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.
We perform a resurgence analysis of the SU(2) Chern-Simons partition function on a Brieksorn homology sphere Σ(2,5,7). Starting from an exact Chern-Simons partition function, we study the Borel resummation of its perturbative expansion.
We study resurgence properties of partition function of SU(2) Chern-Simons theory (WRT invariant) on closed three-manifolds. We check explicitly that in various examples Borel transforms of asymptotic expansions posses expected analytic properties. In examples that we study we observe that contribution of irreducible f…
The purpose of the paper is to introduce some conjectures regarding the analytic continuation and the arithmetic properties of quantum invariants of knotted objects. More precisely, we package the perturbative and nonperturbative invariants of knots and 3-manifolds into two power series of type P and NP, convergent in …
The paper is concerned with the Kontsevich-Zagier formal power series f(q)=∑n=0∞(1−q)...(1−qn) and its analytic properties. To begin with, we give an explicit formula for the Borel transform of the associated formal power series F(x)=e−1/(24x)f(e−1/x) from which its analytic continuation, i…
Our aim is to prove that two formal power series of importance to quantum topology are Gevrey. These series are the Kashaev invariant of a knot (reformulated by Huynh and the second author) and the Gromov norm of the LMO of an integral homology 3-sphere. It follows that the power series associated to a simple Lie algeb…
For a Seifert fibered homology sphere we show that the q-series Z-hat invariant introduced by Gukov, Pei, Putrov and Vafa is a resummation of the Ohtsuki serie. We show that for every even level k there exists a full asymptotic expansion of Z-hat for q tending to a certain k'th root of unity and in particular that the …
In this note we make an attempt to compare a cohomological theory of Hilbert spaces of ground states in the N=(2,2) 2d Landau-Ginzburg theory in models describing link embeddings in R3 to Khovanov and Khovanov-Rozansky homologies. To confirm the equivalence we exploit the invariance of Hilbert sp…
Reliable uncertainty estimation for time series prediction is critical in many fields, including physics, biology, and manufacturing. At Uber, probabilistic time series forecasting is used for robust prediction of number of trips during special events, driver incentive allocation, as well as real-time anomaly detection…
New invariants for 3-manifolds derived from supergroup representations.
problem Developing invariants for 3-manifolds using supergroup analogues.
method Introducing supergroup analogues of 3-manifold invariants for superunitary groups, focusing on SU(2|1). Calculating q-series for specific 3-manifolds and studying their properties.
result Explicit calculation and study of q-series for certain 3-manifolds, providing a formula relating new invariants to quantum invariants.
Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we approach the question of fundamental iteration complexity by providing lower boun…
There is resurging interest, in statistics and machine learning, in solvers for ordinary differential equations (ODEs) that return probability measures instead of point estimates. Recently, Conrad et al. introduced a sampling-based class of methods that are 'well-calibrated' in a specific sense. But the computational c…
Stochastic gradient descent (SGD), which dates back to the 1950s, is one of the most popular and effective approaches for performing stochastic optimization. Research on SGD resurged recently in machine learning for optimizing convex loss functions and training nonconvex deep neural networks. The theory assumes that on…
Machine Learning (ML) is making a strong resurgence in tune with the massive generation of unstructured data which in turn requires massive computational resources. Due to the inherently compute- and power-intensive structure of Neural Networks (NNs), hardware accelerators emerge as a promising solution. However, with …
Why does Deep Learning work? What representations does it capture? How do higher-order representations emerge? We study these questions from the perspective of group theory, thereby opening a new approach towards a theory of Deep learning. One factor behind the recent resurgence of the subject is a key algorithmic step…
Why does Deep Learning work? What representations does it capture? How do higher-order representations emerge? We study these questions from the perspective of group theory, thereby opening a new approach towards a theory of Deep learning. One factor behind the recent resurgence of the subject is a key algorithmic step…
The physical 3d N=2 theory T[Y] was previously used to predict the existence of some 3-manifold invariants Z^a(q) that take the form of power series with integer coefficients, converging in the unit disk. Their radial limits at the roots of unity should recover the Witten-Reshetikhin-Turaev invari…
A method to automatically learn proposal distributions for energy-based regression models.
problem Manual design and initial estimate of proposal distributions for energy-based regression models.
method Introduces a method to learn an effective proposal distribution automatically, parameterized by a separate network head, and derives a unified training objective to minimize KL divergence and negative log-likelihood.
result Consistently outperforms conventional MDN training on four real-world regression tasks within computer vision.