Proteins are traditionally optimized through the costly construction and measurement of many mutants. Active Learning-assisted Directed Evolution (ALDE) alleviates that cost by predicting the best improvements and iteratively testing mutants to inform predictions. However, existing ALDE methods face a critical limitation: selecting the highest-predicted mutants in each round yields homogeneous training data insufficient for accurate prediction models in subsequent rounds. Here we present FolDE, an ALDE method designed to maximize end-of-campaign success. In simulations across 20 protein targets, FolDE discovers 23% more top 10% mutants than the best baseline ALDE method (p=0.005) and is 55% more likely to find top 1% mutants. FolDE achieves this primarily through naturalness-based warm-starting, which augments limited activity measurements with protein language model outputs to improve activity prediction. We also introduce a constant-liar batch selector, which improves batch diversity; this is important in multi-mutation campaigns but had limited effect in our benchmarks. The complete workflow is freely available as open-source software, making efficient protein optimization accessible to any laboratory.

In Autonomous Driving Systems (ADS), Directed Acyclic Graphs (DAGs) are widely used to model complex data dependencies and inter-task communication. However, existing DAG scheduling approaches oversimplify data fusion tasks by assuming fixed triggering mechanisms, failing to capture the diverse fusion patterns found in real-world ADS software stacks. In this paper, we propose a systematic framework for analyzing various fusion patterns and their performance implications in ADS. Our framework models three distinct fusion task types: timer-triggered, wait-for-all, and immediate fusion, which comprehensively represent real-world fusion behaviors. Our Integer Linear Programming (ILP)-based approach enables an optimization of multiple real-time performance metrics, including reaction time, time disparity, age of information, and response time, while generating deterministic offline schedules directly applicable to real platforms. Evaluation using real-world ADS case studies, Raspberry Pi implementation, and randomly generated DAGs demonstrates that our framework handles diverse fusion patterns beyond the scope of existing work, and achieves substantial performance improvements in comparable scenarios.

Structural topology optimization (TO) is central to engineering design but remains computationally intensive due to complex physics and hard constraints. Existing deep-learning methods are limited to fixed square grids, a few hand-coded boundary conditions, and post-hoc optimization, preventing general deployment. We introduce Optimize Any Topology (OAT), a foundation-model framework that directly predicts minimum-compliance layouts for arbitrary aspect ratios, resolutions, volume fractions, loads, and fixtures. OAT combines a resolution- and shape-agnostic autoencoder with an implicit neural-field decoder and a conditional latent-diffusion model trained on OpenTO, a new corpus of 2.2 million optimized structures covering 2 million unique boundary-condition configurations. On four public benchmarks and two challenging unseen tests, OAT lowers mean compliance up to 90% relative to the best prior models and delivers sub-1 second inference on a single GPU across resolutions from 64 x 64 to 256 x 256 and aspect ratios as high as 10:1. These results establish OAT as a general, fast, and resolution-free framework for physics-aware topology optimization and provide a large-scale dataset to spur further research in generative modeling for inverse design. Code & data can be found at https://github.com/ahnobari/OptimizeAnyTopology.

Pretrained diffusion models have demonstrated strong capabilities in zero-shot inverse problem solving by incorporating observation information into the generation process of the diffusion models. However, this presents an inherent dilemma: excessive integration can disrupt the generative process, while insufficient integration fails to emphasize the constraints imposed by the inverse problem. To address this, we propose \emph{Noise Combination Sampling}, a novel method that synthesizes an optimal noise vector from a noise subspace to approximate the measurement score, replacing the noise term in the standard Denoising Diffusion Probabilistic Models process. This enables conditional information to be naturally embedded into the generation process without reliance on step-wise hyperparameter tuning. Our method can be applied to a wide range of inverse problem solvers, including image compression, and, particularly when the number of generation steps $T$ is small, achieves superior performance with negligible computational overhead, significantly improving robustness and stability.

The p-persistent CSMA protocol is central to random-access MAC analysis, but predicting saturation throughput in heterogeneous multi-hop wireless networks remains a hard problem. Simplified models that assume a single, shared interference domain can underestimate throughput by 48-62% in sparse topologies. Exact Markov-chain analyses are accurate but scale exponentially in computation time, making them impractical for large networks. These computational barriers motivate structural machine learning approaches like GNNs for scalable throughput prediction in general network topologies. Yet off-the-shelf GNNs struggle here: a standard GCN yields 63.94% normalized mean absolute error (NMAE) on heterogeneous networks because symmetric normalization conflates a node's direct interference with higher-order, cascading effects that pertain to how interference propagates over the network graph. Building on these insights, we propose the Decoupled Graph Convolutional Network (D-GCN), a novel architecture that explicitly separates processing of a node's own transmission probability from neighbor interference effects. D-GCN replaces mean aggregation with learnable attention, yielding interpretable, per-neighbor contribution weights while capturing complex multihop interference patterns. D-GCN attains 3.3% NMAE, outperforms strong baselines, remains tractable even when exact analytical methods become computationally infeasible, and enables gradient-based network optimization that achieves within 1% of theoretical optima.

