arXiv research

Survey of three geometric frameworks for action-dependent field theories.

Policy gradient methods have enjoyed great success in deep reinforcement learning but suffer from high variance of gradient estimates. The high variance problem is particularly exasperated in problems with long horizons or high-dimensional action spaces. To mitigate this issue, we derive a bias-free action-dependent ba…

In a previous paper we constructed classical spin Chern-Simons for any compact Lie group $G$: a gauge theory whose action depends on the spin structure of the 3-manifold. Here we apply geometric quantization to the classical Hamiltonian theory and investigate the formal properties of the partition function in the Lagra…

We show that J. Lott's equivariant higher analytic torsion for compact group actions depends only on the equivariant Euler characteristic.

Efficient algorithms for second-price auctions with action-dependent censoring.

Study shows observing order book can significantly improve online market making performance.

Policy gradient methods are a widely used class of model-free reinforcement learning algorithms where a state-dependent baseline is used to reduce gradient estimator variance. Several recent papers extend the baseline to depend on both the state and action and suggest that this significantly reduces variance and improv…

Proposes a neural network for efficient deep hedging strategies.

Efficiently handles contextual bandits with diffusion models.

New algorithm tackles multi-agent reinforcement learning with optimal convergence rate.

Policy gradient methods have achieved remarkable successes in solving challenging reinforcement learning problems. However, it still often suffers from the large variance issue on policy gradient estimation, which leads to poor sample efficiency during training. In this work, we propose a control variate method to effe…

Quantum field theory uses Lorentzian bordisms to describe time evolution.

Lectures on topological field theories and differential cohomology.

New framework for fair online allocation in continuous time with deadlines.

Semisimple 4D field theories can't distinguish smooth 4-manifolds.

There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field theory combined.

This thesis proposes a global geometric formulation of Extended Field Theories.

Extends field theory foundations to infinitesimal spaces, simplifying complex concepts.

The paper quantizes hybrid topological-holomorphic field theories on $\mathbb{R}^m imes \mathbb{C}^n$.

The paper reviews a correspondence between Double Field Theory and bundle gerbes.

BRPO optimizes batch RL policies to better exploit state-action differences.

The paper defines strong emergence in field theories and proves it exists between certain theories.

The paper proves UV finiteness and vanishing anomalies for hybrid topological-holomorphic field theories.

Paper introduces Floer theory for field theories, proving periodic solutions for particle-field systems.

Geometrically describes Jacobi equations for field theories with dissipation.

We formulate differential cohomology and Chern-Weil theory -- the theory of connections on fiber bundles and of gauge fields -- abstractly in the context of a certain class of higher toposes that we call "cohesive". Cocycles in this differential cohomology classify higher principal bundles equipped with cohesive struct…

Derives localization formulas in Batalin-Vilkovisky formalism.

The paper axiomatizes strong emergence in parameterized field theories and proves existence theorems.

Machine learning explores symmetries in field theory and algebra.

Develops Hamilton-Jacobi theory for non-conservative field theories in k-contact geometry.

3D dual field theories for Virasoro minimal models constructed using Seifert fiber spaces.

We consider the hypothesis that the C-field 4-flux and 7-flux forms in M-theory are in the image of the non-abelian Chern character map from the non-abelian generalized cohomology theory called J-twisted Cohomotopy theory. We prove for M2-brane backgrounds in M-theory on 8-manifolds that such charge quantization of the…

New geometric framework for non-conservative field theories with time-dependent terms.

Let G be a group and let M be a CAT(0) proper metric space (e.g. a simply connected complete Riemannian manifold of non-positive sectional curvature or a locally finite tree). Isometric actions of G on M are (by definition) points in the space R := Hom(G, Isom(M)) with the compact open topology. Sample theorems: 1. The…

Following the analogies between 3-dimensional topology and number theory, we study an idèlic form of class field theory for 3-manifolds. For a certain set $\mathcal{K}$ of knots in a 3-manifold $M$, we first present a local theory for each knot in $\mathcal{K}$, which is analogous to local class field theory, and then,…

Reduces field theories using Poisson-Poincaré method.

Develops a new geometric framework for non-conservative field theories.

Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construc…

Statistical field theory aids in understanding deep learning complexities.

Analyzes Poisson structures on solution spaces of Hamiltonian field theories.

Defines new canonical lifts for field theories, analyzing Klein-Gordon, Polyakov string, and Einstein-Cartan gravity.

Develops a framework for 1D geometric field theories and proves they are equivalent to vector bundles.

In the paper [4] is presented a theory which unifies the gravitation theory and the mechanical effects, which is different from the Riemannian theories like GTR. Moreover it is built in the style of the electomagnetic field theory. This paper is a continuation of [4] such that the complex variant of that theory yields …

We describe the elements of a novel structural approach to classical field theory, inspired by recent developments in perturbative algebraic quantum field theory. This approach is local and focuses mainly on the observables over field configurations, given by certain spaces of functionals which are studied here in dept…

We survey three different ways in which K-theory in all its forms enters quantum field theory. In Part 1 we give a general argument which relates topological field theory in codimension two with twisted K-theory, and we illustrate with some finite models. Part 2 is a review of pfaffians of Dirac operators, anomalies, a…

Develops Marsden-Meyer-Weinstein reduction for $k$-contact field theories.

Constructs maps from field theories to complexified K-theory and elliptic cohomology.

Finite presentations for skein algebras linked to gauge field theory.