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 new framework for neural network classification using vector quantization.
problem Learning a neural network classifier under the IB principle.
method Aggregated Learning framework, combining vector quantization and variational techniques.
result The effectiveness of Aggregated Learning verified through experiments.
PRISM-VQ combines financial priors with vector quantization for better stock prediction.
problem Predicting cross-sectional stock returns is hard due to low signal-to-noise ratios and changing market conditions.
method Integrates expert priors, vector-quantized latent factors, and dynamic factor loadings.
result Consistent improvements in cross-sectional return prediction and portfolio performance.
New method classifies manifold-valued data using Riemannian geometry.
problem Classifying data on curved Riemannian manifolds.
method Probabilistic Learning Vector Quantization on Symmetric Positive Definite Matrices.
result The method outperforms traditional Euclidean methods on manifold-valued data.
Paper proposes IIQ for compressing embedding vectors.
problem Memory issues in representing large vocabularies.
method Isotropic iterative quantization (IIQ) for binary compression.
result More than 30x compression ratio with comparable performance.
Study shows simple vector quantization measures correlate with deep learning generalization.
problem Understanding and predicting generalization in deep learning models.
method Applying complexity measures from approximation and information theory to deep learning features.
result Simple vector quantization measures correlate well with generalization performance in deep learning.
RATQ is a new quantizer for optimizing noisy gradients in machine learning.
problem Optimizing noisy gradients in stochastic optimization.
method RATQ uses Hadamard transform and adaptive uniform quantization, and achieves near-optimal performance.
result RATQ nearly achieves information theoretic lower bounds for optimization accuracy.
Develops mixed quantization for graph vector bundles.
problem Solving asymptotic spectral problems on graph vector bundles.
method Mixed quantization technique for graph vector bundles.
result Applications to various spectral problems.
This paper compares different activation functions in GLVQ models.
problem Improving performance of GLVQ models using different activation functions.
method Investigates and compares ReLU, sigmoid, and swish activation functions in GLVQ models.
result Different activation functions have varying impacts on GLVQ model performance.
A new method improves maximum inner product search by locally decomposing residual vectors.
problem Maximum inner product search efficiency and accuracy.
method Local Orthogonal Decomposition (LOD) combined with multiscale quantization.
result LOD consistently achieves higher recall than previous methods under the same bitrates.
A new method for multiclass calibration using vector quantization.
problem Challenges in multiclass calibration, especially in high-stakes settings.
method Compositional approach via Vector Quantization (VQ) to learn region-specific calibration maps.
result Significant improvements in local calibration with competitive global calibration and predictive performance.
A new multi-scale vector quantization method for unsupervised data.
problem Efficiently reconstructing unsupervised data with minimal distortion.
method Reconstruction trees, inspired by decision trees, explore data in a multi-scale fashion.
result Analysis of expected distortion under fixed unknown distribution, with asymptotic and finite sample results.
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 …
New vector quantization method reduces relevance of parallel components in database points.
problem Scaling maximum inner product search to massive databases.
method Developed anisotropic vector quantization loss functions.
result Achieves state-of-the-art results on public benchmarks.
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…
Quantizes symplectic fibrations to analyze vector bundles and metrics.
problem Quantizing higher rank vector bundles and understanding their metrics.
method Relates Berezin-Toeplitz quantization to hybrid systems and symplectic fibrations.
result Established refined estimates for computing balanced metrics on Kähler manifolds.
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…
Post-training quantization method using multiple low-precision points achieves higher precision for critical weights.
problem Discretizing pre-trained deep neural networks without re-training.
method Multipoint quantization with efficient greedy selection and adaptive point number.
result Outperforms state-of-the-art methods on ImageNet classification and PASCAL VOC object detection.
Improved vector quantization using Gaussian mixtures for better codebook utilization.
problem Training instability and information loss in discrete vector quantization.
method Generalized vector quantization with Gaussian mixture model and aggregated categorical posterior evidence lower bound.
result GM-VQ improves codebook utilization and reduces information loss without heuristics.
UVeQFed tackles FL model compression over limited channels.
problem Efficiently transmitting trained models over rate-constrained channels.
method Universal vector quantization for FL (UVeQFed).
result UVeQFed minimizes distortion and converges to optimal model.
A new method learns discrete representations for images and videos, improving upon previous models.
problem Learning discrete representations for images and videos to improve performance.
method Depthwise application of Vector Quantized Variational Autoencoders (VQVAE) to feature axis.
result 33% improvement in performance compared to previous discrete models.
Quantizes Kähler manifolds using sheaves and differential operators.
problem Quantizing Kähler manifolds with sheaves and differential operators.
method Constructing a category enriched over sheaves of modules, defining quantizable morphisms, and showing equivalence to differential operator categories.
result Equivalence of quantized categories under certain conditions.
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.
LVQ models robustness evaluated against adversarial attacks.
problem Robustness of LVQ models against adversarial attacks.
method Evaluation of three LVQ models: Generalized LVQ, Generalized Matrix LVQ, and Generalized Tangent LVQ.
result Generalized LVQ and Generalized Tangent LVQ are robust, while Generalized Matrix LVQ is not.
VQ-DRAW compresses images and generates realistic samples.
problem Learning compact discrete representations of images.
method Sequential discrete VAE with vector quantization.
result VQ-DRAW effectively compresses and generates images.
Note on subgaussian bounds for sign-quantized linear maps.
problem Understanding subgaussian behavior of sign-quantized linear maps.
method Developed a dimension-independent subgaussian concentration bound for Gaussian vectors under nonlinear mappings.
result Answered a question about sign-quantized linear maps using a new subgaussian bound.
