On AI solving open math problems

Many people these days are shocked by the OpenAI announcements on results on open (until recently) problems and they ask the company to stop testing frontier models on open math problems. That doesn't sound right. Just because you cannot compete technology you cannot ask it to cease to exist.

Nevertheless, it is reasonable to ask AI companies to make such announcements in a slower pace. Not necessarily to slow down model development, just to make such releases on smaller packages and less frequently, so that the community will have time to digest the results and perhaps even understand the proves.

Bombarding the community with a huge bundle of information can only make the whole task unmanageable. That is if you want to make some serious contribution to scientific progress and not just make good impression to your stockholders.

Schrodinger's cat tired of waiting

 Schrodinger's cat tired of waiting

Algorithmic approach of the unit distance problem

In my latest paper, I present experimental evidence on unit-distance graph density which was introduced by Paul Erdős. My approach is based on a novel algorithmic exploration of the rational plane and the generation of a unit-distance graph that surpasses recent theoretical lower bounds. It achieves a scaling exponent larger than 1.17. 

 

The algorithm essentially utilizes a local-breadth search on a bounded and finite set of elements and generates a graph that potentially encompasses the general properties of a unit-distance graph, not affected by restrictions on its generation. 


Find the paper here and the repository containing code and experimental results here.

Transformer Autoencoder for irregular time series

Transformers are advanced Neural Network architectures useful in Data Analysis, not only for LLMs. 

I recently published a paper that presents a method based on a Transformer Autoencoder architecture for analyzing sparse and irregular time series. The autoencoder utilizes a local attention mechanism to identify similarities and anomalies within the complex structure of irregular datasets. It demonstrates notable clustering capabilities for samples that share similar characteristics.

The method is useful in risk estimation. The application presented in this work focuses on detecting accounts at higher risk of non-technical losses in electrical power systems, mainly electricity theft, using real-world consumption data from Greece.

The proposed framework combines classical data cleaning procedures with a state-of-the-art transformer architecture, exploiting the local attention mechanism to capture meaningful short-range temporal patterns without requiring interpolation of missing data.

The paper is available here. Also a read only version and a preprint.

Java's birthday