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.
Develops methods to simulate rare transitions in molecular systems.
New methods use machine learning to simulate rare transitions in molecular systems.
New relation on paths is not transitive.
Minimum energy paths for transitions such as atomic and/or spin rearrangements in thermalized systems are the transition paths of largest statistical weight. Such paths are frequently calculated using the nudged elastic band method, where an initial path is iteratively shifted to the nearest minimum energy path. The co…
We introduce a geometric transition between two homogeneous three-dimensional geometries: hyperbolic geometry and anti de Sitter (AdS) geometry. Given a path of three-dimensional hyperbolic structures that collapse down onto a hyperbolic plane, we describe a method for constructing a natural continuation of this path i…
Deep reinforcement learning method finds rare events in complex systems.
Convolution operations designed for graph-structured data usually utilize the graph Laplacian, which can be seen as message passing between the adjacent neighbors through a generic random walk. In this paper, we propose PAN, a new graph convolution framework that involves every path linking the message sender and recei…
A new method uses deep learning to efficiently sample rare transitions for estimating committor functions.
Develops a machine learning framework for computing most probable paths in stochastic systems.
New algorithm achieves data-dependent regret bounds in MDPs with unknown transitions.
The paper tackles robust control for insurance contracts under uncertain transition rates.
Causal discovery from empirical data is a fundamental problem in many scientific domains. Observational data allows for identifiability only up to Markov equivalence class. In this paper we first propose a polynomial time algorithm for learning the exact correctly-oriented structure of the transitive reduction of any c…
PAN uses path integrals for graph convolution and pooling, improving GNN performance.
New method reduces discrete flow transitions, improving perplexity estimation.
Two-dimensional transition rates improve life insurance reserve calculations.
Regarding the Specht modules associated to the two-row partition , we provide a combinatorial path model to study the transitioning matrix from the tableau basis to the -web basis (i.e. cup diagrams), and prove that the entries in this matrix are positive in the upper-triangular portion with respect to a ce…
New algorithms for planning with adversarial changes in costs.
Model place cells as spatial embeddings for efficient path planning and cognitive map construction.
The calculation of minimum energy paths for transitions such as atomic and/or spin re-arrangements is an important task in many contexts and can often be used to determine the mechanism and rate of transitions. An important challenge is to reduce the computational effort in such calculations, especially when ab initio …
We study a quantum system in a Riemannian manifold M on which a Lie group G acts isometrically. The path integral on M is decomposed into a family of path integrals on a quotient space Q=M/G and the reduced path integrals are completely classified by irreducible unitary representations of G. It is not necessary to assu…
Study character varieties of a Coxeter group in hyperbolic and Anti-de Sitter spaces.
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a diffusion equation with a diffusion coefficient that inversely depends on the dat…
This article addresses the problem of approximating the price of options on discrete and continuous arithmetic average of the underlying, i.e. discretely and continuously monitored Asian options, in local volatility models. A path-integral-type expression for option prices is obtained using a Brownian bridge representa…
Adjoint sampler targets infinite-dimensional function spaces for efficient sampling.
A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique allows one to obtain remarkably good approximations of the pricing kernels of f…
In this paper, we study the behavior of Ricci-flat Kähler metrics on Calabi-Yau manifolds under algebraic geometric surgeries: extremal transitions or flops. We prove a version of Candelas and de la Ossa's conjecture: Ricci-flat Calabi-Yau manifolds related by extremal transitions and flops can be connected by a path c…
We study the problem of learning the support of transition matrix between random processes in a Vector Autoregressive (VAR) model from samples when a subset of the processes are latent. It is well known that ignoring the effect of the latent processes may lead to very different estimates of the influences among observe…
We study the problem of learning Markov decision processes with finite state and action spaces when the transition probability distributions and loss functions are chosen adversarially and are allowed to change with time. We introduce an algorithm whose regret with respect to any policy in a comparison class grows as t…
Deep learning has become a powerful and popular tool for a variety of machine learning tasks. However, it is challenging to understand the mechanism of deep learning from a theoretical perspective. In this work, we propose a random active path model to study collective properties of deep neural networks with binary syn…
This paper classifies expanding attractors and non-transitive Anosov flows on specific knot and manifold spaces.
Develops new Markov processes with switching rates and past dependence.
New algorithm reduces regret in linear mixture SSPs without cost bounds.
New MCMC method improves sampling from multimodal distributions.
In this note we propose a method based on artificial neural network to study the transition between states governed by stochastic processes. In particular, we aim for numerical schemes for the committor function, the central object of transition path theory, which satisfies a high-dimensional Fokker-Planck equation. By…
Adapts flow matching for MCMC to improve sampling efficiency.
New method for sampling from multivariate distributions using optimal control and quantum mechanics.
This paper presents a general theory that aims at explaining timescales observed empirically in technology transitions and predicting those of future transitions. This framework is used further to derive a theory for exploring the dynamics that underlie the complex phenomenon of irreversible and path dependent price or…
Let G be a closed transitive subgroup of Homeo(S^1) which contains a non-constant continuous path f: [0,1] --> G. We show that up to conjugation G is one of the following groups: SO(2,R), PSL(2,R), PSL_k(2,R), Homeo_k(S^1), Homeo(S^1). This verifies the classification suggested by Ghys [Enseign. Math. 47 (2001) 329-407…
The present work extends the randomized shortest-paths framework (RSP), interpolating between shortest-path and random-walk routing in a network, in three directions. First, it shows how to deal with equality constraints on a subset of transition probabilities and develops a generic algorithm for solving this constrain…
We study a simplification of GAN training: the problem of transporting particles from a source to a target distribution. Starting from the Sobolev GAN critic, part of the gradient regularized GAN family, we show a strong relation with Optimal Transport (OT). Specifically with the less popular dynamic formulation of OT …
Study online learning in MDPs with aggregate bandit feedback, achieving low regret in both stochastic and adversarial settings.
Unified understanding of integrability obstructions for Lie algebroids.
Proposes a thermodynamic work minimization framework for guiding generative models.
The transition of several East and Central European countries and the countries of the Former Soviet Union from the socialist economic system to the capitalist one is studied. A recently developed microeconomic model for the personal income distribution and its evolution and a simple functional relationship between the…
Algorithm samples constrained stochastic differential equations.
ARL bridges non-Markovian decision processes with reinforcement learning, improving foresight and stability.
Value Iteration Networks (VINs) are effective differentiable path planning modules that can be used by agents to perform navigation while still maintaining end-to-end differentiability of the entire architecture. Despite their effectiveness, they suffer from several disadvantages including training instability, random …
We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rules. The polynomial property allows us to study such rules using …