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Solving Probability and Statistics Problems by Program Synthesis

2021-11-16 · ACL ARR November 2021 11 · Anonymous

We solve university level probability and statistics questions by program synthesis using OpenAI's Codex, a Transformer trained on text and fine-tuned on code. We transform course problems from MIT's 18.05 Introduction to Probability and Statistics and Harvard's STAT110 Probability into programming tasks. We then execute the generated code to get a solution. Since these course questions are grounded in probability, we often aim to have Codex generate probabilistic programs that simulate a large number of probabilistic dependencies, to compute its solution. Our approach requires prompt engineering to transform the question from its original form to an explicit, tractable form that results in a correct program and solution. To estimate the amount of work needed to translate an original question into its tractable form, we measure the similarity between original and transformed questions. Our work is the first to introduce a new dataset of university-level probability and statistics problems and solve these problems in a scalable fashion using the program synthesis capabilities of large language models.

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FormProgram SynthesisPrompt Engineering

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Multi-Head Attention 설명 없음
Attention 설명 없음
Linear Layer A Linear Layer is a projection $\mathbf{XW + b}$.
Dropout Dropout is a regularization technique for neural networks that drops a unit (along with connections) at training time with a specified probability $p$ (a common value is…
Label Smoothing Label Smoothing is a regularization technique that introduces noise for the labels. This accounts for the fact that datasets may have mistakes in them, so maximizing the…
BPE Byte Pair Encoding, or BPE, is a subword segmentation algorithm that encodes rare and unknown words as sequences of subword units. The intuition is that various word…
Absolute Position Encodings Absolute Position Encodings are a type of position embeddings for [Transformer-based models] where positional encodings are…
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