Study quantization effects on high-dimensional linear regression learning.
problem Understanding quantization's impact on learning high-dimensional linear regression models.
method Analyzes stochastic gradient descent for high-dimensional linear regression under various quantization targets.
result Establishes precise bounds on excess risk for different quantization schemes.
Paper quantizes heavy-tailed data for near optimal estimation rates.
problem Estimating parameters from heavy-tailed data with quantization.
method Truncate and dither data, then uniformly quantize; achieves near minimax rates.
result Near optimal estimation rates achievable with quantized data.
StatQAT optimizes quantization for deep networks, reducing computational cost and memory usage.
problem Optimal quantization parameters selection for deep neural networks with diverse data distributions.
method Statistical error analysis framework for uniform and floating-point quantization, iterative and analytic quantizers designed for arbitrary and Gaussian-like distributions.
result Improved accuracy and stability in training low-precision neural networks.
This study analyzes quantization in deep learning models using statistical physics methods.
problem The computational resource requirements for large-scale data analysis models.
method Typical case analysis from statistical physics, specifically the replica method.
result Optimal quantization width minimizes error and delays overfitting.
Robustly estimates mean with quantized data and corruption.
problem Mean estimation under quantization and adversarial corruption.
method Constructs multivariate robust estimators in two settings.
result Optimal estimators up to logarithmic factors.
This study optimizes quantized neural networks by considering model architecture and quantization types.
problem Optimizing quantized neural networks for low-power, high-throughput applications.
method Holistic approach including training methods and quantization-friendly architecture design.
result Deeper models are more sensitive to activation quantization, while wider models improve resilience to both weight and activation quantization.
Distributed quantization improves classification accuracy with less data.
problem Efficiently classify features from distributed nodes with limited communication.
method Designs tailored quantization schemes for classification, proving NP-hardness and proposing polynomial-time algorithms.
result Tailored quantizers can reduce bit communication by more than a factor of two for the same accuracy.
Data-free quantization method improves model performance without fine-tuning.
problem Efficient quantization of deep neural networks without performance loss.
method Equalizing weight ranges and correcting biases to achieve 8-bit quantization.
result Achieves state-of-the-art quantized model performance on various architectures.
Proposes a robust neural network quantization method.
problem Training model's dependency on specific quantization methods.
method Intrinsic robustness to various quantization processes.
result Single model capable of operating at various bit-widths and policies.
Paper proposes a 1-bit quantization scheme for high-dimensional statistical estimation.
problem High-dimensional statistical estimation with limited data.
method Uniformly dithered 1-bit quantization for sparse covariance matrix estimation, sparse linear regression, and matrix completion.
result Near minimax rates in sub-Gaussian regime and improved rates in heavy-tailed regime.
This work proposes a complete 8-bit quantization framework for large-scale deep neural networks.
problem Training large-scale deep neural networks with high performance and low memory footprint.
method WAGEUBN framework that quantizes all data paths including weights, activations, gradients, errors, updates, and batch normalization.
result Achieves competitive accuracy on the ImageNet dataset using only 8-bit integers.
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.
This paper develops quantization algorithms for random Fourier features, simplifying the process and improving performance.
problem Efficient quantization of random Fourier features for better performance and storage.
method Developed Lloyd-Max (LM) and LM2-RFF quantization schemes for random Fourier features. result The marginal distribution of RFF is independent of the Gaussian kernel parameter γ, simplifying quantization design.
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…
This paper tackles tensor recovery from noisy and multi-level quantized measurements.
problem Tensors from multi-level quantized measurements.
method Nonconvex optimization problem with alternating proximal gradient descent.
result The recovery error diminishes to zero with increasing tensor dimensions.
Adaptive quantization improves SGD accuracy in data-parallel settings.
problem Fixed gradient quantization schemes lead to suboptimal performance in deep learning.
method Developed adaptive quantization schemes ALQ and AMQ that update compression schemes based on gradient statistics.
result Improved validation accuracy on CIFAR-10 and ImageNet datasets by 2% and 1% respectively.
Paper studies quantized LRMR with random dithering for correlated tasks.
problem Estimating coefficient matrix in quantized multivariate regression.
method Uniform quantization with random dithering, constrained and regularized Lasso estimators.
result Achieves minimax optimal rate with dithering, slightly worsens quantization effect.
Simplified neural network quantization speeds up process by 8 epochs.
problem Efficient quantization of neural networks for mobile devices.
method Trained scale factors for quantization thresholds.
result Significant reduction in training time and model size.
Quantized-TinyLLaVA reduces communication costs in split learning for multimodal models.
problem High communication costs in split learning for multimodal models.
method Integrates a compression module that quantizes intermediate features into discrete representations before transmission.
result Achieves an approximate 87.5% reduction in communication overhead with 2-bit quantization.
We prove several versions of "quantization commutes with reduction" for circle actions on manifolds that are not symplectic. Instead, these manifolds possess a weaker structure, such as a spin^c structure. Our theorems work whenever the quantization data and the reduction data are compatible; this condition always hold…
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.
A G-equivariant spin^c structure on a manifold gives rise to a virtual representation of the group G, called the spin^c quantization of the manifold. We present a cutting construction for S^1-equivariant spin^c manifolds, and show that the quantization of the original manifold is isomorphic to the direct sum of the qua…
A scalable approach to learning from probability measures using quantization.
problem Efficiently comparing and manipulating large sets of probability measures.
method Quantization of probability measures to a fixed support, followed by optimal transport computations.
result Consistency and convergence guarantees for quantized measures in various OT-based tasks.
