We consider the Tree Alternating Optimization (TAO) algorithm to train regression trees with linear predictors in the leaves. Unlike the traditional, greedy recursive partitioning algorithms such as CART, TAO guarantees a monotonic decrease of the objective function and results in smaller trees of much better accuracy. We modify the TAO algorithm so that it produces exactly the same result but is much faster, particularly for high input dimensionality or deep trees. The idea is based on the fact that, at each iteration of TAO, each leaf receives only a subset of the training instances. Thus, the optimization of the leaf model can be done exactly but faster by using the Sherman-Morrison-Woodbury formula. This has the unexpected advantage that, once a tree exceeds a critical depth, then making it deeper makes it faster to train, even though the tree is larger and has more parameters. Indeed, this can make learning a nonlinear model (the tree) asymptotically faster than a regular linear regression model. We analyze the corresponding computational complexity and verify the speedups experimentally in various datasets. The argument can be applied to other types of trees, whenever the optimization of a node can be computed in superlinear time of the number of instances.

Direct Preference Optimization (DPO) has emerged as an effective approach for mitigating hallucination in Multimodal Large Language Models (MLLMs). Although existing methods have achieved significant progress by utilizing vision-oriented contrastive objectives for enhancing MLLMs' attention to visual inputs and hence reducing hallucination, they suffer from non-rigorous optimization objective function and indirect preference supervision. To address these limitations, we propose a Symmetric Multimodal Preference Optimization (SymMPO), which conducts symmetric preference learning with direct preference supervision (i.e., response pairs) for visual understanding enhancement, while maintaining rigorous theoretical alignment with standard DPO. In addition to conventional ordinal preference learning, SymMPO introduces a preference margin consistency loss to quantitatively regulate the preference gap between symmetric preference pairs. Comprehensive evaluation across five benchmarks demonstrate SymMPO's superior performance, validating its effectiveness in hallucination mitigation of MLLMs.

Training-free guidance enables controlled generation in diffusion and flow models, but most methods rely on gradients and assume differentiable objectives. This work focuses on training-free guidance addressing challenges from non-differentiable objectives and discrete data distributions. We propose TreeG: Tree Search-Based Path Steering Guidance, applicable to both continuous and discrete settings in diffusion and flow models. TreeG offers a unified framework for training-free guidance by proposing, evaluating, and selecting candidates at each step, enhanced with tree search over active paths and parallel exploration. We comprehensively investigate the design space of TreeG over the candidate proposal module and the evaluation function, instantiating TreeG into three novel algorithms. Our experiments show that TreeG consistently outperforms top guidance baselines in symbolic music generation, small molecule design, and enhancer DNA design with improvements of 29.01%,26.38%,and

Most existing multi-view clustering methods aim to generate a consensus partition across all views, based on the assumption that all views share the same sample arrangement. However, in real-world scenarios, the collected data across different views is often unsynchronized, making it difficult to ensure consistent sample correspondence between views. To address this issue, we propose a scalable sample-alignment-based multi-view clustering method, referred to as SSA-MVC. Specifically, we first employ a cluster-label matching (CLM) algorithm to select the view whose clustering labels best match those of the others as the benchmark view. Then, for each of the remaining views, we construct representations of nonaligned samples by computing their similarities with aligned samples. Based on these representations, we build a similarity graph between the non-aligned samples of each view and those in the benchmark view, which serves as the alignment criterion. This alignment criterion is then integrated into a late-fusion framework to enable clustering without requiring aligned samples. Notably, the learned sample alignment matrix can be used to enhance existing multi-view clustering methods in scenarios where sample correspondence is unavailable. The effectiveness of the proposed SSA-MVC algorithm is validated through extensive experiments conducted on eight real-world multi-view datasets.

Text-to-motion generation is essential for advancing the creative industry but often presents challenges in producing consistent, realistic motions. To address this, we focus on fine-tuning text-to-motion models to consistently favor highquality, human-preferred motions--a critical yet largely unexplored problem. In this work, we theoretically investigate the DPO under both online and offline settings, and reveal their respective limitation: overfitting in offline DPO, and biased sampling in online DPO. Building on our theoretical insights, we introduce Semi-online Preference Optimization (SoPo), a DPO-based method for training text-to-motion models using "semi-online" data pair, consisting of unpreferred motion from online distribution and preferred motion in offline datasets. This method leverages both online and offline DPO, allowing each to compensate for the other's limitations. Extensive experiments demonstrate that SoPo outperforms other preference alignment methods, with an MM-Dist of 3.25% (vs e.g.

