Bayesian optimization (BO) is a popular, sample-efficient technique for expensive, black-box optimization. One such problem arising in manufacturing is that of maximizing the reliability, or equivalently minimizing the probability of a failure, of a design which is subject to random perturbations - a problem that can involve extremely rare failures ($P_\mathrm{fail} = 10^{-6}-10^{-8}$). In this work, we propose two BO methods based on Thompson sampling and knowledge gradient, the latter approximating the one-step Bayes-optimal policy for minimizing the logarithm of the failure probability. Both methods incorporate importance sampling to target extremely small failure probabilities. Empirical results show the proposed methods outperform existing methods in both extreme and non-extreme regimes.

We present Actron3D, a framework that enables robots to acquire transferable 6-DoF manipulation skills from just a few monocular, uncalibrated, RGB-only human videos. At its core lies the Neural Affordance Function, a compact object-centric representation that distills actionable cues from diverse uncalibrated videos-geometry, visual appearance, and affordance-into a lightweight neural network, forming a memory bank of manipulation skills. During deployment, we adopt a pipeline that retrieves relevant affordance functions and transfers precise 6-DoF manipulation policies via coarse-to-fine optimization, enabled by continuous queries to the multimodal features encoded in the neural functions. Experiments in both simulation and the real world demonstrate that Actron3D significantly outperforms prior methods, achieving a 14.9 percentage point improvement in average success rate across 13 tasks while requiring only 2-3 demonstration videos per task.

Shannon entropy (SE) and its quantum mechanical analogue von Neumann entropy are key components in many tools used in physics, information theory, machine learning (ML) and quantum computing. Besides of the significant amounts of SE computations required in these fields, the singularity of the SE gradient is one of the central mathematical reason inducing the high cost, frequently low robustness and slow convergence of such tools. Here we propose the Fast Entropy Approximation (FEA) - a non-singular rational approximation of Shannon entropy and its gradient that achieves a mean absolute error of $10^{-3}$, which is approximately $20$ times lower than comparable state-of-the-art methods. FEA allows around $50\%$ faster computation, requiring only $5$ to $6$ elementary computational operations, as compared to tens of elementary operations behind the fastest entropy computation algorithms with table look-ups, bitshifts, or series approximations. On a set of common benchmarks for the feature selection problem in machine learning, we show that the combined effect of fewer elementary operations, low approximation error, and a non-singular gradient allows significantly better model quality and enables ML feature extraction that is two to three orders of magnitude faster and computationally cheaper when incorporating FEA into AI tools.

In this paper, we study the inexact Moreau envelope Lagrangian (iMELa) method for solving smooth non-convex optimization problems over a simple polytope with additional convex inequality constraints. By incorporating a proximal term into the traditional Lagrangian function, the iMELa method approximately solves a convex optimization subproblem over the polyhedral set at each main iteration. Under the assumption of a local error bound condition for subsets of the feasible set defined by subsets of the constraints, we establish that the iMELa method can find an $\epsilon$-Karush-Kuhn-Tucker point with $\tilde O(\epsilon^{-2})$ gradient oracle complexity.

In recent years, Graph Neural Networks (GNNs) have become successful in molecular property prediction tasks such as toxicity analysis. However, due to the black-box nature of GNNs, their outputs can be concerning in high-stakes decision-making scenarios, e.g., drug discovery. Facing such an issue, Graph Counterfactual Explanation (GCE) has emerged as a promising approach to improve GNN transparency. However, current GCE methods usually fail to take domain-specific knowledge into consideration, which can result in outputs that are not easily comprehensible by humans. To address this challenge, we propose a novel GCE method, LLM-GCE, to unleash the power of large language models (LLMs) in explaining GNNs for molecular property prediction. Specifically, we utilize an autoencoder to generate the counterfactual graph topology from a set of counterfactual text pairs (CTPs) based on an input graph. Meanwhile, we also incorporate a CTP dynamic feedback module to mitigate LLM hallucination, which provides intermediate feedback derived from the generated counterfactuals as an attempt to give more faithful guidance. Extensive experiments demonstrate the superior performance of LLM-GCE. Our code is released on https://github.com/YinhanHe123/new\_LLM4GNNExplanation.

Contact-rich manipulation remains a major challenge in robotics. Optical tactile sensors like GelSight Mini offer a low-cost solution for contact sensing by capturing soft-body deformations of the silicone gel. However, accurately inferring shear and normal force distributions from these gel deformations has yet to be fully addressed. In this work, we propose a machine learning approach using a U-net architecture to predict force distributions directly from the sensor's raw images. Our model, trained on force distributions inferred from Finite Element Analysis (FEA), demonstrates promising accuracy in predicting normal and shear force distributions. It also shows potential for generalization across sensors of the same type and for enabling real-time application. The codebase, dataset and models are open-sourced and available at https://feats-ai.github.io .

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.

Automated Theorem Proving (ATP) faces significant challenges due to the vast action space and the computational demands of proof generation. Recent advances have utilized Large Language Models (LLMs) for action selection in ATP, but these methods often require substantial computational resources. This study introduces the Functional Equation Automated Solver (FEAS), an agent that builds on the COPRA in-context learning framework within the Lean environment. FEAS innovates by refining prompt generation and response parsing mechanisms, integrating domain-specific heuristics for functional equations, and introducing the FunEq dataset--a rigorously curated collection of functional equation problems categorized into three difficulty levels. The agent's performance is evaluated against established baselines using this dataset, demonstrating improvements in theorem proving accuracy, particularly with the integration of functional equation-specific heuristics. Our results highlight the effectiveness of FEAS in generating and formalizing high-level proof strategies into Lean proofs, emphasizing the potential of tailored approaches in domain-specific ATP challenges.

Inflated-beam soft robots, such as tip-everting vine robots, can control curvature by contracting one beam side via pneumatic actuation. This work develops a general finite element modeling approach to characterize their bending. The model is validated across four pneumatic actuator types (series, compression, embedded, and fabric pneumatic artificial muscles), and can be extended to other designs. These actuators employ two bending mechanisms: geometry-based contraction and material-based contraction. The model accounts for intricate nonlinear effects of buckling and anisotropy. Experimental validation includes three working pressures (10, 20, and 30 kPa) for each actuator type. Geometry-based contraction yields significant deformation (92.1% accuracy) once the buckling pattern forms, reducing slightly to 80.7% accuracy at lower pressures due to stress singularities during buckling. Material-based contraction achieves smaller bending angles but remains at least 96.7% accurate. The open source models available at http://www.vinerobots.org support designing inflated-beam robots like tip-everting vine robots, contributing to waste reduction by optimizing designs based on material properties and stress distribution for effective bending and stress management.