MathDSL: A Domain-Specific Language for Concise Mathematical Solutions Via Program Synthesis

We present MathDSL, a Domain-Specific Language (DSL) for mathematical equation solving, which, when deployed in program synthesis models, outperforms state-of-the-art reinforcement-learning-based methods. We also introduce a quantitative metric for measuring the conciseness of a mathematical solution and demonstrate the improvement in the quality of generated solutions compared to other methods. Our system demonstrates that a program synthesis system (DreamCoder) using MathDSL can generate programs that solve linear equations with greater accuracy and conciseness than using reinforcement learning systems. Additionally, we demonstrate that if we use the action spaces of previous reinforcement learning systems as DSLs, MathDSL outperforms the action-space-DSLs. We use DreamCoder to store equation-solving strategies as learned abstractions in its program library and demonstrate that by using MathDSL, these can be converted into human-interpretable solution strategies that could have applications in mathematical education.

CapText: Large Language Model-based Caption Generation From Image Context and Description

While deep-learning models have been shown to perform well on image-to-text datasets, it is difficult to use them in practice for captioning images. This is because captions traditionally tend to be context-dependent and offer complementary information about an image, while models tend to produce descriptions that describe the visual features of the image. Prior research in caption generation has explored the use of models that generate captions when provided with the images alongside their respective descriptions or contexts. We propose and evaluate a new approach, which leverages existing large language models to generate captions from textual descriptions and context alone, without ever processing the image directly. We demonstrate that after fine-tuning, our approach outperforms current state-of-the-art image-text alignment models like OSCAR-VinVL on this task on the CIDEr metric.