From a variational perspective, many statistical learning criteria involve seeking a distribution that balances empirical risk and regularization. In this paper, we broaden this perspective by introducing a new general class of variational methods based on Fenchel-Young (FY) losses, treated as divergences that generalize (and encompass) the familiar Kullback-Leibler divergence at the core of classical variational learning. Our proposed formulation -- FY variational learning -- includes as key ingredients new notions of FY free energy, FY evidence, FY evidence lower bound, and FY posterior. We derive alternating minimization and gradient backpropagation algorithms to compute (or lower bound) the FY evidence, which enables learning a wider class of models than previous variational formulations. This leads to generalized FY variants of classical algorithms, such as an FY expectation-maximization (FYEM) algorithm, and latent-variable models, such as an FY variational autoencoder (FYVAE). Our new methods are shown to be empirically competitive, often outperforming their classical counterparts, and most importantly, to have qualitatively novel features. For example, FYEM has an adaptively sparse E-step, while the FYVAE can support models with sparse observations and sparse posteriors.

Alignment with human preferences is an important step in developing accurate and safe large language models. This is no exception in machine translation (MT), where better handling of language nuances and context-specific variations leads to improved quality. However, preference data based on human feedback can be very expensive to obtain and curate at a large scale. Automatic metrics, on the other hand, can induce preferences, but they might not match human expectations perfectly. In this paper, we propose an approach that leverages the best of both worlds. We first collect sentence-level quality assessments from professional linguists on translations generated by multiple high-quality MT systems and evaluate the ability of current automatic metrics to recover these preferences. We then use this analysis to curate a new dataset, MT-Pref (metric induced translation preference) dataset, which comprises 18k instances covering 18 language directions, using texts sourced from multiple domains post-2022. We show that aligning TOWER models on MT-Pref significantly improves translation quality on WMT23 and FLORES benchmarks.

We propose a general framework for regularization based on group majorization. In this framework, a group is defined to act on the parameter space and an orbit is fixed; to control complexity, the model parameters are confined to lie in the convex hull of this orbit (the orbitope). Common regularizers are recovered as particular cases, and a connection is revealed between the recent sorted 1 -norm and the hyperoctahedral group. We derive the properties a group must satisfy for being amenable to optimization with conditional and projected gradient algorithms. Finally, we suggest a continuation strategy for orbit exploration, presenting simulation results for the symmetric and hyperoctahedral groups.