{"id":103481,"date":"2025-05-28T07:06:33","date_gmt":"2025-05-28T07:06:33","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%aa%d9%88%d9%84%db%8c%d8%af-%d8%b3%d9%88%d8%a7%d9%84%d8%a7%d8%aa-%d8%af%d8%b4%d9%88%d8%a7%d8%b1-%d8%b1\/"},"modified":"2025-05-28T07:06:33","modified_gmt":"2025-05-28T07:06:33","slug":"%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%aa%d9%88%d9%84%db%8c%d8%af-%d8%b3%d9%88%d8%a7%d9%84%d8%a7%d8%aa-%d8%af%d8%b4%d9%88%d8%a7%d8%b1-%d8%b1","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%aa%d9%88%d9%84%db%8c%d8%af-%d8%b3%d9%88%d8%a7%d9%84%d8%a7%d8%aa-%d8%af%d8%b4%d9%88%d8%a7%d8%b1-%d8%b1\/","title":{"rendered":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u062a\u0648\u0644\u06cc\u062f \u0633\u0648\u0627\u0644\u0627\u062a \u062f\u0634\u0648\u0627\u0631 \u0631\u06cc\u0627\u0636\u06cc \u0628\u0627 \u06a9\u0645\u06a9 \u0647\u0648\u0634 \u0645\u0635\u0646\u0648\u0639\u06cc"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nAI-Assisted Generation of Difficult Math Questions<\/td>\n<\/tr>\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u062a\u0648\u0644\u06cc\u062f \u0633\u0648\u0627\u0644\u0627\u062a \u062f\u0634\u0648\u0627\u0631 \u0631\u06cc\u0627\u0636\u06cc \u0628\u0627 \u06a9\u0645\u06a9 \u0647\u0648\u0634 \u0645\u0635\u0646\u0648\u0639\u06cc<\/td>\n<\/tr>\n
\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\nVedant Shah, Dingli Yu, Kaifeng Lyu, Simon Park, Nan Rosemary Ke, Michael Mozer, Yoshua Bengio, Sanjeev Arora, Anirudh Goyal<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPDF<\/td>\n<\/tr>\n
\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u062d\u0648\u06cc\u0644\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 <\/td>\n\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\n<\/tr>\n
\u0646\u062d\u0648\u0647 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 <\/td>\n\u062f\u0648 \u062a\u0627 \u0633\u0647 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634 (\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u062f\u0627\u0646\u0644\u0648\u062f\u06cc)<\/td>\n<\/tr>\n
\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n30<\/td>\n<\/tr>\n
\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a <\/td>\nArtificial Intelligence,Machine Learning,\u0647\u0648\u0634 \u0645\u0635\u0646\u0648\u0639\u06cc , \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0645\u0627\u0634\u06cc\u0646 ,<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a <\/td>\nSubmitted 2 September, 2024; v1 submitted 30 July, 2024; originally announced July 2024.<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0627\u0631\u0633\u0627\u0644 \u0634\u062f\u0647 \u062f\u0631 2 \u0633\u067e\u062a\u0627\u0645\u0628\u0631 2024 \u061bV1 \u0627\u0631\u0633\u0627\u0644 \u0634\u062f\u0647 30 \u0698\u0648\u0626\u06cc\u0647 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0698\u0648\u0626\u06cc\u0647 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u06af\u0632\u06cc\u0646\u0647\u200c\u0647\u0627\u06cc \u062e\u0631\u06cc\u062f<\/h3>\n
\n

\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647 \u0627\u0635\u0644 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/h4>\n

\u0628\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0627\u06cc\u0646 \u06af\u0632\u06cc\u0646\u0647\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u0641\u0627\u06cc\u0644 PDF \u0645\u0642\u0627\u0644\u0647 \u0627\u0635\u0644\u06cc \u0631\u0627 \u0628\u0647 \u0632\u0628\u0627\u0646 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc \u062f\u0627\u0646\u0644\u0648\u062f \u06a9\u0646\u06cc\u062f.<\/p>\n

\u0642\u06cc\u0645\u062a: 19,000 \u062a\u0648\u0645\u0627\u0646<\/p>\n<\/p><\/div>\n

\n

\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647 \u0627\u0635\u0644 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc + \u062e\u0644\u0627\u0635\u0647 \u062f\u0648 \u0635\u0641\u062d\u0647 \u0627\u06cc \u0645\u0642\u0627\u0644\u0647 + \u067e\u0627\u062f\u06a9\u0633\u062a \u0635\u0648\u062a\u06cc \u0641\u0627\u0631\u0633\u06cc \u062e\u0644\u0627\u0635\u0647 \u0645\u0642\u0627\u0644\u0647<\/h4>\n

