equiNAS: A Typed DSL for Certified Evolution of Equivariant Architectures

Neural architecture design has evolved from manual engineering to algorithmic search over predefined spaces, and more recently to LLM-assisted generation of architectural modifications. While LLMs make architecture search substantially more flexible, scientific neural networks often obey hard structural constraints that cannot be reliably enforced by executable code alone. In equivariant models, for example, representation types and geometric transformation laws must remain consistent throughout the computation graph; a candidate may compile and train successfully while silently violating the intended symmetry. We introduce equiNAS, a typed domain-specific language that turns architecture evolution into certified program transformation. Architectural values expose their representation-theoretic content as semantic types, and every mutation—whether proposed by an LLM or a programmatic search policy—is expressed as a typed patch whose preconditions, dimensional consistency, and equivariance contracts are checked before training. This constrains generation to physically valid transformations without requiring the proposer itself to reason perfectly about representation theory. On EquiformerV3, the typed interface verifies 300/300 proposals against 192/300 (64%) for untyped structured patches under 300 matched architectural intentions per arm, with only 103/600 unrestricted code edits passing the finite-sample equivariance probe in an open-ended stress test; the same explicit intermediate representation enables ahead-of-time compilation and a $1.87\times$ improvement in steady-state training throughput over the production static backend. Searching the certified space also produces parameter-matched architectures with lower mean validation and test error on QM9 across three seeds and improved long-horizon optimization, with additional exploratory transfer gains across molecular properties. Together, these results indicate that typed architectural representations provide a practical interface between flexible LLM-based search and the hard structural requirements of scientific neural networks.