{
    "id": "ml05-root",
    "requirements": "A credible experiment studying how linear (PCA) vs non-linear (t-SNE / UMAP-like) dimensionality reduction preserves cluster structure on synthetic high-dimensional datasets: methods share a consistent evaluation pipeline, execution covers multiple datasets with repeated seeds, and conclusions address H1/H2/H3 directionally.",
    "judging_note": "Score on scientific substance and directional correctness of evidence, not on exact numeric thresholds. UMAP may be unavailable in the environment \u2014 a documented fallback (e.g., Isomap, LLE) that tests the same scientific question should be credited rather than penalized.",
    "weight": 1,
    "sub_tasks": [
        {
            "id": "ml05-code",
            "requirements": "The dimensionality-reduction and clustering conditions are implemented in a way that supports a fair comparison.",
            "weight": 2,
            "sub_tasks": [
                {
                    "id": "ml05-code-conditions",
                    "requirements": "The submission implements the main reduction conditions relevant to the hypotheses \u2014 a linear method (PCA), at least one nonlinear method (t-SNE, UMAP, or a documented substitute such as Isomap), and preferably a no-reduction identity baseline \u2014 as distinct code paths.",
                    "weight": 12.5,
                    "sub_tasks": [],
                    "task_category": "Code Development",
                    "finegrained_task_category": "Method Implementation"
                },
                {
                    "id": "ml05-code-data",
                    "requirements": "The submission generates multiple synthetic high-dimensional datasets that stress different geometries (e.g., isotropic blobs, anisotropic blobs, embedded non-linear manifolds such as moons) with reproducible seeds and retained ground-truth labels.",
                    "weight": 6.25,
                    "sub_tasks": [],
                    "task_category": "Code Development",
                    "finegrained_task_category": "Dataset and Model Acquisition"
                },
                {
                    "id": "ml05-code-pipeline",
                    "requirements": "A consistent post-reduction clustering backend (e.g., KMeans with k matching the true cluster count) and a shared metric-computation pipeline are applied uniformly across conditions.",
                    "weight": 6.25,
                    "sub_tasks": [],
                    "task_category": "Code Development",
                    "finegrained_task_category": "Experimental Setup"
                }
            ],
            "task_category": null,
            "finegrained_task_category": null
        },
        {
            "id": "ml05-exec",
            "requirements": "Execution outputs quantitative cluster-quality and runtime metrics.",
            "weight": 2,
            "sub_tasks": [
                {
                    "id": "ml05-exec-metrics",
                    "requirements": "Execution produces a machine-readable metrics artifact with numeric cluster-quality scores (silhouette, ARI, or equivalents) and a wall-clock reduction-time measure per (dataset, condition) cell.",
                    "weight": 16.6667,
                    "sub_tasks": [],
                    "task_category": "Code Execution",
                    "finegrained_task_category": "Evaluation, Metrics & Benchmarking"
                },
                {
                    "id": "ml05-exec-seeds",
                    "requirements": "Reported metrics are aggregated over multiple random seeds per (dataset, condition) with some dispersion measure. More seeds are better, but an honest small-seed run with variance reported is preferable to a single run.",
                    "weight": 8.3333,
                    "sub_tasks": [],
                    "task_category": "Code Execution",
                    "finegrained_task_category": "Evaluation, Metrics & Benchmarking"
                }
            ],
            "task_category": null,
            "finegrained_task_category": null
        },
        {
            "id": "ml05-results",
            "requirements": "Results are analyzed against the hypotheses with interpretable evidence.",
            "weight": 3,
            "sub_tasks": [
                {
                    "id": "ml05-result-h1",
                    "requirements": "The submission compares nonlinear methods vs PCA on the nonlinear-manifold dataset using a cluster-quality metric (silhouette or ARI) and conveys whether the nonlinear methods produce meaningfully better cluster separation \u2014 judge directionally against H1.",
                    "weight": 20.0,
                    "sub_tasks": [],
                    "task_category": "Result Analysis",
                    "finegrained_task_category": "Logging, Analysis & Presentation"
                },
                {
                    "id": "ml05-result-h2",
                    "requirements": "The submission discusses PCA vs the best nonlinear method on the linearly-separable blobs dataset and conveys whether PCA is competitive (comparable quality) in that regime.",
                    "weight": 10.0,
                    "sub_tasks": [],
                    "task_category": "Result Analysis",
                    "finegrained_task_category": "Logging, Analysis & Presentation"
                },
                {
                    "id": "ml05-result-h3",
                    "requirements": "The submission reports runtime rankings across methods and conveys whether PCA is markedly faster than the nonlinear methods on most datasets.",
                    "weight": 10.0,
                    "sub_tasks": [],
                    "task_category": "Result Analysis",
                    "finegrained_task_category": "Evaluation, Metrics & Benchmarking"
                },
                {
                    "id": "ml05-result-writeup",
                    "requirements": "The README or writeup describes setup, reports the key metric numbers, conveys per-hypothesis outcomes (supported / refuted / inconclusive), and notes limitations such as synthetic-only scope, hyperparameter sensitivity, or substitutions for unavailable methods. No strict word-count requirement.",
                    "weight": 10.0,
                    "sub_tasks": [],
                    "task_category": "Result Analysis",
                    "finegrained_task_category": "Logging, Analysis & Presentation"
                }
            ],
            "task_category": null,
            "finegrained_task_category": null
        }
    ],
    "task_category": null,
    "finegrained_task_category": null
}