In this work, we introduce Boolformer, the first Transformer architecture
trained to perform end-to-end symbolic regression of Boolean functions. First,
we show that it can predict compact formulas for complex functions which were
not seen during training, when provided a clean truth table. Then, we
demonstrate its ability to find approximate expressions when provided
incomplete and noisy observations. We evaluate the Boolformer on a broad set of
real-world binary classification datasets, demonstrating its potential as an
interpretable alternative to classic machine learning methods. Finally, we
apply it to the widespread task of modelling the dynamics of gene regulatory
networks. Using a recent benchmark, we show that Boolformer is competitive with
state-of-the art genetic algorithms with a speedup of several orders of
magnitude. Our code and models are available publicly.

我们介绍了 Boolformer，这是第一个经过训练的 Transformer 架构，能够执行完整的布尔函数符号回归。它能够预测复杂函数的简洁公式，并能够在提供不完整和嘈杂的观测数据时找到近似表达式。我们在广泛的实际二元分类数据集上评估了 Boolformer，展示了它作为解释性机器学习方法的潜力。最后，我们将其应用于基因调控网络动力学建模任务，使用最新的基准测试，展示了 Boolformer 与最先进的遗传算法相竞争，并具有数个量级的加速度。我们的代码和模型公开可用。