Related papers: Barren Plateaus as Destructive Interference: A Dia…
A Bayesian Belief Network (BN) is a model of a joint distribution over a setof n variables, with a DAG structure to represent the immediate dependenciesbetween the variables, and a set of parameters (aka CPTables) to represent thelocal…
Interest is rising in Physics-Informed Neural Networks (PINNs) as a mesh-free alternative to traditional numerical solvers for partial differential equations (PDEs). However, PINNs often struggle to learn high-frequency and multi-scale…
The parameters of the quantum circuit in a variational quantum algorithm induce a landscape that contains the relevant information regarding its optimization hardness. In this work we investigate such landscapes through the lens of…
Barren plateaus in variational quantum algorithms are typically described by gradient concentration at random initialization. In contrast, rigorous results for the Hessian, even at the level of entry-wise variance, remain limited. In this…
Statistical inference for stochastic block models typically relies on the spectrum of the normalized adjacency matrix $\A^*$. In practice, the true probability matrix $\mathbf{B}$ is unknown and must be replaced by a plug-in estimator…
We study conditions under which treatment effect estimators constructed under the no-interference assumption in randomized experiments are asymptotically normal in the presence of interference. We prove that the standard Horvitz-Thompson…
This paper explores the difficulties in solving partial differential equations (PDEs) using physics-informed neural networks (PINNs). PINNs use physics as a regularization term in the objective function. However, a drawback of this approach…
An important inference from Neural Tangent Kernel (NTK) theory is the existence of spectral bias (SB), that is, low frequency components of the target function of a fully connected Artificial Neural Network (ANN) being learnt significantly…
We present an interval-based approach for parameter identification in structural static inverse problems. The proposed inverse formulation exploits the Interval Finite Element Method (IFEM) combined with adjoint-based optimization. The…
A periodically driven quantum system with avoided-level crossing experiences both non-adiabatic transitions and wave-function phase changes. These result in coherent interference fringes in the system's occupation probabilities. For qubits,…
Empirical studies of trained models often report a transient regime in which signal is detectable in a finite gradient descent time window before overfitting dominates. We provide an analytically tractable random-matrix model that…
Physics-informed neural networks (PINNs) have recently emerged as effective methods for solving partial differential equations (PDEs) in various problems. Substantial research focuses on the failure modes of PINNs due to their frequent…
We present a model of a basic recurrent neural network (or bRNN) that includes a separate linear term with a slightly "stable" fixed matrix to guarantee bounded solutions and fast dynamic response. We formulate a state space viewpoint and…
The discovery and understanding of new quantum phases has time and again transformed both fundamental physics and technology, yet progress often relies on slow, intuition-based theoretical considerations or experimental serendipity. Here,…
The spectral form factor is believed to exhibit a special type of behavior called ``dip-ramp-plateau'' in chaotic quantum systems that originates from random matrix theory. This suggests that the shape of the spectral form factor could…
In cognitive radio (CR) technology, the trend of sensing is no longer to only detect the presence of active primary users. A large number of applications demand for more comprehensive knowledge on primary user behaviors in spatial,…
In modern large-scale observational studies, data collection constraints often result in partially labeled datasets, posing challenges for reliable causal inference, especially due to potential labeling bias and relatively small size of the…
H-EFT-VA established a physics-informed solution to the Barren Plateau (BP) problem via a hierarchical EFT UV-cutoff, guaranteeing gradient variance in Omega(1/poly(N)). However, localization restricts the ansatz to a polynomial subspace,…
In this article, the model presented by Shen and Pierre to investigate the transverse vibration behavior of a simply supported beam has been revised. This is done by applying more realistic assumptions. The crack is modeled as a continuous…
Experiments in online platforms frequently suffer from network interference, in which a treatment applied to a given unit affects outcomes for other units connected via the platform. This SUTVA violation biases naive approaches to…