-forward widths under a resource budget, with certified bounds on the best numerically evaluated ResNSC score within a specified finite candidate set. At the 121M and 374M pretraining scales, selected architectures achieve lower mean perplexity than uniform, variable-width, and tapered allocations on FineWeb-Edu, WikiText-2, and LAMBADA…