A monoped's jump height and energy consumption depend on both, its mechanical design and control strategy. Existing co-design frameworks typically optimize for either maximum height or minimum energy, neglecting their trade-off. They also often omit gearbox parameter optimization and use oversimplified actuator mass models, producing designs difficult to replicate in practice. In this work, we introduce a novel three-stage co-design optimization framework that jointly maximizes jump height while minimizing mechanical energy consumption of a monoped. The proposed method explicitly incorporates realistic actuator mass models and optimizes mechanical design (including gearbox) and control parameters within a unified framework. The resulting design outputs are then used to automatically generate a parameterized CAD model suitable for direct fabrication, significantly reducing manual design iterations. Our experimental evaluations demonstrate a 50 percent reduction in mechanical energy consumption compared to the baseline design, while achieving a jump height of 0.8m. Video presentation is available at http://y2u.be/XW8IFRCcPgM

Abstract--Federated split learning (FedSL) has emerged as a promising paradigm for enabling collaborative intelligence in industrial Internet of Things (IoT) systems, particularly in smart factories where data privacy, communication efficiency, and device heterogeneity are critical concerns. In this article, we present a comprehensive study of FedSL frameworks tailored for resource-constrained robots in industrial scenarios. We compare synchronous, asynchronous, hierarchical, and heterogeneous FedSL frameworks in terms of workflow, scalability, adaptability, and limitations under dynamic industrial conditions. Furthermore, we systematically categorize token fusion strategies into three paradigms: input-level (pre-fusion), intermediate-level (intra-fusion), and output-level (post-fusion), and summarize their respective strengths in industrial applications. We also provide adaptive optimization techniques to enhance the efficiency and feasibility of FedSL implementation, including model compression, split layer selection, computing frequency allocation, and wireless resource management. Finally, we outline open issues and research directions of FedSL in future smart manufacturing systems. The rapid evolution of the industrial Internet of Things (IoT) has catalyzed a paradigm shift toward intelligent, autonomous, and interconnected manufacturing systems [1]. At the heart of this transformation are networked robots that perform complex tasks such as quality inspection, predictive maintenance, and multi-device collaboration across dynamic production environments. These robots are increasingly equipped with multimodal sensors and onboard computing units, enabling them to perceive, reason, and act in real time [2].

While semi-structured pruning, particularly 2:4 sparsity, offers a path to practical hardware acceleration, existing methods often incur substantial performance degradation. To bridge this gap, we introduce ARMOR: (Adaptive Representation with Matrix-factORization), a novel one-shot post-training pruning algorithm. Instead of directly pruning weights, ARMOR factorizes each weight matrix into a 2:4 sparse core wrapped by two low-overhead, block diagonal matrices. These wrappers act as efficient pre-and post-transformation error correctors, offering greater flexibility to preserve model quality compared to conventional 2:4 pruning techniques. The sparse core and block diagonal wrappers are chosen through a block coordinate descent algorithm that minimizes a layer-wise proxy loss. We theoretically prove this optimization is guaranteed to converge to a solution with a proxy loss less than or equal to state-of-the-art pruning algorithms. Experiments on Llama (Touvron et al., 2023; Dubey et al., 2024) and Qwen (Y ang et al., 2025) model families demonstrate that ARMOR consistently and significantly outperforms state-of-the-art 2:4 pruning methods across a wide range of downstream tasks and perplexity evaluations. ARMOR achieves this superior performance while retaining the inference speedups and substantial memory usage reductions of 2:4 pruning, establishing a more effective trade-off between model compression and task accuracy. Large Language Models (LLMs) have demonstrated remarkable capabilities (Park et al., 2023; Huang & Y ang, 2025), yet their immense computational and memory requirements pose significant barriers to practical deployment.

Bayesian optimization (BO) is effective for expensive black-box problems but remains challenging in high dimensions. We propose NeST-BO, a local BO method that targets the Newton step by jointly learning gradient and Hessian information with Gaussian process surrogates, and selecting evaluations via a one-step lookahead bound on Newton-step error. We show that this bound (and hence the step error) contracts with batch size, so NeST-BO directly inherits inexact-Newton convergence: global progress under mild stability assumptions and quadratic local rates once steps are sufficiently accurate. To scale, we optimize the acquisition in low-dimensional subspaces (e.g., random embeddings or learned sparse subspaces), reducing the dominant cost of learning curvature from $O(d^2)$ to $O(m^2)$ with $m \ll d$ while preserving step targeting. Across high-dimensional synthetic and real-world problems, including cases with thousands of variables and unknown active subspaces, NeST-BO consistently yields faster convergence and lower regret than state-of-the-art local and high-dimensional BO baselines.

We study a class of misspecified saddle point (SP) problems, where the optimization objective depends on an unknown parameter that must be learned concurrently from data. Unlike existing studies that assume parameters are fully known or pre-estimated, our framework integrates optimization and learning into a unified formulation, enabling a more flexible problem class. To address this setting, we propose two algorithms based on the accelerated primal-dual (APD) by Hamedani & Aybat 2021. In particular, we first analyze the naive extension of the APD method by directly substituting the evolving parameter estimates into the primal-dual updates; then, we design a new learning-aware variant of the APD method that explicitly accounts for parameter dynamics by adjusting the momentum updates. Both methods achieve a provable convergence rate of $\mathcal{O}(\log K / K)$, while the learning-aware approach attains a tighter $\mathcal{O}(1)$ constant and further benefits from an adaptive step-size selection enabled by a backtracking strategy. Furthermore, we extend the framework to problems where the learning problem admits multiple optimal solutions, showing that our modified algorithm for a structured setting achieves an $\mathcal{O}(1/\sqrt{K})$ rate. To demonstrate practical impact, we evaluate our methods on a misspecified portfolio optimization problem and show superior empirical performance compared to state-of-the-art algorithms.

