arXiv research

Quantization techniques have been applied in many challenging finance applications, including pricing claims with path dependence and early exercise features, stochastic optimal control, filtering problems and efficient calibration of large derivative books. Recursive Marginal Quantization of the Euler scheme has recen…

Improved Heston model produces steeper smile for short maturities.

A new method for robust product Markovian quantization overcomes numerical instabilities.

Quantization algorithms have been successfully adopted to option pricing in finance thanks to the high convergence rate of the numerical approximation. In particular, very recently, recursive marginal quantization has been proven to be a flexible and versatile tool when applied to stochastic volatility processes. In th…

The paper develops a method to estimate conditional survival probabilities under noisy firm value data.

Solves a recursion for Gromov-Witten invariants of the unknot.

We revisit the development of grid based recursive approximate filtering of general Markov processes in discrete time, partially observed in conditionally Gaussian noise. The grid based filters considered rely on two types of state quantization: The \textit{Markovian} type and the \textit{marginal} type. We propose a s…

Unified framework for observables in n-plectic geometry.

In this note we describe the recursion relations between two parameter HOMLFY and Kauffman polynomials of framed links These relation correspond to embeddings of quantized universal enveloping algebras. The relation corresponding to embeddings $g_{n}\supset g_{k}\times sl_{n-k}$ where $g_{n}$ is either $so_{2n+1}$, $so…

A new scheme for FBSDEs simplifies computation without Monte Carlo.

This paper provides a methodology for fast and accurate pricing of the long-dated contracts that arise as the building blocks of insurance and pension fund agreements. It applies the recursive marginal quantization (RMQ) and joint recursive marginal quantization (JRMQ) algorithms outside the framework of traditional ri…

Quantizes geodesic lengths in Teichmüller spaces using algebraic methods.

Recursive Marginal Quantization (RMQ) allows fast approximation of solutions to stochastic differential equations in one-dimension. When applied to two factor models, RMQ is inefficient due to the fact that the optimization problem is usually performed using stochastic methods, e.g., Lloyd's algorithm or Competitive Le…

We prove that the colored HOMFLY polynomial of a link, colored by symmetric or exterior powers of the fundamental representation, is q-holonomic with respect to the color parameters. As a result, we obtain the existence of an (a,q) super-polynomial of all knots in 3-space. Our result has implications on the quantizatio…

We sketch a construction of Legendrian Symplectic Field Theory (SFT) for conormal tori of knots and links. Using large $N$ duality and Witten's connection between open Gromov-Witten invariants and Chern-Simons gauge theory, we relate the SFT of a link conormal to the colored HOMFLY-PT polynomials of the link. We presen…

We propose a novel algorithm which allows to sample paths from an underlying price process in a local volatility model and to achieve a substantial variance reduction when pricing exotic options. The new algorithm relies on the construction of a discrete multinomial tree. The crucial feature of our approach is that -- …

Survey on quantization methods on Kähler manifolds.

Recursive neural networks have widely been used by researchers to handle applications with recursively or hierarchically structured data. However, embedded control flow deep learning frameworks such as TensorFlow, Theano, Caffe2, and MXNet fail to efficiently represent and execute such neural networks, due to lack of s…

We introduce a new spatial data structure for high dimensional data called the \emph{approximate principal direction tree} (APD tree) that adapts to the intrinsic dimension of the data. Our algorithm ensures vector-quantization accuracy similar to that of computationally-expensive PCA trees with similar time-complexity…

Paper defines Farey Recursive Functions and explores their properties.

The paper classifies quantizable functions and explores symmetry in quantization methods.

The paper explores generalizations of Mirzakhani's recursion and computes volumes for physical gravity models.

This paper introduces a differentiable, scalable quantization method for neural networks.

StatQAT optimizes quantization for deep networks, reducing computational cost and memory usage.

Smart Quantization adapts binary and ternary quantization for neural networks.

This study optimizes quantized neural networks by considering model architecture and quantization types.

Extends ONNX for quantized neural networks with new formats and operators.

New method for quantizing symplectic manifolds with Lagrangian bundles.

HMQ improves quantization for edge devices with mixed precision.

Introduces sheaf quantization, a topological approach to geometric quantization.

Network quantization is an effective solution to compress deep neural networks for practical usage. Existing network quantization methods cannot sufficiently exploit the depth information to generate low-bit compressed network. In this paper, we propose two novel network quantization approaches, single-level network qu…

The article defines and compares two types of quantizations on compact manifolds.

We present Rotated Adaptive Tetra-iterated Quantizer (RATQ), a fixed-length quantizer for gradients in first order stochastic optimization. RATQ is easy to implement and involves only a Hadamard transform computation and adaptive uniform quantization with appropriately chosen dynamic ranges. For noisy gradients with al…

Quantized Adam reduces communication cost in deep learning training.

Proposes a robust neural network quantization method.

Quantizes neural networks using frame theory for improved accuracy.

The paper studies quantization on symplectic manifolds with real polarizations, comparing different quantization methods.

Unified finetuning of all quantization degrees of freedom achieves state-of-the-art 4-bit quantization.

Tab-TRM uses recursive model for insurance pricing on tabular data.

Geometric quantization of a Poisson manifold need not imply quantization of its symplectic leaves. We provide the leafwise geometric quantization of a Poisson manifold, seen as a foliated one, whose quantum algebra restricted to each leaf is quantized.

Meta learning optimizes neural network quantization for efficient inference.

Study quantization effects on high-dimensional linear regression learning.

We present an overview of techniques for quantizing convolutional neural networks for inference with integer weights and activations. Per-channel quantization of weights and per-layer quantization of activations to 8-bits of precision post-training produces classification accuracies within 2% of floating point networks…

New recursion formula for non-orientable surfaces resolves divergences.

FrostNet improves INT8 quantization efficiency in mobile networks.

Harer and Zagier proved a recursion to enumerate gluings of a $2d$-gon that result in an orientable genus $g$ surface, in their work on Euler characteristics of moduli spaces of curves. Analogous results have been discovered for other enumerative problems, so it is natural to pose the following question: how large is t…

Optimal gradient quantization reduces communication costs in distributed deep learning.

Quantizes symplectic manifolds with bounded geometry using Berezin-Toeplitz method.