Machine learning classifies topological phases in leaky photonic lattices.
problem Classifying topological phases in leaky photonic lattices using limited data.
method A fully connected neural network trained on bulk intensity measurements.
result Accurate determination of topological properties from intensity distributions.
Study on black holes and photon surfaces in 4D spacetimes, proving uniqueness theorems.
problem Uniqueness of black hole and photon surfaces in 4D spacetimes.
method Potential theory approach, self-contained proofs for known and new cases.
result Proves new results for connected photon spheres and photon surfaces in the extremal case, and super-extremal case.
Restricted Boltzmann Machine (RBM) is a bipartite graphical model that is used as the building block in energy-based deep generative models. Due to numerical stability and quantifiability of the likelihood, RBM is commonly used with Bernoulli units. Here, we consider an alternative member of exponential family RBM with…
The paper characterizes photon surfaces in static spacetimes and proves their uniqueness.
problem Characterizing and proving uniqueness of photon surfaces in static spacetimes.
method Local characterization and proof of uniqueness using specific spacetime properties.
result Static, vacuum, asymptotically isotropic spacetimes with equipotential photon surfaces are isometric to Schwarzschild spacetime.
Characterizes photon surfaces in static spacetimes, proving uniqueness.
problem Understanding photon surfaces in static spacetimes of arbitrary dimension.
method Complete characterization and new insights into spacetime geometry.
result Proves uniqueness of certain electrostatic spacetimes.
New insights into how linear classifiers and leaky ReLU networks can overfit without harming generalization.
problem Understanding conditions for benign overfitting in linear classifiers and leaky ReLU networks.
method Utilizing Karush--Kuhn--Tucker (KKT) conditions for margin maximization.
result Satisfaction of KKT conditions leads to benign overfitting in linear classifiers and leaky ReLU networks.
Derives exact gradients for linear optics with single photons.
problem Gradient estimation for linear optics with single photons.
method Generalized parameter shift rule for linear optics.
result Derives analytical formula for gradients in linear optics.
Paper proves uniqueness of black holes and photon surfaces in higher dimensions.
problem Proving uniqueness of static vacuum black holes and photon surfaces in higher dimensions.
method Combining and generalizing techniques from previous works by Müller zum Hagen, Robinson, and Seifert, the authors prove geometric inequalities for connected (n+1)-dimensional spacetimes.
result Recovering and extending known uniqueness results for black holes and photon surfaces in higher dimensions.
In a recent paper the first author established the uniqueness of photon spheres, suitably defined, in static vacuum asymptotically flat spacetimes by adapting Israel's proof of static black hole uniqueness. In this note we establish uniqueness of photon spheres by adapting the argument of Bunting and Masood-ul-Alam, wh…
The paper simplifies FLRW photon propagators using geometric embeddings.
problem Understanding Friedmann-Lemaître-Robertson-Walker (FLRW) spaces.
method Differential-geometric methods applied to FLRW spaces as submanifolds in \(\mathbb{R}^{n+2}\).
result New and simplified expressions for the photon propagator in four dimensions.
Photonic quantum reinforcement learning for control problems.
problem Solving continuous control problems with noisy quantum computers.
method Proximal policy optimization for photonic variational quantum agents.
result Photonic policy learning achieves comparable performance to classical neural networks.
Uniqueness proven for photon spheres in higher-dimensional spacetimes.
problem Proving uniqueness of photon spheres in higher-dimensional electrovacuum spacetimes.
method Combining ideas from earlier works with newer techniques.
result Proven uniqueness of subextremal Reissner-Nordström manifolds with positive mass.
Enhances quantum machine learning models using Fock states.
problem Data-embedding bottleneck in quantum machine learning.
method Photonic-based bosonic data-encoding scheme in Fock space.
result Controlled expressive power via photon number.
Paper finds conditions for benign overfitting in neural networks.
problem Benign overfitting in leaky ReLU two-layer neural networks.
method Established directional convergence and classification error bounds.
result Benign overfitting occurs with high probability on mixture data.
Study improves chiral photonic metasurface design using neural networks and genetic algorithms.
problem Optimizing chiral photonic metasurfaces for high chiral dichroism and reflectivity.
method Combines neural network and genetic algorithm approaches with improved fitness functions and data augmentation.
result Demonstrates a significant increase in chiral dichroism and reflectivity.
New proofs of unique photon surfaces in 4D spacetimes, extending previous work.
problem Proving uniqueness of photon surfaces in 4D static vacuum spacetimes.
method Different proofs based on black hole uniqueness and Willmore inequality.
result Partial proof of Willmore inequality in 3D.
