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.
Develops mixed quantization for graph vector bundles.
Quantizes symplectic fibrations to analyze vector bundles and metrics.
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…
Based on the notion of information bottleneck (IB), we formulate a quantization problem called "IB quantization". We show that IB quantization is equivalent to learning based on the IB principle. Under this equivalence, the standard neural network models can be viewed as scalar (single sample) IB quantizers. It is know…
A simple and computationally efficient scheme for tree-structured vector quantization is presented. Unlike previous methods, its quantization error depends only on the intrinsic dimension of the data distribution, rather than the apparent dimension of the space in which the data happen to lie.
Quantizes Kähler manifolds using sheaves and differential operators.
PRISM-VQ combines financial priors with vector quantization for better stock prediction.
Inverted file and asymmetric distance computation (IVFADC) have been successfully applied to approximate nearest neighbor search and subsequently maximum inner product search. In such a framework, vector quantization is used for coarse partitioning while product quantization is used for quantizing residuals. In the ori…
Paper proposes IIQ for compressing embedding vectors.
Vectors of data are at the heart of machine learning and data mining. Recently, vector quantization methods have shown great promise in reducing both the time and space costs of operating on vectors. We introduce a vector quantization algorithm that can compress vectors over 12x faster than existing techniques while al…
Note on subgaussian bounds for sign-quantized linear maps.
ICQ improves high-dimensional similarity search without sacrificing precision.
A new framework for neural network classification using vector quantization.
vqSGD reduces communication in distributed optimization with convergence guarantees.
Post-training quantization method using multiple low-precision points achieves higher precision for critical weights.
Quantization based techniques are the current state-of-the-art for scaling maximum inner product search to massive databases. Traditional approaches to quantization aim to minimize the reconstruction error of the database points. Based on the observation that for a given query, the database points that have the largest…
A new method for robust product Markovian quantization overcomes numerical instabilities.
The paper examines obstacles to extending deformation quantization of vector bundles.
A new distortion measure optimizes function approximations in vector quantization.
New method classifies manifold-valued data using Riemannian geometry.
A geometric quantization of a Kähler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures. Having a canonical quantization would amount to finding a natural (projectively) flat co…
Improved vector quantization using Gaussian mixtures for better codebook utilization.
We propose a quantization based approach for fast approximate Maximum Inner Product Search (MIPS). Each database vector is quantized in multiple subspaces via a set of codebooks, learned directly by minimizing the inner product quantization error. Then, the inner product of a query to a database vector is approximated …
The paper quantizes concatenated noisy vectors to a common cluster center, improving performance over naive methods.
The paper classifies quantizable functions and explores symmetry in quantization methods.
A new method for multiclass calibration using vector quantization.
Study shows simple vector quantization measures correlate with deep learning generalization.
Let be a holomorphic Hermitian vector bundle over a polarized manifold. We provide a canonical quantization of the Laplacian operator acting on sections of the bundle of Hermitian endomorphisms of . If is simple we obtain an approximation of the eigenvalues and eigenspaces of the Laplacian.
By computing certain cohomology of Vect(M) of smooth vector fields we prove that on 1-dimensional manifolds M there is no quantization map intertwining the action of non-projective embeddings of the Lie algebra sl(2) into the Lie algebra Vect(M). Contrariwise, for projective embeddings sl(2)-equivariant quantization ex…
We study two quantization schemes for compact symplectic manifolds with almost complex structures. The first of these is the Spin-c quantization. We prove the analog of Kodaira vanishing for the Spin-c Dirac operator, which shows that the index space of this operator provides an honest (not virtual) vector space semicl…
Extends geometric quantization to singular spaces.
In this work we present a review of the state of the art of Learning Vector Quantization (LVQ) classifiers. A taxonomy is proposed which integrates the most relevant LVQ approaches to date. The main concepts associated with modern LVQ approaches are defined. A comparison is made among eleven LVQ classifiers using one r…
We adapt the framework of geometric quantization to the polysymplectic setting. Considering prequantization as the extension of symmetries from an underlying polysymplectic manifold to the space of sections of a Hermitian vector bundle, a natural definition of prequantum vector bundle is obtained which incorporates in …
This paper compresses neural networks by permuting and quantizing weights.
In the first part of this article we provide a geometrically oriented approach to the theory of orbispaces which originally had been introduced by Chen. We explain the notion of a vector orbibundle and characterize the good sections of a reduced vector orbibundle as the smooth stratified sections. In the second part of…
VQ-GNN scales GNNs to large graphs using vector quantization.
In this paper, we provide an information-theoretic interpretation of the Vector Quantized-Variational Autoencoder (VQ-VAE). We show that the loss function of the original VQ-VAE can be derived from the variational deterministic information bottleneck (VDIB) principle. On the other hand, the VQ-VAE trained by the Expect…
We discuss the quantization of mechanical systems for which the Hamiltonian vector fields of observables form the deformation of -dimensional oscilator algebra. Because of this fact these systems can be considered as "deformations" of the harmonic oscillator. The set of abovementioned mechanical systems are realized…
Paper proves existence of a universal codebook for low-precision quantization.
The paper quantizes Hessian structures on R^2 using KV-algebras.
A new model trains prior and encoder/decoder networks simultaneously for efficient generation.
Study quantizes topological numbers on degenerating Einstein manifolds.
This work reduces model size by 86.11% for recommender systems using 4-bit quantization.
UVeQFed tackles FL model compression over limited channels.
Quantization can be used to form new vectors/matrices with shared values close to the original. In recent years, the popularity of scalar quantization for value-sharing applications has been soaring as it has been found huge utilities in reducing the complexity of neural networks. Existing clustering-based quantization…
A new method learns discrete representations for images and videos, improving upon previous models.
We propose and study a multi-scale approach to vector quantization. We develop an algorithm, dubbed reconstruction trees, inspired by decision trees. Here the objective is parsimonious reconstruction of unsupervised data, rather than classification. Contrasted to more standard vector quantization methods, such as K-mea…
We give an explicit construction of a deformation quantization of the algebra of functions on a Poisson manifolds, based on Kontsevich's local formula. The deformed algebra of functions is realized as the algebra of horizontal sections of a vector bundle with flat connection.