Post-Training Quantization

Also known as PTQ

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Overview

Post-training quantization (PTQ) converts a trained model to lower-precision numbers without retraining it, reducing memory use and enabling inference on constrained hardware. Methods range from rounding and calibration-based scaling to Hessian-aware reconstruction such as GPTQ, rotations and outlier handling, codebooks, and mixed-precision allocation across layers, experts, or caches. Calibration usually uses a small set of representative inputs, while evaluation spans language-model perplexity and reasoning, vision accuracy, multimodal tasks, and real-device latency and memory. The central tension is that moderate precision often retains task quality, while very low bit widths can amplify errors and alter behavior; calibration and hardware-aware kernels help, but accuracy, behavioral fidelity, and deployment speed do not always move together.

Latest papers

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366 papers72 papers in the last four weeks, up 50% on the four weeks before. 0.4% of all new papers.

Jun 12, 2026

Realizing Native INT8 Compute for Diffusion Transformers on Consumer GPUs: A Fused INT8 GEMM Kernel for Ideogram 4.0

Post-training INT8 (W8A8) quantization of diffusion transformers is widely deployed as a speed optimization, yet on consumer Ampere GPUs it is frequently slower than the FP8 and NF4 alternatives it is meant to beat. We trace this to a software artifact: the production "INT8" forward quantizes weights and activations only to immediately dequantize them back to bf16 and run a bf16 matrix multiply, never engaging the GPU's INT8 tensor cores, so the hardware's compute advantage is left entirely unrealized. We close this gap with a single fused Triton INT8 GEMM (int8xint8->int32 on Ampere tensor cores, with per-token x per-channel dequantization and bias folded into the epilogue, autotuned per GEMM shape) dropped into the Ideogram 4.0 diffusion transformer's linear layers in place of the dequantize-to-bf16 path. In the kernel, the int8xint8->int32 accumulation is bit-exact against torch._int_mm and the dequantized output matches the reference at cosine similarity 1.0 with no NaNs, running 2.8-4.2x faster than bf16 per GEMM. End to end it delivers a ~1.1x (~9-10%) speedup at 768px, and at 1024px it generates an image in 156.5 s on a single RTX 3090, faster than the single-card NF4 (164.5 s) and FP8 (172.9 s) baselines, at no measurable quality cost on these point estimates (PickScore/CLIPScore). INT8 thus goes from the slowest variant to the fastest, and 1024px becomes single-GPU feasible. The primary speed criterion (beat FP8, by ~9.5%) is comfortably met; the NF4 margin (~4.9%, single-run n=4) is within run-to-run variance we did not quantify and is best read as consistent with meeting the stretch target. We close with an honest deployment map: the win is specific to consumer Ampere, and on A100 and B200 the same kernel loses to those cards' fast native bf16/FP8 paths.

Ali Asaria, Tony Salomone, Deep Gandhi

Transformer Lab

GPU Kernel OptimizationDiffusion TransformerDiffusion Model QuantizationPost-Training QuantizationDiffusion Model Inference Acceleration
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Jun 11, 2026

Quantizing Time-Series Models As Dynamical Systems: Trajectory-Based Quantization Sensitivity Score

We introduce the Trajectory-based Quantization Sensitivity Score (TQS), a metric that reframes post-training quantization (PTQ) through the lens of dynamical-systems stability. By modeling the network's rollout as a discrete-time dynamical system, TQS characterizes how quantization-induced errors propagate and amplify over the rollout horizon. Unlike conventional PTQ methods, where sensitivity analysis is often coupled to the quantization procedure, TQS enables a priori sensitivity estimation decoupled from quantizer selection and bit-width assignment. This separation allows for quantization budget planning even for black-box or compiled networks with fused operators. Building on this, we present TQS-PTQ, a flexible mixed-precision framework that requires no calibration data or costly second-order approximations. Our experiments show that a dynamical-systems perspective provides a robust, high-performing pathway for low-precision deployment in resource-constrained settings.

