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We propose a simulation-free algorithm for the solution of generic problems in stochastic optimal control (SOC). Unlike existing methods, our approach does not require the solution of an adjoint problem, but rather leverages Girsanov theorem to directly calculate the gradient of the SOC objective on-policy. This allows us to speed up the optimization of control policies parameterized by neural networks since it completely avoids the expensive back-propagation step through stochastic differential equations (SDEs) used in the Neural SDE framework. In particular, it enables us to solve SOC problems in high dimension and on long time horizons. We demonstrate the efficiency of our approach in various domains of applications, including standard stochastic optimal control problems, sampling from unnormalized distributions via construction of a Schr\"odinger-F\"ollmer process, and fine-tuning of pre-trained diffusion models. In all cases our method is shown to outperform the existing methods in both the computing time and memory efficiency.

Simulating general relativistic hydrodynamics (GRHD) presents challenges such as handling curved spacetime, achieving high-order shock-capturing accuracy, and preserving key physical constraints (positive density, pressure, and subluminal velocity) under nonlinear coupling. This paper introduces high-order, physical-constraint-preserving, oscillation-eliminating discontinuous Galerkin (PCP-OEDG) schemes with Harten-Lax-van Leer flux for GRHD. To suppress spurious oscillations near discontinuities, we incorporate a computationally efficient oscillation-eliminating (OE) procedure based on a linear damping equation, maintaining accuracy and avoiding complex characteristic decomposition. To enhance stability and robustness, we construct PCP schemes using the W-form of GRHD equations with Cholesky decomposition of the spatial metric, addressing the non-equivalence of admissible state sets in curved spacetime. We rigorously prove the PCP property of cell averages via technical estimates and the Geometric Quasi-Linearization (GQL) approach, which transforms nonlinear constraints into linear forms. Additionally, we present provably convergent PCP iterative algorithms for robust recovery of primitive variables, ensuring physical constraints are satisfied throughout. The PCP-OEDG method is validated through extensive tests, demonstrating its robustness, accuracy, and capability to handle extreme GRHD scenarios involving strong shocks, high Lorentz factors, and intense gravitational fields.

We propose a self-supervised approach for visual robot detection and heading estimation by learning to estimate the states (OFF or ON) of four independent robot-mounted LEDs. Experimental results show a median image-space position error of 14 px and relative heading MAE of 17 degrees, versus a supervised upperbound scoring 10 px and 8 degrees, respectively.

This article introduces the Pareto Control Barrier Function (PCBF) algorithm to maximize the inner safe set of dynamical systems under input constraints. Traditional Control Barrier Functions (CBFs) ensure safety by maintaining system trajectories within a safe set but often fail to account for realistic input constraints. To address this problem, we leverage the Pareto multi-task learning framework to balance competing objectives of safety and safe set volume. The PCBF algorithm is applicable to high-dimensional systems and is computationally efficient. We validate its effectiveness through comparison with Hamilton-Jacobi reachability for an inverted pendulum and through simulations on a 12-dimensional quadrotor system. Results show that the PCBF consistently outperforms existing methods, yielding larger safe sets and ensuring safety under input constraints.

Given a high-dimensional covariate matrix and a response vector, ridge-regularized sparse linear regression selects a subset of features that explains the relationship between covariates and the response in an interpretable manner. To select the sparsity and robustness of linear regressors, techniques like k-fold cross-validation are commonly used for hyperparameter tuning. However, cross-validation substantially increases the computational cost of sparse regression as it requires solving many mixed-integer optimization problems (MIOs). Additionally, validation metrics often serve as noisy estimators of test set errors, with different hyperparameter combinations leading to models with different noise levels. Therefore, optimizing over these metrics is vulnerable to out-of-sample disappointment, especially in underdetermined settings. To improve upon this state of affairs, we make two key contributions. First, motivated by the generalization theory literature, we propose selecting hyperparameters that minimize a weighted sum of a cross-validation metric and a model's output stability, thus reducing the risk of poor out-of-sample performance. Second, we leverage ideas from the mixed-integer optimization literature to obtain computationally tractable relaxations of k-fold cross-validation metrics and the output stability of regressors, facilitating hyperparameter selection after solving fewer MIOs. These relaxations result in an efficient cyclic coordinate descent scheme, achieving lower validation errors than via traditional methods such as grid search. On synthetic datasets, our confidence adjustment procedure improves out-of-sample performance by 2%-5% compared to minimizing the k-fold error alone. On 13 real-world datasets, our confidence adjustment procedure reduces test set error by 2%, on average.

This work presents a simple and robust method to construct a B-spline based Everett map, for application in the Preisach model of hysteresis, to predict static hysteresis behavior. Its strength comes from the ability to directly capture the Everett map as a well-founded closed-form B-spline surface expression, while also eliminating model artifacts that plague Everett map based Preisach models. Contrary to other works, that applied numerical descriptions for the Everett map, the presented approach is of completely analytic nature. In this work the B-spline surface fitting procedure and the necessary set of constraints are explained. Furthermore, the B-spline based Everett map is validated by ensuring that model artifacts were properly eliminated. Additionally, the model was compared with four benchmark excitations. Namely, a degaussing signal, a set of first-order reversal curves, an arbitrary excitation with high-order reversal curves, and a PWM like signal. The model was able to reproduce all benchmarks with high accuracy.

Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.

In semi-supervised domain adaptation, a few labeled samples per class in the target domain guide features of the remaining target samples to aggregate around them. However, the trained model cannot produce a highly discriminative feature representation for the target domain because the training data is dominated by labeled samples from the source domain. This could lead to disconnection between the labeled and unlabeled target samples as well as misalignment between unlabeled target samples and the source domain. In this paper, we propose a novel approach called Cross-domain Adaptive Clustering to address this problem. To achieve both inter-domain and intra-domain adaptation, we first introduce an adversarial adaptive clustering loss to group features of unlabeled target data into clusters and perform cluster-wise feature alignment across the source and target domains. We further apply pseudo labeling to unlabeled samples in the target domain and retain pseudo-labels with high confidence. Pseudo labeling expands the number of ``labeled" samples in each class in the target domain, and thus produces a more robust and powerful cluster core for each class to facilitate adversarial learning. Extensive experiments on benchmark datasets, including DomainNet, Office-Home and Office, demonstrate that our proposed approach achieves the state-of-the-art performance in semi-supervised domain adaptation.

Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model---namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)---which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.