arXiv research

Generative diffusion models exhibit phase transitions in statistical mechanics, impacting their performance.

In the Information Bottleneck (IB), when tuning the relative strength between compression and prediction terms, how do the two terms behave, and what's their relationship with the dataset and the learned representation? In this paper, we set out to answer these questions by studying multiple phase transitions in the IB…

We show that for three dimensional gravity with higher genus boundary conditions, if the theory possesses a sufficiently light scalar, there is a second order phase transition where the scalar field condenses. This three dimensional version of the holographic superconducting phase transition occurs even though the pure…

Bayesian theory explains abrupt emergence of copy subcircuit in attention.

This paper proposes a stochastic model using the concept of Markov chains for the inter-state transitions of the millisecond order quasi-stable phase synchronized patterns or synchrostates, found in multi-channel Electroencephalogram (EEG) signals. First and second order transition probability matrices are estimated fo…

Empirical time series of inter-event or waiting times are investigated using a modified Multifractal Detrended Fluctuation Analysis operating on fluctuations of mean detrended dynamics. The core of the extended multifractal analysis is the non-monotonic behavior of the generalized Hurst exponent $h(q)$ -- the fundament…

A neural network model predicts the critical point of the Ising phase transition.

Predicting labels of nodes in a network, such as community memberships or demographic variables, is an important problem with applications in social and biological networks. A recently-discovered phase transition puts fundamental limits on the accuracy of these predictions if we have access only to the network topology…

Modeling financial markets as gas molecules, the paper predicts phase transitions similar to water and steam.

New method identifies common cause in causal insufficiency, revealing complex phase transitions.

New method makes machine learning approximations unbiased and efficient.

New model explains market dynamics with phase transitions and non-linear interactions.

The paper models market crashes as phase transitions, finding dynamic transitions offer better predictions.

Machine learning approximates phase transitions using Fisher information.

We propose convex relaxations for convolutional neural nets with one hidden layer where the output weights are fixed. For convex activation functions such as rectified linear units, the relaxations are convex second order cone programs which can be solved very efficiently. We prove that the relaxation recovers the glob…

If a given behavior of a multi-agent system restricts the phase variable to a invariant manifold, then we define a phase transition as change of physical characteristics such as speed, coordination, and structure. We define such a phase transition as splitting an underlying manifold into two sub-manifolds with distinct…

Diffusion maps help learn complex quantum phase transitions from data.

Double-well transitions are stiffer than minimal surfaces.

Improved robustness in optimization methods using second-order information.

New algorithms handle phase retrieval with rank d measurements, revealing phase transitions.

Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal recovery methods such as $\ell_1$ minimization and nuclear norm minimization are…

Study phase transitions with prescribed mean curvature in Riemannian manifolds.

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

Unsupervised learning is a discipline of machine learning which aims at discovering patterns in big data sets or classifying the data into several categories without being trained explicitly. We show that unsupervised learning techniques can be readily used to identify phases and phases transitions of many body systems…

Descending phase retrieval algorithms show a phase transition with increasing sample complexity.

Clarifies method of phase synchronization for decoupling linear differential equations.

The addition of wealth-attained advantage (WAA) to the Yard-Sale Model (YSM) of asset exchange has been demonstrated to induce wealth condensation. In a model of WAA for which the bias is a continuous function of the wealth difference of the transacting agents, the condensation was shown to arise from a second-order ph…

Study finds phase transition in context-sensitive language model with short-range interactions.

Proves spectra equivalence for Riemannian manifolds.

Deep networks learn features suddenly, akin to a phase transition.

In this paper, we perform statistical segmentation and clustering analysis of the Dow Jones Industrial Average time series between January 1997 and August 2008. Modeling the index movements and log-index movements as stationary Gaussian processes, we find a total of 116 and 119 statistically stationary segments respect…

New model shows natural language exhibits phase transition similar to physics.

High-dimensional random geometry shows phase transitions in various problems.

In this paper we study the phenomenon of phase transitions for the geodesic flow on some geometrically finite negatively curved manifolds. We define a class of potentials going slowly to zero through the cusps of $M$ for which the pressure map exhibits a phase transition. By a careful choice of the metric at the cusp w…

We derive the exact solution of a one-dimensional Markov functional model with log-normally distributed interest rates in discrete time. The model is shown to have two distinct limiting states, corresponding to small and asymptotically large volatilities, respectively. These volatility regimes are separated by a phase …

The classification of phase transitions is a central and challenging task in condensed matter physics. Typically, it relies on the identification of order parameters and the analysis of singularities in the free energy and its derivatives. Here, we propose an alternative framework to identify quantum phase transitions,…

Improved simulation of phase transitions using hierarchical autoregressive networks.

Improved convergence and curvature estimate for parabolic Allen-Cahn equation.

Study shows strong min-max principle for phase transitions.

Framework for multi-scale clustering using phase transitions.

Study phase transitions in shuffled regression problems.

The stability of money value is an important requisite for a functioning economy, yet it critically depends on the actions of participants in the market themselves. Here we model the value of money as a dynamical variable that results from trading between agents. The basic trading scenario can be recast into an Ising t…

The study uses the Merton model to estimate PD and finds a phase transition affecting convergence speed.

Persistent entropy detects phase transitions in complex systems.

In this paper, we study the sensitivity of the spectral clustering based community detection algorithm subject to a Erdos-Renyi type random noise model. We prove phase transitions in community detectability as a function of the external edge connection probability and the noisy edge presence probability under a general…

We fill a void in merging empirical and phenomenological characterisation of the dynamical phase transitions in complex systems by identifying three of them on real-life financial markets. We extract and interpret the empirical, numerical, and semi-analytical evidences for the existence of these phase transitions, by c…

Strong parallels can be drawn between the theory of minimal hypersurfaces and the theory of phase transitions. Borrowing ideas from the former we extend recent results on the regularity of stable phase transition interfaces to the finite Morse index case. As an application we present a PDE-based proof of the celebrated…

CNN detects phase transitions in Potts models without prior knowledge.