Combinatorial optimization problems are ubiquitous in science and engineering. Still, learning-based approaches to accelerate combinatorial optimization often require solving a large number of difficult instances to collect training data, incurring significant computational cost. Existing learning-based methods require training dedicated models for each problem distribution, for each downstream task, severely limiting their scalability and generalization. We introduce Forge: Foundational Optimization Representations from Graph Embeddings, a framework that pre-trains a vector-quantized graph autoencoder on a large, diverse collection of mixed-integer programming (MIP) instances in an unsupervised manner, without relying on optimization solvers or optimal solutions. Vector quantization produces discrete code assignments that serve as a vocabulary for representing optimization instances. We evaluate Forge in both unsupervised and supervised settings. In the unsupervised setting, Forge embeddings effectively cluster unseen instances across problem domains and sizes. In the supervised setting, we fine-tune Forge embeddings and show that a single pre-trained model helps predicting both the integrality gap for cut-generation and variable hints for search guidance across multiple problem and size distributions. In both tasks, we improve the performance of a commercial optimization solver and outperform state-of-the-art learning-based methods. Finally, we open-source our training code, pre-trained Forge weights, and embeddings for multiple MIP distributions to foster further research in representation learning for optimization problems.

Abstract--The increasing demand for intelligent mobile applications has made multi-agent collaboration with Transformer-based large language models (LLMs) essential in mobile edge computing (MEC) networks. However, training LLMs in such environments remains challenging due to heavy computation, high end-to-end latency, and limited model generalization. We introduce CollaPipe, a hybrid distributed learning framework that integrates collaborative pipeline parallelism with federated aggregation to support self-evolving intelligent networks. In Col-laPipe, the encoder part is adaptively partitioned into variable-sized segments and deployed across mobile devices for pipeline-parallel training, while the decoder is deployed on edge servers to handle generative tasks. Then we perform global model update via federated aggregation. T o enhance training efficiency, we formulate a joint optimization problem that adaptively allocates model segments, micro-batches, bandwidth, and transmission power . We derive and use a closed-form convergence bound to design an Dynamic Segment Scheduling and Resource Allocation (DSSDA) algorithm based on Lyapunov optimization, ensuring system stability under long-term constraints. Extensive experiments on downstream tasks with Transformer and BERT models show that CollaPipe improves computation efficiency by up to 15.09%, reduces end-to-end latency by at least 48.98%, and cuts single device memory usage by more than half, enabling online learning in heterogeneous and dynamic communication environments. With the rapid development of artificial intelligence generated content (AIGC) technologies in mobile Internet of Things (IoT), AI agent systems powered by large language models (LLMs) are emerging as a critical enabler for next-generation intelligent applications in mobile edge computing (MEC) networks [1]-[3]. Jiewei Chen, Shaoyong Guo, and Xuesong Qiu are with the State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, China (e-mail: {chenjiewei, syguo, xsqiu}@bupt.edu.cn). Xiumei Deng is with the Singapore University of Technology and Design, Singapore (e-mail: xiumei_deng@sutd.edu.sg). Ze-hui Xiong is with the School of Electronics, Electrical Engineering and Computer Science, Queen's University Belfast, United Kingdom (e-mail: z.xiong@qub.ac.uk).

Planning collision free trajectories in complex environments remains a core challenge in robotics. Existing corridor based planners which rely on decomposition of the free space into collision free subsets scale poorly with environmental complexity and require explicit allocations of time windows to trajectory segments. We introduce a new trajectory parameterization that represents trajectories in a nonconvex collision free corridor as being in a convex cartesian product of balls. This parameterization allows us to decouple problem size from geometric complexity of the solution and naturally avoids explicit time allocation by allowing trajectories to evolve continuously inside ellipsoidal corridors. Building on this representation, we formulate the Orthogonal Trust Region Problem (Orth-TRP), a specialized convex program with separable block constraints, and develop a solver that exploits this parallel structure and the unique structure of each parallel subproblem for efficient optimization. Experiments on a quadrotor trajectory planning benchmark show that our approach produces smoother trajectories and lower runtimes than state-of-the-art corridor based planners, especially in highly complicated environments.

Counterfactual explanation (CE) is a widely used post-hoc method that provides individuals with actionable changes to alter an unfavorable prediction from a machine learning model. Plausible CE methods improve realism by considering data distribution characteristics, but their optimization models introduce a large number of constraints, leading to high computational cost. In this work, we revisit the DACE framework and propose a refined Mixed-Integer Linear Programming (MILP) formulation that significantly reduces the number of constraints in the local outlier factor (LOF) objective component. We also apply the method to a linear SVM classifier with standard scaler. The experimental results show that our approach achieves faster solving times while maintaining explanation quality. These results demonstrate the promise of more efficient LOF modeling in counterfactual explanation and data science applications.

Training robust bimanual manipulation policies via imitation learning requires demonstration data with broad coverage over robot poses, contacts, and scene contexts. However, collecting diverse and precise real-world demonstrations is costly and time-consuming, which hinders scalability. Prior works have addressed this with data augmentation, typically for either eye-in-hand (wrist camera) setups with RGB inputs or for generating novel images without paired actions, leaving augmentation for eye-to-hand (third-person) RGB-D training with new action labels less explored. In this paper, we propose Synthetic Robot Pose Generation for RGB-D Bimanual Data Augmentation (ROPA), an offline imitation learning data augmentation method that fine-tunes Stable Diffusion to synthesize third-person RGB and RGB-D observations of novel robot poses. Our approach simultaneously generates corresponding joint-space action labels while employing constrained optimization to enforce physical consistency through appropriate gripper-to-object contact constraints in bimanual scenarios. We evaluate our method on 5 simulated and 3 real-world tasks. Our results across 2625 simulation trials and 300 real-world trials demonstrate that ROPA outperforms baselines and ablations, showing its potential for scalable RGB and RGB-D data augmentation in eye-to-hand bimanual manipulation. Our project website is available at: https://ropaaug.github.io/.

Classifying hadronic jets using their constituents' kinematic information is a critical task in modern high-energy collider physics. Often, classifiers are designed by targeting the best performance using metrics such as accuracy, AUC, or rejection rates. However, the use of a single metric can lead to the use of architectures that are more model-dependent than competitive alternatives, leading to potential uncertainty and bias in analysis. We explore such trade-offs and demonstrate the consequences of using networks with high performance metrics but low resilience.

Edge intelligence has emerged as a promising strategy to deliver low-latency and ubiquitous services for mobile devices. Recent advances in fine-tuning mechanisms of foundation models have enabled edge intelligence by integrating low-rank adaptation (LoRA) with federated learning. However, in wireless networks, the device heterogeneity and resource constraints on edge devices pose great threats to the performance of federated fine-tuning. To tackle these issues, we propose to optimize federated fine-tuning in heterogenous wireless networks via online learning. First, the framework of switching-based federated fine-tuning in wireless networks is provided. The edge devices switches to LoRA modules dynamically for federated fine-tuning with base station to jointly mitigate the impact of device heterogeneity and transmission unreliability. Second, a tractable upper bound on the inference risk gap is derived based on theoretical analysis. To improve the generalization capability, we formulate a non-convex mixed-integer programming problem with long-term constraints, and decouple it into model switching, transmit power control, and bandwidth allocation subproblems. An online optimization algorithm is developed to solve the problems with polynomial computational complexity. Finally, the simulation results on the SST-2 and QNLI data sets demonstrate the performance gains in test accuracy and energy efficiency.