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.
Develops methods to simulate rare transitions in molecular systems.
problem Rare transitions between metastable states in molecular systems are difficult to study due to limited data.
method Two novel methods: chain-based and midpoint-based approaches.
result Demonstrates effectiveness of methods in both data-rich and data-scarce scenarios.
Develops a flexible model for regime transitions in time series data.
problem Nonlinear and context-dependent regime transitions in time series data.
method Semi-parametric state-space model with learned transition functions.
result Improved recovery of nonlinear transition dynamics and earlier detection of regime changes.
Paper models transition risk using jump-diffusion model to price credit swaps.
problem Capturing transition risk in financial markets.
method Calibrated jump-diffusion model to CDS term structure, using quantile regression.
result Jump-diffusion model captures transition risk, jumps represent green policies.
Study shows Elo models fail to accurately measure transitive strength in competitive games.
problem Elo models fail to correctly identify the transitive component in real-world competitive games.
method Investigated the challenge of identifying the transitive component in games, proposed an extension of the Elo score.
result Disc ranking system assigns two scores: skill and consistency.
Study models forest transitions with deep learning for parameter estimation.
problem Complex dynamics of forest, agricultural, and abandoned lands.
method Developed a stochastic differential equation model and used deep learning for parameter estimation.
result Deep learning approach estimates model parameters from time-series data.
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.
A new method for ILO with transition model disparity using an intermediary policy.
problem Learning tasks from expert observations with different transition dynamics.
method Training an intermediary policy to match the state transitions of the expert dataset.
result Our method outperforms existing ILO approaches with transition model mismatch.
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.
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.
CNN detects phase transitions in Potts models without prior knowledge.
problem Detecting phase transitions in q-state Potts models using deep learning. method Trained a deep CNN on Ising model spin configurations and temperatures, then tested on Potts model images.
result Deep CNN accurately detects phase transitions in Potts models, including high- and low-temperature regions.
A Longitudinal Attribute-Conditioned Neural Network (LANTERN) framework for modeling health-state transition probabilities in irregular longitudinal data.
problem Estimating long-term care transition probabilities in irregular longitudinal health data.
method A neural network that learns from individual health history, incorporates time elapsed, and conditions on demographic and socioeconomic attributes.
result Improves severe disability discrimination and maintains strong calibration.
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…
New model of vague knowledge without strict partitions or transitivity.
problem Standard economic models of information fail to capture real-world vague knowledge.
method Relaxing assumptions of transitivity and partition structure to formalize vague knowledge.
result Vague knowledge can distinguish some states but not partition the state space.
A novel approach models rating transitions using Lie groups and Deep Learning.
problem Modeling rating transitions with geometric properties and stochastic processes.
method Introducing Itô-SDEs on Lie groups, using TimeGAN for calibration, and examining rating matrix properties.
result The geometric approach using Lie groups and Deep Learning generates a good fit for rating transitions.
Neural models learn continuous-time Markov chain transition rates from data.
problem Learning transition rates for complex stochastic systems.
method Neural networks to model nonlinear transition rates from observed data.
result Neural models outperform traditional methods in accuracy.
Develops a new framework for conditional independence.
problem Generalizing previous notions of conditional independence.
method Introduces transition probability spaces and transitional random variables.
result Satisfies all desired relevance relations except symmetry.
The idea of forward rates stems from interest rate theory. It has natural connotations to transition rates in multi-state models. The generalization from the forward mortality rate in a survival model to multi-state models is non-trivial and several definitions have been proposed. We establish a theoretical framework f…
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.
A new method uses deep learning to efficiently sample rare transitions for estimating committor functions.
problem Efficiently sampling rare transitions to estimate committor functions in high-dimensional problems.
method DASTR (Deep Adaptive Sampling on Transition Paths) method using deep generative models.
result Significantly improved accuracy in approximating committor functions through efficient sampling.
In this paper we study how to learn stochastic, multimodal transition dynamics in reinforcement learning (RL) tasks. We focus on evaluating transition function estimation, while we defer planning over this model to future work. Stochasticity is a fundamental property of many task environments. However, discriminative f…
Generative Stochastic Networks (GSNs) have been recently introduced as an alternative to traditional probabilistic modeling: instead of parametrizing the data distribution directly, one parametrizes a transition operator for a Markov chain whose stationary distribution is an estimator of the data generating distributio…
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 …
Proposes a method for approximating transition densities of SDEs driven by gamma processes.
problem Calculating transition densities for SDEs driven by gamma processes.
method Taylor-type approximation and conditional expectation of multiple stochastic integrals.
result Efficiency of the proposed method demonstrated through numerical tests.
At the heart of technology transitions lie complex processes of social and industrial dynamics. The quantitative study of sustainability transitions requires modelling work, which necessitates a theory of technology substitution. Many, if not most, contemporary modelling approaches for future technology pathways overlo…
Faster sampling in discrete diffusion models with predetermined transition time.
problem Efficiency in sampling discrete diffusion models.
method Discrete Non-Markov Diffusion Models (DNDM) with predetermined transition time.
result Significantly reduces the number of function evaluations for faster sampling.
