We present the Materials Learning Algorithms (MALA) package, a scalable machine learning framework designed to accelerate density functional theory (DFT) calculations suitable for large-scale atomistic simulations. Using local descriptors of the atomic environment, MALA models efficiently predict key electronic observables, including local density of states, electronic density, density of states, and total energy. The package integrates data sampling, model training and scalable inference into a unified library, while ensuring compatibility with standard DFT and molecular dynamics codes. We demonstrate MALA's capabilities with examples including boron clusters, aluminum across its solid-liquid phase boundary, and predicting the electronic structure of a stacking fault in a large beryllium slab. Scaling analyses reveal MALA's computational efficiency and identify bottlenecks for future optimization. With its ability to model electronic structures at scales far beyond standard DFT, MALA is well suited for modeling complex material systems, making it a versatile tool for advanced materials research.

Thompson sampling (TS) has optimal regret and excellent empirical performance in multi-armed bandit problems. Yet, in Bayesian optimization, TS underperforms popular acquisition functions (e.g., EI, UCB). TS samples arms according to the probability that they are optimal. A recent algorithm, P-Star Sampler (PSS), performs such a sampling via Hit-and-Run. We present an improved version, Stagger Thompson Sampler (STS). STS more precisely locates the maximizer than does TS using less computation time. We demonstrate that STS outperforms TS, PSS, and other acquisition methods in numerical experiments of optimizations of several test functions across a broad range of dimension. Additionally, since PSS was originally presented not as a standalone acquisition method but as an input to a batching algorithm called Minimal Terminal Variance (MTV), we also demon-strate that STS matches PSS performance when used as the input to MTV.

Abstract-- Optimization based motion planning provides a useful modeling framework through various costs and constraints. Using Graph of Convex Sets (GCS) for trajectory optimization gives guarantees of feasibility and optimality by representing configuration space as the finite union of convex sets. Nonlinear parametrizations can be used to extend this technique to handle cases such as kinematic loops, but this distorts distances, such that solving with convex objectives will yield paths that are suboptimal in the original space. We present a method to extend GCS to nonconvex objectives, allowing us to "undistort" the optimization landscape while maintaining feasibility guarantees. We demonstrate our method's efficacy on three different robotic planning domains: a bimanual robot moving an object with both arms, the set of 3D rotations using Euler angles, and a rational parametrization of kinematics that enables certifying regions as collision free. Across the board, our method significantly improves path length and trajectory duration with only a minimal increase in runtime.

Current methods for initializing state space model (SSM) parameters primarily rely on the HiPPO framework \citep{gu2023how}, which is based on online function approximation with the SSM kernel basis. However, the HiPPO framework does not explicitly account for the effects of the temporal structures of input sequences on the optimization of SSMs. In this paper, we take a further step to investigate the roles of SSM initialization schemes by considering the autocorrelation of input sequences. Specifically, we: (1) rigorously characterize the dependency of the SSM timescale on sequence length based on sequence autocorrelation; (2) find that with a proper timescale, allowing a zero real part for the eigenvalues of the SSM state matrix mitigates the curse of memory while still maintaining stability at initialization; (3) show that the imaginary part of the eigenvalues of the SSM state matrix determines the conditioning of SSM optimization problems, and uncover an approximation-estimation tradeoff when training SSMs with a specific class of target functions.

We address the problem of client participation in federated learning, where traditional methods typically rely on a random selection of a small subset of clients for each training round. In contrast, we propose FedBack, a deterministic approach that leverages control-theoretic principles to manage client participation in ADMM-based federated learning. FedBack models client participation as a discrete-time dynamical system and employs an integral feedback controller to adjust each client's participation rate individually, based on the client's optimization dynamics. We provide global convergence guarantees for our approach by building on the recent federated learning research. Numerical experiments on federated image classification demonstrate that FedBack achieves up to 50\% improvement in communication and computational efficiency over algorithms that rely on a random selection of clients.

Current black-box backdoor attacks in convolutional neural networks formulate attack objective(s) as single-objective optimization problems in single domain. Designing triggers in single domain harms semantics and trigger robustness as well as introduces visual and spectral anomaly. This work proposes a multi-objective black-box backdoor attack in dual domains via evolutionary algorithm (LADDER), the first instance of achieving multiple attack objectives simultaneously by optimizing triggers without requiring prior knowledge about victim model. In particular, we formulate LADDER as a multi-objective optimization problem (MOP) and solve it via multi-objective evolutionary algorithm (MOEA). MOEA maintains a population of triggers with trade-offs among attack objectives and uses non-dominated sort to drive triggers toward optimal solutions. We further apply preference-based selection to MOEA to exclude impractical triggers. We state that LADDER investigates a new dual-domain perspective for trigger stealthiness by minimizing the anomaly between clean and poisoned samples in the spectral domain. Lastly, the robustness against preprocessing operations is achieved by pushing triggers to low-frequency regions. Extensive experiments comprehensively showcase that LADDER achieves attack effectiveness of at least 99%, attack robustness with 90.23% (50.09% higher than state-of-the-art attacks on average), superior natural stealthiness (1.12x to 196.74x improvement) and excellent spectral stealthiness (8.45x enhancement) as compared to current stealthy attacks by the average $l_2$-norm across 5 public datasets.

