arXiv research

Study on Chern-Simons theory at generic levels, revealing universal resurgent structure.

Novel approach for large genus intersection number asymptotics.

Heat kernel resurgent structure from Picard-Lefschetz theory

New method uses resurgent analysis to determine growth rate of quantum field theory coefficients.

Proves a quantum invariant conjecture for specific three-manifolds.

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 abstract discusses resurgent functions in quantum knot invariants.

Proves resurgence properties for Habiro elements from radial limits of theta series.

Geometrically proves WKB solutions of Schrödinger equations are resurgent.

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 …

New resurgent analysis reveals dual $q$-series for Chern-Simons theory crossing natural boundaries.

Resurgent analysis reveals full partition function for 3-manifold invariants.

Novel mathematical approach using resurgent analysis reveals new structures in complex Chern-Simons theory.

Resurgence of Joyce structures gauged to a standard form using gauge transformations.

Proves resurgent nature of a series solution to deformed Painlevé I equation.

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.

The trivial flat connection's Chern-Simons theory is resurgent, revealing its structure.

Quantum dilogarithm function proven from a linear difference equation.

Study non-perturbative quantum geometry of string theories using finite difference equations and resurgence analysis.

Proves summability of state integrals for specific hyperbolic knots.

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 ${\cal N}=(2,2)$ 2d Landau-Ginzburg theory in models describing link embeddings in ${\mathbb{R}}^3$ to Khovanov and Khovanov-Rozansky homologies. To confirm the equivalence we exploit the invariance of Hilbert sp…

Complex Chern-Simons theory reveals peacock patterns in perturbative series.

The paper defines a function for knots in Seifert manifolds and connects it to Witten-Reshetikhin-Turaev invariants.

The paper is concerned with the Kontsevich-Zagier formal power series $f(q)=\sum_{n=0}^\infty (1-q)... (1-q^n)$ 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…

Study compares two methods to extend $\widehat{Z}$ invariants, finding incompatibility for Brieskorn spheres.

Two Alexander polynomials emerge in a Kashaev limit, resolving a paradox.

The physical 3d $\mathcal{N}=2$ theory T[Y] was previously used to predict the existence of some 3-manifold invariants $\hat{Z}_{a}(q)$ 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…

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…

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…

PAC learning simplified as bipartite matching.

New invariants for 3-manifolds derived from supergroup representations.

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…

Multi-agent reinforcement learning (MARL) has long been a significant and everlasting research topic in both machine learning and control. With the recent development of (single-agent) deep RL, there is a resurgence of interests in developing new MARL algorithms, especially those that are backed by theoretical analysis…

Hierarchical abstractions are a methodology for solving large-scale graph problems in various disciplines. Coarsening is one such approach: it generates a pyramid of graphs whereby the one in the next level is a structural summary of the prior one. With a long history in scientific computing, many coarsening strategies…

Few-shot learning is currently enjoying a considerable resurgence of interest, aided by the recent advance of deep learning. Contemporary approaches based on weight-generation scheme delivers a straightforward and flexible solution to the problem. However, they did not fully consider both the representation power for u…

Regularizes GAMs to improve interpretability by reducing concurvity.

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 …

Policy shifts between Trump and Biden impact ESG investments, creating volatility.

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…

A method to automatically learn proposal distributions for energy-based regression models.

New method classifies nonlinear time series using deep CNNs and bispectra.

This paper provides statistical guarantees for WAE's latent space regeneration.

Layer-wise preconditioning methods improve neural network optimization and feature learning.

Supervised contrastive learning improves image classification accuracy.