In this post on the last day of the year, I thought I will share a map of mathematical structures that are useful for thinking about knowledge representation and reasoning (KRR) issues in Artificial Intelligence and Machine Learning. It is built on top of the diagram shown in Max Tegmark’s paper Is “the theory of … More A Map of Mathematical Structures
Artificial Intelligence as a well-defined mathematical problem was solved a number of years ago through the formulation of the AIXI agent by Prof Marcus Hutter — see https://theconversation.com/to-create-a-super-intelligent-machine-start-with-an-equation-20756 for a quick introduction — but a key fundamental issue with the AIXI theory has always been the incomputability of the general solution. In a continuation of … More A Direct Approximation of AIXI using Logical State Abstractions
A few of us have been working with homomorphic encryption for a number of years now, but we never found a paper / book that covers all the foundational mathematical material in one place. So we decided to write one — well my postdoc Kelvin Yang Li decided to write one and Mike Purcell and I assisted … More A Tutorial Introduction to Lattice-based Cryptography and Homomorphic Encryption
A few colleagues and I have just completed a new research paper titled Factored Conditional Filtering: Tracking States and Estimating Parameters in High-Dimensional Spaces. The research took over 3 years and I am really excited about the underlying theory and its possible applications. In particular, the paper shows how we can lift’ Bayesian filtering to … More Bayesian Filtering on Structured Environments
Cyclotomic polynomials are widely used in the construction of lattice cryptography and homomorphic encryption schemes based on the Ring Learning With Error problem. In this short note, Kelvin Li and I attempt a self-contained introduction to the cyclotomic polynomials and the Galois groups of cyclotomic extensions.
Data matching and entity resolution is a common first step in data preparation and there is a thousand academic papers written on the subject in the literature. In practice, for large datasets – anything more than a million records will do as a definition of large here because most data-matching algorithms can’t handle that because … More A Note on Large Scale Data Matching and Entity Resolution
I read the book Divining a Digital Future: Mess and Mythology in Ubiquitous Computing by Genevieve Bell and Paul Dourish almost cover to cover last year and I have to say that finally gave me some understanding of the research agenda being pursued at the 3A Institute at the ANU. I hope I am not … More Book Review: Divining a Digital Future
A few colleagues and I have just put on arXiv a new survey paper on Private Graph Data Release, which took us nearly 9 months to write. Here’s the abstract: The application of graph analytics to various domains have yielded tremendous societal and economical benefits in recent years. However, the increasingly widespread adoption of graph … More Private Graph Data Release using Differential Privacy
One of my PhD students has just released a paper titled Spatially Invariant Unsupervised 3D Object Segmentation Using Graph Neural Networks. Here’s the abstract: In this paper, we tackle the problem of unsupervised 3D object segmentation from a point cloud without RGB information. In particular, we propose a framework, SPAIR3D, to model a point cloud … More Unsupervised 3D Object Segmentation
A friend sent me Safi Bahcall’s book “Loonshots: How to Nurture the Crazy Ideas that Win Wars, Cure Disease, and Transform Industries” a couple of months ago. It’s a fascinating book with many interesting ideas and stories, the most important of which is (arguably) the Innovation Equation, a model that seeks to explain, in a … More Safi Bahcall’s Innovation Equation
Combating terrorist financing
My Irrational Life
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
Mental Models 4 Life 