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Found 16 papers, 4 papers with code
Spectral Graph Matching and Regularized Quadratic Relaxations: Algorithm and Theory
Graph matching, also known as network alignment, aims at recovering the latent vertex correspondence between two unlabeled, edge-correlated weighted graphs.
Nonlinear spiked covariance matrices and signal propagation in deep neural networks
Many recent works have studied the eigenvalue spectrum of the Conjugate Kernel (CK) defined by the nonlinear feature map of a feedforward neural network.
Optimal Automated Market Makers: Differentiable Economics and Strong Duality
The role of a market maker is to simultaneously offer to buy and sell quantities of goods, often a financial asset such as a share, at specified prices.
Mean-field variational inference with the TAP free energy: Geometric and statistical properties in linear models
In settings where it is conjectured that no efficient algorithm can find this local neighborhood, we prove analogous geometric properties for a local minimizer of the TAP free energy reachable by AMP, and show that posterior inference based on this minimizer remains correctly calibrated.
Transfer Learning for Bayesian Optimization on Heterogeneous Search Spaces
Bayesian optimization (BO) is a popular black-box function optimization method, which makes sequential decisions based on a Bayesian model, typically a Gaussian process (GP), of the function.
HyperBO+: Pre-training a universal prior for Bayesian optimization with hierarchical Gaussian processes
However, those prior learning methods typically assume that the input domains are the same for all tasks, weakening their ability to use observations on functions with different domains or generalize the learned priors to BO on different search spaces.
Local convexity of the TAP free energy and AMP convergence for Z2-synchronization
This provides a rigorous foundation for variational inference in high dimensions via minimization of the TAP free energy.
Empirical Bayes PCA in high dimensions
When the dimension of data is comparable to or larger than the number of data samples, Principal Components Analysis (PCA) may exhibit problematic high-dimensional noise.
Tree-Projected Gradient Descent for Estimating Gradient-Sparse Parameters on Graphs
We study estimation of a gradient-sparse parameter vector $\boldsymbol{\theta}^* \in \mathbb{R}^p$, having strong gradient-sparsity $s^*:=\|\nabla_G \boldsymbol{\theta}^*\|_0$ on an underlying graph $G$.
Spectra of the Conjugate Kernel and Neural Tangent Kernel for linear-width neural networks
We study the eigenvalue distributions of the Conjugate Kernel and Neural Tangent Kernel associated to multi-layer feedforward neural networks.
Spectral Graph Matching and Regularized Quadratic Relaxations II: Erdős-Rényi Graphs and Universality
We analyze a new spectral graph matching algorithm, GRAph Matching by Pairwise eigen-Alignments (GRAMPA), for recovering the latent vertex correspondence between two unlabeled, edge-correlated weighted graphs.
Spectral Graph Matching and Regularized Quadratic Relaxations I: The Gaussian Model
Departing from prior spectral approaches that only compare top eigenvectors, or eigenvectors of the same order, GRAMPA first constructs a similarity matrix as a weighted sum of outer products between all pairs of eigenvectors of the two graphs, with weights given by a Cauchy kernel applied to the separation of the corresponding eigenvalues, then outputs a matching by a simple rounding procedure.
Surfing: Iterative optimization over incrementally trained deep networks
When initialized with random parameters $\theta_0$, we show that the objective $f_{\theta_0}(x)$ is "nice'' and easy to optimize with gradient descent.
Iterative Alpha Expansion for estimating gradient-sparse signals from linear measurements
We consider estimating a piecewise-constant image, or a gradient-sparse signal on a general graph, from noisy linear measurements.
Hybrid Actor-Critic Reinforcement Learning in Parameterized Action Space
In this paper we propose a hybrid architecture of actor-critic algorithms for reinforcement learning in parameterized action space, which consists of multiple parallel sub-actor networks to decompose the structured action space into simpler action spaces along with a critic network to guide the training of all sub-actor networks.
How Well Do Local Algorithms Solve Semidefinite Programs?
Several probabilistic models from high-dimensional statistics and machine learning reveal an intriguing --and yet poorly understood-- dichotomy.
