arXiv research

Random hyperbolic surfaces have nearly optimal spectral gaps.

Optimal spectral method found for inhomogeneous spiked Wigner model.

EGO-MDA identifies optimal spectral-bands for process discrimination.

Muon optimizer simplifies matrix optimization with spectral orthogonalization.

New algorithms optimize spectral risk measures, improving interpolation between average and worst-case performance.

We study Spectral Measures of Risk from the perspective of portfolio optimization. We derive exact results which extend to general Spectral Measures M_phi the Pflug--Rockafellar--Uryasev methodology for the minimization of alpha--Expected Shortfall. The minimization problem of a spectral measure is shown to be equivale…

A large class of machine learning techniques requires the solution of optimization problems involving spectral functions of parametric matrices, e.g. log-determinant and nuclear norm. Unfortunately, computing the gradient of a spectral function is generally of cubic complexity, as such gradient descent methods are rath…

Study shows optimal spectral gaps diminish in large genus surfaces.

Accelerates optimal transport computation by 10x with spectral insights.

We present Spectral Inference Networks, a framework for learning eigenfunctions of linear operators by stochastic optimization. Spectral Inference Networks generalize Slow Feature Analysis to generic symmetric operators, and are closely related to Variational Monte Carlo methods from computational physics. As such, the…

Optimizes risk measures given known marginal distributions of two unknown factors.

New method optimizes portfolios for non-stationary markets.

Spectral algorithms solve optimal community detection and related problems.

Self-distillation optimally improves model performance in spiked covariance models.

Study spectral learning for odeco tensors, addressing initialization bottlenecks.

The paper proves optimal estimates and inequalities for spectral functions on certain manifolds.

Optimal spectral estimators and AMP combine for efficient weak recovery in orthogonally invariant GLMs.

Optimizes spectral density estimation for stationary and nonstationary processes.

We study a spectral generalization of classical combinatorial graph spanners to the spectral setting. Given a set of vectors $V\subseteq \Re^d$, we say a set $U\subseteq V$ is an $α$-spectral spanner if for all $v\in V$ there is a probability distribution $μ_v$ supported on $U$ such that $$vv^\intercal \preceq α\cdot\m…

The optimal dividend problem by De Finetti (1957) has been recently generalized to the spectrally negative Lévy model where the implementation of optimal strategies draws upon the computation of scale functions and their derivatives. This paper proposes a phase-type fitting approximation of the optimal strategy. We con…

Paper explores SNN for learning spectral geometric info from data.

Muon optimizer improves deep learning with spectral norm constraints.

Paper proposes a new method for sparse spectral clustering on Stiefel manifold.

This research optimizes Andrews plots for better visual clarity in high-dimensional data.

The paper finds optimal threshold strategies for insurance companies with a positive terminal value at creeping ruin.

We propose a new reinforcement learning algorithm for partially observable Markov decision processes (POMDP) based on spectral decomposition methods. While spectral methods have been previously employed for consistent learning of (passive) latent variable models such as hidden Markov models, POMDPs are more challenging…

Improves learning of spectral mixture kernels with approximate Bayesian inference.

Spectral algorithms improve under covariate shift with novel weighted techniques.

We propose a new reinforcement learning algorithm for partially observable Markov decision processes (POMDP) based on spectral decomposition methods. While spectral methods have been previously employed for consistent learning of (passive) latent variable models such as hidden Markov models, POMDPs are more challenging…

Stochastic optimization problems often involve the expectation in its objective. When risk is incorporated in the problem description as well, then risk measures have to be involved in addition to quantify the acceptable risk, often in the objective. For this purpose it is important to have an adjusted, adapted and eff…

Rewiring GNNs to optimize community and feature alignment improves their performance.

Study minimizes risk in MDPs with spectral measures.

The paper analyzes the generalization performance of spectral clustering algorithms and proposes new methods to improve their effectiveness.

We introduce a new parameterization method for deep learning layers using spectral tensor train decomposition.

This note is devoted to optimal spectral estimates for Schrödinger operators on compact connected Riemannian manifolds without boundary. These estimates are based on the use of appropriate interpolation inequalities and on some recent rigidity results for nonlinear elliptic equations on those manifolds.

Develops an ℓ_p theory for PCA and spectral clustering.

Study confirms learning rates for vector-valued spectral algorithms, proving consistency.

In this paper we consider a modified version of the classical optimal dividends problem of de Finetti in which the dividend payments subject to a penalty at ruin. We assume that the risk process is modeled by a general spectrally positive Levy process before dividends are deducted. Using the fluctuation theory of spect…

Spectral clustering has become one of the most widely used clustering techniques when the structure of the individual clusters is non-convex or highly anisotropic. Yet, despite its immense popularity, there exists fairly little theory about performance guarantees for spectral clustering. This issue is partly due to the…

Gradient descent with small random init mimics spectral methods for low-rank matrix recovery.

New optimizer SF-NorMuon matches tuned AdamW across various horizons.

This paper proposes a new approach to construct high quality space-filling sample designs. First, we propose a novel technique to quantify the space-filling property and optimally trade-off uniformity and randomness in sample designs in arbitrary dimensions. Second, we connect the proposed metric (defined in the spatia…

An important form of prior information in clustering comes in form of cannot-link and must-link constraints. We present a generalization of the popular spectral clustering technique which integrates such constraints. Motivated by the recently proposed $1$-spectral clustering for the unconstrained problem, our method is…

A fast, robust AMP algorithm for quadratic optimization problems.

Hypercube graphs are optimal in spectral rigidity due to Bakry--Émery curvature.

Optimizer choice affects neural scaling laws, changing the exponent $\alpha$.

Algorithm learns dynamics from past observations.

Survey on spectral gaps of random hyperbolic surfaces.