Conformal prediction provides model-agnostic and distribution-free uncertainty quantification through prediction sets that are guaranteed to include the ground truth with any user-specified probability. Yet, conformal prediction is not reliable under poisoning attacks where adversaries manipulate both training and calibration data, which can significantly alter prediction sets in practice. As a solution, we propose reliable prediction sets (RPS): the first efficient method for constructing conformal prediction sets with provable reliability guarantees under poisoning. To ensure reliability under training poisoning, we introduce smoothed score functions that reliably aggregate predictions of classifiers trained on distinct partitions of the training data. To ensure reliability under calibration poisoning, we construct multiple prediction sets, each calibrated on distinct subsets of the calibration data. We then aggregate them into a majority prediction set, which includes a class only if it appears in a majority of the individual sets. Both proposed aggregations mitigate the influence of datapoints in the training and calibration data on the final prediction set. We experimentally validate our approach on image classification tasks, achieving strong reliability while maintaining utility and preserving coverage on clean data. Overall, our approach represents an important step towards more trustworthy uncertainty quantification in the presence of data poisoning.

This paper introduces a local planner that synergizes the decision making and trajectory planning modules towards autonomous driving. The decision making and trajectory planning tasks are jointly formulated as a nonlinear programming problem with an integrated objective function. However, integrating the discrete decision variables into the continuous trajectory optimization leads to a mixed-integer programming (MIP) problem with inherent nonlinearity and nonconvexity. To address the challenge in solving the problem, the original problem is decomposed into two sub-stages, and a two-stage optimization (TSO) based approach is presented to ensure the coherence in outcomes for the two stages. The optimization problem in the first stage determines the optimal decision sequence that acts as an informed initialization. With the outputs from the first stage, the second stage necessitates the use of a high-fidelity vehicle model and strict enforcement of the collision avoidance constraints as part of the trajectory planning problem. We evaluate the effectiveness of our proposed planner across diverse multi-lane scenarios. The results demonstrate that the proposed planner simultaneously generates a sequence of optimal decisions and the corresponding trajectory that significantly improves driving performance in terms of driving safety and traveling efficiency as compared to alternative methods. Additionally, we implement the closed-loop simulation in CARLA, and the results showcase the effectiveness of the proposed planner to adapt to changing driving situations with high computational efficiency.

Inference in large-scale Markov Random Fields (MRFs) is a critical yet challenging task, traditionally approached through approximate methods like belief propagation and mean field, or exact methods such as the Toulbar2 solver. These strategies often fail to strike an optimal balance between efficiency and solution quality, particularly as the problem scale increases. This paper introduces NeuroLifting, a novel technique that leverages Graph Neural Networks (GNNs) to reparameterize decision variables in MRFs, facilitating the use of standard gradient descent optimization. By extending traditional lifting techniques into a non-parametric neural network framework, NeuroLifting benefits from the smooth loss landscape of neural networks, enabling efficient and parallelizable optimization. Empirical results demonstrate that, on moderate scales, NeuroLifting performs very close to the exact solver Toulbar2 in terms of solution quality, significantly surpassing existing approximate methods. Notably, on large-scale MRFs, NeuroLifting delivers superior solution quality against all baselines, as well as exhibiting linear computational complexity growth. This work presents a significant advancement in MRF inference, offering a scalable and effective solution for large-scale problems.

Diffusion probabilistic models learn to remove noise that is artificially added to the data during training. Novel data, like images, may then be generated from Gaussian noise through a sequence of denoising operations. While this Markov process implicitly defines a joint distribution over noise-free data, it is not simple to condition the generative process on masked or partial images. A number of heuristic sampling procedures have been proposed for solving inverse problems with diffusion priors, but these approaches do not directly approximate the true conditional distribution imposed by inference queries, and are often ineffective for large masked regions. Moreover, many of these baselines cannot be applied to latent diffusion models which use image encodings for efficiency. We instead develop a hierarchical variational inference algorithm that analytically marginalizes missing features, and uses a rigorous variational bound to optimize a non-Gaussian Markov approximation of the true diffusion posterior. Through extensive experiments with both pixel-based and latent diffusion models of images, we show that our VIPaint method significantly outperforms previous approaches in both the plausibility and diversity of imputations, and is easily generalized to other inverse problems like deblurring and superresolution.