A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Efficiently solves exploration-exploitation in LQR using Lagrangian relaxation.
Study uses DRL with Lagrangian relaxation to solve temporal control tasks with STL constraints.
Recent results in Compressive Sensing have shown that, under certain conditions, the solution to an underdetermined system of linear equations with sparsity-based regularization can be accurately recovered by solving convex relaxations of the original problem. In this work, we present a novel primal-dual analysis on a …
This work analyzes machine learning for Lagrangian Relaxation in MILP.
In this paper we address the problem of finding the most probable state of a discrete Markov random field (MRF), also known as the MRF energy minimization problem. The task is known to be NP-hard in general and its practical importance motivates numerous approximate algorithms. We propose a submodular relaxation approa…
Improves neural network verification by merging abstract domains and Lagrangian methods.
New conditions prevent gaps in optimal control problems.
Paper proposes distributed optimization for federated learning with theoretical guarantees.
New methods for efficient exploration under unknown linear constraints in bandits.
Stability of Morse index for Yang-Mills connections in 4D.
Statistical image reconstruction (SIR) methods are studied extensively for X-ray computed tomography (CT) due to the potential of acquiring CT scans with reduced X-ray dose while maintaining image quality. However, the longer reconstruction time of SIR methods hinders their use in X-ray CT in practice. To accelerate st…
Improved neural network verification using Lagrangian decomposition and parallel algorithms.
A fundamental component of neural network verification is the computation of bounds on the values their outputs can take. Previous methods have either used off-the-shelf solvers, discarding the problem structure, or relaxed the problem even further, making the bounds unnecessarily loose. We propose a novel approach bas…
We propose an SDP relaxation for the Gromov-Wasserstein distance, providing globally optimal solutions.
This study presents a rapid multiple incremental and decremental mechanism based on Weight-Error Curves (WECs) for support-vector analysis. Recursion-free computation is proposed for predicting the Lagrangian multipliers of new samples. This study examines Ridge Support Vector Models, subsequently devising a recursion-…
Signal estimation problems with smoothness and sparsity priors can be naturally modeled as quadratic optimization with -"norm" constraints. Since such problems are non-convex and hard-to-solve, the standard approach is, instead, to tackle their convex surrogates based on -norm relaxations. In this paper…
We present the min-max construction of critical points of the area using penalization arguments. Precisely, for any immersion of a closed surface into a given closed manifold, we add to the area Lagrangian a term equal to the norm of the second fundamental form of the immersion times a "viscosity" parameter. …
In this paper, we study the nonnegative tensor data and propose an orthogonal nonnegative Tucker decomposition (ONTD). We discuss some properties of ONTD and develop a convex relaxation algorithm of the augmented Lagrangian function to solve the optimization problem. The convergence of the algorithm is given. We employ…
Counterexample shows state-constrained optimal control problems can have Young measure gaps.
The paper studies how adding a 'Gauge Mass' term breaks gauge symmetry in Yang-Mills-Higgs systems and analyzes the resulting behavior.
A major challenge in computed tomography (CT) is to reduce X-ray dose to a low or even ultra-low level while maintaining the high quality of reconstructed images. We propose a new method for CT reconstruction that combines penalized weighted-least squares reconstruction (PWLS) with regularization based on a sparsifying…
This paper introduces resilient constrained learning to adapt learning constraints while solving machine learning tasks.
New method for MAP inference using Benders' decomposition.
Bayesian optimization tackles mixed discrete-continuous problems with Gaussian processes.
Policy gradient algorithms typically combine discounted future rewards with an estimated value function, to compute the direction and magnitude of parameter updates. However, for most Reinforcement Learning tasks, humans can provide additional insight to constrain the policy learning. We introduce a general method to i…
New approach relaxes inductive biases of physics-inspired NNs for better performance.
We study the total least squares (TLS) problem that generalizes least squares regression by allowing measurement errors in both dependent and independent variables. TLS is widely used in applied fields including computer vision, system identification and econometrics. The special case when all dependent and independent…
GCVAE improves disentanglement in VAEs while balancing reconstruction error.
Much effort has been directed at algorithms for obtaining the highest probability configuration in a probabilistic random field model known as the maximum a posteriori (MAP) inference problem. In many situations, one could benefit from having not just a single solution, but the top M most probable solutions known as th…
We advocate Laplacian K-modes for joint clustering and density mode finding, and propose a concave-convex relaxation of the problem, which yields a parallel algorithm that scales up to large datasets and high dimensions. We optimize a tight bound (auxiliary function) of our relaxation, which, at each iteration, amounts…
We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut theorem for boundary regions, applied recently to develop a "bit-thread" interpretation of holographic entanglement entropies. We also prove various properties of the max flow…
This paper studies a classic maximum entropy sampling problem (MESP), which aims to select the most informative principal submatrix of a prespecified size from a covariance matrix. MESP has been widely applied to many areas, including healthcare, power system, manufacturing and data science. By investigating its Lagran…
We consider effort allocation in crowdsourcing, where we wish to assign labeling tasks to imperfect homogeneous crowd workers to maximize overall accuracy in a continuous-time Bayesian setting, subject to budget and time constraints. The Bayes-optimal policy for this problem is the solution to a partially observable Ma…
Constructing translating solitons from Lagrangian Grim Reapers.
This work studies the robustness certification problem of neural network models, which aims to find certified adversary-free regions as large as possible around data points. In contrast to the existing approaches that seek regions bounded uniformly along all input features, we consider non-uniform bounds and use it to …
In this paper, we study the Lagrangian F-stability of closed Lagrangian self-shrinkers immersed in complex Euclidean space. We show that any closed Lagrangian self-shrinker with first Betti number greater than one is Lagrangian F-unstable. In particular, any two-dimensional embedded closed Lagrangian self-shrinker is L…
A new method solves high-dimensional MFGs using particle-based flow matching.
We exhibit infinitely many, explicit special Lagrangian isolated singularities that admit no asymptotically conical special Lagrangian smoothings. The existence/ nonexistence of such smoothings is an important component of the current efforts to understand which singular special Lagrangians arise as limits of smooth sp…
We introduce a notion of vanishing Maslov index for lagrangian varifolds and lagrangian integral cycles in a Calabi-Yau manifold. We construct mass-decreasing flows of lagrangian varifolds and lagrangian cycles which satisfy this condition. The flow of cycles converges, at infinite time, to a sum of special lagrangian …
Study on singularities of Lagrangian immersions with applications in Floer theory.
Internal Lagrangians derived from variational principles.
New method fills cluster seeds with exact Lagrangian structures.
Quantifies closeness of special Lagrangians under Floer conditions.
In this paper, we prove that any Lagrangian translating soliton is Lagrangian -stable.
Proves conditions for generating families on Lagrangian cobordisms.
Ancient solutions and translators identified for Lagrangian flow.
New method improves neural network verification by considering multivariate input space of ReLU neurons.
Geodesics in positive Lagrangian spaces map to special Lagrangian cylinders.