Abstract-- We present closed-form expressions for marginalizing and conditioning Gaussians onto linear manifolds, and demonstrate how to apply these expressions to smooth nonlinear manifolds through linearization. Although marginalization and conditioning onto axis-aligned manifolds are well-established procedures, doing so onto non-axis-aligned manifolds is not as well understood. We demonstrate the utility of our expressions through three applications: 1) approximation of the projected normal distribution, where the quality of our linearized approximation increases as problem nonlinearity decreases; 2) covariance extraction in Koopman SLAM, where our covariances are shown to be consistent on a real-world dataset; and 3) covariance extraction in constrained GTSAM, where our covariances are shown to be consistent in simulation. Figure 1: Marginalizing and conditioning Gaussians onto manifolds defined by linear constraints using Table II. Gaussians have rank-2 covariances, lying on the constraint plane.

Constructing a high-fidelity representation of the 3D scene using a monocular camera can enable a wide range of applications on mobile devices, such as micro-robots, smartphones, and AR/VR headsets. On these devices, memory is often limited in capacity and its access often dominates the consumption of compute energy. Although Gaussian Splatting (GS) allows for high-fidelity reconstruction of 3D scenes, current GS-based SLAM is not memory efficient as a large number of past images is stored to retrain Gaussians for reducing catastrophic forgetting. These images often require two-orders-of-magnitude higher memory than the map itself and thus dominate the total memory usage. In this work, we present GEVO, a GS-based monocular SLAM framework that achieves comparable fidelity as prior methods by rendering (instead of storing) them from the existing map. Novel Gaussian initialization and optimization techniques are proposed to remove artifacts from the map and delay the degradation of the rendered images over time. Across a variety of environments, GEVO achieves comparable map fidelity while reducing the memory overhead to around 58 MBs, which is up to 94x lower than prior works.

Active learning enhances the performance of machine learning methods, particularly in semi-supervised cases, by judiciously selecting a limited number of unlabeled data points for labeling, with the goal of improving the performance of an underlying classifier. In this work, we introduce the Multiclass Active Learning with Auction Dynamics on Graphs (MALADY) framework which leverages the auction dynamics algorithm on similarity graphs for efficient active learning. In particular, we generalize the auction dynamics algorithm on similarity graphs for semi-supervised learning in [24] to incorporate a more general optimization functional. Moreover, we introduce a novel active learning acquisition function that uses the dual variable of the auction algorithm to measure the uncertainty in the classifier to prioritize queries near the decision boundaries between different classes. Lastly, using experiments on classification tasks, we evaluate the performance of our proposed method and show that it exceeds that of comparison algorithms.

While generative models have made significant advancements in recent years, they also raise concerns such as privacy breaches and biases. Machine unlearning has emerged as a viable solution, aiming to remove specific training data, e.g., containing private information and bias, from models. In this paper, we study the machine unlearning problem in Image-to-Image (I2I) generative models. Previous studies mainly treat it as a single objective optimization problem, offering a solitary solution, thereby neglecting the varied user expectations towards the trade-off between complete unlearning and model utility. To address this issue, we propose a controllable unlearning framework that uses a control coefficient $\varepsilon$ to control the trade-off. We reformulate the I2I generative model unlearning problem into a $\varepsilon$-constrained optimization problem and solve it with a gradient-based method to find optimal solutions for unlearning boundaries. These boundaries define the valid range for the control coefficient. Within this range, every yielded solution is theoretically guaranteed with Pareto optimality. We also analyze the convergence rate of our framework under various control functions. Extensive experiments on two benchmark datasets across three mainstream I2I models demonstrate the effectiveness of our controllable unlearning framework.

We introduce HiSC4D, a novel Human-centered interaction and 4D Scene Capture method, aimed at accurately and efficiently creating a dynamic digital world, containing large-scale indoor-outdoor scenes, diverse human motions, rich human-human interactions, and human-environment interactions. By utilizing body-mounted IMUs and a head-mounted LiDAR, HiSC4D can capture egocentric human motions in unconstrained space without the need for external devices and pre-built maps. This affords great flexibility and accessibility for human-centered interaction and 4D scene capturing in various environments. Taking into account that IMUs can capture human spatially unrestricted poses but are prone to drifting for long-period using, and while LiDAR is stable for global localization but rough for local positions and orientations, HiSC4D employs a joint optimization method, harmonizing all sensors and utilizing environment cues, yielding promising results for long-term capture in large scenes. To promote research of egocentric human interaction in large scenes and facilitate downstream tasks, we also present a dataset, containing 8 sequences in 4 large scenes (200 to 5,000 $m^2$), providing 36k frames of accurate 4D human motions with SMPL annotations and dynamic scenes, 31k frames of cropped human point clouds, and scene mesh of the environment. A variety of scenarios, such as the basketball gym and commercial street, alongside challenging human motions, such as daily greeting, one-on-one basketball playing, and tour guiding, demonstrate the effectiveness and the generalization ability of HiSC4D. The dataset and code will be publicated on www.lidarhumanmotion.net/hisc4d available for research purposes.

