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arXiv:2408.15300공식 코드 · Papers with Code

GIFT-SW: Gaussian noise Injected Fine-Tuning of Salient Weights for LLMs

Parameter Efficient Fine-Tuning (PEFT) methods have gained popularity and democratized the usage of Large Language Models (LLMs). Recent studies have shown that a small subset of weights significantly impacts performance. Based on this observation, we introduce a novel PEFT method, called Gaussian noise Injected Fine Tuning of Salient Weights (GIFT-SW). Our method updates only salient columns, while injecting Gaussian noise into non-salient ones. To identify these columns, we developeda generalized sensitivity metric that extends and unifies metrics from previous studies. Experiments with LLaMA models demonstrate that GIFT-SW outperforms full fine-tuning and modern PEFT methods under the same computational budget. Moreover, GIFT-SW offers practical advantages to recover performance of models subjected to mixed-precision quantization with keeping salient weights in full precision.

arXiv:2408.14690공식 코드 · Papers with Code

Training-Free Activation Sparsity in Large Language Models

Activation sparsity can enable practical inference speedups in large language models (LLMs) by reducing the compute and memory-movement required for matrix multiplications during the forward pass. However, existing methods face limitations that inhibit widespread adoption. Some approaches are tailored towards older models with ReLU-based sparsity, while others require extensive continued pre-training on up to hundreds of billions of tokens. This paper describes TEAL, a simple training-free method that applies magnitude-based activation sparsity to hidden states throughout the entire model. TEAL achieves 40-50% model-wide sparsity with minimal performance degradation across Llama-2, Llama-3, and Mistral families, with sizes varying from 7B to 70B. We improve existing sparse kernels and demonstrate wall-clock decoding speed-ups of up to 1.53$\times$ and 1.8$\times$ at 40% and 50% model-wide sparsity. TEAL is compatible with weight quantization, enabling further efficiency gains.

arXiv:2408.13933공식 코드 · Papers with Code

MobileQuant: Mobile-friendly Quantization for On-device Language Models

Large language models (LLMs) have revolutionized language processing, delivering outstanding results across multiple applications. However, deploying LLMs on edge devices poses several challenges with respect to memory, energy, and compute costs, limiting their widespread use in devices such as mobile phones. A promising solution is to reduce the number of bits used to represent weights and activations. While existing works have found partial success at quantizing LLMs to lower bitwidths, e.g. 4-bit weights, quantizing activations beyond 16 bits often leads to large computational overheads due to poor on-device quantization support, or a considerable accuracy drop. Yet, 8-bit activations are very attractive for on-device deployment as they would enable LLMs to fully exploit mobile-friendly hardware, e.g. Neural Processing Units (NPUs). In this work, we make a first attempt to facilitate the on-device deployment of LLMs using integer-only quantization. We first investigate the limitations of existing quantization methods for on-device deployment, with a special focus on activation quantization. We then address these limitations by introducing a simple post-training quantization method, named MobileQuant, that extends previous weight equivalent transformation works by jointly optimizing the weight transformation and activation range parameters in an end-to-end manner. MobileQuant demonstrates superior capabilities over existing methods by 1) achieving near-lossless quantization on a wide range of LLM benchmarks, 2) reducing latency and energy consumption by 20\%-50\% compared to current on-device quantization strategies, 3) requiring limited compute budget, 4) being compatible with mobile-friendly compute units, e.g. NPU.

arXiv:2408.14267공식 코드 · Papers with Code

1-Bit FQT: Pushing the Limit of Fully Quantized Training to 1-bit

Fully quantized training (FQT) accelerates the training of deep neural networks by quantizing the activations, weights, and gradients into lower precision. To explore the ultimate limit of FQT (the lowest achievable precision), we make a first attempt to 1-bit FQT. We provide a theoretical analysis of FQT based on Adam and SGD, revealing that the gradient variance influences the convergence of FQT. Building on these theoretical results, we introduce an Activation Gradient Pruning (AGP) strategy. The strategy leverages the heterogeneity of gradients by pruning less informative gradients and enhancing the numerical precision of remaining gradients to mitigate gradient variance. Additionally, we propose Sample Channel joint Quantization (SCQ), which utilizes different quantization strategies in the computation of weight gradients and activation gradients to ensure that the method is friendly to low-bitwidth hardware. Finally, we present a framework to deploy our algorithm. For fine-tuning VGGNet-16 and ResNet-18 on multiple datasets, our algorithm achieves an average accuracy improvement of approximately 6%, compared to per-sample quantization. Moreover, our training speedup can reach a maximum of 5.13x compared to full precision training.

