Original (McCulloch and Pitts 1943) neuron as logic gate
6
Weighted neuron (perceptron, 1958) as logic gate
7
Differentiable neuron (MLPs, deep learning) as logic gate
8
b. Constrained differentiable neuron (LNN) as logic gate
9
a. Neuron (LNN) as real-valued logic gate
10
a. Neural network inference as logical reasoning
11
a. Data and learning
12
7b. Data and learning
13
Equivalence between neural networks and symbolic logic
14
Comparison to other common neuro-symbolic ideas
15
Use case: Knowledge base question answering (KBQA)
16
KBQA: Why it challenges default Al (end-to-end deep learning)
17
KBQA: an approach via understanding
18
Making the model & inference process human-understandable
19
Learning to reason
20
Logical rule induction (ILP)
21
Optimization/learning
22
Reinforcement learning
23
Policy induction via rule learning
24
AGI: Bengio-Marcus Desiderata
25
Ongoing directions
26
Philosophical shift
27
Summary
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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.
Logical Neural Networks: Unifying Statistical and Symbolic AI