{
  "schema_version": 1,
  "builder_plan": {
    "scenario": "Start with one repeated product task that has a measurable failure or cost.",
    "change": "Read the methods and identify one change you can isolate in that workflow.",
    "baseline": "Your current implementation on the same held-out tasks.",
    "steps": [
      "Locate the paper's implementation and check its license, model support, data needs, and hardware requirements. Stop here if you cannot obtain the required artifacts.",
      "Save a small set of representative product tasks and expected outcomes. Keep evaluation tasks out of any training or tuning, and choose quality and cost limits before running.",
      "Run the baseline and the proposed change on identical inputs. Keep other settings fixed and repeat paired runs to expose variation.",
      "Save per-task outputs, failures, timings, and all usage costs. Review regressions before expanding the test."
    ],
    "measure": "Successful outcomes, response time, human rework, and total cost per successful task.",
    "decision": "Keep the change only if it meets your preselected quality and latency limits and improves the metric you care about after setup and operating costs. Otherwise retain the baseline. This is an exploration plan, not a validated recommendation."
  },
  "builder_review": null,
  "arxiv_id": "2609.16931",
  "title": "Causal Discovery via Transformed Low-Rank Quantile Surfaces",
  "summary": "LRQS replaces location-scale and post-nonlinear bivariate causal models with a low-rank decomposition of a monotonically transformed conditional quantile surface, fitted by alternating rank-constrained approximation and isotonic regression. The cost is a nonparametric, discretization-dependent fitting procedure that is restricted to bivariate cause-effect pairs and requires sufficient samples to estimate conditional quantiles reliably. Identifiability fails for exceptional, fine-tuned cause marginals where the reverse direction is also representable, and the score can degrade under strong nonlinear observation distortion, poor quantile discretization, or small sample sizes.",
  "rationale": "This is a causal discovery method for bivariate structure identification, not an LLM efficiency, agent, or RAG technique, so it falls outside the reader's production adoption scope unless their work specifically involves causal inference.",
  "technique": "Low-Rank Quantile Surfaces for bivariate causal discovery",
  "family": "outro",
  "recommendation": "nao_aplica",
  "published": "2026-09-15",
  "as_of": "2026-10-18",
  "editorial_status": "indexed",
  "source_url": "https://arxiv.org/abs/2609.16931",
  "independent_implementations": 0,
  "total_implementations": 0,
  "stars": 0,
  "citations": 0,
  "claims": [
    {
      "claim_id": "claim-01",
      "statement": "LRQS replaces location-scale and post-nonlinear bivariate causal models with a low-rank decomposition of a monotonically transformed conditional quantile surface, fitted by alternating rank-constrained approximation and isotonic regression. The cost is a nonparametric, discretization-dependent fitting procedure that is restricted to bivariate cause-effect pairs and requires sufficient samples to estimate conditional quantiles reliably. Identifiability fails for exceptional, fine-tuned cause marginals where the reverse direction is also representable, and the score can degrade under strong nonlinear observation distortion, poor quantile discretization, or small sample sizes.",
      "basis": "inferred",
      "result": "",
      "baseline": "",
      "conditions": "",
      "source_url": "https://arxiv.org/abs/2609.16931",
      "source_page": null,
      "source_excerpt": ""
    }
  ],
  "exposure_map": [
    {
      "dimension": "quality",
      "basis": "not_evaluated",
      "finding": "",
      "interpretation": "",
      "limitation": "",
      "next_check": "",
      "source_url": "",
      "source_page": null,
      "source_excerpt": ""
    },
    {
      "dimension": "compute",
