Transparent Semantic Spaces: A Categorical Approach to Explainable Word Embeddings

The paper introduces a novel framework based on category theory to enhance the explainability of artificial intelligence systems, particularly focusing on word embeddings. Key topics include the construction of categories $\mathcal{L}_T$ and $\mathcal{P}_T$, providing schematic representations of the semantics of a text $ T $, and reframing the selection of the element with maximum probability as a categorical notion. Additionally, the monoidal category $\mathcal{P}_T$ is constructed to visualize various methods of extracting semantic information from $T$, offering a dimension-agnostic definition of semantic spaces reliant solely on information within the text. Furthermore, the paper defines the categories of configurations Conf and word embeddings $\mathcal{Emb}$, accompanied by the concept of divergence as a decoration on $\mathcal{Emb}$. It establishes a mathematically precise method for comparing word embeddings, demonstrating the equivalence between the GloVe and Word2Vec algorithms and the metric MDS algorithm, transitioning from neural network algorithms (black box) to a transparent framework. Finally, the paper presents a mathematical approach to computing biases before embedding and offers insights on mitigating biases at the semantic space level, advancing the field of explainable artificial intelligence.

Taxi dispatching strategies with compensations

Urban mobility efficiency is of utmost importance in big cities. Taxi vehicles are key elements in daily traffic activity. The advance of ICT and geo-positioning systems has given rise to new opportunities for improving the efficiency of taxi fleets in terms of waiting times of passengers, cost and time for drivers, traffic density, CO2 emissions, etc., by using more informed, intelligent dispatching. Still, the explicit spatial and temporal components, as well as the scale and, in particular, the dynamicity of the problem of pairing passengers and taxis in big towns, render traditional approaches for solving standard assignment problem useless for this purpose, and call for intelligent approximation strategies based on domain-specific heuristics. Furthermore, taxi drivers are often autonomous actors and may not agree to participate in assignments that, though globally efficient, may not be sufficently beneficial for them individually. This paper presents a new heuristic algorithm for taxi assignment to customers that considers taxi reassignments if this may lead to globally better solutions. In addition, as such new assignments may reduce the expected revenues of individual drivers, we propose an economic compensation scheme to make individually rational drivers agree to proposed modifications in their assigned clients. We carried out a set of experiments, where several commonly used assignment strategies are compared to three different instantiations of our heuristic algorithm. The results indicate that our proposal has the potential to reduce customer waiting times in fleets of autonomous taxis, while being also beneficial from an economic point of view.