arXiv:2408.12691공식 코드 · Papers with Code

Quantization-aware Matrix Factorization for Low Bit Rate Image Compression

Lossy image compression is essential for efficient transmission and storage. Traditional compression methods mainly rely on discrete cosine transform (DCT) or singular value decomposition (SVD), both of which represent image data in continuous domains and, therefore, necessitate carefully designed quantizers. Notably, these methods consider quantization as a separate step, where quantization errors cannot be incorporated into the compression process. The sensitivity of these methods, especially SVD-based ones, to quantization errors significantly degrades reconstruction quality. To address this issue, we introduce a quantization-aware matrix factorization (QMF) to develop a novel lossy image compression method. QMF provides a low-rank representation of the image data as a product of two smaller factor matrices, with elements constrained to bounded integer values, thereby effectively integrating quantization with low-rank approximation. We propose an efficient, provably convergent iterative algorithm for QMF using a block coordinate descent (BCD) scheme, with subproblems having closed-form solutions. Our experiments on the Kodak and CLIC 2024 datasets demonstrate that our QMF compression method consistently outperforms JPEG at low bit rates below 0.25 bits per pixel (bpp) and remains comparable at higher bit rates. We also assessed our method's capability to preserve visual semantics by evaluating an ImageNet pre-trained classifier on compressed images. Remarkably, our method improved top-1 accuracy by over 5 percentage points compared to JPEG at bit rates under 0.25 bpp. The project is available at https://github.com/pashtari/lrf .

arXiv:2408.11743공식 코드 · Papers with Code

MARLIN: Mixed-Precision Auto-Regressive Parallel Inference on Large Language Models

As inference on Large Language Models (LLMs) emerges as an important workload in machine learning applications, weight quantization has become a standard technique for efficient GPU deployment. Quantization not only reduces model size, but has also been shown to yield substantial speedups for single-user inference, due to reduced memory movement, with low accuracy impact. Yet, it remains open whether speedups are achievable also in \emph{batched} settings with multiple parallel clients, which are highly relevant for practical serving. It is unclear whether GPU kernels can be designed to remain practically memory-bound, while supporting the substantially increased compute requirements of batched workloads. This paper resolves this question positively by describing the design of Mixed-precision Auto-Regressive LINear kernels, called MARLIN. Concretely, given a model whose weights are compressed via quantization to, e.g., 4 bits per element, MARLIN shows that batchsizes up to 16-32 can be supported with close to maximum ($4\times$) quantization speedup, and larger batchsizes up to 64-128 with gradually decreasing, but still significant, acceleration. MARLIN accomplishes this via a combination of techniques, such as asynchronous memory access, complex task scheduling and pipelining, and bespoke quantization support. Our experiments show that MARLIN's near-optimal performance on individual LLM layers across different scenarios can also lead to end-to-end LLM inference speedups (of up to $2.8\times$) when integrated with the popular vLLM serving engine. Finally, MARLIN is extensible to further compression techniques, like NVIDIA 2:4 sparsity, leading to additional speedups.

arXiv:2408.09027공식 코드 · Papers with Code

Efficient Autoregressive Audio Modeling via Next-Scale Prediction

Audio generation has achieved remarkable progress with the advance of sophisticated generative models, such as diffusion models (DMs) and autoregressive (AR) models. However, due to the naturally significant sequence length of audio, the efficiency of audio generation remains an essential issue to be addressed, especially for AR models that are incorporated in large language models (LLMs). In this paper, we analyze the token length of audio tokenization and propose a novel \textbf{S}cale-level \textbf{A}udio \textbf{T}okenizer (SAT), with improved residual quantization. Based on SAT, a scale-level \textbf{A}coustic \textbf{A}uto\textbf{R}egressive (AAR) modeling framework is further proposed, which shifts the next-token AR prediction to next-scale AR prediction, significantly reducing the training cost and inference time. To validate the effectiveness of the proposed approach, we comprehensively analyze design choices and demonstrate the proposed AAR framework achieves a remarkable \textbf{35}$\times$ faster inference speed and +\textbf{1.33} Fr\'echet Audio Distance (FAD) against baselines on the AudioSet benchmark. Code: \url{https://github.com/qiuk2/AAR}.