\u0628\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0627\u06cc\u0646 \u06af\u0632\u06cc\u0646\u0647\u060c \u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u062f\u0631\u06cc\u0627\u0641\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0635\u0644\u06cc\u060c \u06cc\u06a9 \u062e\u0644\u0627\u0635\u0647 \u062f\u0648 \u0635\u0641\u062d\u0647\u200c\u0627\u06cc \u0641\u0627\u0631\u0633\u06cc \u0648 \u067e\u0627\u062f\u06a9\u0633\u062a \u0635\u0648\u062a\u06cc \u0641\u0627\u0631\u0633\u06cc \u062e\u0644\u0627\u0635\u0647 \u0645\u0642\u0627\u0644\u0647 \u0631\u0627 \u0646\u06cc\u0632 \u062f\u0631\u06cc\u0627\u0641\u062a \u062e\u0648\u0627\u0647\u06cc\u062f \u06a9\u0631\u062f.<\/p>\n

\u0642\u06cc\u0645\u062a: 99,000 \u062a\u0648\u0645\u0627\u0646<\/p>\n<\/p><\/div>\n

\n

\u0633\u0641\u0627\u0631\u0634 \u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 + \u062e\u0644\u0627\u0635\u0647 \u062f\u0648 \u0635\u0641\u062d\u0647 \u0627\u06cc \u0645\u0642\u0627\u0644\u0647 + \u067e\u0627\u062f\u06a9\u0633\u062a \u0635\u0648\u062a\u06cc \u0641\u0627\u0631\u0633\u06cc \u062e\u0644\u0627\u0635\u0647 \u0645\u0642\u0627\u0644\u0647<\/h4>\n

\u0628\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0627\u06cc\u0646 \u06af\u0632\u06cc\u0646\u0647\u060c \u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u062f\u0631\u06cc\u0627\u0641\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0635\u0644\u06cc \u0648 \u062a\u0631\u062c\u0645\u0647 \u06a9\u0627\u0645\u0644 \u0622\u0646\u060c \u06cc\u06a9 \u062e\u0644\u0627\u0635\u0647 \u062f\u0648 \u0635\u0641\u062d\u0647\u200c\u0627\u06cc \u0641\u0627\u0631\u0633\u06cc \u0648 \u067e\u0627\u062f\u06a9\u0633\u062a \u0635\u0648\u062a\u06cc \u0641\u0627\u0631\u0633\u06cc \u062e\u0644\u0627\u0635\u0647 \u0645\u0642\u0627\u0644\u0647 \u0631\u0627 \u0646\u06cc\u0632 \u062f\u0631\u06cc\u0627\u0641\u062a \u062e\u0648\u0627\u0647\u06cc\u062f \u06a9\u0631\u062f.<\/p>\n

\u0642\u06cc\u0645\u062a: 1,200,000 \u062a\u0648\u0645\u0627\u0646<\/p>\n

\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644: 2 \u062a\u0627 3 \u0631\u0648\u0632 \u06a9\u0627\u0631\u06cc<\/p>\n<\/p><\/div>\n<\/p><\/div>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n

\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n

Current LLM training positions mathematical reasoning as a core capability. With publicly available sources fully tapped, there is unmet demand for diverse and challenging math questions. Relying solely on human experts is both time-consuming and costly, while LLM-generated questions often lack the requisite diversity and difficulty. We present a design framework that combines the strengths of LLMs with a human-in-the-loop approach to generate a diverse array of challenging math questions. We leverage LLM metacognition skills [Didolkar et al., 2024] of a strong LLM to extract core “skills” from existing math datasets. These skills serve as the basis for generating novel and difficult questions by prompting the LLM with random pairs of core skills. The use of two different skills within each question makes finding such questions an “out of distribution” task for both LLMs and humans. Our pipeline employs LLMs to iteratively generate and refine questions and solutions through multiturn prompting. Human annotators then verify and further refine the questions, with their efficiency enhanced via further LLM interactions. Applying this pipeline on skills extracted from the MATH dataset [Hendrycks et al., 2021] resulted in MATH$^2$ – a dataset of higher-quality math questions, as evidenced by: (a) Lower performance of all models on MATH$^2$ than on MATH (b) Higher performance on MATH when using MATH$^2$ questions as in-context examples. Although focused on mathematics, our methodology seems applicable to other domains requiring structured reasoning, and potentially as a component of scalable oversight. Also of interest is a striking relationship observed between models’ performance on the new dataset: the success rate on MATH$^2$ is the square on MATH, suggesting that successfully solving the question in MATH$^2$ requires a nontrivial combination of two distinct math skills.<\/p>\n

