Annealing Machine-assisted Learning of Graph Neural Network for Combinatorial Optimization

While Annealing Machines (AM) have shown increasing capabilities in solving complex combinatorial problems, positioning themselves as a more immediate alternative to the expected advances of future fully quantum solutions, there are still scaling limitations. In parallel, Graph Neural Networks (GNN) have been recently adapted to solve combinatorial problems, showing competitive results and potentially high scalability due to their distributed nature. We propose a merging approach that aims at retaining both the accuracy exhibited by AMs and the representational flexibility and scalability of GNNs. Our model considers a compression step, followed by a supervised interaction where partial solutions obtained from the AM are used to guide local GNNs from where node feature representations are obtained and combined to initialize an additional GNN-based solver that handles the original graph's target problem. Intuitively, the AM can solve the combinatorial problem indirectly by infusing its knowledge into the GNN. Experiments on canonical optimization problems show that the idea is feasible, effectively allowing the AM to solve size problems beyond its original limits.

Perceptual Structure in the Absence of Grounding for LLMs: The Impact of Abstractedness and Subjectivity in Color Language

The need for grounding in language understanding is an active research topic. Previous work has suggested that color perception and color language appear as a suitable test bed to empirically study the problem, given its cognitive significance and showing that there is considerable alignment between a defined color space and the feature space defined by a language model. To further study this issue, we collect a large scale source of colors and their descriptions, containing almost a 1 million examples , and perform an empirical analysis to compare two kinds of alignments: (i) inter-space, by learning a mapping between embedding space and color space, and (ii) intra-space, by means of prompting comparatives between color descriptions. Our results show that while color space alignment holds for monolexemic, highly pragmatic color descriptions, this alignment drops considerably in the presence of examples that exhibit elements of real linguistic usage such as subjectivity and abstractedness, suggesting that grounding may be required in such cases.