arXiv:2408.08554공식 코드 · Papers with Code

ABQ-LLM: Arbitrary-Bit Quantized Inference Acceleration for Large Language Models

Large Language Models (LLMs) have revolutionized natural language processing tasks. However, their practical application is constrained by substantial memory and computational demands. Post-training quantization (PTQ) is considered an effective method to accelerate LLM inference. Despite its growing popularity in LLM model compression, PTQ deployment faces two major challenges. First, low-bit quantization leads to performance degradation. Second, restricted by the limited integer computing unit type on GPUs, quantized matrix operations with different precisions cannot be effectively accelerated. To address these issues, we introduce a novel arbitrary-bit quantization algorithm and inference framework, ABQ-LLM. It achieves superior performance across various quantization settings and enables efficient arbitrary-precision quantized inference on the GPU. ABQ-LLM introduces several key innovations: (1) a distribution correction method for transformer blocks to mitigate distribution differences caused by full quantization of weights and activations, improving performance at low bit-widths. (2) the bit balance strategy to counteract performance degradation from asymmetric distribution issues at very low bit-widths (e.g., 2-bit). (3) an innovative quantization acceleration framework that reconstructs the quantization matrix multiplication of arbitrary precision combinations based on BTC (Binary TensorCore) equivalents, gets rid of the limitations of INT4/INT8 computing units. ABQ-LLM can convert each component bit width gain into actual acceleration gain, maximizing performance under mixed precision(e.g., W6A6, W2A8). Based on W2*A8 quantization configuration on LLaMA-7B model, it achieved a WikiText2 perplexity of 7.59 (2.17$\downarrow $ vs 9.76 in AffineQuant). Compared to SmoothQuant, we realized 1.6$\times$ acceleration improvement and 2.7$\times$ memory compression gain.

arXiv:2408.08437공식 코드 · Papers with Code

PQV-Mobile: A Combined Pruning and Quantization Toolkit to Optimize Vision Transformers for Mobile Applications

While Vision Transformers (ViTs) are extremely effective at computer vision tasks and are replacing convolutional neural networks as the new state-of-the-art, they are complex and memory-intensive models. In order to effectively run these models on resource-constrained mobile/edge systems, there is a need to not only compress these models but also to optimize them and convert them into deployment-friendly formats. To this end, this paper presents a combined pruning and quantization tool, called PQV-Mobile, to optimize vision transformers for mobile applications. The tool is able to support different types of structured pruning based on magnitude importance, Taylor importance, and Hessian importance. It also supports quantization from FP32 to FP16 and int8, targeting different mobile hardware backends. We demonstrate the capabilities of our tool and show important latency-memory-accuracy trade-offs for different amounts of pruning and int8 quantization with Facebook Data Efficient Image Transformer (DeiT) models. Our results show that even pruning a DeiT model by 9.375% and quantizing it to int8 from FP32 followed by optimizing for mobile applications, we find a latency reduction by 7.18X with a small accuracy loss of 2.24%. The tool is open source.

arXiv:2408.05517공식 코드 · Papers with Code

SWIFT:A Scalable lightWeight Infrastructure for Fine-Tuning

Recent development in Large Language Models (LLMs) and Multi-modal Large Language Models (MLLMs) have leverage Attention-based Transformer architectures and achieved superior performance and generalization capabilities. They have since covered extensive areas of traditional learning tasks. For instance, text-based tasks such as text-classification and sequence-labeling, as well as multi-modal tasks like Visual Question Answering (VQA) and Optical Character Recognition (OCR), which were previously addressed using different models, can now be tackled based on one foundation model. Consequently, the training and lightweight fine-tuning of LLMs and MLLMs, especially those based on Transformer architecture, has become particularly important. In recognition of these overwhelming needs, we develop SWIFT, a customizable one-stop infrastructure for large models. With support of over $300+$ LLMs and $50+$ MLLMs, SWIFT stands as the open-source framework that provide the most comprehensive support for fine-tuning large models. In particular, it is the first training framework that provides systematic support for MLLMs. In addition to the core functionalities of fine-tuning, SWIFT also integrates post-training processes such as inference, evaluation, and model quantization, to facilitate fast adoptions of large models in various application scenarios. With a systematic integration of various training techniques, SWIFT offers helpful utilities such as benchmark comparisons among different training techniques for large models. For fine-tuning models specialized in agent framework, we show that notable improvements on the ToolBench leader-board can be achieved by training with customized dataset on SWIFT, with an increase of 5.2%-21.8% in the Act.EM metric over various baseline models, a reduction in hallucination by 1.6%-14.1%, and an average performance improvement of 8%-17%.

