Despite their remarkable capabilities, LLMs learn word representations that exhibit the undesirable yet poorly understood feature of anisotropy.In this paper, we argue that the second moment in Adam is a cause of anisotropic embeddings, and suggest a modified optimizer called Coupled Adam to mitigate the problem.Our experiments demonstrate that Coupled Adam significantly improves the quality of embeddings, while also leading to better upstream and downstream performance on large enough datasets.

We present the mapping of a class of simplified air traffic management problems (strategic conflict resolution) to quadratic unconstrained Boolean optimization problems. The mapping is performed through an original representation of the conflict-resolution problem in terms of a conflict graph, where the nodes of the graph represent flights and the edges represent a potential conflict between flights. The representation allows a natural decomposition of a real-world instance related to wind-optimal trajectories over the Atlantic Ocean into smaller subproblems that can be discretized and are amenable to be programmed in quantum annealers. In this paper, we tested the new programming techniques, and we benchmark the hardness of the instances using both classical solvers and the D-Wave 2X and D-Wave 2000Q quantum chip. The preliminary results show that for reasonable modeling choices, the most challenging subproblems which are programmable in the current devices are solved to optimality with 99% of probability within a second of annealing time.