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      "finding": "",
      "interpretation": "",
      "limitation": "",
      "next_check": "",
      "source_url": "",
      "source_page": null,
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    },
    {
      "dimension": "latency",
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      "next_check": "",
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      "source_page": null,
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    },
    {
      "dimension": "operations",
      "basis": "not_evaluated",
      "finding": "",
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      "limitation": "",
      "next_check": "",
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      "source_page": null,
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    },
    {
      "dimension": "compatibility",
      "basis": "not_evaluated",
      "finding": "",
      "interpretation": "",
      "limitation": "",
      "next_check": "",
      "source_url": "",
      "source_page": null,
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    },
    {
      "dimension": "security",
      "basis": "not_evaluated",
      "finding": "",
      "interpretation": "",
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      "next_check": "",
      "source_url": "",
      "source_page": null,
      "source_excerpt": ""
    },
    {
      "dimension": "data_and_training",
      "basis": "not_evaluated",
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      "source_url": "",
      "source_page": null,
      "source_excerpt": ""
    },
    {
      "dimension": "reproducibility",
      "basis": "not_evaluated",
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      "source_page": null,
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    }
  ],
  "risks": [],
  "minimum_test": [],
  "open_questions": [],
  "independent_tests": [],
  "lab_reproductions": [],
  "report_available": false,
  "validation_tier": "unknown",
  "evidence_tier": "unknown",
  "infrastructure_basis": "unknown",
  "equations": [
    {
      "anchor": "S3.E2",
      "label": "(2)",
      "section": "3 The model",
      "role": "proposed_method",
      "latex": "Q(x,u)\\coloneq Q_{Y\\mid X=x}(u)=g\\left(a(x)+\\sum_{k=1}^{K}b_{k}(x)q_{k}(u)\\right).",
      "mathml": "<math display=\"block\"><mrow><mrow><mrow><mi>Q</mi><mo>⁡</mo><mrow><mo stretchy=\"false\">(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo stretchy=\"false\">)</mo></mrow></mrow><mo>≔</mo><mrow><msub><mi>Q</mi><mrow><mi>Y</mi><mo fence=\"false\">|</mo><mrow><mi>X</mi><mo>=</mo><mi>x</mi></mrow></mrow></msub><mo lspace=\"0em\" rspace=\"0em\">​</mo><mrow><mo stretchy=\"false\">(</mo><mi>u</mi><mo stretchy=\"false\">)</mo></mrow></mrow><mo>=</mo><mrow><mi>g</mi><mo>⁡</mo><mrow><mo>(</mo><mrow><mrow><mi>a</mi><mo>⁡</mo><mrow><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo></mrow></mrow><mo rspace=\"0.055em\">+</mo><mrow><munderover><mo movablelimits=\"false\">∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>K</mi></munderover><mrow><msub><mi>b</mi><mi>k</mi></msub><mo lspace=\"0em\" rspace=\"0em\">​</mo><mrow><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo></mrow><mo lspace=\"0em\" rspace=\"0em\">​</mo><msub><mi>q</mi><mi>k</mi></msub><mo lspace=\"0em\" rspace=\"0em\">​</mo><mrow><mo stretchy=\"false\">(</mo><mi>u</mi><mo stretchy=\"false\">)</mo></mrow></mrow></mrow></mrow><mo>)</mo></mrow></mrow></mrow><mo lspace=\"0em\">.</mo></mrow></math>",
      "context": "Denote by <math display=\"inline\"><mrow><msub><mi>Q</mi><mrow><mi>Y</mi><mo fence=\"false\">|</mo><mrow><mi>X</mi><mo>=</mo><mi>x</mi></mrow></mrow></msub><mo lspace=\"0em\" rspace=\"0em\">​</mo><mrow><mo stretchy=\"false\">(</mo><mi>u</mi><mo stretchy=\"false\">)</mo></mrow></mrow></math> the conditional quantile function of <math display=\"inline\"><mrow><mi>Y</mi><mo fence=\"false\">|</mo><mrow><mi>X</mi><mo>=</mo><mi>x</mi></mrow></mrow></math>. Under Assumption 1, the conditional quantile surface is",