Federated Learning (FL) presents significant potential for collaborative optimization without data sharing. Since synthetic data is sent to the server, leveraging the popular concept of dataset distillation, this FL framework protects real data privacy while alleviating data heterogeneity. However, such methods are still challenged by the redundant information and noise in entire spatial-domain designs, which inevitably increases the communication burden. In this paper, we propose a novel Frequency-Domain aware FL method with high-energy concentration (FedFD) to address this problem. Our FedFD is inspired by the discovery that the discrete cosine transform predominantly distributes energy to specific regions, referred to as high-energy concentration. The principle behind FedFD is that low-energy like high-frequency components usually contain redundant information and noise, thus filtering them helps reduce communication costs and optimize performance. Our FedFD is mathematically formulated to preserve the low-frequency components using a binary mask, facilitating an optimal solution through frequency-domain distribution alignment. In particular, real data-driven synthetic classification is imposed into the loss to enhance the quality of the low-frequency components. On five image and speech datasets, FedFD achieves superior performance than state-of-the-art methods while reducing communication costs. For example, on the CIFAR-10 dataset with Dirichlet coefficient $α= 0.01$, FedFD achieves a minimum reduction of 37.78\% in the communication cost, while attaining a 10.88\% performance gain.

In this paper we present a variational algorithm for the Traveling Salesman Problem (TSP) that combines (i) a compact encoding of permutations, which reduces the qubit requirement too, (ii) an optimize-freeze-reuse strategy: where the circuit topology (``Ansatz'') is first optimized on a training instance by Simulated Annealing (SA), then ``frozen'' and re-used on novel instances, limited to a rapid re-optimization of only the circuit parameters. This pipeline eliminates costly structural research in testing, making the procedure immediately implementable on NISQ hardware. On a set of $40$ randomly generated symmetric instances that span $4 - 7$ cities, the resulting Ansatz achieves an average optimal trip sampling probability of $100\%$ for 4 city cases, $90\%$ for 5 city cases and $80\%$ for 6 city cases. With 7 cities the success rate drops markedly to an average of $\sim 20\%$, revealing the onset of scalability limitations of the proposed method. The results show robust generalization ability for moderate problem sizes and indicate how freezing the Ansatz can dramatically reduce time-to-solution without degrading solution quality. The paper also discusses scalability limitations, the impact of ``warm-start'' initialization of parameters, and prospects for extension to more complex problems, such as Vehicle Routing and Job-Shop Scheduling.

We study bilevel optimization problems where the lower-level problems are strongly convex and have coupled linear constraints. To overcome the potential non-smoothness of the hyper-objective and the computational challenges associated with the Hessian matrix, we utilize penalty and augmented Lagrangian methods to reformulate the original problem as a single-level one. Especially, we establish a strong theoretical connection between the reformulated function and the original hyper-objective by characterizing the closeness of their values and derivatives. Based on this reformulation, we propose a single-loop, first-order algorithm for linearly constrained bilevel optimization (SFLCB). We provide rigorous analyses of its non-asymptotic convergence rates, showing an improvement over prior double-loop algorithms -- form $O(ε^{-3}\log(ε^{-1}))$ to $O(ε^{-3})$. The experiments corroborate our theoretical findings and demonstrate the practical efficiency of the proposed SFLCB algorithm. Simulation code is provided at https://github.com/ShenGroup/SFLCB.

Recent advances in representation learning reveal that widely used objectives, such as contrastive and non-contrastive, implicitly perform spectral decomposition of a contextual kernel, induced by the relationship between inputs and their contexts. Yet, these methods recover only the linear span of top eigenfunctions of the kernel, whereas exact spectral decomposition is essential for understanding feature ordering and importance. In this work, we propose a general framework to extract ordered and identifiable eigenfunctions, based on modular building blocks designed to satisfy key desiderata, including compatibility with the contextual kernel and scalability to modern settings. We then show how two main methodological paradigms, low-rank approximation and Rayleigh quotient optimization, align with this framework for eigenfunction extraction. Finally, we validate our approach on synthetic kernels and demonstrate on real-world image datasets that the recovered eigenvalues act as effective importance scores for feature selection, enabling principled efficiency-accuracy tradeoffs via adaptive-dimensional representations.

Decentralized bilevel optimization has garnered significant attention due to its critical role in solving large-scale machine learning problems. However, existing methods often rely on prior knowledge of problem parameters-such as smoothness, convexity, or communication network topologies-to determine appropriate stepsizes. In practice, these problem parameters are typically unavailable, leading to substantial manual effort for hyperparameter tuning. In this paper, we propose AdaSDBO, a fully problem-parameter-free algorithm for decentralized bilevel optimization with a single-loop structure. AdaSDBO leverages adaptive stepsizes based on cumulative gradient norms to update all variables simultaneously, dynamically adjusting its progress and eliminating the need for problem-specific hyperparameter tuning. Through rigorous theoretical analysis, we establish that AdaSDBO achieves a convergence rate of $\widetilde{\mathcal{O}}\left(\frac{1}{T}\right)$, matching the performance of well-tuned state-of-the-art methods up to polylogarithmic factors. Extensive numerical experiments demonstrate that AdaSDBO delivers competitive performance compared to existing decentralized bilevel optimization methods while exhibiting remarkable robustness across diverse stepsize configurations.