arXiv research

We provide rigorous guarantees on learning with the weighted trace-norm under arbitrary sampling distributions. We show that the standard weighted trace-norm might fail when the sampling distribution is not a product distribution (i.e. when row and column indexes are not selected independently), present a corrected var…

The paper explores weight systems and their applications to graph and embedded graph invariants.

The conformal invariance and universality results of Chelkak-Smirnov on the two-dimensional Ising model hold for isoradial planar graphs with critical weights. Motivated by the problem of extending these results to a wider class of graphs, we define a generalized notion of s-holomorphicity for functions on arbitrary we…

Constructs geometric models for moduli spaces of Higgs bundles over Riemann sphere.

In this letter, we introduce a distributed Nesterov method, termed as $\mathcal{ABN}$, that does not require doubly-stochastic weight matrices. Instead, the implementation is based on a simultaneous application of both row- and column-stochastic weights that makes this method applicable to arbitrary (strongly-connected…

Hardness proven for neural networks with natural weights.

Tropical Geometry and Mathematical Morphology share the same max-plus and min-plus semiring arithmetic and matrix algebra. In this chapter we summarize some of their main ideas and common (geometric and algebraic) structure, generalize and extend both of them using weighted lattices and a max-$\star$ algebra with an ar…

Two-layer neural networks must be robust, even with arbitrary weights.

It is well known that Expected Shortfall (also called Average Value-at-Risk) is a convex risk measure, i. e. Expected Shortfall of a convex linear combination of arbitrary risk positions is not greater than a convex linear combination with the same weights of Expected Shortfalls of the same risk positions. In this shor…

The Penrose theorem and Hawking's topology theorem are extended to weighted spacetimes.

Unified formula for arbitrary liquidity operations in weighted AMMs

Optimal weight windows are symmetric rectangles centered at peak.

Proves existence of curves with constant curvature in a sphere.

We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does not require the prior knowledge of the number of groups or other dimensions of the…

The paper connects Lie bialgebras, Rota-Baxter Lie algebras, and their properties.

We introduce a weighted de Rham operator which acts on arbitrary tensor fields by considering their structure as r-fold forms. We can thereby define associated superpotentials for all tensor fields in all dimensions and, from any of these superpotentials, we deduce in a straightforward and natural manner the existence …

New inequalities for convex hypersurfaces in various spaces.

Establishes Yau-Tian-Donaldson conjecture for weighted metrics.

The paper analyzes prediction error in nonstationary settings using weighted risk minimization.

New bounds for SGD show improved performance in various settings.

The paper studies a new vacuum field equation and its solutions.

Gradient descent with random weights in linear regression analyzed for various noise types.

Power-law portfolios improve diversification by scaling weights sub-linearly.

Derives Selberg trace formula on Riemann surfaces and generalizes to other spaces.

Study Gaussian approximation for deep neural networks with random weights.

Maximizes probability of completing investment schedules with optimal portfolio weights.

Heuristic weighting improves denoising score matching without requiring noise distribution assumptions.

We consider weighted parallel spinors in Lorentzian Weyl geometry in arbitrary dimensions, choosing the weight such that the integrability condition for the existence of such a spinor, implies the geometry to be Einstein-Weyl. We then use techniques developed for the classification of supersymmetric solutions to superg…

Classifies self-shrinkers in arbitrary dimensions under specific curvature conditions.

We prove that the evolution of weight vectors in online gradient descent can encode arbitrary polynomial-space computations, even in very simple learning settings. Our results imply that, under weak complexity-theoretic assumptions, it is impossible to reason efficiently about the fine-grained behavior of online gradie…

Gaussian Processes improve data interpolation from diverse experiments.

The quadric ansatz solves dKP equations in arbitrary dimensions, leading to Einstein-Weyl structures.

We propose $\textit{weighted inner product similarity}$ (WIPS) for neural network-based graph embedding. In addition to the parameters of neural networks, we optimize the weights of the inner product by allowing positive and negative values. Despite its simplicity, WIPS can approximate arbitrary general similarities in…

Estimates causal effects using neural networks for balancing covariates.

Proves conditions for weighted Hermite-Einstein metrics on vector bundles.

Researchers develop method to protect against 'weight poisoning' attacks on pre-trained models.

The paper examines when importance weighting is needed for nonparametric and misspecified models.

Proposes a new RL method to fine-tune flow-based models with arbitrary rewards.

The paper analyzes how re-weighting helps in reducing variance in high-dimensional kernel methods under covariate shifts.

Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to well-defined knot invariants are identified as 1-dimensional cohomology classes of gene…

New algorithm for learning mixtures with mostly uniform weights, improving on previous bounds.

On a complete manifold, such as Euclidean 3-space or hyperbolic 3-space, the limit at infinity of the norm of the Higgs field is called the mass of the monopole. We show the existence, on hypebolic 3-space, of monopoles with given magnetic charge and arbitrary mass. Previously, aside from charge one monopoles, existenc…

Proposes a new portfolio theory that optimizes returns and risk.

For each cardinal $κ$, each natural number $n$ and each simplicial complex $K$ we construct a space $ν^n_κ(K)$ and a map $π\colon ν^n_κ(K) \to K$ such that the following conditions are satisfied. 1. $ν^n_κ(K)$ is a complete metric $n$-dimensional space of weight $κ$. 2. $ν^n_κ(K)$ is an absolute neighborhood extensor i…

WBCP improves conformal prediction for distribution shifts using weighted Dirichlet posteriors.

Let $(M^N, g, e^{-f}dv)$ be a complete smooth metric measure space with $\infty$-Bakry-Émery Ricci tensor bounded from below. We derive elliptic gradient estimates for positive solutions of a weighted nonlinear parabolic equation \begin{align*} \displaystyle \Big(Δ_f - \frac{\partial}{\partial t}\Big) u(x,t) +q(x,t)u^α…

We show that integration over a $G$-manifold $M$ can be reduced to integration over a minimal section $Σ$ with respect to an induced weighted measure and integration over a homogeneous space $G/N$. We relate our formula to integration formulae for polar actions and calculate some weight functions. In case of a compact …

TSC improves causal effect estimation in panel data.