Simone Shao

Lingjing Kong, Shaoan Xie, Yang Jiao et al.

Compositional generalization -- the ability to understand and generate novel combinations of learned concepts -- enables models to extend their capabilities beyond limited experiences. While effective, the data structures and principles that enable this crucial capability remain poorly understood. We propose that compositional generalization fundamentally requires decomposing high-level concepts into basic, low-level concepts that can be recombined across similar contexts, similar to how humans draw analogies between concepts. For example, someone who has never seen a peacock eating rice can envision this scene by relating it to their previous observations of a chicken eating rice. In this work, we formalize these intuitive processes using principles of causal modularity and minimal changes. We introduce a hierarchical data-generating process that naturally encodes different levels of concepts and their interaction mechanisms. Theoretically, we demonstrate that this approach enables compositional generalization supporting complex relations between composed concepts, advancing beyond prior work that assumes simpler interactions like additive effects. Critically, we also prove that this latent hierarchical structure is provably recoverable (identifiable) from observable data like text-image pairs, a necessary step for learning such a generative process. To validate our theory, we apply insights from our theoretical framework and achieve significant improvements on benchmark datasets.

Zhuqing Liu, Chaosheng Dong, Michinari Momma et al.

Recently, multi-objective optimization (MOO) has gained attention for its broad applications in ML, operations research, and engineering. However, MOO algorithm design remains in its infancy and many existing MOO methods suffer from unsatisfactory convergence rate and sample complexity performance. To address this challenge, in this paper, we propose an algorithm called STIMULUS( stochastic path-integrated multi-gradient recursive e\ulstimator), a new and robust approach for solving MOO problems. Different from the traditional methods, STIMULUS introduces a simple yet powerful recursive framework for updating stochastic gradient estimates to improve convergence performance with low sample complexity. In addition, we introduce an enhanced version of STIMULUS, termed STIMULUS-M, which incorporates a momentum term to further expedite convergence. We establish $O(1/T)$ convergence rates of the proposed methods for non-convex settings and $O (\exp{-μT})$ for strongly convex settings, where $T$ is the total number of iteration rounds. Additionally, we achieve the state-of-the-art $O \left(n+\sqrt{n}ε^{-1}\right)$ sample complexities for non-convex settings and $O\left(n+ \sqrt{n} \ln ({μ/ε})\right)$ for strongly convex settings, where $ε>0$ is a desired stationarity error. Moreover, to alleviate the periodic full gradient evaluation requirement in STIMULUS and STIMULUS-M, we further propose enhanced versions with adaptive batching called STIMULUS+/ STIMULUS-M+ and provide their theoretical analysis.