A new method uses higher-order Langevin dynamics with critical damping for better generative modeling.
problem Improving generative models using Langevin dynamics with auxiliary variables.
method Introducing higher-order Langevin dynamics with critical damping, providing closed-form solutions.
result Improved generative models with better performance as measured by FID metric.
This paper studies the critical dynamics of random surfaces, focusing on area and genus evolution.
problem Understanding the time evolution of random surfaces and their genus.
method Analyzes the dynamics of area and genus using Cox-Ingersoll-Ross process and critical phenomena.
result The genus of surfaces evolves into two phases: planar surfaces and foamy surfaces.
TOLD++ improves convergence of diffusion models by critically damping the forward transition matrix.
problem Improving the convergence of Denoising Diffusion Probabilistic Models.
method Critically damping the Third-Order Langevin Dynamics (TOLD) forward transition matrix using eigen-analysis.
result TOLD++ converges faster than TOLD, verified on toy and real datasets.
Investigates multifractal scaling in critical dynamics of random surfaces.
problem Analyzing multifractal scaling in critical dynamics of random surfaces.
method Examined multifractal scaling in various conformal field theories on random surfaces.
result Higher moments of time variations of the order parameter exhibit multifractal scaling.
Urban transformations within large and growing metropolitan areas often generate critical dynamics affecting social interactions, transport connectivity and income flow distribution. We develop a statistical-mechanical model of urban transformations, exemplified for Greater Sydney, and derive a thermodynamic descriptio…
The paper connects reflection groups to maps with specific dynamical properties.
problem Understanding the relationship between reflection groups and anti-rational maps.
method Established a correspondence using planar graphs.
result Complete answers to geometric mating problems for anti-rational maps.
We introduce a scalable measure of curvature for analyzing training dynamics of large language models.
problem Analyzing the training dynamics of large language models due to high computational cost of measuring Hessian sharpness.
method We introduce critical sharpness and relative critical sharpness as computationally efficient measures capturing Hessian sharpness phenomena.
result We provide the first demonstration of sharpness phenomena at scale up to 7B parameters.
A new method identifies critical transitions in high-dimensional data.
problem Challenges in identifying critical transitions in high-dimensional time-series data.
method Spatial-temporal Principal Component Analysis (stPCA)
result Identifies tipping points before critical transitions reliably.
In this short note we discuss recent attempts to describe pre-crash market dynamics with analogies from theory of critical phenomena.
Researchers identify critical protein residues using advanced graph theory.
problem Identifying essential residues in proteins for function.
method Learning Random Geometric Graphs (RGG) with Cramer's V correlation and organic thresholding.
result Advanced RGG methods accurately identify critical residues compared to existing techniques.
The paper analyzes SGD in high-dimensional networks, revealing new scaling limits.
problem Understanding SGD dynamics in high-dimensional networks.
method Analyzing the effective dynamics of SGD using recent work on the subject.
result A new correction term emerges at the critical scaling regime, changing the phase diagram.
DyNODE uses neural ODEs to model system dynamics in continuous control tasks.
problem Modeling the dynamics of systems in continuous control tasks.
method Neural Ordinary Differential Equations (ODEs) combined with actor-critic RL.
result DyNODE outperforms standard neural networks in sample efficiency and predictive performance.
We investigated the critical dynamics on the daily Taiwan stock exchange index (TSE) from 1971 to 2005, and the 5-min intraday data from 1996 to 2005. A global persistence exponent θp was defined for non-equilibrium critical phenomena \cite{Janssen,Majumdar}, and describing dynamic behavior in an economic index \c…
The paper classifies contact 3-manifolds with critical metrics and connects entropy to optimization.
problem Classifying contact 3-manifolds with critical metrics and understanding their entropy.
method Critical metrics optimization and entropy analysis.
result Anosov contact metrics' optimization is linked to Reeb dynamics and entropy.
Actor-critic algorithms converge to an ODE as data samples change dynamically.
problem Challenging to mathematically analyze due to non-i.i.d. data samples.
method Proved convergence to an ODE using time rescaling and geometric ergodicity.
result Convergence to the ODE limit and its properties proven.