arXiv:2408.03735공식 코드 · Papers with Code

Advancing Multimodal Large Language Models with Quantization-Aware Scale Learning for Efficient Adaptation

This paper presents the first study to explore the potential of parameter quantization for multimodal large language models to alleviate the significant resource constraint encountered during vision-language instruction tuning. We introduce a Quantization-aware Scale LeArning method based on multimodal Warmup, termed QSLAW. This method is grounded in two key innovations: (1) The learning of group-wise scale factors for quantized LLM weights to mitigate the quantization error arising from activation outliers and achieve more effective vision-language instruction tuning; (2) The implementation of a multimodal warmup that progressively integrates linguistic and multimodal training samples, thereby preventing overfitting of the quantized model to multimodal data while ensuring stable adaptation of multimodal large language models to downstream vision-language tasks. Extensive experiments demonstrate that models quantized by QSLAW perform on par with, or even surpass, their full-precision counterparts, while facilitating up to 1.4 times reduction in VL tuning time and GPU consumption. Our code is released at https://github.com/xjjxmu/QSLAW.

arXiv:2408.02966공식 코드 · Papers with Code

Fast Point Cloud Geometry Compression with Context-based Residual Coding and INR-based Refinement

Compressing a set of unordered points is far more challenging than compressing images/videos of regular sample grids, because of the difficulties in characterizing neighboring relations in an irregular layout of points. Many researchers resort to voxelization to introduce regularity, but this approach suffers from quantization loss. In this research, we use the KNN method to determine the neighborhoods of raw surface points. This gives us a means to determine the spatial context in which the latent features of 3D points are compressed by arithmetic coding. As such, the conditional probability model is adaptive to local geometry, leading to significant rate reduction. Additionally, we propose a dual-layer architecture where a non-learning base layer reconstructs the main structures of the point cloud at low complexity, while a learned refinement layer focuses on preserving fine details. This design leads to reductions in model complexity and coding latency by two orders of magnitude compared to SOTA methods. Moreover, we incorporate an implicit neural representation (INR) into the refinement layer, allowing the decoder to sample points on the underlying surface at arbitrary densities. This work is the first to effectively exploit content-aware local contexts for compressing irregular raw point clouds, achieving high rate-distortion performance, low complexity, and the ability to function as an arbitrary-scale upsampling network simultaneously.

arXiv:2408.02970공식 코드 · Papers with Code

EC-Guide: A Comprehensive E-Commerce Guide for Instruction Tuning and Quantization

Large language models (LLMs) have attracted considerable attention in various fields for their cost-effective solutions to diverse challenges, especially with advancements in instruction tuning and quantization. E-commerce, with its complex tasks and extensive product-user interactions, presents a promising application area for LLMs. However, the domain-specific concepts and knowledge inherent in e-commerce pose significant challenges for adapting general LLMs. To address this issue, we developed EC-Guide \href{https://github.com/fzp0424/EC-Guide-KDDUP-2024}, a comprehensive e-commerce guide for instruction tuning and quantization of LLMs. We also heuristically integrated Chain-of-Thought (CoT) during inference to enhance arithmetic performance. Our approach achieved the 2nd place in Track 2 and 5th place in Track 5 at the Amazon KDD Cup'24 \href{https://www.aicrowd.com/challenges/amazon-kdd-cup-2024-multi-task-online-shopping-challenge-for-llms}. Additionally, our solution is model-agnostic, enabling effective scalability across larger systems.