Mariya Pavlova, Harrison Bo Hua Zhu, Lidia Vitanova +2

Department of Computing, Imperial College London, London, United Kingdom · Department of Public Health, University of Copenhagen, Copenhagen, Denmark · GATE Institute, Sofia University St. Kliment Ohridski, Sofia, Bulgaria +1

Mixed-Precision QuantizationTime Series ModelingQuantization Sensitivity AnalysisPost-Training QuantizationNeural Network Quantization
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Jun 11, 2026

TWLA: Achieving Ternary Weights and Low-Bit Activations for LLMs via Post-Training Quantization

Large language models (LLMs) exhibit exceptional general language processing capabilities, but their memory and compute costs hinder deployment. Ternarization has emerged as a promising compression technique, offering significant reductions in model size and inference complexity. However, existing methods struggle with heavy-tailed activation distributions and therefore keep activations in high precision, fundamentally limiting end-to-end inference acceleration. To overcome this limitation, we propose TWLA, a post-training quantization (PTQ) framework that achieves 1.58-bit weight compression and 4-bit activation quantization while maintaining high accuracy. TWLA comprises three components: (1) Euclidean-to-Manifold Asymmetric Ternary Quantizer (E2M-ATQ) minimizes layer-output error under weight ternarization via a two-stage optimization from Euclidean initialization to manifold relocation; (2) Kronecker Orthogonal Tri-Modal Shaping (KOTMS) applies a Kronecker-structured orthogonal rotation to reshape weights into ternary-friendly tri-modal distributions, while the shared rotation statistically suppresses activation outliers; and (3) Inter-Layer Aware Activation Mixed Precision (ILA-AMP) explicitly introduces adjacent-layer second-order interaction costs in bit allocation and jointly optimizes for the layer-wise disparity of activation quantization gains induced by the shared orthogonal transform, preventing cascades triggered by a few weak layers. Extensive experiments demonstrate that TWLA maintains high accuracy under W1.58A4, while delivering significant inference acceleration. The code is available at https://github.com/Kishon-zzx/TWLA.

Zhixiong Zhao, Zukang Xu, Zhixuan Chen +3

Houmo AI, China · 2Southeast University, Nanjing, China

Mixed-Precision QuantizationLLM QuantizationTernary QuantizationActivation QuantizationPost-Training QuantizationNeural Network Quantization
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Jun 11, 2026

Multi-Bitwidth Quantization for LLMs Using Additive Codebooks

As large language models (LLMs) are increasingly deployed across heterogeneous hardware with varying resource constraints, the ability to adaptively manage the trade-off between performance and efficiency without retraining is critical. We propose Drop-by-Drop, a novel multi-bitwidth post-training quantization framework that enables inference-time precision control over LLM weights from a single trained model. Our method is theoretically grounded in information theory and successive refinement. We establish that LLM weights, which commonly follow a Gaussian distribution, can be optimally reconstructed with increasing fidelity as additional bits are incorporated, under a weighted mean squared error distortion motivated by LLM loss functions. To realize this in practice, Drop-by-Drop incorporates Matryoshka-style supervision into the loss function, exploiting the structure of additive codebooks. Drop-by-Drop produces a single model where ordered subsets of codebooks yield accurate partial reconstructions at each precision level. This approach significantly reduces storage and memory overhead by allowing a single checkpoint to serve multiple bitwidths, while maintaining competitive perplexity and accuracy across major architectures, such as Qwen, LLaMA, Gemma, and Mistral.

Liza Babaoglu, Shuangyi Chen, Ashish Khisti

University of Toronto

LLM QuantizationWeight-Only QuantizationIterative RefinementPost-Training QuantizationNeural Network Quantization
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Jun 11, 2026

Quantum Reservoir Computing for Short-Term Power Load Forecasting in Resource-Constrained Energy Systems

Short-term load forecasting is essential for reliable energy management, but practical deployment on edge devices requires models that remain accurate under limited memory, finite measurement budgets, and hardware noise. This work proposes a hardware-efficient Quantum Reservoir Computing (QRC) framework for energy load forecasting, where a fixed quantum reservoir transforms temporal input windows into high-dimensional features and only a classical Elastic Net readout is trained. To reduce deployment cost, the trained readout is compressed using post-training fixed-point quantization at bit widths from 8 to 2 bits. The framework is evaluated on the Tetouan and Spain energy load datasets under exact statevector simulation, 512-shot finite sampling, and realistic hardware-noise models from IBM FakeTorino and IBM FakeMarrakesh. Results show that 6-bit readout precision preserves full-precision forecasting performance while reducing readout memory by 81.2%. Below this point, degradation becomes dataset dependent, with Tetouan showing stronger sensitivity and Spain degrading more gradually. Hardware-noise validation further shows that the trained readout transfers to noisy reservoir states without retraining. These findings support quantized QRC as a resource-aware forecasting approach for near-term quantum time-series applications.

