Lotus: A Logic-based Object-centric Topological Unified Solver

In bipartite graph constraint satisfaction problems such as channel error-correction decoding, existing graph neural networks (GNNs) and belief propagation (BP) algorithms suffer from severe error floors caused by trapping set deadlocks induced by overlapping short cycles. To address this bottleneck, we propose Lotus (Logic-based Object-centric Topological Unified Solver), a neuro-algebraic framework that integrates deep unfolded networks with local discrete algebraic elimination across a Base GNN, an Expert GNN, and an algebraic elimination module termed xLoop. Lotus is structured around three core mechanisms: (i) an isotropic Variable Module and parameter-free Check Module devoid of positional encodings, avoiding graph-specific eigenspectrum overfitting to preserve permutation equivariance and enable zero-shot length and topology generalization; (ii) closed-form forward analytical gradients derived from a soft parity potential function, paired with Targeted Constraint Relaxation (TCR) and dual dynamic gating to directly steer forward trajectories without test-time optimization; and (iii) the xLoop module, which pairs weighted Laplacian spectral bisection with streaming Gaussian elimination (SGE) and Local Maximum Likelihood (Local ML) selection to algebraically resolve long-tail trapping sets within size-capped candidate subgraphs. Evaluated on 3GPP 5G New Radio (NR) and regular quasi-cyclic LDPC (QC-LDPC) matrices, Lotus achieves a 75.0%–83.9% hard-instance recovery rate, suppresses suboptimal convergence (SC) by approximately 50%, approaches the near-ML empirical performance bound of ordered statistics decoding (OSD-3) (with BP+xLoop also achieving near-ML performance), and preserves an asymptotic linear latency scaling of O(N) that operates 15x to 41x faster than OSD-3.