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.

Visual reasoning is essential for building intelligent agents that understand the world and perform problem-solving beyond perception. Differentiable forward reasoning has been developed to integrate reasoning with gradient-based machine learning paradigms. However, due to the memory intensity, most existing approaches do not bring the best of the expressivity of first-order logic, excluding a crucial ability to solve abstract visual reasoning, where agents need to perform reasoning by using analogies on abstract concepts in different scenarios. To overcome this problem, we propose NEUro-symbolic Message-pAssiNg reasoNer (NEUMANN), which is a graph-based differentiable forward reasoner, passing messages in a memory-efficient manner and handling structured programs with functors. Moreover, we propose a computationally-efficient structure learning algorithm to perform explanatory program induction on complex visual scenes. To evaluate, in addition to conventional visual reasoning tasks, we propose a new task, visual reasoning behind-the-scenes, where agents need to learn abstract programs and then answer queries by imagining scenes that are not observed. We empirically demonstrate that NEUMANN solves visual reasoning tasks efficiently, outperforming neural, symbolic, and neuro-symbolic baselines.

Reasoning is an essential part of human intelligence and thus has been a long-standing goal in artificial intelligence research. With the recent success of deep learning, incorporating reasoning with deep learning systems, i.e., neuro-symbolic AI has become a major field of interest. We propose the Neuro-Symbolic Forward Reasoner (NSFR), a new approach for reasoning tasks taking advantage of differentiable forward-chaining using first-order logic. The key idea is to combine differentiable forward-chaining reasoning with object-centric (deep) learning. Differentiable forward-chaining reasoning computes logical entailments smoothly, i.e., it deduces new facts from given facts and rules in a differentiable manner. The object-centric learning approach factorizes raw inputs into representations in terms of objects. Thus, it allows us to provide a consistent framework to perform the forward-chaining inference from raw inputs. NSFR factorizes the raw inputs into the object-centric representations, converts them into probabilistic ground atoms, and finally performs differentiable forward-chaining inference using weighted rules for inference. Our comprehensive experimental evaluations on object-centric reasoning data sets, 2D Kandinsky patterns and 3D CLEVR-Hans, and a variety of tasks show the effectiveness and advantage of our approach.

Kandinsky Figures and Kandinsky Patterns are mathematically describable, simple self-contained hence controllable test data sets for the development, validation and training of explainability in artificial intelligence. Whilst Kandinsky Patterns have these computationally manageable properties, they are at the same time easily distinguishable from human observers. Consequently, controlled patterns can be described by both humans and computers. We define a Kandinsky Pattern as a set of Kandinsky Figures, where for each figure an "infallible authority" defines that the figure belongs to the Kandinsky Pattern. With this simple principle we build training and validation data sets for automatic interpretability and context learning. In this paper we describe the basic idea and some underlying principles of Kandinsky Patterns and provide a Github repository to invite the international machine learning research community to a challenge to experiment with our Kandinsky Patterns to expand and thus make progress in the field of explainable AI and to contribute to the upcoming field of explainability and causability.