arXiv research

Equity-Transformer solves NP-hard min-max routing problems efficiently.

Novel ML approach solves complex warehouse routing problem.

Proposes $φ$-balancing for more balanced expert utilization in MoE models.

New insights into $p$-widths of surfaces, proving optimality and calculating constants.

Study shows strong min-max principle for phase transitions.

Upper bound for Morse index of min-max varifolds.

Localized min-max method proves minimal hypersurface existence.

The paper solves min-max widths on a 3-sphere and strengthens multiplicity theorems.

Study introduces statistical mechanics for min-max problems.

Adaptive momentum method solves non-convex min-max problems.

Paper proves finiteness and Morse index estimates for equivariant min-max hypersurfaces.

New proof of Smale conjecture for RP^3 and lens spaces using min-max theory.

Route Choice Models predict the route choices of travelers traversing an urban area. Most of the route choice models link route characteristics of alternative routes to those chosen by the drivers. The models play an important role in prediction of traffic levels on different routes and thus assist in development of ef…

Paper improves Morse index bound for hypersurfaces.

New methods solve min-max problems on manifolds using Riemannian Hamiltonians.

JAMPR learns to solve complex VRP with time windows.

We introduce a new routing algorithm for capsule networks, in which a child capsule is routed to a parent based only on agreement between the parent's state and the child's vote. The new mechanism 1) designs routing via inverted dot-product attention; 2) imposes Layer Normalization as normalization; and 3) replaces seq…

Bound on equivariant index for min-max surfaces.

We prove that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal hypersurfaces associated with the volume spectrum introduced by Gromov, Guth, Marques-Neves, are two-sided and have multiplicity one. This confirms a conjecture by Marques-Neves. We prove that in a bumpy metric each…

A large GPS dataset reveals that a single route often covers 60% of travel observations.

Global routing has been a historically challenging problem in electronic circuit design, where the challenge is to connect a large and arbitrary number of circuit components with wires without violating the design rules for the printed circuit boards or integrated circuits. Similar routing problems also exist in the de…

Survey of advances in non-convex min-max optimization for applications.

We propose and systematically evaluate three strategies for training dynamically-routed artificial neural networks: graphs of learned transformations through which different input signals may take different paths. Though some approaches have advantages over others, the resulting networks are often qualitatively similar…

A new router uses attention-based reinforcement learning to solve detailed routing problems efficiently.

We reformulate LIPs as min-max problems for easier solution.

The paper bounds the min-max width of embedded circles on spheres and manifolds.

Study confirms a 2-sphere metric with three geodesics of minimal length.

Bayesian optimization methods improved for min max optimization problems.

The DEBS Grand Challenge 2018 is set in the context of maritime route prediction. Vessel routes are modeled as streams of Automatic Identification System (AIS) data points selected from real-world tracking data. The challenge requires to correctly estimate the destination ports and arrival times of vessel trips, as ear…

In this paper, we study the shape of the min-max minimal hypersurface produced by Almgren-Pitts-Schoen-Simon \cite{AF62, AF65, P81, SS81} in a Riemannian manifold $(M^{n+1}, g)$ of positive Ricci curvature for all dimensions. The min-max hypersurface has a singular set of Hausdorff codimension $7$. We characterize the …

Unified routing and arbitrage with concave continuation.

A new approach integrates inventory prediction and routing optimization for better supply chain management.

The study proves a generic multiplicity one theorem for $G$-invariant minimal hypersurfaces.

Constructs cmc doublings of minimal surfaces via min-max theory.

This research proves that two min-max theories for hypersurfaces are equivalent.

This study reveals a Min-Max property in LeNet's convolutional layers, enhancing adversarial robustness.

Sparse routing networks with co-training prevent catastrophic forgetting in continual learning.

New Gaussian min-max theorem extends classical results to non-i.i.d. Gaussian matrices.

New algorithm solves non-convex, non-differentiable min-max games.

Generic density of equivariant min-max hypersurfaces in Riemannian manifolds.

We characterize the Zoll Riemannian metrics on a given simply connected spin closed manifold as those Riemannian metrics for which two suitable min-max values in a finite dimensional loop space coincide. We also show that on odd dimensional Riemannian spheres, when certain pairs of min-max values in the loop space coin…

A recently proposed method in deep learning groups multiple neurons to capsules such that each capsule represents an object or part of an object. Routing algorithms route the output of capsules from lower-level layers to upper-level layers. In this paper, we prove that state-of-the-art routing procedures decrease the e…

Polestar optimizes public transportation routes for efficiency and user satisfaction.

Capsules are the multidimensional analogue to scalar neurons in neural networks, and because they are multidimensional, much more complex routing schemes can be used to pass information forward through the network than what can be used in traditional neural networks. This work treats capsules as collections of neurons …

New geometric invariant from min-max width of spheres on Riemannian 2-spheres.

Given a Riemannian manifold and a closed submanifold, we find a geodesic segment with free boundary on the given submanifold. This is a corollary of the min-max theory which we develop in this article for the free boundary variational problem. In particular, we develop a modified Birkhoff curve shortening process to ac…

Anisotropic min-max theory constructs stable minimal surfaces in 3-manifolds.

In this paper, we develop a min-max theory for the construction of constant mean curvature (CMC) hypersurfaces of prescribed mean curvature in an arbitrary closed manifold. As a corollary, we prove the existence of a nontrivial, smooth, closed, almost embedded, CMC hypersurface of any given mean curvature $c$. Moreover…