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…
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48 results for “structural 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 minimization and nuclear norm minimization are…
Descending phase retrieval algorithms show a phase transition with increasing sample complexity.
problem Theoretical limits of descending phase retrieval algorithms.
method Utilizing Random duality theory (RDT), the study develops a generic program to characterize algorithm performance.
result As sample complexity increases, the parametric manifold transitions from multi to single funneling points, leading to a phase transition in algorithm success.
Discovering Phase Transitions with Unsupervised Learningcond-mat.stat-mech
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…
Framework for multi-scale clustering using phase transitions.
problem Clustering datasets with multi-scale structures.
method Cascade of phase transitions in simulated annealing of Expectation-Maximisation algorithm with weighted local covariance.
result Approximation of the number and size of clusters at different scales.
We find numerical and empirical evidence for dynamical, structural and topological phase transitions on the (German) Frankfurt Stock Exchange (FSE) in the temporal vicinity of the worldwide financial crash. Using the Minimal Spanning Tree (MST) technique, a particularly useful canonical tool of the graph theory, two tr…
Aggregation and structural phase transitions of semiflexible polymer bundles: a braided circuit topology approachcond-mat.soft
A new approach uses circuit topology to study complex polymer interactions.
problem Understanding structural phase transitions in entangled polymer systems.
method Braided circuit topology framework for multiple-chain systems.
result Circuit topological motif fractions are effective order parameters for structural transitions.
Stability of money: Phase transitions in an Ising economycond-mat.stat-mech
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…
New model shows natural language exhibits phase transition similar to physics.
problem Understanding critical properties in natural language models.
method Created a context-sensitive random language model.
result Demonstrated a Berezinskii--Kosterlitz--Thouless phase transition.
The paper models market crashes as phase transitions, finding dynamic transitions offer better predictions.
problem Understanding and predicting extreme financial events like market crashes.
method Employing phase transition theory, focusing on endogenous crashes, and comparing DPT, CPT, and SPT.
result Dynamic phase transitions provide more accurate predictions of market crashes compared to critical and stochastic models.
Machine learning approximates phase transitions using Fisher information.
problem Understanding phase transitions from data using machine learning.
method Information geometry and Fisher information.
result Machine learning indicators approximate the square root of Fisher information.
Optimal spectral method found for inhomogeneous spiked Wigner model.
problem Structured noise in learning scenarios.
method Random matrix theory and spectral analysis.
result Optimal threshold for phase transition in block-structured Wigner model.
Diffusion maps help learn complex quantum phase transitions from data.
problem Learning quantum phase transitions from experimental data is challenging.
method Diffusion maps for nonlinear dimensionality reduction and spectral clustering.
result Diffusion maps can learn complex phase transitions unsupervised.
Double-well transitions are stiffer than minimal surfaces.
problem Rigidity of double-well phase transitions compared to minimal hypersurfaces.
method Comparison of rigidity properties between double-well phase transitions and minimal hypersurfaces.
result Double-well phase transitions exhibit more rigidity than minimal hypersurfaces.
Diffusion models reveal a phase transition in reconstructing high-level features.
problem Understanding the hierarchical structure of natural data.
method Study of hierarchical generative models of data using diffusion models.
result The backward diffusion process shows a phase transition at a threshold time, where high-level features suddenly drop in reconstructibility.
New algorithms handle phase retrieval with rank d measurements, revealing phase transitions.
problem Phase retrieval with rank d measurements.
method Random duality theory (RDT) and descending phase retrieval algorithms (dPR).
result Minimal sample complexity ratio for dPR's success exhibits phase transitions.
Study on detecting hierarchical community structures in networks.
problem Detecting hierarchical community structures in networks.
method Analysis of planted hierarchies of partitions in networks, identifying additional detectability phases.
result There are additional phases in which the presence of multiple consistent partitions can either help or hinder detection of hierarchical structures.
New insights into neural networks reveal unexpected phase transitions.
problem Understanding how overparameterized neural networks learn and generalize.
method Statistical physics of disordered systems applied to non-convex binary neural networks.
result Atypical phase transitions lead to better generalization in neural networks.
Bayesian theory explains abrupt emergence of copy subcircuit in attention.
problem Understanding the abrupt emergence of the copy subcircuit in attention during training.
method Deriving a closed-form posterior over the attention matrix and reducing it to a low-dimensional order parameter space.
result Derive a phase transition in the amount of training data.
Study phase transitions with prescribed mean curvature in Riemannian manifolds.
problem Understanding phase transitions with prescribed mean curvature in geometric settings.
method Analyzing solutions to inhomogeneous semilinear elliptic PDEs, establishing bounds and asymptotics.
result Established upper and lower bounds for eigenvalues of phase transition problems.
The paper studies phase transitions in Information Bottleneck for representation learning.
problem Understanding the behavior of compression and prediction terms in IB objective.
method Studied phase transitions in IB objective using second-order calculus of variations and Fisher information matrix.
result IB phase transitions correspond to learning new classes and are related to maximum correlation between input and target orthogonal to the learned representation.
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…
Continuous phase transitions identified in Doi-Onsager, noisy transformer, and Hegselmann-Krause models.
problem Phase transitions in multimodal models and their properties.
method Sharp coercivity estimate and constrained Lebedev--Milin inequality.
result Continuous phase transitions at critical coupling strengths for Doi-Onsager, noisy transformer, and Hegselmann-Krause models.
