Differentiable max-SAT Solver for real world optimization problems (navokoj.shunyabar.foo)

Navokoj is a new GPU-first max‑SAT/SAT solver that claims to combine gradient-based continuous relaxations with thermodynamic-style energy landscapes and a “Chaotic Lotus” annealing architecture to escape local minima. The team advertises dramatic real‑world results — e.g., a 250-person scheduling instance with 2,275 conflicting constraints solved to 97.2% clause satisfaction in 4.7s — and production benchmarks on much larger problems (random 3‑SAT up to ~1M variables with ~92% satisfaction, logistics at 435k variables with ~97% satisfaction). It’s presented as an approximate-but-fast alternative to exact solvers for industrial combinatorial tasks, with beta APIs for pre‑flight diagnostics (unsat probability), engine modes (Mini: Adam gradient descent; Pro: chaotic annealing; DeepThink: ensemble refinement; Navokoj‑X: GF(2) XOR specialist), and direct integration with LLMs (Claude, GPT‑4) to submit natural language constraints. Technically, Navokoj emphasizes millisecond‑latency gradient updates on GPUs (claimed throughput ~24M variable updates/sec, empirical scaling O(N^1.01), 1M variables in 24GB VRAM) and spectral diagnostics (DEFEKT) to detect structural unsolvability before heavy compute. The architecture mixes continuous relaxations, periodic noise injection, and chaotic dynamics to navigate phase‑transition regions (they highlight a β=1 transition) and then ensemble/refinement stages to boost solution quality. For AI/ML practitioners this implies a pragmatic toolchain for embedding fast, approximate combinatorial reasoning into real‑time systems and LLM agents — but note Navokoj’s approach trades exact guarantees for speed and high‑quality approximations, and is currently offered in beta.