arXiv:2408.02561공식 코드 · Papers with Code

HQOD: Harmonious Quantization for Object Detection

Task inharmony problem commonly occurs in modern object detectors, leading to inconsistent qualities between classification and regression tasks. The predicted boxes with high classification scores but poor localization positions or low classification scores but accurate localization positions will worsen the performance of detectors after Non-Maximum Suppression. Furthermore, when object detectors collaborate with Quantization-Aware Training (QAT), we observe that the task inharmony problem will be further exacerbated, which is considered one of the main causes of the performance degradation of quantized detectors. To tackle this issue, we propose the Harmonious Quantization for Object Detection (HQOD) framework, which consists of two components. Firstly, we propose a task-correlated loss to encourage detectors to focus on improving samples with lower task harmony quality during QAT. Secondly, a harmonious Intersection over Union (IoU) loss is incorporated to balance the optimization of the regression branch across different IoU levels. The proposed HQOD can be easily integrated into different QAT algorithms and detectors. Remarkably, on the MS COCO dataset, our 4-bit ATSS with ResNet-50 backbone achieves a state-of-the-art mAP of 39.6%, even surpassing the full-precision one.

arXiv:2408.00023공식 코드 · Papers with Code

On the Perturbed States for Transformed Input-robust Reinforcement Learning

Reinforcement Learning (RL) agents demonstrating proficiency in a training environment exhibit vulnerability to adversarial perturbations in input observations during deployment. This underscores the importance of building a robust agent before its real-world deployment. To alleviate the challenging point, prior works focus on developing robust training-based procedures, encompassing efforts to fortify the deep neural network component's robustness or subject the agent to adversarial training against potent attacks. In this work, we propose a novel method referred to as Transformed Input-robust RL (TIRL), which explores another avenue to mitigate the impact of adversaries by employing input transformation-based defenses. Specifically, we introduce two principles for applying transformation-based defenses in learning robust RL agents: (1) autoencoder-styled denoising to reconstruct the original state and (2) bounded transformations (bit-depth reduction and vector quantization (VQ)) to achieve close transformed inputs. The transformations are applied to the state before feeding it into the policy network. Extensive experiments on multiple MuJoCo environments demonstrate that input transformation-based defenses, i.e., VQ, defend against several adversaries in the state observations. The official code is available at https://github.com/tunglm2203/tirl

arXiv:2407.21517공식 코드 · Papers with Code

A Simple Low-bit Quantization Framework for Video Snapshot Compressive Imaging

Video Snapshot Compressive Imaging (SCI) aims to use a low-speed 2D camera to capture high-speed scene as snapshot compressed measurements, followed by a reconstruction algorithm to reconstruct the high-speed video frames. State-of-the-art (SOTA) deep learning-based algorithms have achieved impressive performance, yet with heavy computational workload. Network quantization is a promising way to reduce computational cost. However, a direct low-bit quantization will bring large performance drop. To address this challenge, in this paper, we propose a simple low-bit quantization framework (dubbed Q-SCI) for the end-to-end deep learning-based video SCI reconstruction methods which usually consist of a feature extraction, feature enhancement, and video reconstruction module. Specifically, we first design a high-quality feature extraction module and a precise video reconstruction module to extract and propagate high-quality features in the low-bit quantized model. In addition, to alleviate the information distortion of the Transformer branch in the quantized feature enhancement module, we introduce a shift operation on the query and key distributions to further bridge the performance gap. Comprehensive experimental results manifest that our Q-SCI framework can achieve superior performance, e.g., 4-bit quantized EfficientSCI-S derived by our Q-SCI framework can theoretically accelerate the real-valued EfficientSCI-S by 7.8X with only 2.3% performance gap on the simulation testing datasets. Code is available at https://github.com/mcao92/QuantizedSCI.

arXiv:2407.21118공식 코드 · Papers with Code

Palu: Compressing KV-Cache with Low-Rank Projection

Post-training KV-Cache compression methods typically either sample a subset of effectual tokens or quantize the data into lower numerical bit width. However, these methods cannot exploit redundancy in the hidden dimension of the KV tensors. This paper presents a hidden dimension compression approach called Palu, a KV-Cache compression framework that utilizes low-rank projection to reduce inference-time LLM memory usage. Palu decomposes the linear layers into low-rank matrices, caches compressed intermediate states, and reconstructs the full keys and values on the fly. To improve accuracy, compression rate, and efficiency, Palu further encompasses (1) a medium-grained low-rank decomposition scheme, (2) an efficient rank search algorithm, (3) low-rank-aware quantization compatibility enhancements, and (4) optimized GPU kernels with operators fusion. Extensive experiments with popular LLMs show that Palu compresses KV-Cache by 50% while maintaining strong accuracy and delivering up to 1.89x on the RoPE-based attention module. When combined with quantization, Palu's inherent quantization-friendly design yields small to negligible extra accuracy degradation while saving additional memory than quantization-only methods and achieving up to 2.91x speedup for the RoPE-based attention. Moreover, it maintains comparable or even better accuracy (up to 1.19 lower perplexity) compared to quantization-only methods. These results demonstrate Palu's superior capability to effectively address the efficiency and memory challenges of LLM inference posed by KV-Cache. Our code is publicly available at: https://github.com/shadowpa0327/Palu

