arXiv research

Continuous phase transitions identified in Doi-Onsager, noisy transformer, and Hegselmann-Krause models.

Convex solutions to a specific equation are smooth when the phase is smooth enough.

The paper proves optimal smoothness for certain Lagrangian graphs with specific Hölder continuity.

Continuous-time mirror descent solves sparse phase retrieval efficiently.

Minimizing non-convex and high-dimensional objective functions is challenging, especially when training modern deep neural networks. In this paper, a novel approach is proposed which divides the training process into two consecutive phases to obtain better generalization performance: Bayesian sampling and stochastic op…

Study detects signal in financial stock correlations using phase-ordering kinetics.

We construct continuous families of scattering manifolds with the same scattering phase. The manifolds are compactly supported metric perturbations of Euclidean $\mathbf{R}^{n}$ for $n\geq8$. The metric perturbation may have arbitrarily small support.

EP learns like BPTT but with local weight updates.

In this note we prove that reconstruction from magnitudes of frame coefficients (the so called "phase retrieval problem") can be performed using Lipschitz continuous maps. Specifically we show that when the nonlinear analysis map $α:{\mathcal H}\rightarrow\mathbb{R}^m$ is injective, with $(α(x))_k=|<x,f_k>|^2$, where $…

Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time sy…

Statistical mechanics reveals phase transitions in $\varepsilon$-SVR error.

The problem of optimizing unknown costly-to-evaluate functions has been studied for a long time in the context of Bayesian Optimization. Algorithms in this field aim to find the optimizer of the function by asking only a few function evaluations at locations carefully selected based on a posterior model. In this paper,…

Classifies regularity for Lagrangian mean curvature type equations.

Paper tackles sparse phase retrieval with a novel Bayesian approach.

EP algorithm improved for CNNs and real-time learning.

Gradient descent dynamics in neural networks show quenching and activation phases.

We consider the eigenvalue equation for the Laplace-Beltrami operator acting on scalar functions on the non-compact Eguchi-Hanson space. The corresponding differential equation is reducible to a confluent Heun equation with Ince symbol [0,2,1_2]. We construct approximations for the eigenfunctions and their asymptotic s…

Financial markets, being spectacular examples of complex systems, display rich correlation structures among price returns of different assets. The correlation structures change drastically, akin to phase transitions in physical phenomena, as do the influential stocks (leaders) and sectors (communities), during market e…

Gradient descent variants improve phase retrieval accuracy.

PH-VAE models heavy-tailed data with flexible Phase-Type distributions.

The paper establishes pressure gaps for manifolds with flat subtori singularities.

Study coevolutionary trading-agent dynamics in continuous strategies.

PHASE dataset simulates complex social interactions in physical environments.

A learning algorithm optimizes beamforming for holographic transceivers in far-field communication.

Analyzing large X-ray diffraction (XRD) datasets is a key step in high-throughput mapping of the compositional phase diagrams of combinatorial materials libraries. Optimizing and automating this task can help accelerate the process of discovery of materials with novel and desirable properties. Here, we report a new met…

Bayesian theory explains abrupt emergence of copy subcircuit in attention.

Anomalous diffusion in SGD reveals interactions between hyperparameters and Hessian.

Binary encoding enables neural networks to extrapolate periodic functions.

Persistent entropy detects phase transitions in complex systems.

Study phase retrieval under misspecified models using generative priors.

One of the most powerful approaches to imaging at the nanometer or subnanometer length scale is coherent diffraction imaging using X-ray sources. For amorphous (non-crystalline) samples, the raw data can be interpreted as the modulus of the continuous Fourier transform of the unknown object. Making use of prior informa…

Near-optimal sample complexity for phase retrieval with generative priors.

New method SF-AdamW trains large models without decay phases or memory overhead.

Using generating functional and replica techniques, respectively, we study the dynamics and statics of a spherical Minority Game (MG), which in contrast with a spherical MG previously presented in J.Phys A: Math. Gen. 36 11159 (2003) displays a phase with broken ergodicity and dependence of the macroscopic stationary s…

New approach to analyze matrix denoising using gradient flow and fixed point equations.

Improved tabular models learn better from real-world data.

The paper characterizes stochastic incompleteness in Riemannian manifolds.

WSD schedule improves model training efficiency by adapting learning rates dynamically.

The paper analyzes the current state of the world economy and offers a short-term forecast of its development. Our analysis of log-periodic oscillations in the DJIA dynamics suggests that in the second half of 2017 the United States and other more developed countries could experience a new recession, due to the third p…

Paper analyzes LPSA algorithm for constrained optimization, revealing phase transitions and bias-variance trade-offs.

Study phase transitions in noisy transformer dynamics on spheres.

In this paper, we propose to adopt the diffusion approximation tools to study the dynamics of Oja's iteration which is an online stochastic gradient descent method for the principal component analysis. Oja's iteration maintains a running estimate of the true principal component from streaming data and enjoys less tempo…

We prove an existence result for the deformed Hermitian Yang-Mills equation for the full admissible range of the phase parameter, i.e., $\hatθ \in (\fracπ{2},\frac{3π}{2})$, on compact complex three-folds conditioned on a necessary subsolution condition. Our proof hinges on a delicate analysis of a new continuity path …

Paper uses deep reinforcement learning for better control of rocket engines during start-up phases.

This paper proposes a new loss using short-time Fourier transform (STFT) spectra for the aim of training a high-performance neural speech waveform model that predicts raw continuous speech waveform samples directly. Not only amplitude spectra but also phase spectra obtained from generated speech waveforms are used to c…

Let $(X,α)$ be a Kähler manifold of dimension n, and let $[ω] \in H^{1,1}(X,\mathbb{R})$. We study the problem of specifying the Lagrangian phase of $ω$ with respect to $α$, which is described by the nonlinear elliptic equation \[ \sum_{i=1}^{n} \arctan(λ_i)= h(x) \] where $λ_i$ are the eigenvalues of $ω$ with respect …

Study Neumann problem for special Lagrangian type equations.

Paper introduces REED for noncoherent OTA-FL, reducing latency without phase alignment.