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In many large language model (LLM) alignment applications, users expect not only high-quality outputs but also substantial diversity. However, existing methods often face a fundamental trade-off between these objectives: approaches that…

We in this paper propose a realizable framework TECU, which embeds task-specific strategies into update schemes of coordinate descent, for optimizing multivariate non-convex problems with coupled objective functions. On one hand, TECU is…

Knowledge graph embedding (KGE) models encode the structural information of knowledge graphs to predicting new links. Effective training of these models requires distinguishing between positive and negative samples with high precision.…

We propose the Limited Multi-Label (LML) projection layer as a new primitive operation for end-to-end learning systems. The LML layer provides a probabilistic way of modeling multi-label predictions limited to having exactly k labels. We…

In this study, we have developed an incremental machine learning (ML) method that efficiently obtains the optimal model when a small number of instances or features are added or removed. This problem holds practical importance in model…

Reinforcement learning with verifiable rewards (RLVR), particularly Group Relative Policy Optimization (GRPO), has advanced LLM reasoning. However, GRPO suffers from three credit assignment failures: uniform token-level granularity that…

Motivated by variational models in continuum mechanics, we introduce a novel algorithm to perform nonsmooth and nonconvex minimizations with linear constraints in Euclidean spaces. We show how this algorithm is actually a natural…

Rapid resource model updating with real-time data is important for making timely decisions in resource management and mining operations. This requires optimal merging of models and observations, which can be achieved through data…

Solving large-scale robust portfolio optimization problems is challenging due to the high computational demands associated with an increasing number of assets, the amount of data considered, and market uncertainty. To address this issue, we…

Evolutionary algorithms are particularly effective for optimisation problems with dynamic and stochastic components. We propose multi-objective evolutionary approaches for the knapsack problem with stochastic profits under static and…

In long-horizon tasks, recent agents based on Large Language Models (LLMs) face a significant challenge that sparse, outcome-based rewards make it difficult to assign credit to intermediate steps. Previous methods mainly focus on creating…

Augmented Lagrangian and optimistic primal--dual methods stabilize equality-constrained optimization through seemingly different mechanisms: the former adds constraint-dependent primal curvature, while the latter adds dual memory. Recent…

In recent years, bilevel optimization (BLO) has attracted significant attention for its broad applications in machine learning. However, most existing works on BLO remain confined to the single-task setting and rely on the lower-level…

Multimodal reward models are crucial for aligning multimodal large language models with human preferences. Recent works have incorporated reasoning capabilities into these models, achieving promising results. However, training these models…

Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing (local) maximum likelihood estimate (MLE). It can be used in an extensive range of problems, including the clustering of data based on the Gaussian…

In inverse problems, the goal is to estimate unknown model parameters from noisy observational data. Traditionally, inverse problems are solved under the assumption of a fixed forward operator describing the observation model. In this…

Motivated by the computation of the non-parametric maximum likelihood estimator (NPMLE) and the Bayesian posterior in statistics, this paper explores the problem of convex optimization over the space of all probability distributions. We…

Combining Chain-of-Thought (CoT) with Reinforcement Learning (RL) improves text-to-image (T2I) generation, yet the underlying interaction between CoT's exploration and RL's optimization remains unclear. We present a systematic entropy-based…

Efficient exploration is a central problem in reinforcement learning and is often formalized as maximizing the entropy of the state-action occupancy measure. While unconstrained maximum-entropy exploration is relatively well understood,…

Autoregressive (AR) architectures have achieved significant successes in LLMs, inspiring explorations for video generation. In LLMs, top-p/top-k sampling strategies work exceptionally well: language tokens have high semantic density and low…