{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"mmlu-pro","formal_name":"MMLU-Pro","introduction":"MMLU-Pro rebuilds MMLU with ten answer options instead of four and removes items that no longer separate models. Questions span fourteen academic and professional subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/TIGER-Lab/MMLU-Pro","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"383ade8b-47e4-59a8-ae98-3d97360db082","task_key":"default--test--10394","task_revision_id":"1","upstream_id":"10394","short_description":"Suppose we have the following objective function: $\\argmin_{w} \\frac{1}{2}…","config":"default","split":"test","body":"{\"category\":\"computer science\",\"options\":\"['$\\\\\\\\nabla_w f(w) = X^\\\\\\\\top X w - X^\\\\\\\\top y + \\\\\\\\lambda w$', '$\\\\\\\\nabla_w f(w) = X^\\\\\\\\top X w - X^\\\\\\\\top y + \\\\\\\\lambda I$', '$\\\\\\\\nabla_w f(w) = X^\\\\\\\\top X w - X^\\\\\\\\top y + (\\\\\\\\lambda+1) w$', '$\\\\\\\\nabla_w f(w) = X^\\\\\\\\top X w - X^\\\\\\\\top y + \\\\\\\\lambda$', '$\\\\\\\\nabla_w f(w) = X^\\\\\\\\top X w + X^\\\\\\\\top y + \\\\\\\\lambda w$', '$\\\\\\\\nabla_w f(w) = X^\\\\\\\\top X w - X^\\\\\\\\top y - \\\\\\\\lambda w$', '$\\\\\\\\nabla_w f(w) = (X^\\\\\\\\top X + \\\\\\\\lambda I)w - X^\\\\\\\\top y + \\\\\\\\lambda w$', '$\\\\\\\\nabla_w f(w) = X^\\\\\\\\top X + \\\\\\\\lambda I)w - X^\\\\\\\\top y$', '$\\\\\\\\nabla_w f(w) = X^\\\\\\\\top X w - X^\\\\\\\\top y + \\\\\\\\lambda^2 w$', '$\\\\\\\\nabla_w f(w) = X^\\\\\\\\top X w + X^\\\\\\\\top y - \\\\\\\\lambda w$']\",\"question\":\"Suppose we have the following objective function: $\\\\argmin_{w} \\\\frac{1}{2} \\\\norm{Xw-y}^2_2 + \\\\frac{1}{2}\\\\gamma \\\\norm{w}^2_2$ What is the gradient of $\\\\frac{1}{2} \\\\norm{Xw-y}^2_2 + \\\\frac{1}{2}\\\\lambda \\\\norm{w}^2_2$ with respect to $w$?\",\"src\":\"ori_mmlu-machine_learning\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/TIGER-Lab/MMLU-Pro","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}