Let's Be Self-generated via Step by Step: A Curriculum Learning Approach to Automated Reasoning with Large Language Models

While Chain of Thought (CoT) prompting approaches have significantly consolidated the reasoning capabilities of large language models (LLMs), they still face limitations that require extensive human effort or have performance needs to be improved. Existing endeavors have focused on bridging these gaps; however, these approaches either hinge on external data and cannot completely eliminate manual effort, or they fall short in effectively directing LLMs to generate high-quality exemplary prompts. To address the said pitfalls, we propose a novel prompt approach for automatic reasoning named LBS3, inspired by curriculum learning which better reflects human learning habits. Specifically, LBS3 initially steers LLMs to recall easy-to-hard proxy queries that are pertinent to the target query. Following this, it invokes a progressive strategy that utilizes exemplary prompts stemmed from easy-proxy queries to direct LLMs in solving hard-proxy queries, enabling the high-quality of the proxy solutions. Finally, our extensive experiments in various reasoningintensive tasks with varying open-and closed-source LLMs show that LBS3 achieves strongly competitive performance compared to the SOTA baselines. Our code is here: https://anonymous.4open.science/r/DFRD-0C83/ . Q: Sarah used to paint a landscape in 2 hours less time than it took David to paint the same landscape. But David started practicing regularly, which increased his painting speed by 15%. If Sarah takes 6 hours to paint the landscape, how long would it take David, with his improved skills, to complete the painting? A: Let's think step by step. ⋯ ⋯ Q: Olivia could solve a math puzzle 5 minutes quicker than Nicholas could. However, Nicholas enrolled in a tutoring program that reduced his solving time by 20%. If Olivia solves the puzzle in 35 minutes, how long will it take Nicholas, after tutoring, to solve the same math puzzle? A: Let's think step by step. ⋯ ⋯ Q: Emma typically finished reading a novel 3 days ahead of Jake. But Jake started reading an extra hour every day, which led to a 25% improvement in his reading speed. If Emma finishes a novel in 12 days, how many days would it take Jake, with his enhanced speed, to read the same book? A: Let's think step by step. ⋯ ⋯ A: Let's think step by step. ⋯ ⋯ The answer is: 40 seconds. Recall three examples of math problems that are relevant to the initial problem. Your problems should be distinct from each other and from the initial problem (e.g., involving different numbers and names). Initial problem: Q: Lee used to be able to run the 400-meter hurdles two seconds faster than Gerald would run the 400-meter hurdles. But Gerald changed his diet, which improved his speed by 10%. If Lee runs the 400-meter hurdles in 38 seconds, how fast can Gerald, with his improved diet, run the 400-meter hurdles, in seconds? Following is an example instance for the task: Solving the math problem. Please come up with three new, diverse, and creative problems for the task. Example instance: Q: Lee used to be able to run the 400-meter hurdles two seconds faster than Gerald would run the 400-meter hurdles. But Gerald changed his diet, which improved his speed by 10%. If Lee runs the 400-meter hurdles in 38 seconds, how fast can Gerald, with his improved diet, run the 400-meter hurdles, in seconds? Self-ICL Generate three questions with the same structure as the given question: Q: Lee used to be able to run the 400-meter hurdles two seconds faster than Gerald would run the 400-meter hurdles. But Gerald changed his diet, which improved his speed by 10%. If Lee runs the 400-meter hurdles in 38 seconds, how fast can Gerald, with his improved diet, run the 400-meter hurdles, in seconds? Auto-ICL Analogical Prompting Generate two different new relevant problems that are easier to solve than the example problem below. Example problem: Q: Lee used to be able to run the 400-meter hurdles two seconds faster than Gerald would run the 400meter hurdles. But Gerald changed his diet, which improved his speed by 10%. If Lee runs the 400meter hurdles in 38 seconds, how fast can Gerald, with his improved diet, run the 400-meter hurdles, in seconds? Generate one new problem that is analogous to the example problem below. Example problem: Q: Lee used to be able to run the 400-meter hurdles two seconds faster than Gerald would run the 400meter hurdles. But Gerald changed his diet, which improved his speed by 10%. If Lee runs the 400meter hurdles in 38 seconds, how fast can Gerald, with his improved diet, run the 400-meter hurdles, in seconds? LBS𝟑(ours) Q: In a science project, Emma initially solves a physics problem in 35 minutes, while her friend Alex takes 20% longer due to a different approach. If Emma improves her method and reduces her time by 25%, how long will it take Alex, now using Emma's optimized approach, to solve the same problem? A: Let's think step by step. ⋯ ⋯ Q: At a cooking competition, Chef Maria can prepare a gourmet pasta dish in 45 m