We study the set of trapped photons of a subcritical (a<M) Kerr spacetime as a subset of the phase space. First, we present an explicit proof that the photons of constant Boyer--Lindquist coordinate radius are the only photons in the Kerr exterior region that are trapped in the sense that they stay away both from the h…
Adapting Israel's proof of static black hole uniqueness, we show that the Schwarzschild spacetime is the only static vacuum asymptotically flat spacetime that possesses a suitably defined photon sphere.
Study on benign overfitting in leaky ReLUs with moderate input dimensions.
problem Understanding when overfitting is beneficial in neural networks.
method Two-layer leaky ReLU networks trained with hinge loss, considering signal-to-noise ratio.
result Characterization of conditions for benign overfitting based on signal-to-noise ratio.
Photonic chip speeds up option pricing with GAN for financial efficiency.
problem Bottleneck in classical computing limits financial industry development.
method Unary approach, photonic chip, quantum amplitude estimation, GAN for asset distribution.
result Quadratic speedup over classical Monte Carlo methods.
In a recent paper, the authors established the uniqueness of photon spheres in static vacuum asymptotically flat spacetimes by adapting Bunting and Masood-ul-Alam's proof of static vacuum black hole uniqueness. Here, we establish uniqueness of suitably defined sub-extremal photon spheres in static electro-vacuum asympt…
Unified framework for photon and massive particle hypersurfaces in stationary spacetimes.
problem Understanding photon and massive particle hypersurfaces in stationary spacetimes.
method Unified framework using Killing-invariant timelike hypersurfaces and associated Finsler structures.
result Conditions for a hypersurface to be a photon or massive particle hypersurface are established.
Leaky ReLU activations improve the calibration of Bayesian neural networks.
problem Bayesian neural networks struggle with mean-field variational inference for ReLU activations.
method Investigated the effect of activation functions on the calibration of Bayesian neural networks.
result Leaky ReLU activations lead to more Gaussian-like weight posteriors and lower expected calibration error.
Designs chiral photonic structures using machine learning for efficient optical properties.
problem Optimizing chiral photonic nanostructures for light-matter interactions.
method Evolutionary algorithm and neural network approach for rapid optimization.
result Frequency-dependent modification in reflected light's degree of circular polarization.
New methods for uncertainty in neural networks with leaky ReLU activations.
problem Uncertainty in feed-forward neural networks with random input perturbations.
method Analytical expressions for PDF and moments of neural network output, linearization of leaky ReLU, Gaussian copula surrogate models.
result Accurate statistical results for large input perturbations, excellent agreement with Monte Carlo simulations.
Photonic co-processor speeds up training of large neural networks.
problem Training large neural networks with backpropagation is inefficient and communication is a bottleneck.
method Direct Feedback Alignment (DFA) with a photonic accelerator.
result Photonic accelerator can compute random projections with trillions of parameters.
In this paper we investigate the performance of different types of rectified activation functions in convolutional neural network: standard rectified linear unit (ReLU), leaky rectified linear unit (Leaky ReLU), parametric rectified linear unit (PReLU) and a new randomized leaky rectified linear units (RReLU). We evalu…
We propose a method to build quantum memristors in quantum photonic platforms. We firstly design an effective beam splitter, which is tunable in real-time, by means of a Mach-Zehnder-type array with two equal 50:50 beam splitters and a tunable retarder, which allows us to control its reflectivity. Then, we show that th…
New approach confirms Kruskal-Szekeres extension for Schwarzschild spacetime.
problem Confirming the Kruskal-Szekeres extension for Schwarzschild spacetime.
method Reformulating the problem as an ODE and showing the ODE admits a solution if and only if the horizon is non-degenerate.
result Photon surfaces approaching the Killing horizon must necessarily cross it.
Study on feature learning in Leaky ResNets, explaining bottleneck structure.
problem Understanding feature learning in deep neural networks.
method Lagrangian and Hamiltonian reformulation of representation geodesics.
result Emergence of a bottleneck structure in large effective depth networks.
Gradient descent biases towards stable rank networks for nearly-orthogonal data.
problem Understanding implicit bias in non-smooth neural networks trained by gradient descent.
method Analysis of two-layer ReLU and leaky ReLU networks trained by gradient descent on nearly-orthogonal data.
result Gradient descent biases towards networks with stable rank and uniform margin for nearly-orthogonal data.
Quantum computing at room temperature achieves high accuracy in image classification.
problem Classifying images with single photons at room temperature.
method Optical transformation of quantum state to exploit interference and entanglement.
result Theoretical accuracy of 41.27% for MNIST and 36.14% for Fashion-MNIST.
Proves a Minkowski inequality for static Einstein-Maxwell space-time.
problem Understanding the photon sphere in static Einstein-Maxwell space-time.
method Inverse mean curvature flow (IMCF) approach.
result Proves a Minkowski-like inequality for asymptotically flat static Einstein-Maxwell space-time.
