We show that the moment explosion time in the rough Heston model [El Euch, Rosenbaum 2016, arxiv:1609.02108] is finite if and only if it is finite for the classical Heston model. Upper and lower bounds for the explosion time are established, as well as an algorithm to compute the explosion time (under some restrictions…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,786 papers · 148 categories
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48 results for “State Space Explosion”
Structured State-Space Duality connects SSMs to masked attention.
problem Connecting SSMs and attention mechanisms for efficient modeling.
method Formalizing and generalizing SSD from scalar-identity to diagonal state matrices.
result Diagonal SSMs match training complexity lower bounds and support richer dynamics.
Bayesian model improves categorization of explosions from sparse data.
problem Challenges in categorizing explosions from limited data.
method Bayesian update to Event Categorization Matrix model with Bayesian Decision Theory.
result Consistent gains in overall accuracy and lower false negative rates.
We prove that the quotient space of a variationally complete group action is a good Riemannian orbifold. The result is generalized to singular Riemannian foliations without horizontal conjugate points.
Study on martingale property and moment explosions in signature volatility models.
problem Analyzing the martingale property and moment explosions in signature volatility models.
method Fine analysis of the explosion time of a signature stochastic differential equation.
result The price process is a true martingale if and only if the order of the linear form is odd and a correlation parameter is negative.
Transformer model estimates keywords for better audio captioning.
problem Indeterminacy in word selection for audio events/scenes.
method Transformer-based model with keyword estimation.
result Achieved state-of-the-art performance in AAC.
Deep RL solves combinatorial selection problems with large item spaces.
problem Solving MDPs with large state and action spaces, especially for combinatorial selection.
method Convert S-MDP to IS-MDP, use weight-shared Q-networks to manage state space explosion.
result Our approach effectively handles large item spaces and scales to diverse environments.
BatchNorm helps train quantized networks by avoiding gradient explosion.
problem Training quantized neural networks is difficult due to gradient issues.
method Investigated the impact of BatchNorm on both full-precision and quantized networks.
result BatchNorm avoids gradient explosion in quantized networks, contrary to expectations.
The search for higher-order feature interactions that are statistically significantly associated with a class variable is of high relevance in fields such as Genetics or Healthcare, but the combinatorial explosion of the candidate space makes this problem extremely challenging in terms of computational efficiency and p…
We study the problem of non-explosion of diffusion processes on a manifold with time-dependent Riemannian metric. In particular we obtain that Brownian motion cannot explode in finite time if the metric evolves under backwards Ricci flow. Our result makes it possible to remove the assumption of non-explosion in the pat…
We study the explosion of the solutions of the SDE in the quasi-Gaussian HJM model with a CEV-type volatility. The quasi-Gaussian HJM models are a popular approach for modeling the dynamics of the yield curve. This is due to their low dimensional Markovian representation which simplifies their numerical implementation …
Affine Processesmath.PR
We put forward a complete theory on moment explosion for fairly general state-spaces. This includes a characterization of the validity of the affine transform formula in terms of minimal solutions of a system of generalized Riccati differential equations. Also, we characterize the class of positive semidefinite process…
Lipschitz normalization boosts deep attention models, especially for graph neural networks.
problem Gradient explosion in deep graph attention networks leads to poor performance.
method Enforcing Lipschitz continuity by normalizing attention scores.
result Deep GAT models with LipschitzNorm achieve state-of-the-art results for tasks with long-range dependencies.
Noise injection before gradient steps helps in regularization for neural networks.
problem Improving generalization in overparametrized neural networks.
method Injecting small noise perturbations before computing gradient steps, especially in layer-wise fashion.
result Small noise perturbations can explicitly regularize neural networks without variance explosion.
