arXiv research

Unconstrained MLIPs outperform constrained ones in accuracy and speed.

New method parameterizes solutions to linearized vacuum constraints on Einstein manifolds.

Properties of steady compressible flow for which geometric constraints have been placed on the potential function are derived, under hypotheses on the flow density and the singular set. Some related unconstrained problems are also considered, including the estimation of a class of fields having nonzero vorticity.

Our paper explains deep neural collapse in multiple layers.

Problems of segmentation, denoising, registration and 3D reconstruction are often addressed with the graph cut algorithm. However, solving an unconstrained graph cut problem is NP-hard. For tractable optimization, pairwise potentials have to fulfill the submodularity inequality. In our learning paradigm, pairwise poten…

New approach reduces unconstrained linear bandits to simpler optimization problems.

We clarify what fairness guarantees we can and cannot expect to follow from unconstrained machine learning. Specifically, we characterize when unconstrained learning on its own implies group calibration, that is, the outcome variable is conditionally independent of group membership given the score. We show that under r…

This paper evaluates conformal prediction for aerial image classification in challenging environments.

Simulated Bifurcation outperforms quantum machines in community detection.

Develops parameter-free online mirror descent for optimal dynamic regret.

Fourier Neural Operators accurately predict dynamics of high-dimensional ionic models.

A new optimization algorithm improves convergence in unconstrained problems.

Structured regularizers enable faster optimization on SPD manifolds with constraints.

Quantum algorithm improves sparse vector recovery from noisy measurements.

Unconstrained models learn physical symmetries effectively with simple data augmentation.

The paper explores solving inverse problems for ODEs with and without constraints.

Proposes ConstraintMatch for semi-supervised clustering with unconstrained data.

Estimates covariance matrices using Markov chain Monte Carlo with improved sample complexity.

This paper extends neural collapse to class-imbalanced datasets using an unconstrained ReLU feature model.

Paper proposes a method to recover accurate labels from partially valid data in multi-label learning.

Shielded LMC samples from non-convex spaces with repulsive drift.

New algorithms reduce online learning regret by tracking gradient variation.

This paper presents a simple method for a posteriori (historical) multi-variate multi-stage optimal trading under transaction costs and a diversification constraint. Starting from a given amount of money in some currency, we analyze the stage-wise optimal allocation over a time horizon with potential investments in mul…

A new L-BFGS method tackles large-scale optimization with fewer evaluations.

New algorithm minimizes cumulative loss in dynamic linear bandits without prior knowledge of comparator switches.

We propose an online convex optimization algorithm (RescaledExp) that achieves optimal regret in the unconstrained setting without prior knowledge of any bounds on the loss functions. We prove a lower bound showing an exponential separation between the regret of existing algorithms that require a known bound on the los…

Proposes a Gaussian process model for constrained dynamics learning.

The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but nontrivial to project onto their intersection. Algorithms based on Newton's metho…

VAV method optimizes learning rate for faster, stable SGD convergence.

We consider a variant of online convex optimization in which both the instances (input vectors) and the comparator (weight vector) are unconstrained. We exploit a natural scale invariance symmetry in our unconstrained setting: the predictions of the optimal comparator are invariant under any linear transformation of th…

Solves VaR-constrained portfolio optimization in markets with stochastic volatility.

An explicit surjection from a set of (locally defined) unconstrained holomorphic functions on a certain submanifold of (Sp_1(C) \times C^{4n}) onto the set HK_{p,q} of local isometry classes of real analytic pseudo-hyperkähler metrics of signature (4p,4q) in dimension 4n is constructed. The holomorphic functions, calle…

Obtaining compact and discriminative features is one of the major challenges in many of the real-world image classification tasks such as face verification and object recognition. One possible approach is to represent input image on the basis of high-level features that carry semantic meaning which humans can understan…

Cookbook transforms constrained statistical inference into unconstrained problems.

DP-GD achieves dimension-independent convergence for unconstrained private GLMs.

Eigen-decomposition simplifies quadratic programming with equality constraints.

Yau's Affine Normal Descent optimizes smooth unconstrained problems with geometrically adapted directions.

Study optimal portfolio management with periodic evaluations in stochastic models, considering convex constraints.

A key problem in financial mathematics is the forecasting of financial crashes: if we perturb asset prices, will financial institutions fail on a massive scale? This was recently shown to be a computationally intractable (NP-hard) problem. Financial crashes are inherently difficult to predict, even for a regulator whic…

Adam converges with high probability under unconstrained non-convex smooth stochastic optimizations.

Paper analyzes regret bounds for unconstrained online optimization.

A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a drawdown constraint, as in the original setup of Grossman and Zhou (1993). We wor…

New methods solve complex optimization problems in machine learning.

New sparse Gaussian process method tackles unconstrained regression problems.

This article presents a new methodology called deep Theory of Functional Connections (TFC) that estimates the solutions of partial differential equations (PDEs) by combining neural networks with TFC. TFC is used to transform PDEs with boundary conditions into unconstrained optimization problems by embedding the boundar…

The paper studies knot densities under various constraints and degenerations.

Develops regularity theory for Beckmann's optimal transport problem.

We consider minimizing a nonconvex, smooth function $f$ on a Riemannian manifold $\mathcal{M}$. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle points on the manifold). The rate of convergence depends as $1/ε^2$ o…