Mansi Od, Param Pathak, Nouhaila Innan +1

University of Greenwich, London, United Kingdom · Fractal Analytics, QuantumAI Lab, Mumbai, Maharashtra, India · eBRAIN Lab, Division of Engineering, New York University Abu Dhabi (NYUAD), Abu Dhabi, UAE +1

Time Series ForecastingReservoir ComputingQuantum Reservoir ComputingElectricity Load ForecastingPost-Training QuantizationLow-Bit Quantization
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Jun 10, 2026

Holding the FP8 Quality Ceiling at 8-Bit Weights and Activations: INT8 and GGUF Post-Training Quantization of Ideogram 4.0 for Consumer GPUs

We study post-training quantization (PTQ) of Ideogram 4.0, a 9.3B flow-matching diffusion transformer (DiT) that realizes classifier-free guidance with two separate-weight copies of a single-stream backbone and is conditioned by a Qwen3-VL text encoder, targeting Ampere RTX3090 GPUs, which lack FP8 tensor cores. Because Ideogram4.0 is trained on structured JSON captions, we evaluate every variant under schema-valid JSON prompts produced by an LLM expander built to Ideogram's published caption specification, and score them with a battery spanning human-preference (HPSv2), CLIP, and PickScore for standalone quality; PP-OCR exact-match and edit distance for text; and PSNR/SSIM/LPIPS for fidelity to the FP8 reference (the highest-precision public checkpoint) output. On a 300-prompt benchmark with paired bootstrap confidence intervals, an INT8 W8A8 recipe (per-channel weights, per-token dynamic activations, SmoothQuant, and bf16 protection of a small high-fragility layer set) is statistically indistinguishable from FP8 on CLIP and PickScore (paired CIs include zero) and within ~0.004 HPSv2, and, at its 8-bit size, is the most faithful reproduction of the FP8 output (LPIPS 0.243 vs 0.277/0.306 for the half-size 4-bit baselines; the INT8-Q4_K gap excludes zero). A GGUF Q4_K quantization reaches the same standalone quality as the published NF4 baseline at the same on-disk size, making it the Pareto choice on the quality-memory frontier. We further show that under JSON prompts all four variants reach parity on standalone quality, the variants separate on fidelity and text rendering, not on aggregate image-quality scores, and that text legibility, near-zero when the model is prompted with raw strings, reaches 55% OCR exact-match under the JSON captions it expects. We release the INT8 W8A8 and GGUF Q4_K quantized weights on Hugging Face under a gated, non-commercial license.

Deep Gandhi, Ali Asaria, Tony Salomone

Transformer Lab

Mixed-Precision QuantizationDiffusion TransformerDiffusion Model QuantizationActivation QuantizationPost-Training QuantizationNeural Network Quantization
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Jun 10, 2026

PhaseQuant: Mitigating Activation Quantization Collapse via Residual-Stream Dynamics

Post-training quantization (PTQ) is essential for efficient large language model (LLM) inference, but reliably quantizing activations remains challenging when weights, activations, and KV caches are all quantized to 4-bit precision. A key difficulty lies in massive activations, whose extreme values dominate the activation range and amplify quantization error. State-of-the-art methods mitigate massive activations through transformation-based smoothing, such as orthogonal rotations and affine scaling, but overlook the cross-layer dynamics of the residual stream. In this paper, we show that massive activations emerge and disappear in a phase-wise pattern across network depth, injecting abrupt updates into the residual stream. These updates cause the newly injected layer-wise signal to dominate the 4-bit quantization scale and weaken the accumulated residual information. To characterize this behavior, we introduce two metrics, the Update Dominance Ratio (UDR) and the Historical Retention Score (HRS), and show that static transformation-based smoothing cannot fully resolve the resulting dynamic quantization instability. Based on this analysis, we propose PhaseQuant, a phase-aware mixed-precision post-training quantization policy for activation quantization. PhaseQuant identifies quantization-sensitive layers from residual-stream dynamics and assigns 8-bit activation precision only to these layers, while keeping weights, KV caches, and all remaining activations at 4-bit precision. It can be directly integrated with strong PTQ baselines such as QuaRot, SpinQuant, and FlatQuant. Experiments on LLaMA-2 and LLaMA-3 show that PhaseQuant consistently improves perplexity and zero-shot QA performance under W4A4KV4 quantization, while achieving 1.05×\times--1.07×\times throughput improvement with modest memory overhead. These results demonstrate a practical path toward robust low-bit LLM inference.

