This paper formalizes an emerging learning paradigm that uses a trained model as a reference to guide and enhance the training of a target model through strategic data selection or weighting, named **model steering**. While ad-hoc methods have been used in various contexts, including the training of large foundation models, its underlying principles remain insufficiently understood, leading to sub-optimal performance. In this work, we propose a theory-driven framework for model steering called **DRRho risk minimization**, which is rooted in Distributionally Robust Optimization (DRO). Through a generalization analysis, we provide theoretical insights into why this approach improves generalization and data efficiency compared to training without a reference model. To the best of our knowledge, this is the first time such theoretical insights are provided for the new learning paradigm, which significantly enhance our understanding and practice of model steering. Building on these insights and the connection between contrastive learning and DRO, we introduce a novel method for Contrastive Language-Image Pretraining (CLIP) with a reference model, termed DRRho-CLIP. Extensive experiments validate the theoretical insights, reveal a superior scaling law compared to CLIP without a reference model, and demonstrate its strength over existing heuristic approaches. Code is released at [github.com/Optimization-AI/DRRho-CLIP](https://github.com/Optimization-AI/DRRho-CLIP)

Contrastive Language-Image Pre-training (CLIP) generates versatile multimodal embeddings for diverse applications, yet the specific information captured within these representations is not fully understood. Current explainability techniques often target specific tasks, overlooking the rich, general semantics inherent in the representations. Our objective is to reveal the concepts encoded in CLIP embeddings by learning a surrogate representation, which is expressed as a linear combination of human-understandable concepts evident in the image. Our method, which we term EXPLAIN-R, introduces a novel approach that leverages CLIP's learned instance-instance similarity to train a surrogate model that faithfully mimics CLIP's behavior. From the trained surrogate, we derive concept scores for each input image; these scores quantify the contribution of each concept and act as the explanation for the representation. Quantitative evaluations on multiple datasets demonstrate our method's superior faithfulness over the baseline. Moreover, a user study confirms that our explanations are perceived as more relevant, complete, and useful. Our work provides a novel approach for interpreting CLIP image representations, enhancing the user interpretability of representations and fostering more trustworthy AI systems.

Many machine learning tasks can be formulated as a stochastic compositional optimization (SCO) problem such as reinforcement learning, AUC maximization and meta-learning, where the objective function involves a nested composition associated with an expectation. Although many studies have been devoted to studying the convergence behavior of SCO algorithms, there is little work on understanding their generalization, that is, how these learning algorithms built from training data would behave on future test examples. In this paper, we provide the stability and generalization analysis of stochastic compositional gradient descent algorithms in the framework of statistical learning theory. Firstly, we introduce a stability concept called *compositional uniform stability* and establish its quantitative relation with generalization for SCO problems. Then, we establish the compositional uniform stability results for two notable stochastic compositional gradient descent algorithms, namely SCGD and SCSC. Finally, we derive *dimension-independent* excess risk bounds for SCGD and SCSC by balancing stability results and optimization errors. To the best of our knowledge, these are the first-ever known results on stability and generalization analysis of stochastic compositional gradient descent algorithms.

Zeroth-order (ZO) optimization has been the key technique for various machine learning applications especially for black-box adversarial attack, where models need to be learned in a gradient-free manner. Although many ZO algorithms have been proposed, the high function query complexities hinder their applications seriously. To address this challenging problem, we propose two stagewise black-box reduction frameworks for ZO algorithms under convex and non-convex settings respectively, which lower down the function query complexities of ZO algorithms. Moreover, our frameworks can directly derive the convergence results of ZO algorithms under convex and non-convex settings without extra analyses, as long as convergence results under strongly convex setting are given. To illustrate the advantages, we further study ZO-SVRG, ZO-SAGA and ZO-Varag under strongly-convex setting and use our frameworks to directly derive the convergence results under convex and non-convex settings. The function query complexities of these algorithms derived by our frameworks are lower than that of their vanilla counterparts without frameworks, or even lower than that of state-of-the-art algorithms. Finally we conduct numerical experiments to illustrate the superiority of our frameworks.