Equity-Transformer solves NP-hard min-max routing problems efficiently.
problem Min-max routing problems with multiple agents and large-scale applications.
method Sequential planning approach with Transformer and equitable workload distribution inductive biases.
result Significant runtime and cost reductions in min-max mTSP and min-max mPDP tasks.
Novel ML approach solves complex warehouse routing problem.
problem Efficiently routing pickers in mixed-shelves warehouses.
method Hierarchical and parallel multi-agent reinforcement learning.
result State-of-the-art performance in solution quality and inference speed.
Proposes φ φ φ -balancing for more balanced expert utilization in MoE models.
problem Balanced expert utilization in MoE models to avoid bias.
method Directly targets population-level balance by minimizing a convex potential function.
result Consistently outperforms prior methods in stability and effectiveness.
New insights into p p p -widths of surfaces, proving optimality and calculating constants.
problem Understanding p p p -widths of surfaces and their relationship to geodesics. method Analyzing min-max sequences of minimal submanifolds and sweepouts of surfaces.
result Optimal sweepouts of the round two-sphere by ⌊ p f l o o r \lfloor \sqrt{p}
floor ⌊ p f l oor great circles. Study shows strong min-max principle for phase transitions.
problem Understanding nodal sets near minimal hypersurfaces.
method Analogous to White's principle, applies to Allen-Cahn energy.
result Strong min-max principle for phase transitions.
Upper bound for Morse index of min-max varifolds.
problem Bounding Morse index of varifolds.
method Proving upper bound for Morse index of min-max stationary integral varifolds.
result Upper bound for Morse index of min-max stationary integral varifolds.
Localized min-max method proves minimal hypersurface existence.
problem Existence of minimal hypersurfaces in complete manifolds.
method Localized min-max approach to prove existence.
result Existence of complete embedded minimal hypersurface with index at most one.
The paper solves min-max widths on a 3-sphere and strengthens multiplicity theorems.
problem Which min-max widths of the unit 3-sphere lie between 2 π 2 2π^2 2 π 2 and 8 π 8π 8 π ? method Homological min-max theory and stronger versions of multiplicity one theorems.
result Proves the 10th to 13th min-max widths of the unit 3-sphere lie between 2 π 2 2π^2 2 π 2 and 8 π 8π 8 π . Study introduces statistical mechanics for min-max problems.
problem Understanding the properties of min-max problems in high dimensions.
method Statistical mechanical formalism for analyzing min-max problems.
result Derives the relationship between training data and generalization error.
Adaptive momentum method solves non-convex min-max problems.
problem Non-convex min-max optimization problems in training generative adversarial networks.
method Proposes an adaptive momentum algorithm for non-convex min-max optimization.
result Establishes non-asymptotic convergence rates for the proposed algorithm.
Paper proves finiteness and Morse index estimates for equivariant min-max hypersurfaces.
problem Existence and finiteness of G G G -invariant minimal hypersurfaces. method Equivariant min-max theory, compactness theorem, bumpy metrics theorem.
result Generalization of Morse index estimates to equivariant setting.
Capsule networks improve performance on image classification tasks with fewer parameters.
problem Improving performance of capsule networks with fewer parameters.
method Inverted dot-product attention routing, Layer Normalization, concurrent iterative routing.
result Improves performance on benchmark datasets CIFAR-10 and CIFAR-100, and performs at-par with ResNet-18.
New proof of Smale conjecture for RP^3 and lens spaces using min-max theory.
problem Proving the Smale conjecture for specific spaces.
method Minimal surfaces and min-max theory.
result New proof of Smale conjecture for R P 3 \mathbb{RP}^3 RP 3 and lens spaces. 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.
problem Improving Morse index bound for hypersurfaces.
method Construction of hierarchical deformations and restrictive min-max theory.
result Generalizes a result by X. Zhou for 3 ≤ n + 1 ≤ 7 3 \leq n+1 \leq 7 3 ≤ n + 1 ≤ 7 . New methods solve min-max problems on manifolds using Riemannian Hamiltonians.
problem Min-max optimization on Riemannian manifolds.
method Riemannian Hamiltonian methods (RHM) to minimize the Hamiltonian function.
result RHM leads to correct search directions and global optimality in min-max problems.
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…
Bound on equivariant index for min-max surfaces.
problem Bounding the index of equivariant min-max surfaces.
method Equivariant min-max procedure with group action.
result Equivariant index bound by number of parameters.
JAMPR learns to solve complex VRP with time windows.
problem Vehicle routing problems with time windows and vehicle capacities.
method Joint attention to construct multiple routes concurrently.
result JAMPR outperforms existing models on different problem sizes.
A large GPS dataset reveals that a single route often covers 60% of travel observations.
problem Limited insights from small GPS datasets on route choice behavior.
method Evaluation of path generation algorithms including link penalty, link elimination, simulation, and via-node methods.
result Modified link penalty method achieves 97% coverage, significantly higher than previous studies.
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.
problem Finding optimal solutions in non-convex, non-concave min-max problems.
method Selective review of theoretical and algorithmic advances.
result Exciting recent advances in solving non-convex min-max problems.
We reformulate LIPs as min-max problems for easier solution.
problem Recovering signals from few linear measurements.
method Proposed a min-max reformulation of LIPs.
result Saddle points characterize solutions to LIPs.
