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.
Mixed-precision CA-SGD for generalized linear models on GPUs
problem SGD communication bottleneck
method Mixed-precision CA-SGD
result Matches FP32 SGD loss within 0.5% on various problems
Cheetah framework optimizes DNNs for edge devices using low-precision formats.
problem Reducing DNN model size for edge devices while maintaining accuracy.
method Mixed low-precision hardware and software co-design framework using posit and other formats.
result 16-bit posits outperform 16-bit floating point in training, and [5..8]-bit posits improve inference performance.
This paper enables deep network inference on microcontrollers with improved accuracy and reduced memory usage.
problem Deploying deep networks on resource-constrained edge-devices with low memory and computational constraints.
method Mixed low-bitwidth compression, rule-based iterative procedure for bit precision determination, quantization-aware retraining, and integer-only model conversion.
result Improved Top1 accuracy of 68% on a 2MB FLASH memory STM32H7 microcontroller, 8% higher than 8-bit implementations.
SINGD improves KFAC for memory-efficiency and stability in low-precision training.
problem Memory inefficiency and numerical instability of KFAC in low-precision training.
method Formulated inverse-free KFAC update and imposed structures in Kronecker factors.
result SINGD is memory-efficient and numerically robust, often outperforming AdamW in half precision.
The study analyzes numerical stability in large language models using mixed-precision arithmetic.
problem Numerical stability of large language models using low-precision arithmetic.
method Developed a mixed-precision analysis of transformer inference, deriving bounds for condition numbers and forward error.
result Established that numerical stability is determined by the interplay between weight magnitude and the growth of the residual stream.
Bayesian Bits unifies quantization and pruning through gradient optimization.
problem Joint mixed precision quantization and pruning for efficient neural networks.
method Gradient-based optimization with a novel bit width decomposition and learnable stochastic gates.
result Bayesian Bits achieves better accuracy vs. efficiency trade-off compared to static bit width networks.
A new quantization strategy reduces Transformer model size and inference time.
problem Heavy computation load and memory overhead in Transformer models for mobile devices.
method Mixed precision quantization with varying bits per word in embedding blocks.
result 11.8x smaller model size and 3.5x speed up for on-device NMT.
HMQ improves quantization for edge devices with mixed precision.
problem Efficient quantization for edge devices with uniform, power-of-two thresholds.
method Introduces HMQ, a mixed precision quantization block that repurposes Gumbel-Softmax for searching over quantization schemes.
result Achieves competitive and state-of-the-art results on ImageNet despite restrictions.
Improved deep learning model deployment on tiny MCUs with mixed-precision quantization.
problem Memory limitations prevent accurate deployment of DNN models on tiny MCUs.
method Automated mixed-precision quantization using Reinforcement Learning for MCU constraints.
result Mixed-precision models achieve high accuracy with uniform quantization policies.
New framework reduces cost of financial option pricing simulations on FPGAs.
problem Efficiently simulate financial option pricing with reduced computational cost.
method Nested MLMC framework with low precision calculations on FPGAs.
result Higher computational savings compared to existing mixed-precision MLMC frameworks.
Efficient Bitwidth Search optimizes neural network quantization for better performance.
problem Finding optimal bitwidth for weights and activations of each layer efficiently.
method EBS algorithm reusing meta weights and binary decomposition for efficient mixed precision convolution.
result Mixed precision QNN outperforms uniform bitwidth and other techniques on CIFAR10 and ImageNet.
EMPIR combines low and full precision DNNs to enhance robustness against adversarial attacks.
problem Vulnerability of DNNs to adversarial attacks that misclassify inputs with small perturbations.
method Ensemble of quantized DNN models with different numerical precisions.
result EMPIR ensembles increase adversarial robustness by 42.6% on average across different tasks.
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.
MobileNet-v2 improves re-ID on edge devices with mixed precision.
problem Real-time person re-identification in edge devices with limited resources.
method Mixed precision training (FP32 and FP16) for MobileNet-v2 on edge nodes.
result Mixed precision training improves inference throughput and reduces power consumption.
