Article series
Logic Tensor Networks
Code on GitHubA step-by-step series on Logic Tensor Networks, a neuro-symbolic framework where first-order logic becomes a differentiable loss: from grounding symbols as tensors to learning by satisfying a knowledge base.
Chapters 5/5
- 01
Grounding: from symbols to tensors
How Logic Tensor Networks turns the constants, predicates, functions and variables of first-order logic into tensors and differentiable functions.
16 min read
- 02
Connectives and quantifiers
How LTN replaces truth tables with differentiable fuzzy operators, and the quantifiers ∀ and ∃ with generalized means, along with diagonal quantification and guarded quantifiers.
19 min read
- 03
Operators and their gradients
Why fuzzy operators are not all equally good for learning: vanishing gradients, single-passing gradients, exploding gradients, and the stable product configuration that avoids them.
10 min read
- 04
Learning by satisfying a knowledge base
How LTN turns a knowledge base into a loss function: a classifier learns to label 19 points from only two examples and a proximity rule, then 10,000 points in mini-batches.
20 min read
- 05
Case study: adding digits without ever labeling them
An LTN learns to recognize handwritten MNIST digits from the sum of two digits alone, and stays at 95% accuracy on adding two-digit numbers, where a purely supervised network drops to 45%.
42 min read