Federated Logic Gate Networks via Boolean Feature Selection

Federating a LGN is challenging because each gate is parameterised by a distribution over 16 Boolean operations, so averaging parameters across clients does not correspond to averaging the underlying functions. Under non-IID data, such parameter-space merging collapses to near-chance accuracy. Boolean Feature Selection (BFS) avoids this issue by selecting discrete Boolean functions rather than averaging parameters. We propose Federated Boolean Feature Selection (FBFS), which extends BFS to LGNs by treating hardened last-layer gates as candidate Boolean features and aggregating per-class, per-gate sufficient statistics across clients. Clients share only firing aggregates computed on a held-out split, allowing the server to reconstruct discriminative scores, defined as the gap between a gate's mean firing for a class and for the remaining classes, without accessing raw data. This procedure is equivalent to centralized BFS on the union of client data. We further introduce a diversity-regularized variant of FBFS that encourages complementary feature selection across gates. Empirically, FBFS is the only data-free method we evaluate whose performance remains stable under extreme non-IID settings, outperforming parameter-space merging and other baselines by large margins. It maintains high accuracy across a wide range of heterogeneity levels and scales to large architectures. In addition, FBFS enables efficient deployment: the resulting models compile to hardware-efficient logic representations with substantially fewer post-synthesis cells than ensemble-based alternatives while remaining bit-exact with their software counterparts.