Paper introduces TtT, market-implied transition time, from greenium term structure.
problem Estimating market-implied transition time to a low-carbon economy.
method Develops inference theory for TtT, introduces two stochastic models.
result Combines two-layer analysis for consistent estimation of diffusion parameters.
Deep reinforcement learning finds optimal learning policies for adaptive systems.
problem Finding individualized learning plans for learners with unknown latent traits.
method Formulated as a Markov decision process, applied deep Q-learning with a transition model estimator.
result The algorithm efficiently discovers optimal learning policies with small data sets.
New methods use machine learning to simulate rare transitions in molecular systems.
problem Simulating rare transitions between metastable states in molecular dynamics.
method Generative models and reinforcement learning for importance sampling.
result Efficiently generated transition paths linking metastable states.
New algorithm reduces performance loss in IRL with mismatched transition dynamics.
problem Performance degradation in inverse reinforcement learning due to mismatched transition dynamics.
method Proposed a robust Maximum Causal Entropy (MCE) IRL algorithm leveraging robust reinforcement learning insights.
result Empirically demonstrated stable performance improvement under transition dynamics mismatches.
ISOKANN learns collective variables and effective dynamics for metastable transitions.
problem Understanding metastable transitions in complex molecular systems.
method Integrates Koopman operators with neural networks to extract CVs and effective dynamics.
result Reconstructs coarse-grained kinetics and reproduces transition times across barriers.
Develops M2 model for next-basket recommendation considering user preferences, item popularity, and transition patterns.
problem Next-basket recommendation problem considering user preferences, item popularity, and transition patterns.
method Mixed model with preferences, popularities, and transitions (M2) using ed-Trans for transition patterns among items.
result Significantly outperforms state-of-the-art methods on all datasets in all tasks, with up to 22.1% improvement.
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.
Study shows depth improves generalization in deep learning models.
problem Understanding why and when depth improves generalization in deep learning.
method Implementation-agnostic state-transition model to analyze depth and generalization.
result Identifies geometric and semigroup mechanisms that keep entropy contribution saturated or polynomial, clarifying depth's statistical advantage.
A multi-task GP model tracks time-varying transition probabilities between two states.
problem Tracking time-varying transition probabilities between 'moves' and 'pauses' states.
method Kernel-based multi-task Gaussian Process model with time-variability and constraints.
result Enforces constraints while learning transition probabilities.
We present a representation for describing transition models in complex uncertain domains using relational rules. For any action, a rule selects a set of relevant objects and computes a distribution over properties of just those objects in the resulting state given their properties in the previous state. An iterative g…
Curiosity-Critic improves world model training by focusing on cumulative prediction error.
problem Training world models with intrinsic rewards that consider cumulative prediction error.
method Curiosity-Critic uses a surrogate reward based on the difference between current and asymptotic prediction errors, estimated online by a co-trained critic.
result Curiosity-Critic outperforms other methods in training speed and final world model accuracy.
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…
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.
Modeling poverty transitions in India over 54 years, showing rising but persistent poverty.
problem Understanding and addressing poverty dynamics in India over long periods.
method Stochastic model of Geometric Brownian Motion with reallocation (RGBM).
result Annual poverty transitions are common, but poverty persists, especially among the poorest.
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.
New model for pairwise comparisons without stochastic transitivity.
problem Suboptimal performance of models assuming stochastic transitivity in real-world scenarios.
method Proposes a general family of statistical models using a skew-symmetric matrix.
result Achieves minimax-rate optimality and adapts to data sparsity.
Lecture notes on conifold transitions between Calabi-Yau manifolds.
problem Understanding conifold transitions in complex threefolds.
method Differential geometric approach, focusing on explicit calculations and examples.
result Necessary condition for smoothings of nodal Calabi-Yau threefolds proved.
There are various parametric models for analyzing pairwise comparison data, including the Bradley-Terry-Luce (BTL) and Thurstone models, but their reliance on strong parametric assumptions is limiting. In this work, we study a flexible model for pairwise comparisons, under which the probabilities of outcomes are requir…
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.
In Maslov (2003), a two level model of the occurrence of financial pyramid (bubbles) has been considered. We also considered the mathematical analogy of this model to Bose condensation. In the present paper, we explain why Ponzi schemes and bubbles result in a crisis in real economics. In Maslov (2005), the law of incr…
Deep reinforcement learning has recently shown many impressive successes. However, one major obstacle towards applying such methods to real-world problems is their lack of data-efficiency. To this end, we propose the Bottleneck Simulator: a model-based reinforcement learning method which combines a learned, factorized …
The paper develops ML algorithms for calibrating credit rating transition models for high and low default portfolios.
problem Calibration of credit rating transition models for high and low default portfolios.
method Developed Maximum likelihood (ML) algorithms, including Laplace approximation for high-default portfolios and particle filter with Gaussian process regression for low-default portfolios.
result Both algorithms produce accurate approximations of the likelihood function and ML estimates of model parameters.