Zimo Zhao, Maolin Wang, Bowen Yu +3

City University of Hong Kong Hong Kong, China · Zhejiang University of Technology Hangzhou, China

Mixed-Precision QuantizationLLM Quantization4-Bit QuantizationActivation QuantizationPost-Training Quantization
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Jun 9, 2026

Optimal Post-Training Quantization Scales and Where to Find Them

Post-training quantization (PTQ) compresses large language models by mapping weights to low-bit representations. While much work has focused on how weights are rounded onto the quantization grid, the scaling factor that defines the grid is typically chosen with simple, data-free heuristics. We observe that, under round-to-nearest (RTN) quantization, the grid assignments are piecewise constant in the scale, making the output reconstruction error piecewise quadratic over finitely many intervals, each admitting a closed-form optimization. Building on this insight, we present PiSO (Piecewise Scale Optimization), an algorithm that leverages calibration data to efficiently select channel-wise scales to achieve globally optimal output reconstruction error to arbitrary accuracy. We extend PiSO to group-wise quantization via tractable objectives. We also propose strategies for integrating it with error-correction methods such as GPTQ and Qronos, which greedily adjust weight assignments to compensate for the rounding errors of previously quantized weights. Experiments on Llama and Qwen models across multiple sizes and bit-widths show consistent improvements in perplexity and zero-shot accuracy, both standalone and combined with error correction, with gains increasing as the bit-width narrows. For instance, on Llama-3, PiSO reduces the 2-bit perplexity of Qronos by up to 7x, and at 3 bits, PiSO without error correction outperforms GPTQ with absmax scales.

Juan Amboage, Pablo Monteagudo-Lago, Ian Colbert +2

AMD

LLM QuantizationWeight-Only QuantizationPost-Training QuantizationLow-Bit QuantizationNeural Network Quantization
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Jun 9, 2026

UniSVQ: 2-bit Unified Scalar-Vector Quantization

Post-training quantization at the 2-bit level enables low-cost deployment and inference acceleration for large language models (LLMs). Scalar quantization (SQ) and vector quantization (VQ) are two primary quantization methods, however, the former suffers from significant performance degradation, and the latter incurs computational and storage overhead. We propose UniSVQ, a unified 2-bit quantization framework that bridges scalar and vector quantization by parameterizing codewords as an affine transform of integer lattices. This structure preserves compatibility with optimized integer kernels while retaining much of VQ's flexibility. We further introduce a data-driven block-wise fine-tuning strategy to directly minimize quantization reconstruction error. Extensive experiments across multiple LLM families and zero-shot benchmarks demonstrate that UniSVQ consistently outperforms state-of-the-art SQ methods and achieves performance comparable to advanced VQ methods, while providing higher inference throughput. Codes are publicly available at https://github.com/AI9Stars/UniSVQ.

Haoyu Wang, Haiyan Zhao, Xingyu Yu +4

Department of Computer Science and Technology, Tsinghua University, Beijing, China · School of Software and Microelectronics, Peking University, Beijing, China · School of Physics, Beihang University, Beijing, China

LLM QuantizationVector QuantizationPost-Training QuantizationLow-Bit QuantizationNeural Network Quantization
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Jun 8, 2026

Quality Is Not a Safety Proxy Under Quantization

Quantized checkpoints are often screened first with quality metrics and only later, if at all, with direct safety tests. This paper audits that shortcut on a matched 51-row matrix spanning 6 models, 4 families, a 7-level GGUF ladder, and AWQ/GPTQ INT4 checkpoints. In this matrix the shortcut fails: all 36 quality-safety pairings split direction across models, and 9 hidden-danger rows plus 1 near-hidden-danger row show quality stable or improved while refusal falls by 12-68 percentage points. Seven of the 11 AWQ/GPTQ rows are hidden-danger. A four-probe mechanistic follow-up over the 17 Hugging Face-backed FP16/AWQ/GPTQ cells does not rescue it: entropy, refusal-direction, and calibration probes are weak or null separators of dangerous rows, and although probe-identified safety-associated neurons absorb 1.39×\times more quantization error overall (p<5×10−7p < 5 \times 10^{-7}), the effect is not regime-specific. Claude Sonnet 4 relabels 11,470 items in a predefined stratified set, agrees with the primary gemma3:12b judge on 89.9% of rows (κ=0.873κ= 0.873, 95% CI [0.866, 0.881]), and changes 0/10 hidden-danger cells. A calibrated study-internal behavioral screen -- the Refusal Template Stability Index (RTSI), built from four refusal-template drift features and calibrated on this matrix -- routes 10/10 hidden- or near-hidden-danger rows to direct safety testing (Wilson 95% CI lower bound 0.72) while leaving 23 of 45 non-baseline rows in a low-risk bucket under both in-sample scoring and row-level leave-one-out validation; on the same matrix, the best single-feature baselines (unique-prefix-rate-delta, raw refusal-rate delta) recover 9/10 and 8/10 respectively at matched bucket size, and cross-stack transfer requires recalibration. For the quantized checkpoints, model families, and safety outcomes studied here, retained quality cannot waive direct safety evaluation.

