SWALP averages SGD iterates for low-precision training, improving scalability and performance.
problem Improving scalability and performance in low-precision training.
method Averages low-precision SGD iterates with a modified learning rate schedule.
result SWALP matches full-precision SGD performance with 8-bit quantization and converges to optimal solutions.
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.
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.
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.
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.
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…
Posits improve DNN training efficiency on edge devices.
problem Training deep neural networks with low-precision formats.
method Used posits (5-8 bit) for DNN training compared to floating point.
result 16-bit posits outperform 16-bit floating point for end-to-end training.
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.
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.
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.
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.
Currently, deep neural networks are deployed on low-power portable devices by first training a full-precision model using powerful hardware, and then deriving a corresponding low-precision model for efficient inference on such systems. However, training models directly with coarsely quantized weights is a key step towa…
Low precision RL distillation enables real-time game play on neuromorphic hardware.
problem Limited use of low precision networks in reinforcement learning.
method Policy distillation from high precision to low precision networks.
result Low precision distillation enables real-time game play on low-power hardware.
The study analyzes convergence of adaptive optimizers under low-precision training.
problem Understanding why low-precision training remains effective for large models.
method Developed a theoretical framework for analyzing convergence of adaptive optimizers under floating-point quantization.
result Adaptive optimizers retain convergence rates close to full-precision methods under logarithmic mantissa scaling.
Training of large-scale deep neural networks is often constrained by the available computational resources. We study the effect of limited precision data representation and computation on neural network training. Within the context of low-precision fixed-point computations, we observe the rounding scheme to play a cruc…
Recently there has been significant interest in training machine-learning models at low precision: by reducing precision, one can reduce computation and communication by one order of magnitude. We examine training at reduced precision, both from a theoretical and practical perspective, and ask: is it possible to train …
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.
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.
A new method quantizes neural networks to low-precision without STE, improving accuracy.
problem Quantization of neural networks to low-precision without a complete theoretical understanding.
method Alpha-blending (AB) using stochastic gradient descent (SGD) to quantize weights and gradually increase the coefficient α. result Improves top-1 accuracy by 0.9% on 1-bit BinaryNet, 0.82% on 8-bit MobileNet v1, and 2.93% on 4-bit ResNet_50 v1/2 compared to STE.
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…
A method improves deep network accuracy with low precision quantization.
problem Maintaining high accuracy in low precision deep networks.
method Learned Step Size Quantization, improving quantizer configuration and gradient estimation.
result Achieves highest accuracy on ImageNet with 2-4 bit precision models.
MCQ uses Monte Carlo methods to efficiently quantize neural networks without re-training.
problem Efficiently quantizing neural networks for lower power consumption.
method Importance sampling for quantization of weights and activations.
result Minimal accuracy loss with quantized networks compared to full-precision networks.
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.
Paper proposes efficient DNN inference using low precision arithmetic.
problem High computational complexity and memory requirement of DNNs.
method Combining 2bit or 3bit integer arithmetics with binary shift and clipping for float32 accuracy.
result Efficient DNN inference on low precision hardware with minimal performance loss.
CALDERA compresses large language models by approximating weight matrices with low-rank, low-precision factors.
problem The large sizes of Large Language Models (LLMs) hinder deployment on edge devices.
method CALDERA approximates weight matrices W as Q+LR, where L and R are low-rank factors quantized to low precision. result CALDERA achieves better zero-shot performance than existing techniques, especially with low bit precision.
The use of low-precision fixed-point arithmetic along with stochastic rounding has been proposed as a promising alternative to the commonly used 32-bit floating point arithmetic to enhance training neural networks training in terms of performance and energy efficiency. In the first part of this paper, the behaviour of …
Paper explores reducing precision in SVM for faster text classification.
problem Efficiency in multi-class text classification training.
method Comparison of SVM trained with reduced precision (16-bit, half) vs original.
result Reduced precision training maintains text classification accuracy.
Gradient descent stagnates in low-precision, but unbiased rounding schemes improve convergence.
problem Stagnation of gradient descent in low-precision computation.
method Proposed unbiased stochastic rounding schemes that trade zero bias for larger probability of preserving small gradients.
result Unbiased rounding methods typically improve convergence rate of gradient descent for convex problems.
This study improves Ernie's accuracy for INT8 inference by modifying its training process.
problem Improving the accuracy of pre-trained models like Ernie for low precision inference.
method Integrates a regularizer into the training process to make it more robust to quantization.
result Increased INT8 accuracy for Ernie models.
Quantization-aware training can recover accuracy lost by post-training quantization.
problem Post-training quantization (PTQ) can fail sharply at aggressive bitwidths.
method A unified geometric framework that explains PTQ failure and QAT recovery.
result QAT has a useful bias that steers iterates back into the basin.
