[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"skill:01M7980Z7VRNJ0VEASHCT8C6FF":3,"skill-same:01M7980Z7VRNJ0VEASHCT8C6FF":54},{"skillNo":4,"name":5,"nameZh":6,"description":7,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":15,"categories":16,"keywords":17,"publishedAt":18,"linkOnly":19,"markdownContent":20,"markdownBody":21,"frontMatter":22,"refName":23,"commitSha":24,"skillDirectory":25,"forksCount":26,"repositoryHtmlUrl":27,"repositoryHomepageUrl":6,"ownerHtmlUrl":28,"ownerBlogUrl":6,"ownerDescription":6,"updatedAt":29,"install":30,"resources":43},"01M7980Z7VRNJ0VEASHCT8C6FF","ksd_bootstrap_gof",null,"Calibrate a KSD U-statistic goodness-of-fit test with the centered multinomial bootstrap for degenerate U-statistics.","VectorSpaceLab\u002FAREX-Skill","VectorSpaceLab","https:\u002F\u002Favatars.githubusercontent.com\u002Fu\u002F180637102?v=4","01M7538C5WPSJGWF7KHR4EFZ9F","01M7538C6R2GFP53NPXTCZNBRT",351,"Apache-2.0","https:\u002F\u002Fgithub.com\u002FVectorSpaceLab\u002FAREX-Skill\u002Fblob\u002Fmain\u002Fskills\u002Ftask-oriented\u002FPaperBench\u002Fskills\u002Fbam\u002Fskill\u002Fstein_discrepancy_sample_quality\u002Fksd_bootstrap_gof\u002FSKILL.md",[],[],"2026-11-15 14:19:17",false,"---\nname: ksd_bootstrap_gof\ndescription: Calibrate a KSD U-statistic goodness-of-fit test with the centered multinomial bootstrap for degenerate U-statistics.\n---\n\n# KSD Bootstrap Goodness-of-fit Test\n\nUse this skill when you already have a pairwise Stein kernel matrix and need the paper's KSD-U goodness-of-fit decision. The skill implements Algorithm 1's centered multinomial bootstrap, which is designed for the degenerate U-statistic null distribution.\n\nDo not use this skill for ordinary non-degenerate bootstrap tests, V-statistic-only diagnostics, or linear-time KSD calibration.\n\n## Inputs\n\n- `stein_matrix`: finite square matrix `U` where `U[i,j] = u_q(x_i, x_j)`.\n- `alpha`: significance level, usually `0.05`.\n- `num_bootstrap`: bounded number of bootstrap replicates.\n- `seed`: integer random seed for reproducibility.\n\n## Outputs\n\n- `ksd_u`: unbiased KSD U-statistic.\n- `scaled_observed`: `n * ksd_u`.\n- `bootstrap_scaled`: bootstrap null samples.\n- `p_value`: fraction of bootstrap statistics greater than the observed statistic.\n- `reject`: boolean decision `p_value \u003C alpha`.\n\n## Workflow\n\n1. Validate the square Stein matrix and exclude diagonal entries for observed KSD-U.\n2. Draw multinomial bootstrap counts of size `n` with uniform category probabilities.\n3. Center the counts as `(w_i - 1\u002Fn)` before forming pairwise products.\n4. Compare the observed scaled statistic against the bootstrap scaled statistics using the strict `>` tail rule.\n5. Log the seed and bootstrap count for reproducibility.\n\n## Validation\n\nRun:\n\n```bash\npython tests\u002Ftest_ksd_bootstrap_gof.py\n```\n\nThe tests cover U-statistic calculation, reproducibility, and rejection behavior for a strongly positive Stein matrix.\n\n## Limitations\n\n- Bootstrap counts are intended for bounded recovery and smoke checks; large paper-scale replicates may be expensive.\n- The skill assumes the Stein matrix was computed correctly by a scoring skill.\n\n## Refinement Notes\n\nRefinement invariant: treat multinomial draws as empirical probabilities before centering. For a draw count `count_i`, Equation (16) is implemented as `(count_i \u002F n - 1 \u002F n)`, not raw `count_i - 1 \u002F n`; raw counts make the bootstrap null too wide and suppress valid KSD-U rejections.\n","# KSD Bootstrap Goodness-of-fit Test\n\nUse this skill when you already have a pairwise Stein kernel matrix and need the paper's KSD-U goodness-of-fit decision. The skill implements Algorithm 1's centered multinomial bootstrap, which is designed for the degenerate U-statistic null distribution.\n\nDo not use this skill for ordinary non-degenerate bootstrap tests, V-statistic-only diagnostics, or linear-time KSD calibration.\n\n## Inputs\n\n- `stein_matrix`: finite square matrix `U` where `U[i,j] = u_q(x_i, x_j)`.