ICQ improves high-dimensional similarity search without sacrificing precision.
problem High-dimensional similarity search is computationally expensive.
method Interleaved Composite Quantization (ICQ) reduces code length and quantization error.
result ICQ achieves fast similarity search without using shorter codes.
Develops a faster soybean genome clustering method combining spectral and vector quantization.
problem Clustering soybean whole genome sequences efficiently.
method Combines Spectral Clustering and Vector Quantization for computational efficiency.
result Significantly outperforms existing methods in cluster quality and time complexity.
Paper presents a semi-supervised grasp detection method using VQ-VAE.
problem Robotic grasp detection difficulty due to insufficient labelled data.
method Semi-supervised learning with VQ-VAE in a latent space.
result Model performs better than existing approaches using unlabelled images.
A new framework enhances generative modeling by learning local flows over complex manifolds.
problem Limited expressivity of current normalizing flows for low-dimensional manifolds.
method Vector quantized local normalizing flows (VQ-Flows) using a VQ-AE atlas and conditional flows.
result Enhanced modeling of complex data distributions over manifolds.
vqSGD reduces communication in distributed optimization with convergence guarantees.
problem Reduction of communication cost in distributed optimization.
method Vector quantization schemes based on convex hull of a point set.
result Asymptotic reduction in communication cost with convergence guarantees.
This paper introduces a quantization-based regularizer for autoencoders to improve latent representations.
problem Autoencoders can overfit and collapse, leading to poor latent representations.
method The authors combine VQ-VAE and denoising methods to introduce a bottleneck Bayesian estimator that soft quantizes latent codes.
result The method results in better latent representations for supervised and clustering tasks.
A new method for robust product Markovian quantization overcomes numerical instabilities.
problem Numerical instabilities in the PMQ algorithm limit its adoption, especially for stochastic volatility models.
method Reformulated PMQ as standard vector quantization, applying accelerated Lloyd's algorithm for robustness.
result The method overcomes numerical instabilities and extends applicability to stochastic volatility models.
We propose in this contribution a method for l one regularization in prototype based relevance learning vector quantization (LVQ) for sparse relevance profiles. Sparse relevance profiles in hyperspectral data analysis fade down those spectral bands which are not necessary for classification. In particular, we consider …
The paper examines obstacles to extending deformation quantization of vector bundles.
problem Obstructing the extension of deformation quantization to higher orders.
method Analyzes the obstruction class and proves its necessity and sufficiency under certain conditions.
result Establishes that extending deformation quantization to higher orders is possible under specific conditions.
A new distortion measure optimizes function approximations in vector quantization.
problem Measuring the quality of vector quantization points for natural signals.
method A canonical distortion measure (CDM) is introduced, induced by an environment of functions on input space.
result Optimizing reconstruction error with respect to CDM yields optimal piecewise constant approximations.
A new model trains prior and encoder/decoder networks simultaneously for efficient generation.
problem Complex autoregressive prior in VQ-VAE models leads to slow generation.
method Builds a diffusion bridge between continuous and non-informative prior distributions.
result Model is competitive and efficient in optimization and sampling.
Paper proves existence of a universal codebook for low-precision quantization.
problem Optimizing low-precision approximation of matrix products in machine learning.
method Develops a universal codebook that is near-optimal for all possible statistics of input data.
result Proves existence of a universal codebook with a 0.11 bit per dimension reduction in rate.
It is of fundamental importance to find algorithms obtaining optimal performance for learning of statistical models in distributed and communication limited systems. Aiming at characterizing the optimal strategies, we consider learning of Gaussian Processes (GPs) in distributed systems as a pivotal example. We first ad…
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…
VQ-GNN scales GNNs to large graphs using vector quantization.
problem Scaling GNNs to large graphs with stable performance and speed.
method VQ-GNN uses vector quantization to preserve all messages passed to a mini-batch of nodes, avoiding the 'neighbor explosion' problem.
result VQ-GNN achieves competitive performance on large-graph node classification and link prediction benchmarks.
Geometric quantization adapted to polysymplectic manifolds.
problem Quantization of polysymplectic manifolds.
method Adapted geometric quantization framework to polysymplectic setting.
result Polysymplectic Guillemin-Sternberg conjecture is shown to be false with a complex polarization.
The nearest neighbor method together with the dynamic time warping (DTW) distance is one of the most popular approaches in time series classification. This method suffers from high storage and computation requirements for large training sets. As a solution to both drawbacks, this article extends learning vector quantiz…
The paper quantizes concatenated noisy vectors to a common cluster center, improving performance over naive methods.
problem Clustering concatenated noisy vectors from multiple sources.
method Asymptotic analysis of weighted sum of distances to a common cluster center.
result The clustering approach outperforms naive methods in terms of average distortion.
The paper classifies quantizable functions and explores symmetry in quantization methods.
problem Classifying quantizable functions and understanding symmetry in quantization methods.
method Deformation quantization and geometric quantization methods are compared and classified.
result Formal quantizable functions are of a specific form and relate to Hamiltonian Killing vector fields.
Discretizing multi-dimensional data distributions is a fundamental step of modern indexing methods. State-of-the-art techniques learn parameters of quantizers on training data for optimal performance, thus adapting quantizers to the data. In this work, we propose to reverse this paradigm and adapt the data to the quant…
Paper introduces a technique to simplify RNN policies for better understanding and analysis.
problem Difficulty in explaining and analyzing RNN policies due to continuous-valued memory vectors and observation features.
method Quantized Bottleneck Insertion technique to learn finite representations of RNN vectors and features.
result Finite representations of RNN policies can be as small as 3 discrete memory states and 10 observations, improving interpretability.
Prototype-based methods improve neural networks' robustness and interpretability.
problem Neural networks lack robustness and interpretability.
method Prototype-based vector quantization methods are integrated into neural networks.
result Established a strong theoretical framework for prototype-based neural network layers.