The paper finds local minimizers for obstacle avoidance on curved spaces.
problem Finding optimal paths on curved spaces avoiding obstacles.
method Minimizing an action functional with bi-Jacobi fields and biconjugate points.
result Local minimizers are classified into two categories with local uniqueness results.
The paper simplifies conditions for optimal paths on manifolds avoiding obstacles.
problem Finding optimal paths on manifolds avoiding obstacles.
method Study of sufficient conditions for optimality on Riemannian manifolds and Lie groups.
result New conditions for optimality are provided in terms of matrix invertibility.
In this paper we prove two extensions of Hamilton's maximal principle for systems pf parabolic equations which sould be useful for the study of the Ricci flow and some other geometric evolution equations. One extension is a time-dependent maximum principle and the other is a time-dependent maximum principle subject to …
Reduces necessary conditions for collision avoidance on curved spaces.
problem Finding non-intersecting trajectories for multiple agents on curved spaces.
method Reduction by Lie group symmetries of variational collision avoidance problems.
result Derives necessary conditions for reduced extremals.
The paper extends the avoidance principle for mean curvature flows, proving new intersection dimension monotonicity results.
problem Understanding the behavior of intersections in mean curvature flows.
method Proving new intersection dimension monotonicity results for mean curvature flows, Brakke flows, and level set flows.
result The dimension of the intersection of mean curvature flows is non-increasing over time.
Paper studies stochastic optimization methods with momentum, proving convergence and avoiding traps.
problem Optimizing non-convex functions with momentum.
method Unified analysis of stochastic gradient descent variants, including S-NAG and Adam.
result Convergence to critical points and avoidance of undesired critical points like local maxima or saddle points.
Invariant Causal Set Covering Machines avoid spurious associations.
problem Learning algorithms for rule-based models are vulnerable to spurious associations.
method Building on invariant causal prediction, propose Invariant Causal Set Covering Machines for conjunctions/disjunctions of binary-valued rules.
result The method can identify causal parents of a variable of interest in polynomial time.
SafeMIL learns safer policies by avoiding risky behavior from non-preferred trajectories.
problem Learning safe imitation policies from non-preferred trajectories in risky environments.
method SafeMIL uses Multiple Instance Learning to learn a cost function from non-preferred trajectories.
result SafeMIL learns a safer policy that avoids non-preferred behaviors without sacrificing reward performance.
Method controls extrapolation in prediction profiles for statistical and machine learning models.
problem Avoiding invalid predictions due to extrapolation in prediction profiles.
method Genetic algorithm optimization over constrained factor regions.
result Optimal factor settings without constraint are often invalid and extrapolated.
New theory shows how learning algorithms can create a bias towards negative outcomes.
problem Negativity bias in adaptive learning algorithms.
method Generalization of the Hot Stove Effect to settings with negative estimates leading to smaller sample sizes.
result Negativity bias persists even when negative estimates do not lead to avoidance.
GP-ND avoids obstacles in trajectory planning using Gaussian Process regression.
problem Avoiding obstacles in trajectory planning for real-world systems.
method GP-ND models negative data pairs using Gaussian distributions and maximizes their KL divergence from the GP to avoid them.
result GP-ND outperforms traditional GP learning in obstacle-aware trajectory planning.
New method reduces synchronization costs in parallel optimization.
problem Inhibiting scalability of optimization methods due to communication costs.
method Extending Communication-Avoiding Krylov subspace methods to first-order, block coordinate descent methods.
result SA-variants attain large speedups of up to 5.1x on a supercomputer.
We prove diffeomorphisms of polygonal linkage moduli spaces to Euclidean spaces.
problem Moduli spaces of self-avoiding polygonal linkages and configurations.
method Construct Lyapunov-Reeb functions to show diffeomorphisms.
result Moduli spaces are diffeomorphic to Euclidean spaces.
New statistic κ-profile helps monitor weather, soundscapes, and dynamical systems.
problem Monitoring intrinsic dimensionality of large data sets.
method Optimization problem to find κ-profile, which is the norm of the shortest projected secant. result The κ-profile provides a useful statistic for understanding and monitoring large data sets. The study uses heat flow to analyze properties of Laplace eigenfunctions on manifolds and domains.
problem Analyzing mass concentration and nodal domains of Laplace eigenfunctions.
method Heat diffusion technique to study eigenfunctions and their nodal sets.
result Discovers new insights into the decay and behavior of Laplace eigenfunctions.
