The KANDY Benchmark: Incremental Neuro-Symbolic Learning and Reasoning with Kandinsky Patterns

Artificial intelligence is continuously seeking novel challenges and benchmarks to effectively measure performance and to advance the state-of-the-art. In this paper we introduce KANDY, a benchmarking framework that can be used to generate a variety of learning and reasoning tasks inspired by Kandinsky patterns. By creating curricula of binary classification tasks with increasing complexity and with sparse supervisions, KANDY can be used to implement benchmarks for continual and semi-supervised learning, with a specific focus on symbol compositionality. Classification rules are also provided in the ground truth to enable analysis of interpretable solutions. Together with the benchmark generation pipeline, we release two curricula, an easier and a harder one, that we propose as new challenges for the research community. With a thorough experimental evaluation, we show how both state-of-the-art neural models and purely symbolic approaches struggle with solving most of the tasks, thus calling for the application of advanced neuro-symbolic methods trained over time.