Given a sub-hyperbolic semi-rational branched covering which is not CLH-equivalent a rational map, it must have the non-empty canonical Thurston obstruction. By using this canonical Thurston obstruction, we decompose this dynamical system in this paper into several sub-dynamical systems. Each of these sub-dynamical sys…
Machine learning detects tipping points in complex systems.
problem Detecting abrupt shifts in complex dynamical systems.
method Equilibrium-informed neural networks (EINNs) trained on candidate equilibrium states.
result EINNs can identify critical thresholds in nonlinear systems.
New framework analyzes SGD dynamics in large samples and dimensions.
problem Analyzing stochastic gradient descent in large-scale settings.
method Inspired by random matrix theory, new framework for fixed stepsize and finite sum settings.
result SGD dynamics become deterministic in the large sample and dimensional limit, governed by a Volterra integral equation.
We study the dynamics of the vector field on an open surface given by the gradient of a Green's function. This dynamical approach enables us to show that this field induces an invariant decomposition of the surface as the union of a disk and a 1-skeleton that encodes the topology of the surface. We analyze the structur…
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.
We show that financial correlations exhibit a non-trivial dynamic behavior. We introduce a simple phenomenological model of a multi-asset financial market, which takes into account the impact of portfolio investment on price dynamics. This captures the fact that correlations determine the optimal portfolio but are affe…
AEA dynamically aggregates ensemble targets for actor-critic learning.
problem Static ensemble aggregation methods struggle with overestimation bias and variance.
method Adaptive Ensemble Aggregation (AEA) dynamically constructs ensemble-based targets.
result AEA converges to optimal variance reduction and maximal Fisher information.
We study the problem of predicting rare critical transition events for a class of slow-fast nonlinear dynamical systems. The state of the system of interest is described by a slow process, whereas a faster process drives its evolution and induces critical transitions. By taking advantage of recent advances in reservoir…
LC-SAC tackles non-stationary dynamics in reinforcement learning.
problem Degradation of deep RL methods in non-stationary environments.
method LC-SAC uses latent context encoders and contrastive loss for dynamic information capture.
result LC-SAC outperforms SAC on environments with drastic dynamics changes.
Riemannian gradient descent escapes some spurious critical points on low-rank matrix manifold.
problem Spurious critical points on the boundary of low-rank matrix manifold.
method Riemannian gradient descent with dynamical low-rank approximation and rescaled gradient flow.
result Riemannian gradient descent escapes some spurious critical points on the boundary of the manifold.
We study the maximum mean discrepancy (MMD) in the context of critical transitions modelled by fast-slow stochastic dynamical systems. We establish a new link between the dynamical theory of critical transitions with the statistical aspects of the MMD. In particular, we show that a formal approximation of the MMD near …
Develops RL for dynamic risk assessment in stochastic optimization.
problem Time-consistent risk assessment in stochastic optimization problems.
method Model-free reinforcement learning with dynamic convex risk measures, time-consistent dynamic programming, policy gradient updates, actor-critic neural network optimization.
result Demonstrates optimal policies for statistical arbitrage, financial hedging, and robot control.
New method evaluates personalized treatment in critical care, robust to death.
problem Truncation by death in critical care makes traditional DTR evaluation ineffective.
method Principal stratification-based approach, focusing on always-survivor value function, with a semiparametrically efficient, multiply robust estimator.
result Demonstrates robustness and efficiency of the method for personalized treatment optimization.
New theory predicts deep neural networks can operate in an extended critical regime without fine-tuning.
problem Understanding the dynamics and computational principles of deep neural networks.
method Combining theories of heavy-tailed random matrices and non-equilibrium statistical physics.
result Deep neural networks can operate in an extended critical regime without fine-tuning parameters.
CARL safely adapts RL agents for safety-critical tasks.
problem Safety hazards in RL for safety-critical tasks.
method CARL combines model-based RL and cautious adaptation.
result CARL achieves higher rewards with fewer failures in safety-critical tasks.
Proves properties of Morse vector fields on compact manifolds.
problem Properties of gradient vector fields of Morse functions.
method Analyzes connectedness of critical points and shrinkage of flow.
result Shows connectedness of critical points through orbits and exponential shrinkage.
Physics-guided reinforcement learning optimizes swimming in turbulent flows.
problem Optimizing swimming efforts to maintain proximity in turbulent environments.
method Physics-informed actor-physicist reinforcement learning algorithm.
result Physics-informed reinforcement learning outperforms standard methods in turbulent flow control.