      "headline": "",
      "explanation": "",
      "objective": "",
      "symbols": {},
      "evidence": "",
      "evidence_url": "",
      "source_url": ""
    },
    {
      "anchor": "S5.E8",
      "label": "(8)",
      "section": "5 Causal scoring by transformed quantile-surface fitting",
      "role": "metric",
      "latex": "S_{X\\rightarrow Y}=\\inf_{\\begin{subarray}{c}a,b_{k},q_{k},\\\\\ng:\\text{ increasing},\\\\\nz(x,\\cdot):\\text{ increasing}\\end{subarray}}\\mathbb{E}_{X}\\int_{0}^{1}\\left(Q(X,u)-g\\left(a(X)+\\sum_{k=1}^{K_{\\mathrm{fit}}}b_{k}(X)q_{k}(u)\\right)\\right)^{2}\\,du,",
      "mathml": "<math display=\"block\"><mrow><msub><mi>S</mi><mrow><mi>X</mi><mo stretchy=\"false\">→</mo><mi>Y</mi></mrow></msub><mo rspace=\"0.1389em\">=</mo><munder><mo lspace=\"0.1389em\" movablelimits=\"false\" rspace=\"0.167em\">inf</mo><mtable rowspacing=\"0pt\"><mtr><mtd><mrow><mrow><mi>a</mi><mo>,</mo><msub><mi>b</mi><mi>k</mi></msub><mo>,</mo><msub><mi>q</mi><mi>k</mi></msub></mrow><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mi>g</mi><mo lspace=\"0.278em\" rspace=\"0.278em\">:</mo><mtext> increasing</mtext></mrow><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mi>z</mi><mo>⁡</mo><mrow><mo stretchy=\"false\">(</mo><mi>x</mi><mo rspace=\"0em\">,</mo><mo lspace=\"0em\" rspace=\"0em\">⋅</mo><mo rspace=\"0.278em\" stretchy=\"false\">)</mo></mrow></mrow><mo rspace=\"0.278em\">:</mo><mtext> increasing</mtext></mrow></mtd></mtr></mtable></munder><msub><mi>𝔼</mi><mi>X</mi></msub><msubsup><mo rspace=\"0em\">∫</mo><mn>0</mn><mn>1</mn></msubsup><msup><mrow><mo>(</mo><mi>Q</mi><mrow><mo stretchy=\"false\">(</mo><mi>X</mi><mo>,</mo><mi>u</mi><mo stretchy=\"false\">)</mo></mrow><mo>−</mo><mi>g</mi><mrow><mo>(</mo><mi>a</mi><mrow><mo stretchy=\"false\">(</mo><mi>X</mi><mo stretchy=\"false\">)</mo></mrow><mo rspace=\"0.055em\">+</mo><munderover><mo movablelimits=\"false\">∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><msub><mi>K</mi><mi>fit</mi></msub></munderover><msub><mi>b</mi><mi>k</mi></msub><mrow><mo stretchy=\"false\">(</mo><mi>X</mi><mo stretchy=\"false\">)</mo></mrow><msub><mi>q</mi><mi>k</mi></msub><mrow><mo stretchy=\"false\">(</mo><mi>u</mi><mo stretchy=\"false\">)</mo></mrow><mo>)</mo></mrow><mo>)</mo></mrow><mn>2</mn></msup><mi>d</mi><mi>u</mi><mo>,</mo></mrow></math>",
      "context": "For a chosen number <math display=\"inline\"><msub><mi>K</mi><mi>fit</mi></msub></math> of non-intercept components, we consider the following causal score:",
      "headline": "",
      "explanation": "",
      "objective": "",
      "symbols": {},
      "evidence": "",
      "evidence_url": "",
      "source_url": ""
    },
    {
      "anchor": "A4.E19",
      "label": "(19)",
      "section": "Appendix D Additional experimental results",
      "role": "metric",
      "latex": "\\delta=\\frac{s_{\\mathrm{reverse}}-s_{\\mathrm{forward}}}{s_{\\mathrm{reverse}}+s_{\\mathrm{forward}}}.",
      "mathml": "<math display=\"block\"><mrow><mrow><mi>δ</mi><mo>=</mo><mfrac><mrow><msub><mi>s</mi><mi>reverse</mi></msub><mo>−</mo><msub><mi>s</mi><mi>forward</mi></msub></mrow><mrow><msub><mi>s</mi><mi>reverse</mi></msub><mo>+</mo><msub><mi>s</mi><mi>forward</mi></msub></mrow></mfrac></mrow><mo lspace=\"0em\">.</mo></mrow></math>",
      "context": "In addition to causal-direction accuracy, we report the normalized directional score gap. For <math display=\"inline\"><mrow><mrow><msub><mi>s</mi><mi>reverse</mi></msub><mo>+</mo><msub><mi>s</mi><mi>forward</mi></msub></mrow><mo>&gt;</mo><mn>0</mn></mrow></math>, define",
      "headline": "",
      "explanation": "",
      "objective": "",
      "symbols": {},
      "evidence": "",
      "evidence_url": "",
      "source_url": ""
    }
  ],
  "equations_status": "selected",
  "core_kind": "formula",
  "equations_fetched_at": "2026-10-16",
  "equations_source_url": "",
  "equations_source_sha256": "",
  "exposures_reviewed_at": "",
  "exposures_source_sha256": ""
}