The rapid development of LLMs has raised concerns about their potential misuse, leading to various watermarking schemes that typically offer high detectability. However, existing watermarking techniques often face trade-off between watermark detectability and generated text quality. In this paper, we introduce Learning to Watermark (LTW), a novel selective watermarking framework that leverages multi-objective optimization to effectively balance these competing goals. LTW features a lightweight network that adaptively decides when to apply the watermark by analyzing sentence embeddings, token entropy, and current watermarking ratio. Training of the network involves two specifically constructed loss functions that guide the model toward Pareto-optimal solutions, thereby harmonizing watermark detectability and text quality. By integrating LTW with two baseline watermarking methods, our experimental evaluations demonstrate that LTW significantly enhances text quality without compromising detectability. Our selective watermarking approach offers a new perspective for designing watermarks for LLMs and a way to preserve high text quality for watermarks.

Training deep neural networks (DNNs) is a structured optimization problem, because the parameters are naturally represented by matrices and tensors rather than simple vectors. Under this structural representation, it has been widely observed that gradients are low-rank and Hessians are approximately block-wise diagonal. These structured properties are crucial for designing efficient optimization algorithms but may not be utilized by current popular optimizers like Adam. In this paper, we present a novel optimization algorithm ASGO that capitalizes on these properties by employing a preconditioner that is adaptively updated using structured gradients. By fine-grained theoretical analysis, ASGO is proven to achieve superior convergence rates compared to existing structured gradient methods. Based on the convergence theory, we further demonstrate that ASGO can benefit from the low-rank and block-wise diagonal properties. We also discuss practical modifications of ASGO and empirically verify the effectiveness of the algorithm on language model tasks.

Learning representations for solutions of constrained optimization problems (COPs) with unknown cost functions is challenging, as models like (Variational) Autoencoders struggle to enforce constraints when decoding structured outputs. We propose an Inverse Optimization Latent Variable Model (IO-LVM) that learns a latent space of COP cost functions from observed solutions and reconstructs feasible outputs by solving a COP with a solver in the loop. Our approach leverages estimated gradients of a Fenchel-Young loss through a non-differentiable deterministic solver to shape the latent space. Unlike standard Inverse Optimization or Inverse Reinforcement Learning methods, which typically recover a single or context-specific cost function, IO-LVM captures a distribution over cost functions, enabling the identification of diverse solution behaviors arising from different agents or conditions not available during the training process. We validate our method on real-world datasets of ship and taxi routes, as well as paths in synthetic graphs, demonstrating its ability to reconstruct paths and cycles, predict their distributions, and yield interpretable latent representations.

Many real-world black-box optimization problems have multiple conflicting objectives. Rather than attempting to approximate the entire set of Pareto-optimal solutions, interactive preference learning, i.e., optimization with a decision maker in the loop, allows to focus the search on the most relevant subset. However, few previous studies have exploited the fact that utility functions are usually monotonic. In this paper, we address the Bayesian Optimization with Preference Exploration (BOPE) problem and propose using a neural network ensemble as a utility surrogate model. This approach naturally integrates monotonicity and allows to learn the decision maker's preferences from pairwise comparisons. Our experiments demonstrate that the proposed method outperforms state-of-the-art approaches and exhibits robustness to noise in utility evaluations. An ablation study highlights the critical role of monotonicity in enhancing performance.

While recent success of large reasoning models (LRMs) significantly advanced LLMs' reasoning capability by optimizing the final answer accuracy using reinforcement learning, they may also drastically increase the output length due to --characterized by unnecessarily complex reasoning paths that waste computation and potentially degrade the performance. We hypothesize that such inefficiencies stem from LRMs' limited capability to dynamically select the proper modular reasoning strategies, termed at the right position. To investigate this hypothesis, we propose a dynamic optimization framework that segments model-generated reasoning paths into distinct thinking patterns, systematically identifying and promoting beneficial patterns that improve the answer while removing detrimental ones. Empirical analysis confirms that our optimized thinking paths yield more concise yet sufficiently informative trajectories, enhancing reasoning efficiency by reducing attention FLOPs by up to 47% while maintaining accuracy for originally correct responses. Moreover, a non-trivial portion of originally incorrect responses are transformed into correct ones, achieving a 15.6% accuracy improvement with reduced length. Motivated by the improvement brought by the optimized thinking paths, we apply a preference optimization technique supported by a pairwise dataset contrasting suboptimal and optimal reasoning paths. Experimental evaluations across multiple mathematical reasoning benchmarks reveal that our method notably reduces computational overhead while simultaneously improving reasoning accuracy, achieving up to a 12% accuracy improvement and reducing token usage from approximately 5,000 to 3,000 tokens.

