Many deep learning models involve optimizing multiple objectives. Since objectives are often conflicting, we aim to get diverse and representative trade-off solutions among these objectives. Gradient-based multi-objective optimization (MOO) algorithms using reference vectors have shown promising performance. However, they may still produce undesirable solutions due to mismatch between the pre-specified reference vectors and the problem's underlying Pareto front. In this paper, we propose a novel gradient-based MOO algorithm with adaptive reference vectors. We formulate reference vector adaption as a bilevel optimization problem, and solve it with an efficient solver.

Over the past decades, Linear Programming (LP) has been widely used in different areas and considered as one of the mature technologies in numerical optimization. However, the complexity offered by state-of-the-art algorithms (i.e.

As large language models continue to scale up in both size and context length, the memory and communication cost of key-value (KV) cache storage has become a major bottleneck in multi-GPU and multi-node inference. While MoE-based architectures sparsify computation across experts, the corresponding KV caches remain dense and globally synchronized, resulting in significant overhead. We introduce \textbf{PiKV}, a parallel and distributed KV cache serving framework tailored for MoE architecture. PiKV leverages \textit{expert-sharded KV storage} to partition caches across GPUs, \textit{PiKV routing} to reduce token-to-KV access, and a \textit{PiKV Scheduling} to adaptively retain query-relevant entries. To further reduce memory usage, PiKV integrates \textit{PiKV Compression} modules the caching pipeline for acceleration. PiKV is recently publicly available as an open-source software library: \href{https://github.com/NoakLiu/PiKV}{https://github.com/NoakLiu/PiKV}. Experiments details is recorded at: \href{https://github.com/NoakLiu/PiKV/blob/main/downstream_tasks/README.md}{https://github.com/NoakLiu/PiKV/Experimental\_Results}. We also have PiKV integrated with Nvidia kvpress for acceleration, details see \href{https://github.com/NoakLiu/PiKVpress}{https://github.com/NoakLiu/PiKVpress}. PiKV is still a living project, aiming to become a comprehesive KV Cache management system for MoE Architectures.

Recent advances in learning rate (LR) scheduling have demonstrated the effectiveness of decay-free approaches that eliminate the traditional decay phase while maintaining competitive performance. Model merging techniques have emerged as particularly promising solutions in this domain. We present Warmup-Stable and Merge (WSM), a general framework that establishes a formal connection between learning rate decay and model merging. WSM provides a unified theoretical foundation for emulating various decay strategies-including cosine decay, linear decay and inverse square root decay-as principled model averaging schemes, while remaining fully compatible with diverse optimization methods. Through extensive experiments, we identify merge duration-the training window for checkpoint aggregation-as the most critical factor influencing model performance, surpassing the importance of both checkpoint interval and merge quantity. Our framework consistently outperforms the widely-adopted Warmup-Stable-Decay (WSD) approach across multiple benchmarks, achieving significant improvements of +3.5% on MATH, +2.9% on HumanEval, and +5.5% on MMLU-Pro. The performance advantages extend to supervised fine-tuning scenarios, highlighting WSM's potential for long-term model refinement.

Machine learning (ML) systems are increasingly deployed in high-stakes domains where reliability is paramount. This thesis investigates how uncertainty estimation can enhance the safety and trustworthiness of ML, focusing on selective prediction -- where models abstain when confidence is low. We first show that a model's training trajectory contains rich uncertainty signals that can be exploited without altering its architecture or loss. By ensembling predictions from intermediate checkpoints, we propose a lightweight, post-hoc abstention method that works across tasks, avoids the cost of deep ensembles, and achieves state-of-the-art selective prediction performance. Crucially, this approach is fully compatible with differential privacy (DP), allowing us to study how privacy noise affects uncertainty quality. We find that while many methods degrade under DP, our trajectory-based approach remains robust, and we introduce a framework for isolating the privacy-uncertainty trade-off. Next, we then develop a finite-sample decomposition of the selective classification gap -- the deviation from the oracle accuracy-coverage curve -- identifying five interpretable error sources and clarifying which interventions can close the gap. This explains why calibration alone cannot fix ranking errors, motivating methods that improve uncertainty ordering. Finally, we show that uncertainty signals can be adversarially manipulated to hide errors or deny service while maintaining high accuracy, and we design defenses combining calibration audits with verifiable inference. Together, these contributions advance reliable ML by improving, evaluating, and safeguarding uncertainty estimation, enabling models that not only make accurate predictions -- but also know when to say "I do not know".

