Building Smarter Generative AI: The Art of Algorithmic Reasoning in Language Models

Large language models (LLMs) like GPT-4 and PaLM have made significant advancements in natural language processing due to scaling model and training data sizes. However, there is ongoing debate about whether these models can perform symbolic reasoning, which involves manipulating symbols based on logical rules. While LLMs can handle arithmetic operations with small numbers effectively, their performance declines with larger numbers, indicating that they do not learn the fundamental arithmetic rules.

Neural networks, despite their strong pattern recognition capabilities, tend to overfit to spurious statistical patterns. This issue becomes apparent in tasks requiring rule-based reasoning, where LLMs often rely on spurious correlations rather than true solutions, leading to challenges in out-of-distribution generalization.

The paper titled "Teaching Algorithmic Reasoning Through In-Context Learning" aims to improve algorithmic reasoning in LLMs using in-context learning. This technique allows the model to learn tasks from a few examples provided via prompts without updating the model weights. Additionally, appropriate prompting strategies can lead to better performance on out-of-distribution problems.

Imparting Algorithmic Expertise to Models

Algorithmic prompting is a technique designed to teach large language models (LLMs) to perform tasks using algorithmic reasoning. It builds on rationale-augmented methods like scratchpad and chain-of-thought prompting, but with two key distinctions: (1) it generates step-by-step solutions for tasks, and (2) it provides detailed explanations for each step to ensure the model interprets them correctly.

An example of two-number addition illustrates the approach. In a scratchpad-style prompt, digits are added from right to left, tracking the carry value when necessary. However, the carry rule can become ambiguous for the model after seeing only a few examples. Algorithmic prompting resolves this by introducing explicit equations to define each step, such as how to handle carry values and indexing operations, making the task clearer for the model. By using clear, non-ambiguous instructions, algorithmic prompting helps LLMs improve their performance in tasks requiring algorithmic reasoning. Illustration of various prompt strategies for addition.

Using only three prompt examples of addition with answer length up to five digits, we evaluate performance on additions of up to 19 digits. Accuracy is measured over 2,000 total examples sampled uniformly over the length of the answer. As shown below, the use of algorithmic prompts maintains high accuracy for questions significantly longer than what’s seen in the prompt, which demonstrates that the model is indeed solving the task by executing an input-agnostic algorithm.

Applying Algorithmic Skills for Enhanced Problem Solving

To assess whether models can effectively use algorithmic reasoning within broader tasks, this study applies algorithmic prompting to grade school math word problems (GSM8k). Specifically, it replaces addition calculations in GSM8k with algorithmic solutions. Due to constraints on context length and potential interference between different algorithms, the study employs a dual-model approach. One model is tasked with informal mathematical reasoning using chain-of-thought prompting, while another model focuses on addition through algorithmic prompting. The informal reasoning model generates specialized tokens to call upon the addition model for arithmetic steps. Queries are extracted from these tokens, sent to the addition model, and the results are fed back to the reasoning model. The reasoning model then continues processing based on the arithmetic answers provided.This approach is tested with difficult GSM8k problems (GSM8k-Hard), where 50 addition-only questions with increased numerical values are randomly selected. The goal is to determine if leveraging algorithmic skills through interaction between specialized models improves the overall performance on complex math problems, demonstrating the ability to integrate algorithmic reasoning into more extensive problem-solving processes.

The study shows that using separate models with specialized prompts effectively addresses GSM8k-Hard problems. Specifically, the model utilizing algorithmic prompting for addition performs 2.3 times better than the chain-of-thought baseline. This approach demonstrates how interacting models, each specialized in different skills, can solve complex tasks through in-context learning. By combining models with distinct expertise, the strategy improves overall problem-solving performance and showcases the benefits of integrating specialized capabilities in handling challenging math problems.

Conclusion

The approach combines in-context learning with a new algorithmic prompting technique to enhance algorithmic reasoning in large language models (LLMs). Results indicate that providing more detailed explanations can improve reasoning performance, even with longer contexts. This suggests that simulating extended contexts and generating comprehensive rationales could be effective research avenues for further advancing LLM capabilities.As Leveragai, we strive to provide you with a better quality service by using the latest technologies in our consultancy services. Join Leveragai now and enjoy the latest technologies.

References

Zhou, H., Nova, A., Larochelle, H., Courville, A., Neyshabur, B., & Sedghi, H. (2022). Teaching algorithmic reasoning via in-context learning. arXiv preprint arXiv:2211.09066.

Zhou, H., Sedghi, H. (2022). Teaching language models to reason algorithmically. Google Research Blog.

Cobbe, K., Kosaraju, V., Bavarian, M., Chen, M., Jun, H., Kaiser, L., Plappert, M., Tworek, J., Hilton, J., Nakano, R., Hesse, C., & Schulman, J. (2021). Training verifiers to solve math word problems. arXiv preprint arXiv:2110.14168.