From Neural Activations to Concepts: A Survey on Explaining Concepts in Neural Networks

In this paper, we review recent approaches for explaining concepts in neural networks. Concepts can act as a natural link between learning and reasoning: once the concepts are identified that a neural learning system uses, one can integrate those concepts with a reasoning system for inference or use a reasoning system to act upon them to improve or enhance the learning system. On the other hand, knowledge can not only be extracted from neural networks but concept knowledge can also be inserted into neural network architectures. Since integrating learning and reasoning is at the core of neuro-symbolic AI, the insights gained from this survey can serve as an important step towards realizing neuro-symbolic AI based on explainable concepts.Comment: Submitted to Neurosymbolic Artificial Intelligence (https://neurosymbolic-ai-journal.com/paper/neural-activations-concepts-survey-explaining-concepts-neural-networks

Neural Expectation Maximization

Many real world tasks such as reasoning and physical interaction require identification and manipulation of conceptual entities. A first step towards solving these tasks is the automated discovery of distributed symbol-like representations. In this paper, we explicitly formalize this problem as inference in a spatial mixture model where each component is parametrized by a neural network. Based on the Expectation Maximization framework we then derive a differentiable clustering method that simultaneously learns how to group and represent individual entities. We evaluate our method on the (sequential) perceptual grouping task and find that it is able to accurately recover the constituent objects. We demonstrate that the learned representations are useful for next-step prediction.Comment: Accepted to NIPS 201

Neural-Symbolic Relational Reasoning on Graph Models: Effective Link Inference and Computation from Knowledge Bases

The recent developments and growing interest in neural-symbolic models has shown that hybrid approaches can offer richer models for Artificial Intelligence. The integration of effective relational learning and reasoning methods is one of the key challenges in this direction, as neural learning and symbolic reasoning offer complementary characteristics that can benefit the development of AI systems. Relational labelling or link prediction on knowledge graphs has become one of the main problems in deep learning-based natural language processing research. Moreover, other fields which make use of neural-symbolic techniques may also benefit from such research endeavours. There have been several efforts towards the identification of missing facts from existing ones in knowledge graphs. Two lines of research try and predict knowledge relations between two entities by considering all known facts connecting them or several paths of facts connecting them. We propose a neural-symbolic graph neural network which applies learning over all the paths by feeding the model with the embedding of the minimal subset of the knowledge graph containing such paths. By learning to produce representations for entities and facts corresponding to word embeddings, we show how the model can be trained end-to-end to decode these representations and infer relations between entities in a multitask approach. Our contribution is two-fold: a neural-symbolic methodology leverages the resolution of relational inference in large graphs, and we also demonstrate that such neural-symbolic model is shown more effective than path-based approachesComment: Under review: ICANN 202

Neural disjunctive normal form: Vertically integrating logic with deep learning for classification

Inspired by the limitations of pure deep learning and symbolic logic-based models, in this thesis we consider a specific type of neuro-symbolic integration called vertical integration to bridge logic reasoning and deep learning and address their limitations. The motivation of vertical integration is to combine perception and reasoning as two separate stages of computation, while still being able to utilize simple and efficient end-to-end learning. It uses a perceptive deep neural network (DNN) to learn abstract concepts from raw sensory data and uses a symbolic model that operates on these abstract concepts to make interpretable predictions. As a preliminary step towards this direction, we tackle the task of binary classification and propose the Neural Disjunctive Normal Form (Neural DNF). Specifically, we utilize a per- ceptive DNN module to extract features from data, then after binarization (0 or 1), feed them into a Disjunctive Normal Form (DNF) module to perform logical rule-based classi- fication. We introduce the BOAT algorithm to optimize these two normally-incompatible modules in an end-to-end manner. Compared to standard DNF, Neural DNF can handle prediction tasks from raw sensory data (such as images) thanks to the neurally-extracted concepts. Compared to standard DNN, Neural DNF offers improved interpretability via an explicit symbolic representation while being able to achieve comparable accuracy despite the reduction of model flexibility, and is particularly suited for certain classification tasks that require some logical composition. Our experiments show that BOAT can optimize Neural DNF in an end-to-end manner, i.e. jointly learn the logical rules and concepts from scratch, and that in certain cases the rules and the meanings of concepts are aligned with human understanding. We view Neural DNF as an important first step towards more sophisticated vertical inte- gration models, which use symbolic models of more powerful rule languages for advanced prediction and algorithmic tasks, beyond using DNF (propositional logic) for classification tasks. The BOAT algorithm introduced in this thesis can potentially be applied to such advanced hybrid models