The last few years have seen an explosion of academic and popular interest in algorithmic fairness. Despite this interest and the volume and velocity of work that has been produced recently, the fundamental science of fairness in machine learning is still in a nascent state. In March 2018, we convened a group of expert…
The randomised Heston modelq-fin.PR
We propose a randomised version of the Heston model-a widely used stochastic volatility model in mathematical finance-assuming that the starting point of the variance process is a random variable. In such a system, we study the small-and large-time behaviours of the implied volatility, and show that the proposed random…
Gaussian stochastic volatility models: Scaling regimes, large deviations, and moment explosionsq-fin.MF
In this paper, we establish sample path large and moderate deviation principles for log-price processes in Gaussian stochastic volatility models, and study the asymptotic behavior of exit probabilities, call pricing functions, and the implied volatility. In addition, we prove that if the volatility function in an uncor…
Study of stochastic differential equations on non-compact manifolds, solving open problem on strong completeness.
problem Open problem on strong completeness of SDEs on non-compact spaces.
method Systematic study of stochastic differential equations, solving open problem on strong completeness.
result Existence of global smooth solution flow of SDEs on R^n, including substantial growth of coefficients.
We determine the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a Robertson-Walker space-time. We prove in particular that when approaching the explosion time of the diffusion, its projection on the base manifold almost surely converges to a random point of the …
Generative model learns spin-glass dynamics and properties.
problem Complex behavior of many-body systems in statistical physics and computer science.
method Self-supervised learning with normalizing flows.
result Key physical and computational properties of spin-glasses are learned.
SCOPE-FE improves feature engineering efficiency for high-dimensional datasets.
problem Expanding and reducing feature space in tabular learning becomes computationally expensive with increased dimensionality.
method SCOPE-FE controls the search space by regulating operator and feature-pair spaces, using OperatorProbing and FeatureClustering.
result SCOPE-FE reduces feature engineering time while maintaining competitive predictive performance.
CoTj improves diffusion model quality and stability via graph planning.
problem Rigidity in diffusion models due to high-dimensional state space.
method Chain-of-Trajectories (CoTj) framework using Diffusion DNA for graph planning.
result CoTj discovers context-aware trajectories improving output quality and stability.
Stringy orbifoldsmath.AG
Recently, there is an explosive growth of activities to understand stringy properties of orbifolds. In this article, we survey some of recent developments.
Quasi-Gaussian HJM models are a popular approach for modeling the dynamics of the yield curve. This is due to their low dimensional Markovian representation, which greatly simplifies their numerical implementation. We present a qualitative study of the solutions of the quasi-Gaussian log-normal HJM model. Using a small…
We consider Markov Decision Problems defined over continuous state and action spaces, where an autonomous agent seeks to learn a map from its states to actions so as to maximize its long-term discounted accumulation of rewards. We address this problem by considering Bellman's optimality equation defined over action-val…
Finding statistically significant interactions between binary variables is computationally and statistically challenging in high-dimensional settings, due to the combinatorial explosion in the number of hypotheses. Terada et al. recently showed how to elegantly address this multiple testing problem by excluding non-tes…
VIX options in the SABR modelq-fin.PR
Study on VIX options pricing in SABR model, showing infinite prices due to volatility explosion.
problem Infinite VIX futures and call prices due to volatility explosion in SABR model.
method Analyzing SABR model, showing as unique solution to diffusion process, proving explosion using Feller test, proposing capped volatility process.
result VIX futures and call prices are infinite for any maturity due to volatility explosion, but capped volatility process mitigates this issue.
RestoreAI predicts landmine risk from patterns, improving clearance efficiency.
problem Predicting landmine risk from spatial patterns to enhance clearance efficiency.
method RestoreAI uses landmine patterns for risk prediction, implementing three deminers: linear, curved, and Bayesian.
result RestoreAI significantly boosts clearance efficiency, achieving a 14.37 percentage point increase in cleared landmines per timestep.
