Problem Reductions at Scale: Agentic Integration of Computationally Hard Problems

Agentic coding makes code generation cheap, but reliable completion remains difficult: the agent that writes the code is a weak judge of whether it is done. We present Humanize, a multi-agent orchestration workflow for agentic coding built around judgement engineering: explicit, mechanically enforced decisions at the boundaries between planning, implementation, review, and learning. A human approves a plan contract, a builder agent implements it in rounds, and a reviewer agent from another vendor decides completion; deterministic hooks, not a model, route work between these roles and enforce 72 mechanical gates. Viewed as a Markov chain over repository states, alternating builder and reviewer samples jointly from two models, so a defect survives only if both miss it. We study Humanize through its deployment, 118 public postmortems of real loops, and its applications. Over 68 versions in 108 days, it gathered 1,468 GitHub stars. Applications include a 567-file gem5 build-system migration under upstream review; Kernel Design Agents, which extend the loop with a kernel knowledge base and profiling feedback and placed in the top three of all three Full-Agent tracks of the MLSys 2026 FlashInfer contest; and, through Humanize Olympiad Agents (HOA), full scores in IOI 2026, IMO 2026, IPhO 2026, and IBO 2024, 418.5/437 in IChO 2026 (gold-medal). Humanize also achieves 672/672 on PutnamBench and ranks first (251/303) on Lean-Eval's leaderboard even competiting with professional mathematicians. The postmortems show that independent review catches unsupported builder claims, but stopping remains a key weakness. In reports that separate rounds by phase, two thirds of rounds occurred after implementation was accepted. This evidence is observational, not a controlled comparison of workflows.

Many optimization problems are solved repeatedly on instances drawn from the same underlying distribution. In this setting, a system can begin with a general-purpose solver and use experience from previous instances to learn a cheaper way to solve future ones. We formalize this as distribution-aware programming: samples from an unknown deployment distribution are used to produce executable solver code whose quality and runtime generalize to new instances. A simple analysis shows how sample access interpolates between distribution-oblivious and distribution-informed algorithm design, and when the offline cost of specialization is recovered through lower deployment cost. We instantiate this framework with an LLM agent that proposes structural hypotheses, analyzes training instances, and synthesizes specialized solver code; the LLM is used only before deployment. Across $21$ structured combinatorial-optimization distributions, the synthesized solvers achieve high quality while often replacing generic search or optimization with smaller distribution-specific computations. Against released PACE competition solvers, our method remains competitive while using substantially less runtime: $75$--$125\times$ less on PACE 2025 Dominating Set, $80$--$96\times$ less on Hitting Set, and more than $34{,}000\times$ less on the PACE 2024 OCM exact track. More broadly, the results suggest using AI not only to solve optimization problems, but to learn how recurring distributions should be solved.

The harness surrounding a language model is a central determinant of agent performance. Recent methods optimize harnesses by searching over complete programs, where individual mechanisms are difficult to isolate and reuse. We introduce PluginRSI, which represents a harness as a composition of atomized plugins and organizes harness evolution around these plugins. Individual plugins are improved independently and accumulated in a shared library, then recombined into new harnesses at each iteration. PluginRSI improves over existing harness optimization methods across software engineering, command-line interaction, and question-answering tasks. The resulting harnesses retain their advantage when transferred to other solver models without further optimization. The evolved plugin library accelerates subsequent optimization from the initial harness, which helps faster and higher convergence on unseen tasks. These results show that accumulating reusable mechanisms provides an effective basis for continued harness improvement.