We specialize techniques from topological data analysis to the problem of characterizing the topological complexity (as defined in the body of the paper) of a multi-class data set. As a by-product, a topological classifier is defined that uses an open sub-covering of the data set. This sub-covering can be used to construct a simplicial complex whose topological features (e.g., Betti numbers) provide information about the classification problem. We use these topological constructs to study the impact of topological complexity on learning in feedforward deep neural networks (DNNs). We hypothesize that topological complexity is negatively correlated with the ability of a fully connected feedforward deep neural network to learn to classify data correctly. We evaluate our topological classification algorithm on multiple constructed and open source data sets. We also validate our hypothesis regarding the relationship between topological complexity and learning in DNN's on multiple data sets.

We present a prototype hybrid prediction market and demonstrate the avenue it represents for meaningful human-AI collaboration. We build on prior work proposing artificial prediction markets as a novel machine-learning algorithm. In an artificial prediction market, trained AI agents buy and sell outcomes of future events. Classification decisions can be framed as outcomes of future events, and accordingly, the price of an asset corresponding to a given classification outcome can be taken as a proxy for the confidence of the system in that decision. By embedding human participants in these markets alongside bot traders, we can bring together insights from both. In this paper, we detail pilot studies with prototype hybrid markets for the prediction of replication study outcomes. We highlight challenges and opportunities, share insights from semi-structured interviews with hybrid market participants, and outline a vision for ongoing and future work.

Explainably estimating confidence in published scholarly work offers opportunity for faster and more robust scientific progress. We develop a synthetic prediction market to assess the credibility of published claims in the social and behavioral sciences literature. We demonstrate our system and detail our findings using a collection of known replication projects. We suggest that this work lays the foundation for a research agenda that creatively uses AI for peer review.