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.
Study shows non-polyhedral structure in moduli spaces for n≥8.
Reductive quotients preserve klt singularities in algebraic geometry.
Classifies 3D spaces using specific invariants.
It is the aim of this article to determine curvature quantities of an arbitrary Riemannian monotone metric on the space of positive matrices resp. nonsingular density matrices. Special interest is focused on the scalar curvature due to its expected quantum statistical meaning. The scalar curvature is explained in more …
Regression learns Mori-Zwanzig operators for dynamical systems.
DREAM learns optimal strategies in imperfect games without needing a simulator.
In the present paper we prove that, on a hyperkähler manifold, walls of the kähler cone and extremal rays of the Mori cone are determined by all divisors satisfying certain numerical conditions.
DREAM model improves computational efficiency for non-linear effects in relational event models.
The curvature tensor and the scalar curvature are computed in the space of positive definite real matrices endowed by the Kubo-Mori inner product as a Riemannian metric.
Learning to control robots directly based on images is a primary challenge in robotics. However, many existing reinforcement learning approaches require iteratively obtaining millions of robot samples to learn a policy, which can take significant time. In this paper, we focus on learning a realistic world model capturi…
We give an introduction to the theory of varieties of minimal rational tangents, emphasizing its aspect as a fusion of algebraic geometry and differential geometry, more specifically, a fusion of Mori geometry of minimal rational curves and Cartan geometry of cone structures.
LiDER refreshes past experiences in RL by dreaming about them.
Model compression is eminently suited for deploying deep learning on IoT-devices. However, existing model compression techniques rely on access to the original or some alternate dataset. In this paper, we address the model compression problem when no real data is available, e.g., when data is private. To this end, we p…
Novel autoencoder method approximates Koopman operator in low dimensions.
Develops a new deep learning formulation using Mori-Zwanzig formalism.
We survey our recent papers (some being joint ones) about the relation between the geometry of a compact Kähler manifold and the existence of automorphisms of positive entropy on it. We also use the language of log minimal model program (LMMP) in biraitonal geometry, but not its more sophisticated technical part. We gi…
Reduces symplectic Hamiltonian systems to contact systems, realizing Poincaré's dream.
The authors give a complete classification of projective threefolds admitting a holomorphic normal projective connection. Moreover, they prove a general structure theorem on complex projective manifolds admitting a holomorphic normal projective connection, saying in particular, that any such manifold is either the proj…
In this paper we show that the Chern numbers of a smooth Mori fibre space in dimension three are bounded in terms of the underlying topological manifold. We also generalise a theorem of Cascini and the second named author on the boundedness of Chern numbers of certain threefolds to the case of negative Kodaira dimensio…
ESCHER avoids importance sampling to estimate regret in large games.
Model reduction methods aim to describe complex dynamic phenomena using only relevant dynamical variables, decreasing computational cost, and potentially highlighting key dynamical mechanisms. In the absence of special dynamical features such as scale separation or symmetries, the time evolution of these variables typi…
RL research overhypes potential but lacks deployable solutions.
We show that, in finite dimensions, the only monotone metrics for which the (+1) and (-1) affine connections are mutually dual are constant multiples of Bogoliubov-Kubo-Mori metric
The well-known Mori-Zwanzig theory tells us that model reduction leads to memory effect. For a long time, modeling the memory effect accurately and efficiently has been an important but nearly impossible task in developing a good reduced model. In this work, we explore a natural analogy between recurrent neural network…
New meta-RL method avoids exploration-exploitation trade-off.
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…
Machine learning models learn what we teach them to learn. Machine learning is at the heart of recommender systems. If a machine learning model is trained on biased data, the resulting recommender system may reflect the biases in its recommendations. Biases arise at different stages in a recommender system, from existi…
A new method predicts non-Markovian closure terms for complex systems.
New Dreamer model tackles object vanishing in robot learning.
In this paper, we introduce playing games on shadows of knots. We demonstrate two novel games, namely, To Knot or Not to Knot and Much Ado about Knotting. We also discuss winning strategies for these games on certain families of knot shadows. Finally, we suggest variations of these games for further study.
We generalize a result of Giroux which says that a closed surface in a contact -manifold with Morse-Smale characteristic foliation is convex. Specifically, we show that the result holds in contact manifolds of arbitrary dimension. As an application, we show that a particular closed hypersurface introduced by A. Mori…
We posit that hippocampal place cells encode information about future locations under a transition distribution observed as an agent explores a given (physical or conceptual) space. The encoding of information about the current location, usually associated with place cells, then emerges as a necessary step to achieve t…
We show that any bounded zero-angular momentum solution for the Newtonian three-body problem must suffer infinitely many eclipses, or collinearities, provided that it does not suffer a triple collision. Motivation for the result comes from the dream of building a symbolic dynamics for the three-body problem, one whose …
Study optimal degenerations of Fano threefolds, proving K-polystability and Kähler-Ricci solitons.
iLED framework offers interpretable dynamics for multiscale systems.
Given a (meromorphic) fibration where and are compact complex manifolds of dimensions and , we define to be the invertible subsheaf of the sheaf of holomorphic -forms of given by the saturation of , where is the canonical sheaf of . We define the Kodaira dimension…
A neural network learns from examples and optimizes by dreaming.
Develops a method to estimate optimal policy value in online learning.
Dimofte, Gaiotto and Gukov introduced a powerful invariant, the 3D-index, associated to a suitable ideal triangulation of a 3-manifold with torus boundary components. The 3D-index is a collection of formal power series in with integer coefficients. Our goal is to explain how the 3D-index is a generating serie…
Develops a new geometric framework for quantum metrics.
By using analytic method, we prove that there exist rational curves on compact Hermitian manifolds with positive holomorphic bisectional curvature. It confirms a question of S.-T. Yau. It is well-known that Mori proved in \cite{Mori79} that every compact complex manifold with contains at least one ration…
In a previous paper, we proved that a projective Kähler manifold of positive total scalar curvature is uniruled. At the other end of the spectrum, it is a well-known theorem of Campana and Kollár-Miyaoka-Mori that a projective Kähler manifold of positive Ricci curvature is rationally connected. In the present work, we …
Paper uses diffusion models to design electric aircraft quickly.
We explore building generative neural network models of popular reinforcement learning environments. Our world model can be trained quickly in an unsupervised manner to learn a compressed spatial and temporal representation of the environment. By using features extracted from the world model as inputs to an agent, we c…
We consider projective rational strong Calabi dream surfaces: projective smooth rational surfaces which admit a constant scalar curvature Kähler metric for every Kähler class. We show that there are only two such rational surfaces, namely the projective plane and the quadric surface. In particular, we show that all rat…
Kähler-Ricci flow shows type II singularity on Fano threefolds.
Quantum connections replace metrics with operator inner products.
We propose generative neural network methods to generate DNA sequences and tune them to have desired properties. We present three approaches: creating synthetic DNA sequences using a generative adversarial network; a DNA-based variant of the activation maximization ("deep dream") design method; and a joint procedure wh…