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Found 18 papers, 0 papers with code
Barriers for the performance of graph neural networks (GNN) in discrete random structures. A comment on~\cite{schuetz2022combinatorial},\cite{angelini2023modern},\cite{schuetz2023reply}
In particular, critical commentaries~\cite{angelini2023modern} and~\cite{boettcher2023inability} point out that simple greedy algorithm performs better than GNN in the setting of random graphs, and in fact stronger algorithmic performance can be reached with more sophisticated methods.
Self-Regularity of Non-Negative Output Weights for Overparameterized Two-Layer Neural Networks
Using a simple covering number argument, we establish that under quite mild distributional assumptions on the input/label pairs; any such network achieving a small training error on polynomially many data necessarily has a well-controlled outer norm.
Hardness of Random Optimization Problems for Boolean Circuits, Low-Degree Polynomials, and Langevin Dynamics
For the case of Boolean circuits, our results improve the state-of-the-art bounds known in circuit complexity theory (although we consider the search problem as opposed to the decision problem).
Neural Networks and Polynomial Regression. Demystifying the Overparametrization Phenomena
Thus a message implied by our results is that parametrizing wide neural networks by the number of hidden nodes is misleading, and a more fitting measure of parametrization complexity is the number of regression coefficients associated with tensorized data.
Stationary Points of Shallow Neural Networks with Quadratic Activation Function
Next, we show that initializing below this barrier is in fact easily achieved when the weights are randomly generated under relatively weak assumptions.
Sparse High-Dimensional Isotonic Regression
We consider the problem of estimating an unknown coordinate-wise monotone function given noisy measurements, known as the isotonic regression problem.
Inference in High-Dimensional Linear Regression via Lattice Basis Reduction and Integer Relation Detection
Using a novel combination of the PSLQ integer relation detection, and LLL lattice basis reduction algorithms, we propose a polynomial-time algorithm which provably recovers a $\beta^*\in\mathbb{R}^p$ enjoying the mixed-support assumption, from its linear measurements $Y=X\beta^*\in\mathbb{R}^n$ for a large class of distributions for the random entries of $X$, even with one measurement $(n=1)$.
The Landscape of the Planted Clique Problem: Dense subgraphs and the Overlap Gap Property
Using the first moment method, we study the densest subgraph problems for subgraphs with fixed, but arbitrary, overlap size with the planted clique, and provide evidence of a phase transition for the presence of Overlap Gap Property (OGP) at $k=\Theta\left(\sqrt{n}\right)$.
High Dimensional Linear Regression using Lattice Basis Reduction
We consider a high dimensional linear regression problem where the goal is to efficiently recover an unknown vector $\beta^*$ from $n$ noisy linear observations $Y=X\beta^*+W \in \mathbb{R}^n$, for known $X \in \mathbb{R}^{n \times p}$ and unknown $W \in \mathbb{R}^n$.
Sparse High-Dimensional Linear Regression. Algorithmic Barriers and a Local Search Algorithm
The presence of such an Overlap Gap Property phase transition, which originates in statistical physics, is known to provide evidence of an algorithmic hardness.
Matrix Completion from $O(n)$ Samples in Linear Time
Under a certain incoherence assumption on $M$ and for the case when both the rank and the condition number of $M$ are bounded, it was shown in \cite{CandesRecht2009, CandesTao2010, keshavan2010, Recht2011, Jain2012, Hardt2014} that $M$ can be recovered exactly or approximately (depending on some trade-off between accuracy and computational complexity) using $O(n \, \text{poly}(\log n))$ samples in super-linear time $O(n^{a} \, \text{poly}(\log n))$ for some constant $a \geq 1$.
High-Dimensional Regression with Binary Coefficients. Estimating Squared Error and a Phase Transition
c) We establish a certain Overlap Gap Property (OGP) on the space of all binary vectors \beta when n\le ck\log p for sufficiently small constant c. We conjecture that OGP is the source of algorithmic hardness of solving the minimization problem \min_{\beta}\|Y-X\beta\|_{2} in the regime n<n_{\text{LASSO/CS}}.
A Message Passing Algorithm for the Problem of Path Packing in Graphs
We consider the problem of packing node-disjoint directed paths in a directed graph.
A Note on Alternating Minimization Algorithm for the Matrix Completion Problem
We consider the problem of reconstructing a low rank matrix from a subset of its entries and analyze two variants of the so-called Alternating Minimization algorithm, which has been proposed in the past.
Structure learning of antiferromagnetic Ising models
In this paper we investigate the computational complexity of learning the graph structure underlying a discrete undirected graphical model from i. i. d.
Learning graphical models from the Glauber dynamics
In this paper we consider the problem of learning undirected graphical models from data generated according to the Glauber dynamics.
Hardness of parameter estimation in graphical models
Our proof gives a polynomial time reduction from approximating the partition function of the hard-core model, known to be hard, to learning approximate parameters.
Performance of the Survey Propagation-guided decimation algorithm for the random NAE-K-SAT problem
We show that the Survey Propagation-guided decimation algorithm fails to find satisfying assignments on random instances of the "Not-All-Equal-$K$-SAT" problem if the number of message passing iterations is bounded by a constant independent of the size of the instance and the clause-to-variable ratio is above $(1+o_K(1)){2^{K-1}\over K}\log^2 K$ for sufficiently large $K$.