Motivated by applications in Optimization, Game Theory, and the training of Generative Adversarial Networks, the convergence properties of first order methods in min-max problems have received extensive study. It has been recognized that they may cycle, and there is no good understanding of their limit points when they…
A simple model economy with locally interacting producers and consumers is introduced. When driven by extremal dynamics, the model self-organizes {\em not} to an attractor state, but to an asymptote, on which the economy has a constant rate of deflation, is critical, and exhibits avalanches of activity with power-law d…
New pricing algorithm learns demand curves and optimizes prices in dynamic markets.
problem Dynamic pricing in markets with incomplete demand information and shifting conditions.
method Actor-Critic Information-Directed Pricing (ACIDP) using IDS algorithms and auditing procedures.
result ACIDP outperforms UCB and TS in market environment shifts.
Reinforcement learning, mathematically described by Markov Decision Problems, may be approached either through dynamic programming or policy search. Actor-critic algorithms combine the merits of both approaches by alternating between steps to estimate the value function and policy gradient updates. Due to the fact that…
To make efficient use of limited spectral resources, we in this work propose a deep actor-critic reinforcement learning based framework for dynamic multichannel access. We consider both a single-user case and a scenario in which multiple users attempt to access channels simultaneously. We employ the proposed framework …
The study of Reeb dynamics on contact manifolds without periodic orbits.
problem Existence of periodic Reeb orbits on bm-contact manifolds. method Generalization of the Weinstein conjecture, proof of periodic orbits, existence of traps.
result In dimension 3, there are infinitely many periodic orbits on the critical set.
We consider the static and dynamic models of Cournot duopoly with tax evasion. In the dynamic model we introduce the time delay and we analyze the local stability of the stationary state. There is a critical value of the delay when the Hopf bifurcation occurs.
Proposes a new framework for risk-sensitive RL using deep nets.
problem Risk-sensitive reinforcement learning problems.
method Conditional elicitability, scoring functions, deep neural networks.
result Dynamic spectral risk measures can be approximated by deep nets.
General equilibrium is the dominant theoretical framework for economic policy analysis at the level of the whole economy. In practice, general equilibrium treats economies as being always in equilibrium, albeit in a sequence of equilibria as driven by external changes in parameters. This view is sometimes defended on t…
Entropy of critical points generalizes Morse theory.
problem Extending Morse theory to group actions.
method Entropy of homologically detectable critical points.
result Entropy lower bound on critical points.
Model criticism is usually carried out by assessing if replicated data generated under the fitted model looks similar to the observed data, see e.g. Gelman, Carlin, Stern, and Rubin [2004, p. 165]. This paper presents a method for latent variable models by pulling back the data into the space of latent variables, and c…
Gradient flow in phase retrieval escapes spurious minima with high probability.
problem Understanding gradient-based optimization in high-dimensional non-convex functions.
method Analytical and numerical study of gradient dynamics in phase retrieval.
result Gradient flow avoids spurious minima by drifting along unstable directions.
Constructs initial data leading to apparent horizons and tests Penrose Inequality.
problem Testing Penrose Inequality in dynamical spacetimes.
method Scale critical initial data for Einstein vacuum system, constructing Cauchy data.
result Penrose Inequality holds in an open region of the future of initial data.
Paper uses DDPG to learn optimal execution strategies in dynamic markets.
problem Learning non-Markovian optimal execution strategies in dynamic financial markets.
method Introduces a novel actor-critic algorithm based on DDPG for transient price impact modeling.
result Successfully approximates optimal execution strategy through numerical experiments.
High-dimensional SGD limits show surprising dynamics and phase transitions.
problem Understanding SGD in high dimensions and its scaling limits.
method Proving limit theorems for SGD trajectories in high dimensions, choosing summary statistics, initialization, and step-size.
result Critical scaling regime for step-size, new correction term, and complex diffusive limits.
SGD converges to critical points of normalized margin in late-stage training for homogeneous neural networks.
problem Analyzing the implicit bias of SGD on homogeneous neural networks.
method Interpreting SGD dynamics as an Euler-like discretization of a conservative field flow associated with the normalized classification margin.
result Normalized SGD iterates converge to the set of critical points of the normalized margin at late-stage training.