Wasserstein gradient flow (WGF) is a common method to perform optimization over the space of probability measures. While WGF is guaranteed to converge to a first-order stationary point, for nonconvex functionals the converged solution does not necessarily satisfy the second-order optimality condition; i.e., it could converge to a saddle point. In this work, we propose a new algorithm for probability measure optimization, perturbed Wasserstein gradient flow (PWGF), that achieves second-order optimality for general nonconvex objectives. PWGF enhances WGF by injecting noisy perturbations near saddle points via a Gaussian process-based scheme. By pushing the measure forward along a random vector field generated from a Gaussian process, PWGF helps the solution escape saddle points efficiently by perturbing the solution towards the smallest eigenvalue direction of the Wasserstein Hessian. We theoretically derive the computational complexity for PWGF to achieve a second-order stationary point. Furthermore, we prove that PWGF converges to a global optimum in polynomial time for strictly benign objectives.

This paper addresses the problem of learning avoidance behavior within the context of offline imitation learning. In contrast to conventional methodologies that prioritize the replication of expert or near-expert demonstrations, our work investigates a setting where expert (or desirable) data is absent, and the objective is to learn to eschew undesirable actions by leveraging demonstrations of such behavior (i.e., learning from negative examples). To address this challenge, we propose a novel training objective grounded in the maximum entropy principle. We further characterize the fundamental properties of this objective function, reformulating the learning process as a cooperative inverse Q-learning task. Moreover, we introduce an efficient strategy for the integration of unlabeled data (i.e., data of indeterminate quality) to facilitate unbiased and practical offline training. The efficacy of our method is evaluated across standard benchmark environments, where it consistently outperforms state-of-the-art baselines.

Zeroth-order Optimization (ZO) has received wide attention in machine learning, especially when computing full gradient is expensive or even impossible. Recently, ZO has emerged as an important paradigm for memory-efficient fine-tuning of large language models (LLMs), circumventing the memory overhead of backpropagation. However, existing ZO gradient estimators exhibit dimension-dependent variance scaling as $\Theta(d)$, leading to dimension-dependent convergence rates without further assumptions on the objective function, which is prohibitive for large-scale LLM parameters.

We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M $-component mixture distributions, we propose a family of estimators derived from the stochastic mirror descent (SMD) algorithm. This optimization-based approach provides a principled and flexible framework that generalizes traditional estimators and proposes a variety of novel estimators through the choice of Bregman divergences. A key advantage of our method is that it scales efficiently with the number of candidate components $ f_i $; that is, one can employ a large set of basis distributions in the mixture model without incurring significant computational overhead. This enables richer approximations and improved estimation accuracy. Moreover, in the case of categorical distribution (discrete outcomes) our estimators do not require a strict lower bound, in other words our framework does not require the precise knowledge of the support of the distribution. We demonstrate that, under mild conditions, the proposed $ φ$-SMD estimators achieve near-optimal convergence rates in both Kullback-Leibler (KL) divergence and $ \ell_2 $-norm and offer practical benefits when computation is expensive. Our numerical analysis highlights improved performance guaranties over classical estimators, particularly in terms of sample efficiency and scalability.

In complex multivariate systems, interactions among variables are defined by dependency structures, often encoded as directed acyclic graphs ($\text{DAGs}$). However, dependency structures can vary across subjects, and ignoring this structural heterogeneity introduces bias and obscures subpopulation-specific dependencies. To address this, we propose Directed Acyclic Graph-based Dependency Clustering via Alternating Direction Method of Multipliers (DAG-DC-ADMM), a unified framework built upon Structural Equation Modeling (SEM) that jointly learns cluster assignments and cluster-specific dependency structures. We encode acyclicity via a smooth constraint and integrate a groupwise truncated Lasso fusion penalty (gTLP) to cluster subjects based on their structural similarity. This yields a nonconvex optimization problem that incorporates sparsity, acyclicity, and structural consensus constraints. We address the nonconvexity by using the augmented Lagrangian method and solve it with an adapted version of the Alternating Direction Method of Multipliers (ADMM) for difference-of-convex programs. For certain graph structures, such as upper triangular adjacency matrices, our algorithm is guaranteed to converge to a Karush-Kuhn-Tucker (KKT) point. Experiments demonstrate that our method recovers cluster-specific causal dependency structures with a high true positive rate and a low false discovery rate. This capability enables the robust discovery of heterogeneous dependencies across subjects where the subpopulation label is unknown.