Logic Encoding: Creating Embeddings For Logical And Arithmetic Functions
Link to Colab Notebook: https://colab.research.google.com/dri...
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This video discusses logic and coding, focusing on utilizing different programming languages to code logic [00:05]. It covers several approaches:
Prolog: Created in the 1960s, Prolog uses facts, rules, and queries to process logical queries with an inference engine [00:21]. It excels in logic but has limitations with arithmetic and inductive reasoning [01:24].
Higher Order Logic: This encodes higher-order predicates, offering more data than Prolog. It allows mapping variables and entities to structured numerical representations, enabling training a neural network [02:07].
First Order Predicate Calculus: An advanced form of higher-order logic, it incorporates arithmetic to some extent [03:47].
Arithmetic Encoding: The video transitions to a language focused on arithmetic and algebraic relationships, contrasting with the logic-based languages discussed earlier [05:18]. This method encodes operations as binary for the model to perform arithmetic calculations [06:21].
Universal Logic Encoding Neural Network: Combines both arithmetic and logic encoding methods [08:35].
Probabilistic Fractal Activation Function (Paaf): The video introduces Paaf, a method developed by the presenter to teach models how to utilize their weights probabilistically [11:11]. Paaf uses geometry and calculus, differing from the linear algebra-based approaches [13:15].