arXiv research

Geometric Mean Market Makers super-hedge impermanent loss without models.

GCML preserves geometric structure in manifold clustering for diverse data types.

Researchers discover pathways connecting optima in complex loss functions of deep neural networks.

Proposes a new loss function for distributional learning.

We analyze impermanent loss in AMMs and show G3Ms are simplest.

Regularizers change the geometric properties of loss functions in neural networks.

We analyze the optimization landscape of α-loss in logistic models.

Equivalence found between algorithmic regularization and convex penalization for convex losses.

Geometric study of linear neural networks identifies pure and spurious critical points.

Optimizes exp-concave losses with a new risk bound.

Explains deep learning models and their geometric properties.

This paper extends stock trading results to include stop-loss orders.

GGA improves untrustworthy prediction detection in neural networks without retraining.

Topology-enhanced loss improves 3D object reconstruction from 2D images.

OLÉ simplifies deep learning by enforcing class orthogonality.

Focal loss reduces model curvature for better calibration.

The paper improves Kaczmarz algorithm with momentum for linear least squares.

BAEN-SVM improves SVM robustness to noisy data.

Study geometric properties of loss functions to understand neural network performance.

New method for high-fidelity shape representations from raw data.

Benguria and Loss have conjectured that, amongst all smooth closed curves of length $2π$ in the plane, the lowest possible eigenvalue of the operator $L=-Δ+κ^2$ was one. They observed that this value was achieved on a two-parameter family, $\mathcal{O}$, of geometrically distinct ovals containing the round circle and c…

Second-order optimizers retain residual information after data deletion, affecting machine unlearning.

Geometric focusing affects dispersive estimates for Schrödinger and wave equations.

Improved online learning for hidden-convex losses achieves optimal regret.

We analyze the generalization and robustness of the batched weighted average algorithm for V-geometrically ergodic Markov data. This algorithm is a good alternative to the empirical risk minimization algorithm when the latter suffers from overfitting or when optimizing the empirical risk is hard. For the generalization…

Gradient descent struggles to achieve zero loss in deep learning models due to non-generic data distributions.

Quantization-aware training can recover accuracy lost by post-training quantization.

Proposes IIKL for preserving geometric properties of non-Euclidean data.

Geometric framework explains and controls implicit bias in machine learning.

Geometric framework links clustering accuracy to structural recovery.

Paper proves stability of multi-dimensional rarefaction waves in gas dynamics.

New deep clustering network uses divergence measures for unlabeled data.

Transforms solutions of Davey-Stewartson II equation geometrically.

We consider regression with square loss and general classes of functions without the boundedness assumption. We introduce a notion of offset Rademacher complexity that provides a transparent way to study localization both in expectation and in high probability. For any (possibly non-convex) class, the excess loss of a …

Paper tackles dynamic pricing in a geometrically decaying environment, achieving better occupancy with lower rates.

Introduces generalized Orlicz premia for broader applicability.

PINNs solve differential geometry problems in complex shapes.

Generative models learn complex data from low-dimensional manifolds.

Optimal exit strategies of CPT gamblers in unfair gambles

Researchers interpret SGD using diffusion metrics for clearer geometric understanding.

This paper introduces SRPR for robust phase retrieval with smoothed loss functions.

Equivariant networks improve geometric prediction without scalar approximations.

We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We provide, in a general setup, a relaxed geometric dynamic programming principle for this problem and derive, for the case of …

A method to identify important features without solving the full problem.

Proposes a new metric learning method for image recognition.

We propose a geometric algorithm for topic learning and inference that is built on the convex geometry of topics arising from the Latent Dirichlet Allocation (LDA) model and its nonparametric extensions. To this end we study the optimization of a geometric loss function, which is a surrogate to the LDA's likelihood. Ou…

A geometric theory explains loss functions for robust representation learning.

Unified approach to optimal reinsurance models for insurers and reinsurers.