A new neural network framework avoids iterations and achieves fast, low-error predictions.
problem Training neural networks efficiently and avoiding overfitting.
method Gradient-free approach based on Universal Approximation Theorem, using local approximation matrices.
result Highly accurate predictions on complex datasets, including the Griewank function and MNIST.
Aims to teach agents to avoid dangerous behaviors observed in experts.
problem Teaching agents to avoid dangerous behaviors observed in experts.
method Developed a framework for avoidance learning involving a distance measure between state occupancy distributions of expert and demonstrator policies.
result Improves sample efficiency during training compared to existing methods.
In this paper, we propose several "measurements" of the "non-stopping timeness" of ends g of previsible sets, such that g avoids stopping times, in an ambiant filtration. We then study several explicit examples, involving last passage times of some remarkable martingales.
We present techniques for effective Gaussian process (GP) modelling of multiple short time series. These problems are common when applying GP models independently to each gene in a gene expression time series data set. Such sets typically contain very few time points. Naive application of common GP modelling techniques…
Hybrid regularization avoids double descent in random feature models.
problem Avoiding the double descent phenomenon in random feature models.
method Combines early stopping and weight decay, using GCV for hyperparameter selection.
result Hybrid method successfully avoids double descent and achieves comparable generalization.
Paper tackles zeroth-order optimization for nonconvex problems with constraints, high-dimensions, and saddle-points.
problem Optimization of nonconvex functions with constraints and high-dimensionality, avoiding saddle-points.
method Proposes zeroth-order stochastic approximation algorithms, including conditional gradient and truncated gradient methods, and a zeroth-order cubic regularization Newton's method.
result Demonstrates algorithms achieving rates similar to standard stochastic gradient methods, with rates dependent on poly-logarithmic dimensionality.
Deep neural network approximates collision avoidance table for aircraft systems.
problem High dimensionality of collision avoidance state space leads to large numeric tables.
method Used deep neural networks to approximate the numeric tables, using asymmetric loss functions and gradient descent.
result Reduced storage space by a factor of 1000, enabling current avionics systems.
Study on connectivity of Morse boundaries of Coxeter groups.
problem Connectivity of Morse boundaries of Coxeter groups.
method Defined conditions on defining graphs (wide-avoidant, wide-spherical-avoidant) and characterized Morse boundaries based on these conditions.
result Characterization of Morse boundary connectivity for different classes of Coxeter groups.
Develops a learning model predictive controller for competitive racing.
problem Lack of exploration in state space and complexity in obstacle avoidance.
method Explores state space through multiple initializations and develops a new method for convex terminal set selection.
result Yields a richer terminal safe set and maintains convexity.
GUM tackles MARL by avoiding overestimation through state-marginal restriction.
problem Overestimation of values in large joint state-action spaces.
method Greedy UnMixing through state-marginal restriction and unmixing.
result Superior performance compared to existing Q-learning and general MARL algorithms.
We study Thom Transversality Theorem using a point of view, suggested by Gromov, which allows to avoid the use of Sard Theorem and gives finer informations on the structure of the set of non-transverse maps.
New study shows MLE can avoid model collapse with gradual synthetic data addition.
problem Model collapse in generative models trained on synthetic data.
method Theoretical study of maximum likelihood estimation (MLE) under iterative training with accumulating synthetic data.
result Non-asymptotic bounds show MLE can avoid model collapse even as real data fraction vanishes.
Optimal CL requires perfect memory and is NP-hard.
problem Designing CL algorithms that perform reliably and avoid catastrophic forgetting.
method Theoretical approach to derive computational properties of optimal CL algorithms.
result Optimal CL algorithms generally solve an NP-hard problem and require perfect memory.
Self-training avoids spurious features in domain adaptation.
problem Domain shift with large differences between source and target domains.
method Entropy minimization on unlabeled target data, initialized with a source classifier.
result Entropy minimization avoids using spurious features in large domain shifts.
Paper finds unavoidable set for spherical curves with reductivity four.
problem Unknown if there exists a spherical curve with reductivity four.
method Considered 4-gons to find an unavoidable set.
result Found an unavoidable set for spherical curves with reductivity four.
We describe a simplification of Donaldson's arguments for the construction of symplectic hypersurfaces or Lefschetz pencils that makes it possible to avoid any reference to Yomdin's work on the complexity of real algebraic sets.
New algorithm avoids spurious sharpness minimization for NLP models.
problem SAM fails in NLP, leading to performance degradation.
method Developed Functional-SAM, which modifies logit statistics instead of function geometry.
result Functional-SAM and combined methods outperform AdamW and SAM in NLP tasks.