Pipeline parallelism (PP) has become a standard technique for scaling large language model (LLM) training across multiple devices. However, despite recent progress in reducing memory consumption through activation offloading, existing approaches remain largely heuristic and coarse-grained, often overlooking the fine-grained trade-offs between memory, computation, and scheduling latency. In this work, we revisit the pipeline scheduling problem from a principled optimization perspective. We observe that prevailing strategies either rely on static rules or aggressively offload activations without fully leveraging the interaction between memory constraints and scheduling efficiency. To address this, we formulate scheduling as a constrained optimization problem that jointly accounts for memory capacity, activation reuse, and pipeline bubble minimization. Solving this model yields fine-grained schedules that reduce pipeline bubbles while adhering to strict memory budgets. Our approach complements existing offloading techniques: whereas prior approaches trade memory for time in a fixed pattern, we dynamically optimize the tradeoff with respect to model structure and hardware configuration. Experimental results demonstrate that our method consistently improves both throughput and memory utilization. In particular, we reduce idle pipeline time by up to 50% under the same per-device memory limit, and in some cases, enable the training of larger models within limited memory budgets.

Prompt engineering is crucial for fully leveraging large language models (LLMs), yet most existing optimization methods follow a single trajectory, resulting in limited adaptability, gradient conflicts, and high computational overhead. We propose MAPGD (Multi-Agent Prompt Gradient Descent), a novel framework that reconceptualizes prompt optimization as a collaborative process among specialized agents. Each agent focuses on a distinct refinement dimension, such as instruction clarity, example selection, format structure, or stylistic adaptation, and their contributions are coordinated through semantic gradient embedding, conflict detection, and fusion. To further enhance robustness and stability, MAPGD introduces two new mechanisms: Hypersphere Constrained Gradient Clustering (HCGC), which enforces angular margin constraints for compact and well-separated clusters, and Channel Adaptive Agent Weighting (CAAW), which dynamically reweights agent contributions based on validation performance. Experiments on classification and reasoning benchmarks show that MAPGD consistently surpasses single-agent and random baselines in both accuracy and efficiency. Ablation studies confirm the effectiveness of gradient fusion, agent specialization, and conflict resolution. Together, these components establish MAPGD as a unified, gradient-based, and interpretable framework for robust prompt optimization with theoretical convergence guarantees.

A quantum thermodynamic system is described by a Hamiltonian and a list of conserved, non-commuting charges, and a fundamental goal is to determine the minimum energy of the system subject to constraints on the charges. Recently, [Liu et al., arXiv:2505.04514] proposed first- and second-order classical and hybrid quantum-classical algorithms for solving a dual chemical potential maximization problem, and they proved that these algorithms converge to global optima by means of gradient-ascent approaches. In this paper, we benchmark these algorithms on several problems of interest in thermodynamics, including one- and two-dimensional quantum Heisenberg models with nearest and next-to-nearest neighbor interactions and with the charges set to the total x, y, and z magnetizations. We also offer an alternative compelling interpretation of these algorithms as methods for designing ground and thermal states of controllable Hamiltonians, with potential applications in molecular and material design. Furthermore, we introduce stabilizer thermodynamic systems as thermodynamic systems based on stabilizer codes, with the Hamiltonian constructed from a given code's stabilizer operators and the charges constructed from the code's logical operators. We benchmark the aforementioned algorithms on several examples of stabilizer thermodynamic systems, including those constructed from the one-to-three-qubit repetition code, the perfect one-to-five-qubit code, and the two-to-four-qubit error-detecting code. Finally, we observe that the aforementioned hybrid quantum-classical algorithms, when applied to stabilizer thermodynamic systems, can serve as alternative methods for encoding qubits into stabilizer codes at a fixed temperature, and we provide an effective method for warm-starting these encoding algorithms whenever a single qubit is encoded into multiple physical qubits.

This paper presents a state representation framework for Markov decision processes (MDPs) that can be learned solely from state trajectories, requiring neither reward signals nor the actions executed by the agent. We propose learning the minimum action distance (MAD), defined as the minimum number of actions required to transition between states, as a fundamental metric that captures the underlying structure of an environment. MAD naturally enables critical downstream tasks such as goal-conditioned reinforcement learning and reward shaping by providing a dense, geometrically meaningful measure of progress. Our self-supervised learning approach constructs an embedding space where the distances between embedded state pairs correspond to their MAD, accommodating both symmetric and asymmetric approximations. We evaluate the framework on a comprehensive suite of environments with known MAD values, encompassing both deterministic and stochastic dynamics, as well as discrete and continuous state spaces, and environments with noisy observations. Empirical results demonstrate that the proposed approach not only efficiently learns accurate MAD representations across these diverse settings but also significantly outperforms existing state representation methods in terms of representation quality.

Non-convex constrained optimizations are ubiquitous in robotic applications such as multi-agent navigation, UAV trajectory optimization, and soft robot simulation. For this problem class, conventional optimizers suffer from small step sizes and slow convergence. We propose BC-ADMM, a variant of Alternating Direction Method of Multiplier (ADMM), that can solve a class of non-convex constrained optimizations with biconvex constraint relaxation. Our algorithm allows larger step sizes by breaking the problem into small-scale sub-problems that can be easily solved in parallel. We show that our method has both theoretical convergence speed guarantees and practical convergence guarantees in the asymptotic sense. Through numerical experiments in a row of four robotic applications, we show that BC-ADMM has faster convergence than conventional gradient descent and Newton's method in terms of wall clock time.