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Sun, Aug 2

# First, read the challenge instructions: curl -sL https://huggingface.co/datasets/ICML-2026-agent-repro/challenge/resolve/main/README.md Your job is to reproduce the ICML 2026 paper #166 — Row-Stochastic Matrices Can Provably Outperform Doubly Stochastic Matrices in Decentralized Learning (OpenReview id: GAQE4Wr53f). Here are the major claims that you should verify: - Claim 1: In the weighted Hilbert space L²(λ;R^d), the λ-induced row-stochastic mixing matrix W is self-adjoint whereas the doubly stochastic matrix W^ds is not, and this non-self-adjointness introduces additional multiplicative penalty terms (κ_λ > 1 and λ_max² > 1) that amplify consensus error under the doubly stochastic design (Section 5.2, Section 6.2). - Claim 2: Theorem 6.5 gives O(1/T) convergence rates for both row-stochastic and doubly stochastic strategies, but the row-stochastic strategy achieves strictly smaller non-asymptotic consensus error and can converge faster even when its spectral gap is smaller than that of the doubly stochastic strategy (Theorem 6.5). - Claim 3: Theorem 7.1 derives a sufficient condition on the spectral gaps, 1 − ρ*Λ ≥ max{(1+η)κ*λ^(-1/3), λ_max^(-1/2)}(1 − ρ_J), under which the row-stochastic design provably converges strictly faster than the doubly stochastic design (Theorem 7.1). - Claim 4: Corollary 7.3 and Algorithm 2 give topology construction guidelines showing that when node degrees scale proportionally with their assigned weights (d_i/d_j matching λ_i/λ_j within bounds set by R), the row-stochastic design outperforms the doubly stochastic design, satisfying a Loewner order condition on the graph Laplacians (Corollary 7.3, Remark 7.4, Algorithm 2). Logbook structure (fixed order): - Index: title + Pages table only - Executive summary: pinned summary + Scope & cost table + pinned Chenruishuo/posterly poster (`poster_embed.html`) - Claim 1 … Claim N: one page per claim - Conclusion: overall findings and reproducibility notes Try to verify the claims as much as you can locally or using Hugging Face Jobs. Link every Hub model, dataset, Job, Bucket, and GitHub repo in logbook cells. # Last step — validate, then publish: curl -sL https://huggingface.co/spaces/ICML-2026-agent-repro/challenge/raw/main/scripts/validate_icml_logbook.py | python3 - --space /repro-row-stochastic-matrices-can-provably-outperform-doubly-stochastic-matrices-in-decentralize && trackio logbook publish /repro-row-stochastic-matrices-can-provably-outperform-doubly-stochastic-matrices-in-decentralize Print the published logbook link here when done. 1 message 29 tools

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