Paper explores low-precision SGLD for neural networks, reducing costs without sacrificing performance.
problem Infeasibility of low-precision sampling in large-scale scenarios.
method Developed low-precision SGLD with quantization function and full-precision gradient accumulators.
result Low-precision SGLD achieves comparable performance to full-precision SGLD with only 8 bits.
This paper improves low-precision sampling using SGHMC for deep learning models.
problem Enhancing training efficiency of deep neural networks with low-precision training.
method Investigates low-precision sampling via Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) for both log-concave and non-log-concave distributions.
result Low-precision SGHMC achieves quadratic improvement in error compared to SGLD for non-log-concave distributions.
QPyTorch simplifies low-precision training simulations.
problem Empirical evaluation of low-precision training algorithms.
method Native PyTorch framework with efficient fused-kernel approach.
result Supports various low-precision configurations and rounding options.
Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables. We give a precise graph-theoretic characterization of when submatrices of the cov…
New method for robust matrix completion with mixed data types.
problem Recovering a structured low rank matrix with mixed data types.
method Proposes a computationally feasible statistical approach with strong recovery guarantees for mixed data types.
result Strong recovery guarantees for low rank matrix completion with mixed data types.
Low precision operations can provide scalability, memory savings, portability, and energy efficiency. This paper proposes SWALP, an approach to low precision training that averages low-precision SGD iterates with a modified learning rate schedule. SWALP is easy to implement and can match the performance of full-precisi…
We improve Gaussian copula models for imputing mixed data types with precise approximations.
problem Imputing missing values with mixed data types in surveys and medical applications.
method We use randomized quasi-Monte Carlo procedures for direct and arbitrarily precise approximations of model estimation and imputation.
result Our method yields lower errors for model parameters and imputed values compared to existing methods.
Efficient deep neural network (DNN) inference on mobile or embedded devices typically involves quantization of the network parameters and activations. In particular, mixed precision networks achieve better performance than networks with homogeneous bitwidth for the same size constraint. Since choosing the optimal bitwi…
Three RFF-based methods for nonlinear causal discovery in mixed data.
problem Nonlinear causal discovery in mixed data with computational constraints.
method FFML, TRFF, and FFCI methods for score-based, constraint-based, and hybrid causal discovery.
result FFML and TRFF methods provide complementary performance in causal discovery.
Unified formula for training dynamics of linear networks combining lazy and balanced regimes.
problem Training dynamics of linear networks in two distinct setups: lazy and balanced/active.
method Unified formula for the evolution of the learned matrix, combining lazy and balanced regimes.
result Unified formula allows for rapid convergence and low rank bias, proving a complete phase diagram.
Low-precision computation is often used to lower the time and energy cost of machine learning, and recently hardware accelerators have been developed to support it. Still, it has been used primarily for inference - not training. Previous low-precision training algorithms suffered from a fundamental tradeoff: as the num…
PAIN network improves imputation for mixed datasets.
problem Missing data in diverse scientific domains.
method Dynamic adaptive imputation using statistical methods, random forests, and autoencoders.
result PAIN outperforms traditional imputation methods in preserving data distributions.
Spectral methods improve signal recovery in mixed GLMs with precise asymptotics.
problem Estimating multiple signals from unlabeled observations in mixed GLMs.
method Developed exact asymptotics for spectral methods in a proportional regime.
result Optimized spectral method combined with a linear estimator minimizes estimation error.
Adaptive loss scaling speeds up and improves deep learning training.
problem Numerical underflow in mixed precision training.
method Adaptive loss scaling that automatically computes layer-wise loss scale values during training.
result Adaptive loss scaling leads to shorter convergence time and improved accuracy.
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.
Low precision networks in the reinforcement learning (RL) setting are relatively unexplored because of the limitations of binary activations for function approximation. Here, in the discrete action ATARI domain, we demonstrate, for the first time, that low precision policy distillation from a high precision network pro…
The paper proposes methods for predicting missing values in mixed data matrices.
problem Matrix completion for mixed data types (continuous, binary, ordinal).
method Generalized latent factor models for low-rank matrix estimation with entrywise consistency.
result Tight probabilistic error bounds for the proposed estimators.
