Logical Neural Networks: Unifying Statistical and Symbolic AI

Explore the concept of Logical Neural Networks in this comprehensive lecture that aims to unify statistical and symbolic AI. Delve into a new neuro-symbolic framework that establishes a one-to-one correspondence between artificial neurons and logic gates in weighted real-valued logic. Discover how this approach enables logical inference within neural networks and introduces contradiction loss to maximize logical consistency. Learn about the framework's unique features, including full disentanglement, exact logical deduction, and compositional knowledge representation. Examine state-of-the-art results in question answering and other applications. Follow the evolution of neural networks from McCulloch and Pitts to modern deep learning, and understand how Logical Neural Networks bridge the gap between neural and symbolic approaches. Gain insights into knowledge base question answering, logical rule induction, and the potential implications for artificial general intelligence.

Intro
Logical Neural Networks
Neuro-symbolic methods so far
Neuro-symbolic methods: another category
Original (McCulloch and Pitts 1943) neuron as logic gate
Weighted neuron (perceptron, 1958) as logic gate
Differentiable neuron (MLPs, deep learning) as logic gate
b. Constrained differentiable neuron (LNN) as logic gate
a. Neuron (LNN) as real-valued logic gate
a. Neural network inference as logical reasoning
a. Data and learning
7b. Data and learning
Equivalence between neural networks and symbolic logic
Comparison to other common neuro-symbolic ideas
Use case: Knowledge base question answering (KBQA)
KBQA: Why it challenges default Al (end-to-end deep learning)
KBQA: an approach via understanding
Making the model & inference process human-understandable
Learning to reason
Logical rule induction (ILP)
Optimization/learning
Reinforcement learning
Policy induction via rule learning
AGI: Bengio-Marcus Desiderata
Ongoing directions
Philosophical shift
Summary