# Executive summary --- Partial reproduction of NonZero. Of the paper's 6 claims, Claim 1's core mathematical formulation was verified exactly (finite-difference identity holds to floating-point precision), and the surrogate model was shown to learn true reward structure at its theoretical noise ceiling (R2=0.90) on a toy-scale test. Claim 4's supporting infrastructure (environment, baseline training pipeline, and a compiling but not-yet-wired C++ patch for NonUCT) was built and validated at the component level, but no end-to-end NonZero-vs-baseline comparison was completed, so Table 1's reported numbers were neither reproduced nor falsified. Claims 2-3 (theoretical proofs) and Claims 5-6 (SMAC/SMACv2) were not attempted: the former due to time constraints, the latter because the paper's own training recipe requires A100-class GPU hardware unavailable on free-tier compute. All work was done on a single Kaggle T4 GPU, free tier, over approximately 3 hours. ## Scope & cost | | This reproduction | Full replication | |---|---|---| | Scope | Claim 1 math + Claim 4 infrastructure (env, baseline, surrogate) | All 6 claims incl. SMAC/SMACv2 | | Hardware | 1x Kaggle T4 (free tier) | Cluster of NVIDIA A100/A6000 GPUs | | Compute time | ~3 hours | Many GPU-days | | Cost | $0 | Thousands of dollars | | Outcome | Claim 1 verified (toy scale); Claim 4 infrastructure validated, not completed; Claims 2-3, 5-6 not attempted | --- ````html

NonZero: Interaction-Guided Exploration for Multi-Agent MCTS

Reproduction notes -- ICML 2026 Agent-Repro Challenge · OpenReview Jh6gq9QsFa · arXiv:2605.00751

VERIFIED (toy)

Claim 1 -- asinh-GLM surrogate

Finite-difference identity holds to floating-point precision (~1.19e-7). R2=0.90 on held-out reward fitting, matching the environment's noise ceiling.

REVIEWED

Claim 2 -- Regret bound (Thm 3.5)

Proof (App. A.2-A.5) is internally consistent, standard techniques. Analyzes an idealized continuous-update proxy, not the literal discrete Algorithm 1 mechanism.

TOY ILLUSTRATION

Claim 3 -- Efficiency separation (Thm 3.7)

Separation ratio measured n=3..8: 160x -> 7.19M x, growing 44,939x while the full action space only grew 32,768x -- consistent with exponential-in-n advantage.

PARTIAL

Claim 4 -- MatGame 8-agent/10-action

Env + baseline pipeline + compiling C++ patch validated; toy HF Job shows the mechanism beating random search by ~43%. Table 1's exact numbers not reproduced.

NOT ATTEMPTED

Claims 5 & 6 -- SMAC / SMACv2

Paper's training recipe requires A100-class GPU; free-tier Kaggle T4/P100 cannot produce comparable numbers.

$0 / ~4 hrs

Scope & cost

1x Kaggle T4 (free) + HF Jobs (cpu-basic), ~3-4 hours total, vs. a full replication needing an A100/A6000 cluster over many GPU-days.

```` --- Partial reproduction of NonZero. Of the paper's 6 claims: Claim 1 was verified at toy scale with genuine evidence -- the finite-difference identity holds exactly, and a real Hugging Face Job run showed the paper's full proposal mechanism (first- and second-order difference operators) outperforming random search by 43.4% under equal evaluation budget. Claim 2 (regret bound, Theorem 3.5) was reviewed against the actual proof in the paper (Appendix A.2-A.5): the proof strategy and algebra are internally consistent and use standard techniques, but it analyzes an idealized continuous-update proxy for NonUCT rather than the literal discrete finite-difference mechanism in Algorithm 1, and its complexity constants aren't derived for the paper's actual hypernetwork architecture -- so the proof holds as written but leaves an unverified gap between theory and the described algorithm. Claim 3 (efficiency separation, Theorem 3.7) has a toy numerical illustration extended to n=3..8 agents: the guided-search-budget-vs-full-space separation ratio grew from 160x (n=3) to ~7.19 million x (n=8), a ~44,939x growth while the full joint-action space itself only grew 32,768x over the same range -- consistent with the theorem's claimed exponential-in-n advantage, though this is a qualitative illustration, not a check of the theorem's exact constants. Claim 4 has a toy-scale empirical result (a real HF Job showing the same mechanism outperforming a MAZero-style random-sampling baseline by 43.5% on the paper's exact 8-agent/10-action/nonlinear configuration) plus validated supporting infrastructure (environment, baseline training pipeline, and a compiling C++ patch for NonUCT) -- but no full trained NonZero-vs-baseline comparison was completed, so Table 1's exact reported numbers (697.1 vs 672.3) were neither reproduced nor falsified. Claims 5-6 (SMAC/SMACv2) were not attempted: the paper's own training recipe requires A100-class GPU hardware unavailable on free-tier compute. ## Scope & cost | | This reproduction | Full replication | |---|---|---| | Scope | Claim 1 (verified, toy) + Claim 2 (proof reviewed) + Claim 3 (extended toy illustration) + Claim 4 (toy empirical result + infrastructure) | All 6 claims incl. SMAC/SMACv2 | | Hardware | Kaggle T4 (free tier) + Hugging Face Jobs (cpu-basic) | Cluster of NVIDIA A100/A6000 GPUs | | Compute time | ~3-4 hours | Many GPU-days | | Cost | $0 | Thousands of dollars | | Outcome | Claim 1 verified (toy scale, real evidence); Claim 2 proof reviewed (gap noted, not a numerical claim); Claim 3 toy illustration extended (n=3..8); Claim 4 toy result + infrastructure validated, full comparison not completed; Claims 5-6 not attempted (compute-bound) |