Continuously extending combinatorial optimization objectives is a powerful technique commonly applied to the optimization of set functions. However, few such methods exist for extending functions on permutations, despite the fact that many combinatorial optimization problems, such as the quadratic assignment problem (QAP) and the traveling salesperson problem (TSP), are inherently optimization over permutations.

Machine unlearning aims to remove the influence of specific training samples (i.e., forget data) from a trained model while preserving its performance on the remaining samples (i.e., retain data). Existing approximate unlearning approaches, such as fine-tuning or negative gradient, often suffer from either insufficient forgetting or significant degradation on retain data. In this paper, we introduce Unlearning-Aware Minimization (UAM), a novel min-max optimization framework for machine unlearning. UAM perturbs model parameters to maximize the forget loss and then leverages the corresponding gradients to minimize the retain loss. We derive an efficient optimization method for this min-max problem, which enables effective removal of forget data and uncovers better optima that conventional methods fail to reach. Extensive experiments demonstrate that UAM outperforms existing methods across diverse benchmarks, including image classification datasets (CIFAR-10, CIFAR-100, TinyImageNet) and multiple-choice question-answering benchmarks for large language models (WMDP-Bio, WMDP-Cyber).

Binary (0-1) integer programming (BIP) is pivotal in scientific domains requiring discrete decision-making. As the advance of AI computing, recent works explore neural network-based solver for integer linear programming (ILP) problems. Yet, they lack scalability for tackling nonlinear challenges. To handle nonlinearities, state-of-the-art Branch-and-Cut solvers employ linear relaxations, leading to exponential growth in auxiliary variables and severe computation limitations. To overcome these limitations, we propose BIPNN, an unsupervised learning framework to solve BIP problems via hypergraph neural networks (HyperGNN). Specifically, (i) BIPNN reformulates BIPs-constrained, discrete, and nonlinear (sin, log, exp) optimization problems-into unconstrained, differentiable, and polynomial loss functions.

Recent advances in 3D Gaussian Splatting have shown remarkable potential for novel view synthesis. However, most existing large-scale scene reconstruction methods rely on the divide-and-conquer paradigm, which often leads to the loss of global scene information and requires complex parameter tuning due to scene partitioning and local optimization. To address these limitations, we propose MixGS, a novel holistic optimization framework for large-scale 3D scene reconstruction. MixGS models the entire scene holistically by integrating camera pose and Gaussian attributes into a view-aware representation, which is decoded into fine-detailed Gaussians. Furthermore, a novel mixing operation combines decoded and original Gaussians to jointly preserve global coherence and local fidelity. Extensive experiments on large-scale scenes demonstrate that MixGS achieves state-of-the-art rendering quality and competitive speed, while significantly reducing computational requirements, enabling large-scale scene reconstruction training on a single 24GB VRAM GPU.

Decentralized federated learning (DFL) enables clients (e.g., hospitals and banks) to jointly train machine learning models without a central orchestration server. In each global training round, each client trains a local model on its own training data and then they exchange local models for aggregation. In this work, we propose SelfishAttack, a new family of attacks to DFL. In SelfishAttack, a set of selfish clients aim to achieve competitive advantages over the remaining non-selfish ones, i.e., the final learnt local models of the selfish clients are more accurate than those of the non-selfish ones. Towards this goal, the selfish clients send carefully crafted local models to each remaining non-selfish one in each global training round. We formulate finding such local models as an optimization problem and propose methods to solve it when DFL uses different aggregation rules. Theoretically, we show that our methods find the optimal solutions to the optimization problem. Empirically, we show that SelfishAttack successfully increases the accuracy gap (i.e., competitive advantage) between the final learnt local models of selfish clients and those of non-selfish ones. Moreover, SelfishAttack achieves larger accuracy gaps than poisoning attacks when extended to increase competitive advantages.