Daily Papers

In this paper, we extend mean-field Langevin dynamics to minimax optimization over probability distributions for the first time with symmetric and provably convergent updates. We propose mean-field Langevin averaged gradient (MFL-AG), a single-loop algorithm that implements gradient descent ascent in the distribution spaces with a novel weighted averaging, and establish average-iterate convergence to the mixed Nash equilibrium. We also study both time and particle discretization regimes and prove a new uniform-in-time propagation of chaos result which accounts for the dependency of the particle interactions on all previous distributions. Furthermore, we propose mean-field Langevin anchored best response (MFL-ABR), a symmetric double-loop algorithm based on best response dynamics with linear last-iterate convergence. Finally, we study applications to zero-sum Markov games and conduct simulations demonstrating long-term optimality.

Figurative language generation is the task of reformulating a given text in the desired figure of speech while still being faithful to the original context. We take the first step towards multi-figurative language modelling by providing a benchmark for the automatic generation of five common figurative forms in English. We train mFLAG employing a scheme for multi-figurative language pre-training on top of BART, and a mechanism for injecting the target figurative information into the encoder; this enables the generation of text with the target figurative form from another figurative form without parallel figurative-figurative sentence pairs. Our approach outperforms all strong baselines. We also offer some qualitative analysis and reflections on the relationship between the different figures of speech.