We introduce ANTIDOTE, a new class of objectives for learning under noisy labels which are defined in terms of a relaxation over an information-divergence neighborhood. Using convex duality, we provide a reformulation as an adversarial training method that has similar computational cost to training with standard cross-entropy loss. We show that our approach adaptively reduces the influence of the samples with noisy labels during learning, exhibiting a behavior that is analogous to forgetting those samples. ANTIDOTE is effective in practical environments where label noise is inherent in the training data or where an adversary can alter the training labels. Extensive empirical evaluations on different levels of symmetric, asymmetric, human annotation, and real-world label noise show that ANTIDOTE outperforms leading comparable losses in the field and enjoys a time complexity that is very close to that of the standard cross entropy loss.

Rare but critical events in complex systems, such as protein folding, chemical reactions, disease progression, and extreme weather or climate phenomena, are governed by complex, high-dimensional, stochastic dynamics. Identifying an optimal reaction coordinate (RC) that accurately captures the progress of these dynamics is crucial for understanding and simulating such processes. This work introduces a nonparametric RC optimization framework that incorporates trajectory histories, enabling robust analysis even for irregular or incomplete data. The power of the method is demonstrated through increasingly challenging analyses of protein folding dynamics, where it provides accurate committor estimates that pass a stringent validation test and yield high-resolution free energy profiles. Its generality is further illustrated through applications to dynamics in phase space, a conceptual ocean circulation model, and a longitudinal clinical dataset. These results demonstrate that rare event dynamics can be accurately characterized without exhaustive sampling of the configuration space, establishing a general, flexible, and robust framework for analyzing complex dynamical systems and longitudinal datasets.

We propose a joint learning framework for Byzantine-resilient spectrum sensing and secure intelligent reflecting surface (IRS)--assisted opportunistic access under channel state information (CSI) uncertainty. The sensing stage performs logit-domain Bayesian updates with trimmed aggregation and attention-weighted consensus, and the base station (BS) fuses network beliefs with a conservative minimum rule, preserving detection accuracy under a bounded number of Byzantine users. Conditioned on the sensing outcome, we pose downlink design as sum mean-squared error (MSE) minimization under transmit-power and signal-leakage constraints and jointly optimize the BS precoder, IRS phase shifts, and user equalizers. With partial (or known) CSI, we develop an augmented-Lagrangian alternating algorithm with projected updates and provide provable sublinear convergence, with accelerated rates under mild local curvature. With unknown CSI, we perform constrained Bayesian optimization (BO) in a geometry-aware low-dimensional latent space using Gaussian process (GP) surrogates; we prove regret bounds for a constrained upper confidence bound (UCB) variant of the BO module, and demonstrate strong empirical performance of the implemented procedure. Simulations across diverse network conditions show higher detection probability at fixed false-alarm rate under adversarial attacks, large reductions in sum MSE for honest users, strong suppression of eavesdropper signal power, and fast convergence. The framework offers a practical path to secure opportunistic communication that adapts to CSI availability while coherently coordinating sensing and transmission through joint learning.

This paper introduces a novel Large Language Models (LLMs)-assisted agent that automatically converts natural-language descriptions of power system optimization scenarios into compact, solver-ready formulations and generates corresponding solutions. In contrast to approaches that rely solely on LLM to produce solutions directly, the proposed method focuses on discovering a mathematically compatible formulation that can be efficiently solved by off-the-shelf optimization solvers. Directly using LLMs to produce solutions often leads to infeasible or suboptimal results, as these models lack the numerical precision and constraint-handling capabilities of established optimization solvers. The pipeline integrates a domain-aware prompt and schema with an LLM, enforces feasibility through systematic validation and iterative repair, and returns both solver-ready models and user-facing results. Using the unit commitment problem as a representative case study, the agent produces optimal or near-optimal schedules along with the associated objective costs. Results demonstrate that coupling the solver with task-specific validation significantly enhances solution reliability. This work shows that combining AI with established optimization frameworks bridges high-level problem descriptions and executable mathematical models, enabling more efficient decision-making in energy systems

It is a challenging task for ground robots to autonomously navigate in harsh environments due to the presence of non-trivial obstacles and uneven terrain. This requires trajectory planning that balances safety and efficiency. The primary challenge is to generate a feasible trajectory that prevents robot from tip-over while ensuring effective navigation. In this paper, we propose a capsizing-aware trajectory planner (CAP) to achieve trajectory planning on the uneven terrain. The tip-over stability of the robot on rough terrain is analyzed. Based on the tip-over stability, we define the traversable orientation, which indicates the safe range of robot orientations. This orientation is then incorporated into a capsizing-safety constraint for trajectory optimization. We employ a graph-based solver to compute a robust and feasible trajectory while adhering to the capsizing-safety constraint. Extensive simulation and real-world experiments validate the effectiveness and robustness of the proposed method. The results demonstrate that CAP outperforms existing state-of-the-art approaches, providing enhanced navigation performance on uneven terrains.