Detecting a change point is a crucial task in statistics that has been recently extended to the quantum realm. A source state generator that emits a series of single photons in a default state suffers an alteration at some point and starts to emit photons in a mutated state. The problem consists in identifying the poin…
This paper investigates the effect of leak in spiking neural networks.
problem Comparative analysis of leaky and non-leaky spiking neuron models.
method Experimental and frequency domain analysis of spiking neural networks.
result Leaky spiking neuron models provide improved robustness and generalization but decrease sparsity of computation.
Active learning method for neural population dynamics using optogenetics.
problem Efficiently selecting neurons to stimulate for identifying neural population dynamics.
method Developed active learning procedure for low-rank regression to determine informative photostimulation patterns.
result Demonstrated a two-fold reduction in data required for predictive power using low-rank linear dynamical systems model.
GKP codes connect quantum gates to algebraic curves, enabling fault-tolerant quantum computation.
problem Implementing fault-tolerant quantum computation in quantum harmonic oscillator systems.
method Exploring the topological and algebraic structure of GKP codes, showing how gates correspond to symplectic automorphisms and mapping class groups of surfaces.
result GKP Clifford gates are identified with symplectic automorphisms of GKP lattices and mapping class groups of surfaces, providing a topological interpretation of fault tolerance.
The paper extends IPC framework to stationary physical systems and validates it with a photonic system.
problem Characterizing the computational capabilities of stationary physical systems in a principled, data-efficient way.
method Extended IPC framework, established fundamental results, derived asymptotic bias, introduced data-efficient estimation methods.
result IPC strongly correlates with machine-learning performance and provides a reliable estimate of system dimensionality.
This study investigates how gradient-based methods bias neural networks trained on high-dimensional data.
problem The implicit biases of gradient-based optimization algorithms in neural networks trained on high-dimensional data.
method Investigation of gradient flow and gradient descent in two-layer fully-connected neural networks with leaky ReLU activations.
result Gradient flow and gradient descent lead to neural networks with low-rank solutions and linear decision boundaries.
New model enhances SPIM for solving low-rank combinatorial optimization and statistical learning problems.
problem Solving large-scale combinatorial optimization problems efficiently.
method Proposed a new computing model for SPIM that can handle low-rank interaction matrices.
result Demonstrated efficient learning, classification, and sampling of MNIST images using the model.
Study maximal representations of surface groups via pleated surfaces in pseudo-Riemannian space.
problem Maximal representations of surface groups and their geometric properties.
method Introduction of ρ-invariant pleated surfaces and construction of shear cocycles. result Properties of ρ-invariant pleated surfaces, including embeddedness, acausality, and hyperbolic structure. Learning and memory are intertwined in our brain and their relationship is at the core of several recent neural network models. In particular, the Attention-Gated MEmory Tagging model (AuGMEnT) is a reinforcement learning network with an emphasis on biological plausibility of memory dynamics and learning. We find that …
This study uses neural networks to solve interpolation problems with sparse, infinitely wide layers.
problem Exact data interpolation using sparse, infinitely wide neural networks.
method Atomic norm framework to derive convex hulls and equivalent convex formulations.
result Simple characterizations of convex hulls for different constraints on network weights and biases.
Early training of deep neural networks leads to small, directionally converging weights.
problem Training dynamics of deep homogeneous neural networks with small initializations.
method Gradient flow analysis and study of KKT points for neural correlation function.
result Weights converge in direction to KKT points during early training stages.
The paper develops methods for monitoring TPL machine health.
problem Inaccurate and untimely maintenance of TPL systems leads to poor quality and inefficiencies.
method Physics-informed data-driven predictive models integrated with statistical approaches.
result The methods achieve high accuracy across various scenarios and conditions.
oPoW proposes a new PoW algorithm to reduce mining costs and environmental impact.
problem Scalability issues, environmental concerns, and systemic risks in Bitcoin PoW.
method oPoW is a novel PoW algorithm that shifts mining costs from electricity to hardware (CAPEX).
result oPoW reduces mining costs and improves network scalability, decentralization, and issuance.
Study null energy condition impacts on special hypersurfaces in static spacetimes.
problem Effects of null energy condition on totally umbilic hypersurfaces.
method Characterization of embedded surfaces and photon surfaces using Alexandrov Theorem and other methods.
result Full characterization of embedded surfaces with constant spacetime mean curvature.
We apply numerical methods in combination with finite-difference-time-domain (FDTD) simulations to optimize transmission properties of plasmonic mirror color filters using a multi-objective figure of merit over a five-dimensional parameter space by utilizing novel multi-fidelity Gaussian processes approach. We compare …