Avoids noncompact hypersurfaces from touching in evolving flows.
problem Preventing noncompact hypersurfaces from touching in evolving flows.
method Analyzes mean curvature flow and weak set flows in Euclidean and Riemannian spaces.
result Proves that noncompact hypersurfaces remain disjoint in evolving flows.
This paper solves a complex differential relation using a novel 'avoidance trick'.
problem Classifying tangent distributions satisfying non-involutivity conditions.
method Convex integration with an 'avoidance trick'.
result First example of a differential relation that is ample in some directions but not all.
New algorithms optimize constrained problems faster, avoiding full set optimization.
problem Optimizing constrained problems efficiently and quickly.
method Designing accelerated first-order algorithms that avoid full set optimization.
result Proved convergence to stationary points in nonconvex settings and accelerated rates in convex settings.
Deep learning networks have connected sublevel sets, avoiding local minima.
problem Finding local minima in deep learning networks.
method Analyzing sublevel sets of loss functions in over-parameterized neural nets.
result Sublevel sets are connected and unbounded, ensuring all global minima are accessible.
Study of Willmore energy on sphere sublevel sets and flow singularities.
problem Understanding the Willmore energy landscape and singularities of the Willmore flow.
method Gluing different instances of the Willmore flow and using an invariant for triple-point-free spheres.
result Classification of initial surfaces with energy at most 12π leading to unavoidable singularities.
This paper extends Newton's method to distributed learning, avoiding saddle points and handling Byzantine workers.
problem Avoiding saddle points in distributed non-convex optimization, especially in the presence of Byzantine workers.
method Extends cubic-regularized Newton method to distributed framework, addressing communication bottlenecks and Byzantine attacks.
result The method achieves improved iteration complexity compared to first-order methods, with a 25% improvement in experiments.
New approach to avoid bad incentives in reinforcement learning agents.
problem Designing safe reinforcement learning agents that avoid unnecessary disruptions.
method Break down side effects penalties into baseline state and deviation measure; introduce new stepwise inaction baseline and relative reachability deviation measure.
result Combination of new design choices avoids undesirable incentives, while simpler alternatives fail.
Industrial vehicle uses LiDAR and camera to detect and avoid restricted areas.
problem Avoiding collisions in industrial settings with automated vehicles.
method Combining LiDAR and camera data, using deep learning for projection, and model-predictive control.
result Reduces false positives in LiDAR detection of reflective beacons.
CARML uses meta-learning to avoid obstacles in 2D vehicle navigation.
problem Collision avoidance in 2D vehicle navigation.
method Model-Agnostic Meta-Learning for multi-objective reinforcement learning.
result CARML outperforms a baseline TD3 solution in obstacle avoidance.
New model predicts sets from feature vectors without discontinuity issues.
problem Discontinuity issues in predicting sets from feature vectors.
method General model that respects set structure, auto-encodes point sets, predicts bounding boxes, and attributes.
result Model successfully predicts sets from a single feature vector without discontinuity.
Improves data-driven reachability estimation for complex systems.
problem Estimating reachable states in complex dynamical systems with unknown parameters.
method Uses Christoffel functions and conformal prediction to improve sample efficiency and robustness.
result Guaranteed convergence to the true reach set with improved sample efficiency and robustness.
Distillation works even with hard labels from overparameterized teacher, leading to better performance.
problem Improving model performance with hard labels from overparameterized teacher.
method Training a student model on a large held-out dataset labeled by a highly overparameterized teacher.
result Student model outperforms traditional approaches due to double descent phenomenon.
Study motion planning for points avoiding obstacles in a plane.
problem Avoiding collisions for multiple points in a plane with unknown obstacles.
method Algebraic and topological tools for motion planning.
result New topological complexity for planar motion planning.
Generative method avoids function estimation for data generation.
problem Challenges in function estimation for generative models.
method Deterministic point transport with gradient descent.
result Data generation possible without function estimation.
Framework trains safe agents avoiding deceptive behavior.
problem Training safe agents from unsafe incentives.
method Formal settings, causal influence analysis, maximizing non-mediated effects.
result Agents avoid manipulating delicate state for rewards.
First-order methods avoid saddle points for most initializations.
problem Avoiding saddle points in optimization problems.
method First-order methods, including gradient descent and variants, analyzed using dynamical systems and the Stable Manifold Theorem.
result First-order methods avoid saddle points for almost all initializations.