We conduct mathematical analysis on the effect of batch normalization (BN) on gradient backpropogation in residual network training, which is believed to play a critical role in addressing the gradient vanishing/explosion problem, in this work. By analyzing the mean and variance behavior of the input and the gradient i…
We present transductive Boltzmann machines (TBMs), which firstly achieve transductive learning of the Gibbs distribution. While exact learning of the Gibbs distribution is impossible by the family of existing Boltzmann machines due to combinatorial explosion of the sample space, TBMs overcome the problem by adaptively …
Constraint-based causal discovery from limited data is a notoriously difficult challenge due to the many borderline independence test decisions. Several approaches to improve the reliability of the predictions by exploiting redundancy in the independence information have been proposed recently. Though promising, existi…
Intelligent Transportation Systems (ITSs) are envisioned to play a critical role in improving traffic flow and reducing congestion, which is a pervasive issue impacting urban areas around the globe. Rapidly advancing vehicular communication and edge cloud computation technologies provide key enablers for smart traffic …
Using unitary (instead of general) matrices in artificial neural networks (ANNs) is a promising way to solve the gradient explosion/vanishing problem, as well as to enable ANNs to learn long-term correlations in the data. This approach appears particularly promising for Recurrent Neural Networks (RNNs). In this work, w…
Wide-band Electromagnetic Induction Sensors (WEMI) have been used for a number of years in subsurface detection of explosive hazards. While WEMI sensors have proven effective at localizing objects exhibiting large magnetic responses, detecting objects lacking or containing very low amounts of conductive materials can b…
This paper investigates optimal consumption in the stochastic Ramsey problem with the Cobb-Douglas production function. Contrary to prior studies, we allow for general consumption processes, without any a priori boundedness constraint. A non-standard stochastic differential equation, with neither Lipschitz continuity n…
In the LIBOR market model, forward interest rates are log-normal under their respective forward measures. This note shows that their distributions under the other forward measures of the tenor structure have approximately log-normal tails.
We present a number of related comparison results, which allow to compare moment explosion times, moment generating functions and critical moments between rough and non-rough Heston models of stochastic volatility. All results are based on a comparison principle for certain non-linear Volterra integral equations. Our u…
We consider a class of asset pricing models, where the risk-neutral joint process of log-price and its stochastic variance is an affine process in the sense of Duffie, Filipovic and Schachermayer [2003]. First we obtain conditions for the price process to be conservative and a martingale. Then we present some results o…
Framework detects and ranks suspicious market manipulation using temporal convolutions and expert assessment.
problem Detecting and deterring rogue agents in financial markets.
method Weakly supervised learning, expert assessment, similarity search.
result Promising preliminary results in detecting and ranking suspicious market manipulation.
AxCell automates results extraction from machine learning papers.
problem Difficulty in tracking progress in machine learning due to many papers.
method AxCell uses table segmentation and learns structural knowledge to extract results.
result AxCell significantly improves results extraction compared to existing methods.
The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function defined over the nodes of a network. This work presents a versatile kernel-base…
A high-order recombination algorithm for weak approximation of stochastic differential equationsmath.PR
Paper develops a high-order recombination algorithm for financial modeling.
problem Creating accurate approximations of stochastic differential equations in finance.
method High-order recombination method applied to practical financial problems.
result Algorithm effectively avoids explosive growth in support cardinality for high-order approximations.
Ripple Walk Training: A Subgraph-based training framework for Large and Deep Graph Neural Networkcs.LG
Ripple Walk Training tackles graph neural network training issues for large and deep graphs.
problem Neighbors explosion, node dependence, and oversmoothing in large and deep GNNs.
method Subgraph-based training framework with Ripple Walk Sampler for high-quality subgraph sampling.
result RWT improves training efficiency and reduces space complexity for deep and large GNNs.
We propose a K-sparse exhaustive search (ES-K) method and a K-sparse approximate exhaustive search method (AES-K) for selecting variables in linear regression. With these methods, K-sparse combinations of variables are tested exhaustively assuming that the optimal combination of explanatory variables is K-sparse. By co…
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…
SDIFT generates full-field dynamics from sparse, irregular data.
problem Modeling and reconstructing physical dynamics from sparse, off-grid observations.
method SDIFT uses a functional Tucker model and sequential diffusion for generating full-field evolution from irregular sparse observations.
result Significant improvements in reconstruction accuracy and computational efficiency compared to state-of-the-art approaches.
This paper presents a novel one-factor stochastic volatility model where the instantaneous volatility of the asset log-return is a diffusion with a quadratic drift and a linear dispersion function. The instantaneous volatility mean reverts around a constant level, with a speed of mean reversion that is affine in the in…
Smart city surveillance benefits from sound event recognition.
problem Improving monitoring capabilities in smart cities.
method Exploration of several classifiers on the SESA dataset.
result SGD achieved 72.13% accuracy in sound event recognition.