Einsum, Tensors, and Logic: The Core Insight

Pedro Domingos, author of the bestselling book "The Master Algorithm," introduces his latest work: Tensor Logic - a new programming language he believes could become the fundamental language for artificial intelligence.

Think of it like this: Physics found its language in calculus. Circuit design found its language in Boolean logic. Pedro argues that AI has been missing its language - until now.

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Current AI is split between two worlds that don't play well together:

Deep Learning (neural networks, transformers, ChatGPT) - great at learning from data, terrible at logical reasoning

Symbolic AI (logic programming, expert systems) - great at logical reasoning, terrible at learning from messy real-world data

Tensor Logic unifies both. It's a single language where you can:

Write logical rules that the system can actually learn and modify

Do transparent, verifiable reasoning (no hallucinations)

Mix "fuzzy" analogical thinking with rock-solid deduction

INTERACTIVE TRANSCRIPT:

https://app.rescript.info/public/share/NP4vZQ-GTETeN_roB2vg64vbEcN7isjJtz4C86WSOhw

TOC:

00:00:00 - Introduction

00:04:41 - What is Tensor Logic?

00:09:59 - Tensor Logic vs PyTorch & Einsum

00:17:50 - The Master Algorithm Connection

00:20:41 - Predicate Invention & Learning New Concepts

00:31:22 - Symmetries in AI & Physics

00:35:30 - Computational Reducibility & The Universe

00:43:34 - Technical Details: RNN Implementation

00:45:35 - Turing Completeness Debate

00:56:45 - Transformers vs Turing Machines

01:02:32 - Reasoning in Embedding Space

01:11:46 - Solving Hallucination with Deductive Modes

01:16:17 - Adoption Strategy & Migration Path

01:21:50 - AI Education & Abstraction

01:24:50 - The Trillion-Dollar Waste

REFS

Tensor Logic: The Language of AI [Pedro Domingos]

https://arxiv.org/abs/2510.12269

The Master Algorithm [Pedro Domingos]

https://www.amazon.co.uk/Master-Algorithm-Ultimate-Learning-Machine/dp/0241004543

Einsum is All you Need (TIM ROCKTÄSCHEL)

https://rockt.ai/2018/04/30/einsum

https://www.youtube.com/watch?v=6DrCq8Ry2cw

Autoregressive Large Language Models are Computationally Universal (Dale Schuurmans et al - GDM)

https://arxiv.org/abs/2410.03170

Memory Augmented Large Language Models are Computationally Universal [Dale Schuurmans]

https://arxiv.org/pdf/2301.04589

On the computational power of NNs [95/Siegelmann]

https://binds.cs.umass.edu/papers/1995_Siegelmann_JComSysSci.pdf

Sebastian Bubeck

https://www.reddit.com/r/OpenAI/comments/1oacp38/openai_researcher_sebastian_bubeck_falsely_claims/

I am a strange loop - Hofstadter

https://www.amazon.co.uk/Am-Strange-Loop-Douglas-Hofstadter/dp/0465030793

Stephen Wolfram

https://www.youtube.com/watch?v=dkpDjd2nHgo

The Complex World: An Introduction to the Foundations of Complexity Science [David C. Krakauer]

https://www.amazon.co.uk/Complex-World-Introduction-Foundations-Complexity/dp/1947864629

Geometric Deep Learning

https://www.youtube.com/watch?v=bIZB1hIJ4u8

Andrew Wilson (NYU)

https://www.youtube.com/watch?v=M-jTeBCEGHc

Yi Ma

https://www.patreon.com/posts/yi-ma-scientific-141953348

Roger Penrose - road to reality

https://www.amazon.co.uk/Road-Reality-Complete-Guide-Universe/dp/0099440687

Artificial Intelligence: A Modern Approach [Russel and Norvig]

https://www.amazon.co.uk/Artificial-Intelligence-Modern-Approach-Global/dp/1292153962