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.
problem Solving detailed routing in integrated circuits while adhering to complex design rules.
method Attention-based reinforcement learning applied to track-assignment detailed routing.
result The attention router achieves over 100x acceleration compared to a genetic router without sacrificing solution quality.
Epoch-GDA achieves optimal convergence rate for SCSC min-max problems.
problem Solving stochastic min-max problems with strong convexity and strong concavity.
method Epoch-wise stochastic gradient descent ascent method (Epoch-GDA) without additional assumptions.
result Achieves the optimal rate of O ( 1 / T ) O(1/T) O ( 1/ T ) for the duality gap of general SCSC min-max problems. The paper bounds the min-max width of embedded circles on spheres and manifolds.
problem Bounding the min-max width of embedded circles on spheres and manifolds.
method Inducing a sweepout by pairs of points in embedded circles from a given sweepout of the sphere by closed curves.
result Lower bounds for the Birkhoff min-max invariant of a Riemannian sphere in terms of the min-max width of its embedded circles.
Study confirms a 2-sphere metric with three geodesics of minimal length.
problem Understanding the systolic, width, and Gromov-Guth metrics on a 2-sphere.
method Classical min-max and hyperbolic geometry tools.
result Figure-eight geodesics achieve the systolic, width, and Gromov-Guth metrics on a 2-sphere.
Bayesian optimization methods improved for min max optimization problems.
problem Min-max optimization for unknown functions.
method Extended Bayesian optimization to min-max problems with new acquisition functions.
result Improved acquisition functions lead to better solutions.
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 ) (M^{n+1}, g) ( M n + 1 , g ) of positive Ricci curvature for all dimensions. The min-max hypersurface has a singular set of Hausdorff codimension 7 7 7 . We characterize the …
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…
Unified routing and arbitrage with concave continuation.
problem Combining routing and arbitrage in financial markets.
method Extending AMM trade functions to negative inputs via concave continuation.
result Unified approach unifies routing and arbitrage.
The study proves a generic multiplicity one theorem for G G G -invariant minimal hypersurfaces.
problem Proving a generic multiplicity one theorem for G G G -invariant minimal hypersurfaces. method Equivariant min-max theory and analysis of G G G -homology classes. result Shows a generic multiplicity one theorem for G G G -invariant minimal hypersurfaces. Constructs cmc doublings of minimal surfaces via min-max theory.
problem Construct cmc doublings of minimal surfaces.
method Uses min-max theory and catenoid estimate.
result Constructs ε-cmc doublings of Σ for small ε > 0.
This research proves that two min-max theories for hypersurfaces are equivalent.
problem Comparing two min-max theories for hypersurfaces.
method Developed and proved the equivalence of Almgren-Pitts and Allen-Cahn min-max theories.
result The Almgren-Pitts widths and Allen-Cahn widths are equivalent.
A new approach integrates inventory prediction and routing optimization for better supply chain management.
problem Optimizing efficient route selection in supply chain management with uncertain inventory demand.
method Decision-focused learning approach using neural networks to directly integrate inventory prediction and routing optimization.
result Direct integration of inventory prediction and routing optimization leads to better supply chain decisions.
This study reveals a Min-Max property in LeNet's convolutional layers, enhancing adversarial robustness.
problem Uncertainty in the connection weights of convolutional layers in neural networks.
method Demonstrates the Min-Max property through back propagation-based training and a simplified convolution formulation.
result The Min-Max property improves adversarial robustness, indicating a stronger uncertainty in the model parameters.
Sparse routing networks with co-training prevent catastrophic forgetting in continual learning.
problem Catastrophic forgetting in neural networks trained on a sequence of tasks.
method Sparse routing networks with co-training to minimize interference between dissimilar tasks.
result Sparse routing networks with co-training outperform densely connected networks on benchmarks.
New Gaussian min-max theorem extends classical results to non-i.i.d. Gaussian matrices.
problem Extending classical Gaussian min-max theorems to non-i.i.d. Gaussian matrices.
method Identifying a new pair of Gaussian processes that satisfy comparison inequalities.
result New Gaussian min-max and convex Gaussian min-max theorems with applications in multi-source Gaussian regression and binary classification.
New algorithm solves non-convex, non-differentiable min-max games.
problem Limited theoretical understanding of non-smooth min-max games.
method Proximal gradient descent-ascent algorithm for convex-strongly convex games.
result Algorithm converges to ε-Nash equilibrium with polynomial gradient evaluations.
Neural LNS improves vehicle routing performance.
problem Optimizing vehicle routes with constraints.
method Integrates deep learning with large neighborhood search.
result Significantly outperforms existing methods on CVRP.
Generic density of equivariant min-max hypersurfaces in Riemannian manifolds.
problem Finding generic density of equivariant min-max hypersurfaces in Riemannian manifolds.
method Weyl asymptotic law for G G G -equivariant volume spectrum, generic density result. result 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…
Polestar optimizes public transportation routes for efficiency and user satisfaction.
problem Difficulty in finding optimal public transportation routes due to complex networks and dynamic situations.
method Developed a Public Transportation Graph (PTG) and a route search algorithm with station binding and ranking modules.
result Demonstrated superior efficiency and user satisfaction compared to existing systems.
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…
New geometric invariant from min-max width of spheres on Riemannian 2-spheres.
problem Understanding the min-max width of spheres associated to distance functions.
method Application of min-max methods to pairs of points on Riemannian 2-spheres.
result The min-max width does not always equal half the length of a simple closed geodesic.
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 …
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…