Abstract Visual Reasoning: An Algebraic Approach for Solving Raven's Progressive Matrices

We introduce algebraic machine reasoning, a new reasoning framework that is well-suited for abstract reasoning. Effectively, algebraic machine reasoning reduces the difficult process of novel problem-solving to routine algebraic computation. The fundamental algebraic objects of interest are the ideals of some suitably initialized polynomial ring. We shall explain how solving Raven's Progressive Matrices (RPMs) can be realized as computational problems in algebra, which combine various well-known algebraic subroutines that include: Computing the Gr\"obner basis of an ideal, checking for ideal containment, etc. Crucially, the additional algebraic structure satisfied by ideals allows for more operations on ideals beyond set-theoretic operations. Our algebraic machine reasoning framework is not only able to select the correct answer from a given answer set, but also able to generate the correct answer with only the question matrix given. Experiments on the I-RAVEN dataset yield an overall $93.2\%$ accuracy, which significantly outperforms the current state-of-the-art accuracy of $77.0\%$ and exceeds human performance at $84.4\%$ accuracy.

How Robust are Limit Order Book Representations under Data Perturbation?

The success of machine learning models in the financial domain is highly reliant on the quality of the data representation. In this paper, we focus on the representation of limit order book data and discuss the opportunities and challenges for learning representations of such data. We also experimentally analyse the issues associated with existing representations and present a guideline for future research in this area.