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arXiv research

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.

168,742 papers · 148 categories

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7142128 · May 201919922001200920172026
48 results for 1-bit quantization

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.

New protocols show 1-bit mean estimation can be order-optimal without interaction.

problem Can 1-bit mean estimation be optimal without interaction?
method Adaptive and non-adaptive threshold and interval queries, with one adaptive transition.
result Arbitrary non-adaptive quantizers can match the adaptive rate, suggesting interaction is not necessary.

Paper offers robust recovery for 1-bit sensing with partial Gaussian circulant matrices.

problem Accurately recovering vectors from 1-bit measurements using structured matrices.
method Correlation-based optimization with randomly signed partial Gaussian circulant matrices and generative models.
result Recovery guarantees match those for i.i.d. Gaussian matrices but with faster computation.

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

problem Previous quantization methods lacked differentiability and scalability.
method The approach is differentiable and scalable, using bit-shifting and logarithmic quantization.
result The method achieves comparable accuracy to state-of-the-art approaches with less training time and lower inference cost.

Binary Iterative Hard Thresholding converges with optimal number of 1-bit measurements.

problem Recovering sparse signals from 1-bit compressed measurements.
method Binary Iterative Hard Thresholding (BIHT) algorithm.
result BIHT converges with only O(k/ε) measurements, optimal for recovery.

New algorithm tackles batched stochastic linear bandits with 1-bit communication constraints.

problem Stochastic linear bandits with 1-bit communication constraints.
method Phased-elimination algorithms based on G-optimal designs and 1-bit mean estimation.
result Achieves near-optimal regret bounds for broad scaling regimes.

BiTAT improves neural network quantization for edge devices by focusing on weight dependencies and disentangling them.

problem Performance degradation of compact neural networks under extreme quantization.
method Task-dependent Aggregated Transformation (BiTAT) method that orthonormalizes weights and progressively quantizes them.
result BiTAT effectively preserves model performance on ImageNet and CIFAR-100 with compact backbones.

Unified framework for uniform signal recovery in nonlinear GCS with 1-bit/quantized measurements.

problem Uniform recovery guarantees for nonlinear generative compressed sensing.
method Unified framework using generalized Lasso and Lipschitz approximation.
result Uniform recovery of all signals in the ball up to an error of ε using approximately O(k/ε^2) samples.

New quantization methods improve accuracy of Random Fourier Features.

problem Improving accuracy of Random Fourier Features for machine learning.
method Sigma-Delta and distributed noise-shaping quantization methods for 1-bit and low bit-depth quantization.
result Quantized RFFs allow high accuracy approximation of underlying kernels with polynomial error decay.

Paper analyzes BIHT for noisy 1-bit CS, improving results with up to τ-fraction of incorrect measurements.

problem Estimating sparse vectors from noisy sign measurements in 1-bit compressed sensing.
method Binary Iterative Hard Thresholding (BIHT) algorithm, using Gaussian matrices and high-dimensional geometry analysis.
result BIHT provides estimates within ε+τ error with τ-fraction of incorrect measurements, maintaining universality of measurements.

Enhances LLM quantization with MDBF, improving perplexity and accuracy.

problem Limited performance of Double Binary Factorization in extreme quantization.
method Introduces Multi-envelope DBF, retaining sign matrices and replacing single envelope with rank-ll envelope.
result Improves perplexity and zero-shot accuracy over previous binary formats.

The recent framework of compressive statistical learning aims at designing tractable learning algorithms that use only a heavily compressed representation-or sketch-of massive datasets. Compressive K-Means (CKM) is such a method: it estimates the centroids of data clusters from pooled, non-linear, random signatures of …

2018-04-26abs ↗pdf ↗

Study 1-bit compressive sensing with generative models, improving recovery accuracy.

problem Accurately recover sparse vectors from binary measurements with generative models.
method Analyzes noiseless and noisy 1-bit measurements with i.i.d.~Gaussian and Lipschitz continuous generative priors, proving sample complexity bounds and stability properties.
result Proves sample complexity bounds and stability properties for 1-bit compressive sensing with generative models.

Matrix completion has a long-time history of usage as the core technique of recommender systems. In particular, 1-bit matrix completion, which considers the prediction as a ``Recommended'' or ``Not Recommended'' question, has proved its significance and validity in the field. However, while customers and products aggre…

2019-04-07abs ↗pdf ↗

New method predicts binary matrix entries using empirical Bayes and low-rank structure.

problem Predicting unobserved entries in binary matrices.
method Empirical Bayes method motivated by Efron--Morris estimator, exploiting low-rank structure.
result Superior performance in predictive accuracy, calibration, and efficiency compared to existing methods.

The paper develops a robust signal estimation method for noisy measurements from generative models.

problem Signal estimation from noisy non-linear measurements with adversarial corruptions.
method Generalized Lasso approach with sub-Gaussian measurements and adversarial noise consideration.
result The method requires $O\left(\frac{k}{ε^2}\log L ight)$ samples for εε-error recovery, robust to adversarial noise.

Study improves fractional posterior for 1-bit matrix completion.

problem Estimating a binary matrix from observed entries.
method Fractional posterior approach with low-rank factorization and spectral scaled Student priors.
result Concentration results for fractional posterior, demonstrating effectiveness in matrix recovery.

We consider the problem of noisy 1-bit matrix completion under an exact rank constraint on the true underlying matrix MM^*. Instead of observing a subset of the noisy continuous-valued entries of a matrix MM^*, we observe a subset of noisy 1-bit (or binary) measurements generated according to a probabilistic model. W…

2015-02-24abs ↗pdf ↗

Paper studies signal detection in noisy environments with limited communication.

problem Signal detection in Gaussian noise with 1-bit communication constraints.
method Derives lower bounds and exhibits optimal testing strategies.
result Optimal distributed testing strategies attain the derived lower bound.

We consider in this paper the problem of noisy 1-bit matrix completion under a general non-uniform sampling distribution using the max-norm as a convex relaxation for the rank. A max-norm constrained maximum likelihood estimate is introduced and studied. The rate of convergence for the estimate is obtained. Information…

2013-09-24abs ↗pdf ↗

Binary Neural Networks (BNNs) show promising progress in reducing computational and memory costs but suffer from substantial accuracy degradation compared to their real-valued counterparts on large-scale datasets, e.g., ImageNet. Previous work mainly focused on reducing quantization errors of weights and activations, w…

2019-06-19abs ↗pdf ↗

Autoencoders fail to capture sparse structure in 1-bit data compression.

problem Proving the performance of shallow autoencoders on sparse data compression.
method Gradient descent analysis and approximate message passing.
result Gradient descent minimizer for sparse data is the identity (up to permutation) above critical sparsity.

Study on recovering supports of multiple sparse vectors from mixed linear measurements.

problem Recovering supports of multiple sparse vectors from a mixture of linear measurements.
method Developed algorithms to identify the support of all component vectors using polynomial and quasi-polynomial number of measurements.
result Polynomial and quasi-polynomial number of measurements sufficient for recovering the supports of all component vectors.

State of the art deep learning models have made steady progress in the fields of computer vision and natural language processing, at the expense of growing model sizes and computational complexity. Deploying these models on low power and mobile devices poses a challenge due to their limited compute capabilities and str…

2018-10-25abs ↗pdf ↗

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.

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.