arXiv:2407.20708공식 코드 · Papers with Code

Integer-Valued Training and Spike-Driven Inference Spiking Neural Network for High-performance and Energy-efficient Object Detection

Brain-inspired Spiking Neural Networks (SNNs) have bio-plausibility and low-power advantages over Artificial Neural Networks (ANNs). Applications of SNNs are currently limited to simple classification tasks because of their poor performance. In this work, we focus on bridging the performance gap between ANNs and SNNs on object detection. Our design revolves around network architecture and spiking neuron. First, the overly complex module design causes spike degradation when the YOLO series is converted to the corresponding spiking version. We design a SpikeYOLO architecture to solve this problem by simplifying the vanilla YOLO and incorporating meta SNN blocks. Second, object detection is more sensitive to quantization errors in the conversion of membrane potentials into binary spikes by spiking neurons. To address this challenge, we design a new spiking neuron that activates Integer values during training while maintaining spike-driven by extending virtual timesteps during inference. The proposed method is validated on both static and neuromorphic object detection datasets. On the static COCO dataset, we obtain 66.2% mAP@50 and 48.9% mAP@50:95, which is +15.0% and +18.7% higher than the prior state-of-the-art SNN, respectively. On the neuromorphic Gen1 dataset, we achieve 67.2% mAP@50, which is +2.5% greater than the ANN with equivalent architecture, and the energy efficiency is improved by 5.7*. Code: https://github.com/BICLab/SpikeYOLO

arXiv:2407.20584공식 코드 · Papers with Code

Pruning Large Language Models with Semi-Structural Adaptive Sparse Training

The remarkable success of Large Language Models (LLMs) relies heavily on their substantial scale, which poses significant challenges during model deployment in terms of latency and memory consumption. Recently, numerous studies have attempted to compress LLMs using one-shot pruning methods. However, these methods often suffer from considerable performance degradation on complex language understanding tasks, raising concerns about the feasibility of pruning in LLMs. To address this issue, we propose Adaptive Sparse Trainer (AST), a novel and efficient retraining framework tailored for semi-structured sparse models. AST enables models to learn optimal masks during the weight update process without incurring additional computational overhead. Furthermore, we demonstrate that incorporating knowledge distillation significantly improves retraining efficiency and enhances model performance under fixed computational constraints. Additionally, a supplementary set of well-initialized parameters is integrated to further augment the model's efficacy. AST achieves state-of-the-art performance with minimal training cost. When applied to the LLaMA2-7B model, AST reduces the perplexity and zero-shot accuracy gap between dense and 2:4 semi-structured sparse models to 0.6 and 1.16%, respectively, utilizing less than 0.4% of the pretraining tokens and GPU hours. Our work demonstrates the feasibility of deploying semi-structured sparse LLMs and offers a promising alternative for achieving highly compressed models when combined with existing quantization techniques.

arXiv:2407.18437공식 코드 · Papers with Code

Mixed Non-linear Quantization for Vision Transformers

The majority of quantization methods have been proposed to reduce the model size of Vision Transformers, yet most of them have overlooked the quantization of non-linear operations. Only a few works have addressed quantization for non-linear operations, but they applied a single quantization method across all non-linear operations. We believe that this can be further improved by employing a different quantization method for each non-linear operation. Therefore, to assign the most error-minimizing quantization method from the known methods to each non-linear layer, we propose a mixed non-linear quantization that considers layer-wise quantization sensitivity measured by SQNR difference metric. The results show that our method outperforms I-BERT, FQ-ViT, and I-ViT in both 8-bit and 6-bit settings for ViT, DeiT, and Swin models by an average of 0.6%p and 19.6%p, respectively. Our method outperforms I-BERT and I-ViT by 0.6%p and 20.8%p, respectively, when training time is limited. We plan to release our code at https://gitlab.com/ones-ai/mixed-non-linear-quantization.