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Quantum noise limits the sensitivity of precision measurement devices, such as laser interferometer gravitational-wave observatories and axion detectors. In the shot-noise-limited regime, these resonant detectors are subject to a trade-off…
The most promising concept for low frequency gravitational wave observatories are laser interferometric detectors in space. It is usually assumed that the noise floor for such a detector is dominated by optical shot noise in the signal…
Quasi-Newton methods are widely used in practise for convex loss minimization problems. These methods exhibit good empirical performance on a wide variety of tasks and enjoy super-linear convergence to the optimal solution. For large-scale…
The astrophysical reach of current and future ground-based gravitational-wave detectors is mostly limited by quantum noise, induced by vacuum fluctuations entering the detector output port. The replacement of this ordinary vacuum field with…
Second-order information -- such as curvature or data covariance -- is critical for optimisation, diagnostics, and robustness. However, in many modern settings, only the gradients are observable. We show that the gradients alone can reveal…
We study the robustness of accelerated first-order algorithms to stochastic uncertainties in gradient evaluation. Specifically, for unconstrained, smooth, strongly convex optimization problems, we examine the mean-squared error in the…
The recent discovery of merging black holes suggests that a stochastic gravitational-wave background is within reach of the advanced detector network operating at design sensitivity. However, correlated magnetic noise from Schumann…
Quantum advantage requires overcoming noise-induced degradation of quantum systems. Conventional methods for reducing noise such as error mitigation face scalability issues in deep circuits. Specifically, noise hampers the extraction of…
We present a theoretical background for the data analysis of the gravitational-wave signals from spinning neutron stars for Earth-based laser interferometric detectors. We introduce a detailed model of the signal including both the…
Theoretical analysis of the error landscape of deep neural networks has garnered significant interest in recent years. In this work, we theoretically study the importance of noise in the trajectories of gradient descent towards optimal…
Motivated by a recently-invented scheme of displacement-noise-free gravitational-wave detection, we demonstrate the existence of gravitational-wave detection schemes insusceptible to both displacement and timing (laser) noises, and are thus…
We consider stochastic zeroth-order optimization over Riemannian submanifolds embedded in Euclidean space, where the task is to solve Riemannian optimization problem with only noisy objective function evaluations. Towards this, our main…
Deep neural networks provide state-of-the-art performance for image denoising, where the goal is to recover a near noise-free image from a noisy observation. The underlying principle is that neural networks trained on large datasets have…
The choice of batch-size in a stochastic optimization algorithm plays a substantial role for both optimization and generalization. Increasing the batch-size used typically improves optimization but degrades generalization. To address the…
Gravitational wave detectors from the advanced generation onwards are expected to be limited in sensitivity by thermal noise of the optics, making the reduction of this noise a key factor in the success of such detectors. A proposed method…
Gradient Smoothing is an efficient approach to reducing noise in gradient-based model explanation method. SmoothGrad adds Gaussian noise to mitigate much of these noise. However, the crucial hyper-parameter in this method, the variance…
Stochastic gradient descent (SGD) forms the core optimization method for deep neural networks. While some theoretical progress has been made, it still remains unclear why SGD leads the learning dynamics in overparameterized networks to…
Interferometers with kilometer-scale arms have been built for gravitational-wave detections on the ground; ones with much longer arms are being planned for space-based detection. One fundamental motivation for long baseline interferometry…
Stochastic gradient descent (SGD) still is the workhorse for many practical problems. However, it converges slow, and can be difficult to tune. It is possible to precondition SGD to accelerate its convergence remarkably. But many attempts…
The representation of functions by artificial neural networks depends on a large number of parameters in a non-linear fashion. Suitable parameters of these are found by minimizing a 'loss functional', typically by stochastic gradient…