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…
Here we present a novel approach to statistical analysis of financial time series. The approach is based on n-grams frequency dictionaries derived from the quantized market data. Such dictionaries are studied by evaluating their information capacity using relative entropy. A specific quantization of (originally conti…
We analyze the effect of quantizing weights and activations of neural networks on their loss and derive a simple regularization scheme that improves robustness against post-training quantization. By training quantization-ready networks, our approach enables storing a single set of weights that can be quantized on-deman…
Study quantized models' privacy against membership inference attacks.
problem Privacy risk in quantized machine learning models.
method Proposed a new MIS indicator for post-training quantization procedures, minimizing empirical loss.
result Demonstrated effectiveness of new MIS indicator in assessing and ranking privacy risk.
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.
BiQGEMM efficiently multiplies quantized DNN weights using lookup tables.
problem Efficiently multiplying quantized DNN weights on CPUs/GPUs with limited memory.
method BiQGEMM pre-computes and stores redundant intermediate results in lookup tables.
result BiQGEMM achieves lower overall computations and higher performance.
Survey on quantization methods on Kähler manifolds.
problem None explicitly stated; focuses on methods.
method Deformation quantization, geometric quantization, Berezin-Toeplitz quantization, BV quantization.
result New relationships among quantization methods on Kähler manifolds.
A new gradient quantization scheme improves communication efficiency in distributed training.
problem Efficiently compressing gradients for parallel training of large models.
method Proposes a new gradient quantization scheme with theoretical guarantees and empirical performance.
result The new scheme matches and exceeds the performance of existing methods.
Study proves convergence of quantized geodesics to Mabuchi geodesics.
problem Convergence of quantized geodesics to Mabuchi geodesics in short time.
method Real-analytic initial data and convergence proof.
result Proves convergence of quantized Bergman geodesics to Mabuchi geodesics.
Analyzes quantization of flux observables in gauge theories.
problem Lifting Poisson-brackets of flux observables to higher moduli stacks.
method Systematic analysis of canonical quantization and flux quantization laws.
result Topological quantum observables form homology Pontrjagin algebra of loop space.
Paper proposes method to recover quantized data with missing info.
problem Recovering quantized data with missing information.
method Regularized convex cost function with Bi-factorization and Augmented Lagrangian Method.
result The method finds global minimizer of the cost function.
Estimates means in metric spaces using quantization.
problem No practical estimator for Fréchet means in all metric spaces.
method Introduced estimators based on random quantization and data-driven partitioning.
result Universal consistency of estimators across separable metric spaces and Banach spaces.
Low-precision streaming PCA estimates the leading eigenvector with limited precision.
problem Estimating the leading eigenvector in a streaming setting with limited precision.
method Oja's algorithm with linear and nonlinear stochastic quantization.
result A batched version of the quantized variants achieves the lower bound on quantization error up to logarithmic factors.
Decentralized detection avoids sharing data, controls false discoveries.
problem Global false discovery rate control in decentralized novelty detection.
method Quantized surrogate models for low-precision sharing, preserving exchangeability.
result Quantized composite scores maintain competitive statistical power with reduced communication.
Paper proposes a fast stochastic algorithm for neural network quantization with error bounds.
problem Error analysis for quantized neural networks with non-convex loss functions and nonlinear activations.
method Greedy path-following mechanism combined with stochastic quantizer.
result Established full-network error bounds for quantized neural networks.
New method for flux quantization on phase space stacks.
problem Defining and constructing flux-quantized phase space stacks.
method Observation of flux densities and characterization of Cauchy data.
result Flux-quantized phase space stacks have classifying spaces with rational Whitehead L-infinity algebra.
AdaRound improves post-training quantization of neural networks.
problem Improving the accuracy of quantized weights in neural networks.
method Adaptive rounding mechanism that adapts to data and task loss.
result AdaRound outperforms rounding-to-nearest and achieves state-of-the-art performance.
The paper offers error bounds for quantized dynamical models.
problem Accuracy of dynamical models from dependent data sequences.
method Developed uniform error bounds for quantized models and imperfect optimization algorithms.
result Unified bounds for slow and fast rates, scaling with model encoding bits.
CoDeQ simplifies joint model compression by integrating pruning and quantization.
problem Joint pruning and quantization methods are complex and require additional procedures.
method CoDeQ uses a dead-zone quantizer to directly induce sparsity and learn quantization parameters.
result CoDeQ achieves high sparsity and low-precision accuracy with minimal bit operations.
QDSB accelerates Schrödinger bridge learning with quantized approximations.
problem Learning generative models from unpaired samples.
method Quantized diffusion Schrödinger bridges (QDSB) using anchor-quantized distributions and cell-wise sampling.
result QDSB achieves sample quality similar to existing methods but with significantly less computational time.
Deep task-based quantization improves MIMO signal processing.
problem Improving performance of MIMO signal processing with scalar ADCs.
method Data-driven task-oriented quantization using deep learning.
result Deep task-based quantization can approach optimal performance limits.
This work studies scaling laws for low-precision training in high-dimensional linear regression.
problem Optimizing trade-off between model quality and training costs in high-dimensional linear regression.
method Theoretical study of scaling laws for low-precision training within a high-dimensional sketched linear regression framework, analyzing multiplicative and additive quantization.
result Multiplicative quantization maintains full-precision model size, while additive quantization reduces effective model size.
A new method reduces communication in distributed learning by skipping less informative gradient updates.
problem Efficient communication in distributed machine learning.
method Quantizes and skips less informative gradients to reduce communication overhead.
result Proves linear convergence rate similar to gradient descent with significant communication savings.
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.
Recent research implies that training and inference of deep neural networks (DNN) can be computed with low precision numerical representations of the training/test data, weights and gradients without a general loss in accuracy. The benefit of such compact representations is twofold: they allow a significant reduction o…