To address unfairness issues in federated learning (FL), contemporary approaches typically use frequent model parameter updates and transmissions between the clients and server. In such a process, client-specific information (e.g., local dataset size or data-related fairness metrics) must be sent to the server to compute, e.g., aggregation weights. All of this results in high transmission costs and the potential leakage of client information. As an alternative, we propose a strategy that promotes fair predictions across clients without the need to pass information between the clients and server iteratively and prevents client data leakage. For each client, we first use their local dataset to obtain a synthetic dataset by solving a bilevel optimization problem that addresses unfairness concerns during the learning process. We then pass each client's synthetic dataset to the server, the collection of which is used to train the server model using conventional machine learning techniques (that do not take fairness metrics into account). Thus, we eliminate the need to handle fairness-specific aggregation weights while preserving client privacy. Our approach requires only a single communication between the clients and the server, thus making it computationally cost-effective, able to maintain privacy, and able to ensuring fairness. We present empirical evidence to demonstrate the advantages of our approach. The results illustrate that our method effectively uses synthetic data as a means to mitigate unfairness and preserve client privacy.

Learning uncertain dynamics models using Gaussian process~(GP) regression has been demonstrated to enable high-performance and safety-aware control strategies for challenging real-world applications. Yet, for computational tractability, most approaches for Gaussian process-based model predictive control (GP-MPC) are based on approximations of the reachable set that are either overly conservative or impede the controller's safety guarantees. To address these challenges, we propose a robust GP-MPC formulation that guarantees constraint satisfaction with high probability. For its tractable implementation, we propose a sampling-based GP-MPC approach that iteratively generates consistent dynamics samples from the GP within a sequential quadratic programming framework. We highlight the improved reachable set approximation compared to existing methods, as well as real-time feasible computation times, using two numerical examples.

In this paper, we address the problem of reducing the computational burden of Model Predictive Control (MPC) for real-time robotic applications. We propose TransformerMPC, a method that enhances the computational efficiency of MPC algorithms by leveraging the attention mechanism in transformers for both online constraint removal and better warm start initialization. Specifically, TransformerMPC accelerates the computation of optimal control inputs by selecting only the active constraints to be included in the MPC problem, while simultaneously providing a warm start to the optimization process. This approach ensures that the original constraints are satisfied at optimality. TransformerMPC is designed to be seamlessly integrated with any MPC solver, irrespective of its implementation. To guarantee constraint satisfaction after removing inactive constraints, we perform an offline verification to ensure that the optimal control inputs generated by the MPC solver meet all constraints. The effectiveness of TransformerMPC is demonstrated through extensive numerical simulations on complex robotic systems, achieving up to 35x improvement in runtime without any loss in performance.

Nonreciprocal thermal emitters that break Kirchhoff's law of thermal radiation promise exciting applications for thermal and energy applications. The design of the bandwidth and angular range of the nonreciprocal effect, which directly affects the performance of nonreciprocal emitters, typically relies on physical intuition. In this study, we present a general numerical approach to maximize the nonreciprocal effect. We choose doped magneto-optic materials and magnetic Weyl semimetal materials as model materials and focus on pattern-free multilayer structures. The optimization randomly starts from a less effective structure and incrementally improves the broadband nonreciprocity through the combination of Bayesian optimization and reparameterization. Optimization results show that the proposed approach can discover structures that can achieve broadband nonreciprocal emission at wavelengths from 5 to 40 micrometers using only a fewer layers, significantly outperforming current state-of-the-art designs based on intuition in terms of both performance and simplicity.

Robotic locomotion often relies on sequenced gaits to efficiently convert control input into desired motion. Despite extensive studies on gait optimization, achieving smooth and efficient gait transitions remains challenging. In this paper, we propose a general solver based on geometric optimal control methods, leveraging insights from previous works on gait efficiency. Building upon our previous work, we express the effort to execute the trajectory as distinct geometric objects, transforming the optimization problems into boundary value problems. To validate our approach, we generate gait transition trajectories for three-link swimmers across various fluid environments. This work provides insights into optimal trajectory geometries and mechanical considerations for robotic locomotion.