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.
E2-Train reduces training energy by 80%+ for state-of-the-art CNNs.
problem Efficient training of energy-hungry CNNs on edge devices.
method Selective layer update, stochastic mini-batch dropping, and sign prediction for low-precision backpropagation.
result Achieves >90% energy savings for training ResNet-74 on CIFAR-10.
This paper introduces a new method to train normalizing flows using precision-recall divergences.
problem Training generative models with mode dropping and low-quality samples.
method Introduces PR-divergences and proposes a novel generative model to minimize precision-recall trade-offs.
result Normalizing flows can be trained to achieve specific precision-recall trade-offs using PR-divergences.
Low-precision quantization improves kernel approximation under memory constraints.
problem Training kernel approximation methods efficiently with limited memory.
method Low-precision quantization of random Fourier features (LP-RFFs).
result LP-RFFs can match the performance of full-precision RFFs and Nyström method with significantly less memory.
BCGD algorithm improves training of quantized neural networks.
problem Training quantized deep neural networks at low bit-widths.
method Introduces coarse gradient descent and blended correction for training.
result BCGD achieves high accuracy in quantized neural networks.
New method analyzes accumulation precision in deep learning networks.
problem Lack of precision analysis for accumulation in deep learning training.
method Statistical approach to analyze partial sum accumulations and derive equations for minimum required bits.
result Reduced accumulation precision can lead to loss of information and degraded network quality.
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.
Gradient descent with biased rounding errors converges faster under certain conditions.
problem Stagnation or negative impact of rounding errors in neural network training with low precision.
method Analysis of gradient descent with stochastic fixed-point rounding errors under the Polyak-Lojasiewicz inequality.
result Biased rounding errors can improve convergence rates, especially when the Polyak-Lojasiewicz inequality holds.
This paper explains how low-precision arithmetic causes loss spikes in deep learning models.
problem Loss spikes during long-term training of deep neural networks.
method Analyzes the impact of floating-point precision limits on gradient updates and feature means.
result Numerical Feature Inflation (NFI) explains loss spikes and rapid parameter norm growth.
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.
This paper automates the creation of low precision deep learning operators for mobile devices.
problem Deploying large deep learning models on low power devices is challenging due to limited compute capabilities and energy budgets.
method Introduces a workflow to generate high-performance low precision deep learning operators for multiple CPU architectures, including optimizations like memory tiling and vectorization.
result 1-bit and 2-bit convolutions achieve up to 16x and 2.3x speedups over 16-bit integer baselines on ARM Cortex-A53 CPU.
Low-bit training framework reduces energy consumption in CNNs.
problem Reducing energy consumption in convolutional neural networks.
method Low-bit training framework using MLS tensor format with dynamic quantization.
result Achieves superior trade-off between accuracy and bit-width.
Flexible deep learning models for dynamic accuracy and speed trade-offs.
problem Dynamic accuracy and speed trade-offs in real-world applications.
method Training deep neural networks with a new method allowing flexible numerical precision during inference.
result Achieved comparable accuracy to dedicated models trained at the same precision with dynamic precision settings.
Paper addresses quantization bias in neural networks, proposing a simple method to improve performance.
problem Quantization bias causes performance degradation in low-precision neural networks.
method Compensating for quantization-induced shift by adding a constant to the bias term.
result Simple methods for estimating correction constants can match training-based quantization performance at lower cost.
SGMs can generate samples from low-dimensional data manifolds.
problem Understanding the conditions under which SGMs can produce samples from a low-dimensional data manifold.
method Analyzing the conditions for SGMs to approximate the scores and generate samples from a manifold.
result Precise conditions for SGMs to generate samples from a low-dimensional data manifold.
OverQ increases model accuracy by handling outliers in neural networks with minimal hardware changes.
problem Handling outliers in neural network weights and activations for low-precision quantization.
method Overwrite quantization (OverQ) that opportunistically increases bitwidth for activation outliers.
result OverQ can handle over 90% of outliers and achieve +5% ImageNet Top-1 accuracy on a quantized ResNet-50 at 4 bits.
Paper improves DNN accelerator robustness against bit errors with energy savings.
problem Bit errors in quantized DNN weights reduce energy efficiency.
method Combines robust fixed-point quantization, weight clipping, and random bit error training.
result Significantly improves robustness against random bit errors with high energy savings.
CoNNTrA trains DNNs with low-power, low-memory constraints.
problem Training deep neural networks on edge computing systems with low power and memory usage.
method Coordinate gradient descent-based approach for training DNNs with constrained learning parameters.
result CoNNTrA models use 32x less memory and have comparable errors to Backpropagation models.