Low precision weights, activations, and gradients have been proposed as a way to improve the computational efficiency and memory footprint of deep neural networks. Recently, low precision networks have even shown to be more robust to adversarial attacks. However, typical implementations of low precision DNNs use unifor…
GNMR controls runtime stability in low-precision language model training.
problem Efficient low-precision training faces numerical risks at specific operators.
method GNMR compares gradient norms to historical means, applying bounded recovery actions.
result GNMR preserves high-fidelity quality with sparse, budgeted recovery.
The study prevents model collapse in overparameterized linear regression by mixing real and synthetic labels.
problem Preventing model collapse in overparameterized linear regression.
method Iterative mixing of real and synthetic labels, deriving generalization error formulae.
result Optimal mixing ratio converges to the reciprocal of the golden ratio for isotropic features.
Generalized Precision Matrix for scalable estimation of nonparametric Markov networks.
problem Estimating conditional independence structure in general distributions for all data types.
method Generalized Precision Matrix (GPM) for mixed-type variables, regularized score matching framework for scalability.
result Validated theoretical results and demonstrated scalability in various settings.
The paper explores knotoids, pseudo knotoids, braidoids, and pseudo braidoids on the torus.
problem The study of knotoids, pseudo knotoids, braidoids, and pseudo braidoids on the torus.
method Introducing new knotoid and braidoid concepts, isotopy theorems, state sum formulas, and Alexander and Markov theorems.
result Formulation and proof of Alexander and Markov theorems for mixed knotoids and mixed pseudo knotoids.
A new method for Gaussian Processes handles mixed continuous and categorical inputs.
problem Modeling cross-correlations between continuous and categorical data.
method Low-Rank Correlation (LRC) method for Gaussian Processes with flexible rank approximation.
result LRC outperforms existing methods in estimating cross-correlations and predicting response surfaces.
We study the regular conditional law of mixed Gaussian Volterra processes under the influence of model disturbances. More precisely, we study prediction of Gaussian Volterra processes driven by a Brownian motion in a case where the Brownian motion is not observable, but only a noisy version is observed. As an applicati…
Proposes a convex model for mixed logit to handle individual heterogeneity.
problem Non-convex optimization in mixed logit models for individual heterogeneity.
method Sparse and low-rank decomposition for convex formulation.
result Convex formulation avoids simulation-based approximation and unstable model interpretation.
FQ-Conv quantizes CNNs for efficient inference with low-precision weights and activations.
problem Reducing precision in DNNs leads to reduced accuracy.
method Fully quantized convolutional neural networks (FQ-Conv) using novel quantization and training techniques.
result Ternary-weight CNNs perform nearly as well as full-precision networks.
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…
We prove the existence of C^{\infty} local solutions to a class of mixed type Monge-Ampere equations in the plane. More precisely, the equation changes type to finite order across two smooth curves intersecting transversely at a point. Existence of C^{\infty} global solutions to a corresponding class of linear mixed ty…
New method detects essential tori in mixed singularity links.
problem Detecting essential tori in mixed singularity link complements.
method Analyzing properties of defining mixed polynomials.
result Explicit criteria for essential tori existence.
SQWA improves low-precision DNNs with model averaging and quantization.
problem Designing good generalization DNNs with quantized weights.
method Floating-point model training, direct quantization, multiple low-precision models, weight averaging, re-quantization, fine-tuning, loss visualization.
result State-of-the-art results for 2-bit QDNNs on CIFAR-100 and ImageNet datasets.
The paper develops new inequalities for Markov chain sums, linking them to mixing time.
problem Establishing concentration inequalities for Markov chain sums.
method Developed novel concentration inequalities for geometrically ergodic Markov chains, linking bounds to mixing time constants.
result Explicit bounds for additive functionals of Markov chains, linked to Rosenthal inequality constants and mixing properties.
Log-Normal Multiplicative Dynamics improves low-precision training of neural networks.
problem Training large neural networks with low precision is unstable.
method Derive a Bayesian learning rule with log-normal posterior distributions and multiplicative updates.
result LMD achieves stable and accurate training for Vision Transformer and GPT-2.
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.