arXiv research

Characterizes optimal-speed quantum state evolution Hamiltonians.

New method predicts state evolution for non-first-order algorithms on nonconvex problems.

Geometric approach to Dirac operator evolution on spacetimes.

This paper introduces SS-MAMP to address convergence issues in AMP algorithms.

We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum s…

DISCO predicts system states from short trajectories using an evolved operator.

Investigates Q value evolution in Stable Baselines for DQL in simple vs complex environments.

Model financial markets using open quantum systems to understand market imperfections.

Approximate message passing (AMP) refers to a class of efficient algorithms for statistical estimation in high-dimensional problems such as compressed sensing and low-rank matrix estimation. This paper analyzes the performance of AMP in the regime where the problem dimension is large but finite. For concreteness, we co…

Autoregressive state transitions, where predictions are conditioned on past predictions, are the predominant choice for both deterministic and stochastic sequential models. However, autoregressive feedback exposes the evolution of the hidden state trajectory to potential biases from well-known train-test discrepancies.…

GDB bridges geometric states with improved accuracy and generality.

Mackey showed that for a compact Lie group $K$, the pair $(K,C^{0}(K))$ has a unique non-trivial irreducible covariant pair of representations. We study the relevance of this result to the unitary equivalence of quantizations for an infinite-dimensional family of $K\times K$ invariant polarizations on $T^{\ast}K$. The …

Tree-AMP simplifies inference in complex tree-structured models.

Graph neural network using Beltrami flow for feature and topology evolution.

New model explains volatility after extreme stock market events.

In this work, sequence-to-sequence (seq2seq) models, originally developed for language translation, are used to predict the temporal evolution of complex, multi-physics computer simulations. The predictive performance of seq2seq models is compared to state transition models for datasets generated with multi-physics cod…

New setting combines state evolution and corrupted context for better decision-making.

For the cotangent bundle $T^{*}K$ of a compact Lie group $K$, we study the complex-time evolution of the vertical tangent bundle and the associated geometric quantization Hilbert space $L^{2}(K)$ under an infinite-dimensional family of Hamiltonian flows. For each such flow, we construct a generalized coherent state tra…

Generative model predicts remaining life of damaged structures.

New algorithm improves signal reconstruction from noisy measurements with side information.

CoMGNN models heterogeneous graphs with evolving nodes and edges.

AMP algorithm for matrix tensor product model provides recovery conditions.

We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is governed via (a kind of) a parallel transport in this bundle. Some problems concernin…

Word evolution refers to the changing meanings and associations of words throughout time, as a byproduct of human language evolution. By studying word evolution, we can infer social trends and language constructs over different periods of human history. However, traditional techniques such as word representation learni…

Paper confirms Thom's conjecture for nonlinear evolutions on manifolds.

New AMP algorithm estimates signals and latent variables in mixed regression models.

Quantum methods model uncertain volatility in financial markets.

The combination of high-dimensionality and disparity of time scales encountered in many problems in computational physics has motivated the development of coarse-grained (CG) models. In this paper, we advocate the paradigm of data-driven discovery for extract- ing governing equations by employing fine-scale simulation …

Quantum method prices options by evolving a state in imaginary time.

A generative recurrent neural network is quickly trained in an unsupervised manner to model popular reinforcement learning environments through compressed spatio-temporal representations. The world model's extracted features are fed into compact and simple policies trained by evolution, achieving state of the art resul…

Study bi-harmonic flow with forcing term on smooth curves.

Quantum computer method for pricing lookback options with jumps.

We analyze the sectoral dynamics of startup venture financing. Based on a dataset of 52000 start-ups and 110000 funding rounds in the United States from 2000 to 2017, and by applying both Principal Component Analysis (PCA) and Tensor Component Analysis (TCA) in sector space, we visualize and measure the evolution of th…

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…

Unified framework for AMP iterations using graph indexing.

This study examines cores within superclusters, highlighting their transitional nature and dynamical state.

We consider a quasi-metric topological structure for the construction of a new reinforcement learning model in the framework of financial markets. It is based on a Lipschitz type extension of reward functions defined in metric spaces. Specifically, the McShane and Whitney extensions are considered for a reward function…

The study of the critical dynamics in complex systems is always interesting yet challenging. Here, we choose financial market as an example of a complex system, and do a comparative analyses of two stock markets - the S&P 500 (USA) and Nikkei 225 (JPN). Our analyses are based on the evolution of crosscorrelation struct…

An array system of coupled maps is proposed as a model for economy evolution. The local dynamics of each map or agent is controlled by two parameters. One of them represents the growth capacity of the agent and the other one is a control term representing the local environmental pressure which avoids an exponential gro…

Novel AMP framework for multi-environment transfer learning.

Clusters cryptocurrency market states via cross correlation analysis.

In automatic financial feature construction task, the state-of-the-art technic leverages reverse polish expression to represent the features, then use genetic programming (GP) to conduct its evolution process. In this paper, we propose a new framework based on neural network, alpha discovery neural network (ADNN). In t…

Geometric QHD tests improve hub detection in correlated data.

Motivation: Driver (epi)genomic alterations underlie the positive selection of cancer subpopulations, which promotes drug resistance and relapse. Even though substantial heterogeneity is witnessed in most cancer types, mutation accumulation patterns can be regularly found and can be exploited to reconstruct predictive …

Based on the stochastic model proposed by Patriarca-Kaski-Chakraborti that describes the exchange of wealth between $n$ economic agents, we analyze the evolution of the corresponding economies under the assumption of a Gaussian background, modeling the exchange parameter $ε$. We demonstrate, that within Gaussian noise,…

New method clusters strong and weak views effectively, improving performance by up to 40%.

CR-FM-NES improves NES for high-dimensional optimization.

The goal of this note is to prove a compact embedding result for spaces of forward rate curves. As a consequence of this result, we show that any forward rate evolution can be approximated by a sequence of finite dimensional processes in the larger state space.