Optimal spectral initializers impact phase retrieval phase transitions.
problem Understanding the limits of phase retrieval algorithms.
method Developed Random duality theory (RDT) to characterize optimal spectral initializers.
result Optimal spectral initializers can fall into flat regions of the phase retrieval manifold, making phase retrieval difficult.
We study the crash dynamics of the Warsaw Stock Exchange (WSE) by using the Minimal Spanning Tree (MST) networks. We find the transition of the complex network during its evolution from a (hierarchical) power law MST network, representing the stable state of WSE before the recent worldwide financial crash, to a superst…
Paper analyzes latent space geometry in generative models using Fisher information.
problem Understanding the structure of latent spaces in generative models.
method Reconstructs Fisher information metric from generated samples and posterior distribution.
result Reveals fractal structure and abrupt changes in Fisher metric at phase boundaries.
Study finds phase transition in context-sensitive language model with short-range interactions.
problem Understanding phase transitions in language models with short-range interactions.
method Constructed a random language model with short-range interactions and investigated its statistical properties.
result Phase transition occurs in context-sensitive language models with constant context length.
One of the longstanding open problems in spectral graph clustering (SGC) is the so-called model order selection problem: automated selection of the correct number of clusters. This is equivalent to the problem of finding the number of connected components or communities in an undirected graph. We propose automated mode…
Proves spectra equivalence for Riemannian manifolds.
problem Equivalence of Almgren-Pitts and phase-transition half-volume spectra.
method Proof of spectra equivalence for Riemannian manifolds.
result Confirms conjecture about spectra equivalence.
Deep networks learn features suddenly, akin to a phase transition.
problem Understanding sudden feature learning in deep networks.
method Adaptive kernel approach applied to two teacher-student models.
result Feature learning and Grokking are analogous to a first-order phase transition.
This paper is partly based on a lecture delivered by the author at the ERC workshop "Geometric Partial Differential Equations" held in Pisa in September 2012. What is presented here is an expanded version of that lecture.
PLS-SVD struggles with missing data in multimodal datasets, showing a phase transition in performance.
problem Missing data in PLS-SVD for multimodal datasets.
method Replica-symmetric analysis of spiked rectangular random matrices with missing entries.
result PLS-SVD performance transitions from uninformative to informative singular vectors at a critical signal-to-noise threshold.
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…
Study finds a phase transition in flash crashes involving large and liquid stocks.
problem Systemic risk and propagation of shocks in high frequency trading.
method In-depth investigation of co-crashes in high frequency trading.
result Large co-crashes involve mostly illiquid stocks, while small crashes involve a mix of liquid and illiquid stocks.
Aspects of a phase transition in high-dimensional random geometrycond-mat.stat-mech
High-dimensional random geometry shows phase transitions in various problems.
problem Phase transitions in high-dimensional random geometry.
method Analysis of various financial, optimization, and ecological problems.
result Links between seemingly distant fields and further ramifications.
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 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 …
Unveiling phase transitions with machine learningcond-mat.str-el
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.
problem Simulating phase transitions in complex systems.
method Hierarchical Autoregressive Neural (HAN) network sampling algorithm.
result Significant improvement in statistical uncertainty compared to the Wolff cluster algorithm.
Generative diffusion models exhibit phase transitions in statistical mechanics, impacting their performance.
problem Understanding the performance and capabilities of generative diffusion models.
method Reformulating generative diffusion models using statistical mechanics, focusing on phase transitions and symmetry breaking.
result Generative diffusion models undergo second-order phase transitions with mean-field universality, critical instability, and mean-field critical exponents.
Study shows strong min-max principle for phase transitions.
problem Understanding nodal sets near minimal hypersurfaces.
method Analogous to White's principle, applies to Allen-Cahn energy.
result Strong min-max principle for phase transitions.
We consider the classical stochastic multi-armed bandit problem with a constraint that limits the total cost incurred by switching between actions to be no larger than a given switching budget. For this problem, we prove matching upper and lower bounds on the optimal (i.e., minimax) regret, and provide efficient rate-o…
Study phase transitions in shuffled regression problems.
problem Phase transitions in shuffled regression problems.
method Transformed permutation recovery into probabilistic graphical model, used message passing (MP) algorithm and branching random walk process.
result Characterized impact of signal-to-noise-ratio ($\snr$) on permutation recovery, proposed Gaussian approximation method.
The study uses the Merton model to estimate PD and finds a phase transition affecting convergence speed.
problem Estimating the probability of default (PD) using limited historical data.
method Adopted the Merton model and analyzed phase transitions in default correlation.
result PD estimation converges slowly when temporal correlation decays by power law less than one.
Persistent entropy detects phase transitions in complex systems.
problem Detecting phase transitions in complex systems.
method Established a general theorem for persistent entropy to reliably detect phase transitions, introduced operational framework for finite-time computations.
result Persistent entropy exhibits an asymptotically non-vanishing gap across phases, robust numerical signatures across experiments.
The paper studies dynamical systems with evolving geometric structure using numerical methods.
problem Qualitative behavior of ODEs with varying geometric structure.
method Fourth-order Runge-Kutta scheme for numerical analysis.
result Qualitative transitions in system dynamics as rotation parameter varies.
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…