\n- `alpha`: significance level, usually `0.05`.\n- `num_bootstrap`: bounded number of bootstrap replicates.\n- `seed`: integer random seed for reproducibility.\n\n## Outputs\n\n- `ksd_u`: unbiased KSD U-statistic.\n- `scaled_observed`: `n * ksd_u`.\n- `bootstrap_scaled`: bootstrap null samples.\n- `p_value`: fraction of bootstrap statistics greater than the observed statistic.\n- `reject`: boolean decision `p_value \u003C alpha`.\n\n## Workflow\n\n1. Validate the square Stein matrix and exclude diagonal entries for observed KSD-U.\n2. Draw multinomial bootstrap counts of size `n` with uniform category probabilities.\n3. Center the counts as `(w_i - 1\u002Fn)` before forming pairwise products.\n4. Compare the observed scaled statistic against the bootstrap scaled statistics using the strict `>` tail rule.\n5. Log the seed and bootstrap count for reproducibility.\n\n## Validation\n\nRun:\n\n```bash\npython tests\u002Ftest_ksd_bootstrap_gof.py\n```\n\nThe tests cover U-statistic calculation, reproducibility, and rejection behavior for a strongly positive Stein matrix.\n\n## Limitations\n\n- Bootstrap counts are intended for bounded recovery and smoke checks; large paper-scale replicates may be expensive.\n- The skill assumes the Stein matrix was computed correctly by a scoring skill.\n\n## Refinement Notes\n\nRefinement invariant: treat multinomial draws as empirical probabilities before centering. For a draw count `count_i`, Equation (16) is implemented as `(count_i \u002F n - 1 \u002F n)`, not raw `count_i - 1 \u002F n`; raw counts make the bootstrap null too wide and suppress valid KSD-U rejections.\n",{"name":5,"description":7},"main","ac3fe1afa80fb9a09775ecfb2b6cc3ba850a2db6","skills\u002Ftask-oriented\u002FPaperBench\u002Fskills\u002Fbam\u002Fskill\u002Fstein_discrepancy_sample_quality\u002Fksd_bootstrap_gof",27,"https:\u002F\u002Fgithub.com\u002FVectorSpaceLab\u002FAREX-Skill","https:\u002F\u002Fgithub.com\u002FVectorSpaceLab","2026-09-03 10:25:21",{"source":8,"skillName":5,"commands":31,"prompt":41,"zipAvailable":42},[32,35,38],{"tool":33,"command":34},"npx","npx skills add VectorSpaceLab\u002FAREX-Skill --skill ksd_bootstrap_gof",{"tool":36,"command":37},"bunx","bunx skills add VectorSpaceLab\u002FAREX-Skill --skill ksd_bootstrap_gof",{"tool":39,"command":40},"pnpm","pnpm dlx skills add VectorSpaceLab\u002FAREX-Skill --skill ksd_bootstrap_gof","安装技能，技能地址：https:\u002F\u002Fgithub.com\u002FVectorSpaceLab\u002FAREX-Skill\u002Fblob\u002Fmain\u002Fskills\u002Ftask-oriented\u002FPaperBench\u002Fskills\u002Fbam\u002Fskill\u002Fstein_discrepancy_sample_quality\u002Fksd_bootstrap_gof\u002FSKILL.md",true,[44,50],{"path":45,"resourceType":46,"resourceTypeDesc":47,"sizeBytes":48,"sourceHtmlUrl":49},"scripts\u002Fbootstrap_ksd.py","SCRIPT","脚本",3713,"https:\u002F\u002Fgithub.com\u002FVectorSpaceLab\u002FAREX-Skill\u002Fblob\u002Fmain\u002Fskills\u002Ftask-oriented\u002FPaperBench\u002Fskills\u002Fbam\u002Fskill\u002Fstein_discrepancy_sample_quality\u002Fksd_bootstrap_gof\u002Fscripts\u002Fbootstrap_ksd.py",{"path":51,"resourceType":46,"resourceTypeDesc":47,"sizeBytes":52,"sourceHtmlUrl":53},"tests\u002Ftest_ksd_bootstrap_gof.py",1181,"https:\u002F\u002Fgithub.com\u002FVectorSpaceLab\u002FAREX-Skill\u002Fblob\u002Fmain\u002Fskills\u002Ftask-oriented\u002FPaperBench\u002Fskills\u002Fbam\u002Fskill\u002Fstein_discrepancy_sample_quality\u002Fksd_bootstrap_gof\u002Ftests\u002Ftest_ksd_bootstrap_gof.py",[55,62,69,76,83,90],{"skillNo":56,"name":57,"nameZh":6,"description":58,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":59,"categories":60,"keywords":61,"publishedAt":18},"01M799NYSH1R3RVAHSM2D88Y84","passnet-triton-opt","Make a single PassNet Triton kernel fast AND numerically faithful: performance model (when a replacement can win at all), block\u002Fgrid\u002Fwarp tuning, autotune policy, launch overhead, and per-op numeric recipes to pass the dtype baseline tolerances. Use when a pass matches and is correct but