\u0686\u06a9\u06cc\u062f\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc (\u062a\u0631\u062c\u0645\u0647 \u0645\u0627\u0634\u06cc\u0646\u06cc)<\/h2>\n

\u0622\u0645\u0648\u0632\u0634 LLM \u0641\u0639\u0644\u06cc \u0627\u0633\u062a\u062f\u0644\u0627\u0644 \u0631\u06cc\u0627\u0636\u06cc \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u062a\u0648\u0627\u0646\u0627\u06cc\u06cc \u0627\u0635\u0644\u06cc \u0642\u0631\u0627\u0631 \u0645\u06cc \u062f\u0647\u062f.\u0628\u0627 \u0648\u062c\u0648\u062f \u0645\u0646\u0627\u0628\u0639 \u062f\u0631 \u062f\u0633\u062a\u0631\u0633 \u0639\u0645\u0648\u0645 \u060c \u062a\u0642\u0627\u0636\u0627\u06cc \u0628\u0631\u0622\u0648\u0631\u062f\u0647 \u0646\u0634\u062f\u0647 \u0628\u0631\u0627\u06cc \u0633\u0648\u0627\u0644\u0627\u062a \u0631\u06cc\u0627\u0636\u06cc \u0645\u062a\u0646\u0648\u0639 \u0648 \u0686\u0627\u0644\u0634 \u0628\u0631\u0627\u0646\u06af\u06cc\u0632 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f.\u062a\u06a9\u06cc\u0647 \u0641\u0642\u0637 \u0628\u0647 \u0645\u062a\u062e\u0635\u0635\u0627\u0646 \u0628\u0634\u0631 \u0647\u0645 \u0648\u0642\u062a \u06af\u06cc\u0631 \u0648 \u0647\u0645 \u067e\u0631 \u0647\u0632\u06cc\u0646\u0647 \u0627\u0633\u062a \u060c \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0633\u0624\u0627\u0644\u0627\u062a \u0627\u06cc\u062c\u0627\u062f \u0634\u062f\u0647 \u062a\u0648\u0633\u0637 LLM \u0627\u063a\u0644\u0628 \u0641\u0627\u0642\u062f \u062a\u0646\u0648\u0639 \u0648 \u062f\u0634\u0648\u0627\u0631\u06cc \u0644\u0627\u0632\u0645 \u0627\u0633\u062a.\u0645\u0627 \u06cc\u06a9 \u0686\u0627\u0631\u0686\u0648\u0628 \u0637\u0631\u0627\u062d\u06cc \u0631\u0627 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0646\u0642\u0627\u0637 \u0642\u0648\u062a LLM \u0647\u0627 \u0631\u0627 \u0628\u0627 \u06cc\u06a9 \u0631\u0648\u06cc\u06a9\u0631\u062f \u0627\u0646\u0633\u0627\u0646 \u062f\u0631 \u062d\u0644\u0642\u0647 \u062a\u0631\u06a9\u06cc\u0628 \u0645\u06cc \u06a9\u0646\u062f \u062a\u0627 \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u06cc \u0645\u062a\u0646\u0648\u0639 \u0627\u0632 \u0633\u0624\u0627\u0644\u0627\u062a \u0631\u06cc\u0627\u0636\u06cc \u0686\u0627\u0644\u0634 \u0628\u0631\u0627\u0646\u06af\u06cc\u0632 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u062f.\u0645\u0627 \u0627\u0632 \u0645\u0647\u0627\u0631\u062a \u0647\u0627\u06cc \u0641\u0631\u0627\u0634\u0646\u0627\u062e\u062a LLM [Didolkar et al. \u060c 2024] \u0627\u0632 LLM \u0642\u0648\u06cc \u0628\u0631\u0627\u06cc \u0627\u0633\u062a\u062e\u0631\u0627\u062c “\u0645\u0647\u0627\u0631\u062a \u0647\u0627\u06cc \u0627\u0635\u0644\u06cc” \u0627\u0632 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0631\u06cc\u0627\u0636\u06cc \u0645\u0648\u062c\u0648\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645.\u0627\u06cc\u0646 \u0645\u0647\u0627\u0631\u062a \u0647\u0627 \u0628\u0627 \u0633\u0648\u0642 \u062f\u0627\u062f\u0646 LLM \u0628\u0627 \u062c\u0641\u062a \u0647\u0627\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u0627\u0632 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\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n","protected":false},"excerpt":{"rendered":"

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