ANPL: Compiling Natural Programs with Interactive Decomposition

The advents of Large Language Models (LLMs) have shown promise in augmenting programming using natural interactions. However, while LLMs are proficient in compiling common usage patterns into a programming language, e.g., Python, it remains a challenge how to edit and debug an LLM-generated program. We introduce ANPL, a programming system that allows users to decompose user-specific tasks. In an ANPL program, a user can directly manipulate sketch, which specifies the data flow of the generated program. The user annotates the modules, or hole with natural language descriptions offloading the expensive task of generating functionalities to the LLM. Given an ANPL program, the ANPL compiler generates a cohesive Python program that implements the functionalities in hole, while respecting the dataflows specified in sketch. We deploy ANPL on the Abstraction and Reasoning Corpus (ARC), a set of unique tasks that are challenging for state-of-the-art AI systems, showing it outperforms baseline programming systems that (a) without the ability to decompose tasks interactively and (b) without the guarantee that the modules can be correctly composed together. We obtain a dataset consisting of 300/400 ARC tasks that were successfully decomposed and grounded in Python, providing valuable insights into how humans decompose programmatic tasks. See the dataset at https://iprc-dip.github.io/DARC.

Online Symbolic Regression with Informative Query

Symbolic regression, the task of extracting mathematical expressions from the observed data $\{ \vx_i, y_i \}$, plays a crucial role in scientific discovery. Despite the promising performance of existing methods, most of them conduct symbolic regression in an \textit{offline} setting. That is, they treat the observed data points as given ones that are simply sampled from uniform distributions without exploring the expressive potential of data. However, for real-world scientific problems, the data used for symbolic regression are usually actively obtained by doing experiments, which is an \textit{online} setting. Thus, how to obtain informative data that can facilitate the symbolic regression process is an important problem that remains challenging. In this paper, we propose QUOSR, a \textbf{qu}ery-based framework for \textbf{o}nline \textbf{s}ymbolic \textbf{r}egression that can automatically obtain informative data in an iterative manner. Specifically, at each step, QUOSR receives historical data points, generates new $\vx$, and then queries the symbolic expression to get the corresponding $y$, where the $(\vx, y)$ serves as new data points. This process repeats until the maximum number of query steps is reached. To make the generated data points informative, we implement the framework with a neural network and train it by maximizing the mutual information between generated data points and the target expression. Through comprehensive experiments, we show that QUOSR can facilitate modern symbolic regression methods by generating informative data.