speedup below expected, or when correctness fails by small numeric margins.","https:\u002F\u002Fgithub.com\u002FVectorSpaceLab\u002FAREX-Skill\u002Fblob\u002Fmain\u002Fskills\u002Ftask-oriented\u002FPassNet\u002Fskills\u002Fpassnet-triton-opt\u002FSKILL.md",[],[],{"skillNo":63,"name":64,"nameZh":6,"description":65,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":66,"categories":67,"keywords":68,"publishedAt":18},"01M799NS5APEC0N1FZ7XZVW6BN","passnet-solve","END-TO-END playbook for solving one PassNet sample: analyze the computation graphs, decide the optimization strategy (what to fuse, what to replace, what to leave alone), drive the iteration loop, and maximize the sample score. This is the ENTRY skill — invoke it first for any PassNet optimization task; it tells you when to use passnet-pattern-fusion, passnet-triton-opt and passnet-feedback.","https:\u002F\u002Fgithub.com\u002FVectorSpaceLab\u002FAREX-Skill\u002Fblob\u002Fmain\u002Fskills\u002Ftask-oriented\u002FPassNet\u002Fskills\u002Fpassnet-solve\u002FSKILL.md",[],[],{"skillNo":70,"name":71,"nameZh":6,"description":72,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":73,"categories":74,"keywords":75,"publishedAt":18},"01M799NNY9BKSM21V5R7QVTBJX","passnet-skill","PassNet GPU kernel optimization via compiler passes. Design and implement Triton-based optimization passes, create pass files under .\u002Fpass_dir\u002F, self-evaluate with pass_evaluator, and iterate to maximize GPU speedup.","https:\u002F\u002Fgithub.com\u002FVectorSpaceLab\u002FAREX-Skill\u002Fblob\u002Fmain\u002Fskills\u002Ftask-oriented\u002FPassNet\u002Fskills\u002Fpassnet-skill\u002FSKILL.md",[],[],{"skillNo":77,"name":78,"nameZh":6,"description":79,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":80,"categories":81,"keywords":82,"publishedAt":18},"01M799NHH6NP7Z1RK77KGXAN6S","passnet-pattern-fusion","Author PassNet pass files: write patterns that actually MATCH the FX graph, pick fusion regions (which ops to absorb into one Triton kernel), and structure multi-pass submissions with the mandatory shared-dispatch architecture. Use when creating or fixing pattern()\u002Freplacement_args()\u002Freplacement_func() files, when a pass \"failed to match\", or when deciding how to fuse multiple kernels\u002Fops.","https:\u002F\u002Fgithub.com\u002FVectorSpaceLab\u002FAREX-Skill\u002Fblob\u002Fmain\u002Fskills\u002Ftask-oriented\u002FPassNet\u002Fskills\u002Fpassnet-pattern-fusion\u002FSKILL.md",[],[],{"skillNo":84,"name":85,"nameZh":6,"description":86,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":87,"categories":88,"keywords":89,"publishedAt":18},"01M799ND2J4WNC2PGAZ0A06NDF","passnet-orchestrate","Round\u002Fbatch planning and decision support for PassNet graph optimization. Use for multi-sample triage, worker allocation, eval-budget policy, and post-eval keep\u002Frevert decisions. For solving one concrete sample end to end, use passnet-solve as the entry skill; consult this skill only when you need broader planning or a specific decision gate.","https:\u002F\u002Fgithub.com\u002FVectorSpaceLab\u002FAREX-Skill\u002Fblob\u002Fmain\u002Fskills\u002Ftask-oriented\u002FPassNet\u002Fskills\u002Fpassnet-orchestrate\u002FSKILL.md",[],[],{"skillNo":91,"name":92,"nameZh":6,"description":93,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":94,"categories":95,"keywords":96,"publishedAt":18},"01M799N8SBTMY02ZDG2AZF5ZWE","passnet-feedback","Fast, deterministic feedback for PassNet work: pre-flight pattern\u002Fmatch verification WITHOUT burning a GPU evaluation, per-node bottleneck analysis of a sample's graphs, and eval-log parsing into per-variant status + estimated score + failure classification. Use BEFORE every GPU evaluation (check_pattern), at the START of a sample (analyze_graph), and AFTER every evaluation (parse_eval_log).","https:\u002F\u002Fgithub.com\u002FVectorSpaceLab\u002FAREX-Skill\u002Fblob\u002Fmain\u002Fskills\u002Ftask-oriented\u002FPassNet\u002Fskills\u002Fpassnet-feedback\u002FSKILL.md",[],[]]