Sahil Kadadekar

Independent Researcher

LLM QuantizationLLM Refusal BehaviorLLM Safety EvaluationRefusal Behavior in Language ModelsPost-Training Quantization
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Jun 8, 2026

Understanding Quantization-Aware Training: Gradients at Quantized Weights Bias to the Low-Loss Basin

Post-training quantization (PTQ) converts a trained full-precision model into low-bit weights without task-level retraining, while quantization-aware training (QAT) incorporates quantization into the training loop. Although PTQ is efficient and often accurate at moderate bitwidths, it can fail sharply at aggressive bitwidths; QAT is more expensive but can often recover the lost accuracy. We propose a unified geometric framework that explains both PTQ failure and QAT recovery. We model full-precision training as following a low-loss river inside a wider valley: a normal neighborhood of the river forms a nearly flat basin, while leaving this basin incurs a sharp loss increase. When the quantization grid is comparable to the basin width, local PTQ objectives, including rounding and Hessian-based second-order reconstruction, can select a high-loss deployed quantized point outside the basin even when nearby low-loss quantized points exist. In this regime, straight-through-estimator-based QAT has a useful bias: it evaluates gradients at the deployed quantized weights while updating latent full-precision weights, causing the gradient to sense the valley wall and acquire an inward component that steers subsequent quantized iterates back into the basin. We formalize this mechanism through a local landscape model, construct a geometric PTQ failure mode, and prove finite-time QAT recovery under local quantizer-compatibility assumptions. Experiments across vision and language models under multiple neural-network quantization schemes corroborate the predicted basin-crossing failure of PTQ and the corresponding recovery mechanism of QAT.

Hanyang Li, Jianhao Ma, Ying Cui

Department of IEOR, University of California, Berkeley · Department of Statistics and Data Science, University of Pennsylvania

Neural Network OptimizationStraight-Through EstimatorQuantization-Aware TrainingNeural Network QuantizationPost-Training QuantizationLow-Bit Quantization+1
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Jun 7, 2026

Trainable Smooth-Rotation Transforms with Learned Channel Scales for LLM Quantization

Post-training quantization (PTQ) is one of the most practical ways to reduce the serving cost of Large Language Models (LLMs), but activation quantization remains difficult because outlier-dominated channels lead to large quantization errors. This paper investigates whether part of this degradation is caused by over-migration in scaling-based equivalent transformations. We introduce a quantile-robust scaling policy for SmoothRot-style transforms by replacing max-based activation statistics with high quantiles, and we complement it with constrained gradient-based optimization of channel scales. On LLaMA-3.2-1B under W4A4 quantization, quantile-only policy search improves selected-layer error by 11.1% over the SmoothRot baseline, joint (alpha, q) search improves it by 12%, and training reaches 18.5%. Replaying the best selected-layer policy on all decoder-block down-projection layers reduces the corresponding full-layer mean error from 97.51 to 78.08 (19.9%). The results show that robust migration control and lightweight scale learning provide consistent gains over max-based fixed policies while preserving the equivalent-transform framework.

Patrik Czakó, Gábor Kertész, Sándor Szénási

Doctoral School of Applied Informatics and Applied Mathematics, Obuda University Budapest, Hungary · John von Neumann Faculty of Informatics, Obuda University Budapest, Hungary

LLM Quantization4-Bit QuantizationRotation-Based QuantizationActivation QuantizationPost-Training QuantizationQuantization Robustness
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Jun 5, 2026

Joint Structural Pruning and Mixed-Precision Quantization for LLM Compression

Recently, the efficiency of Large Language Models (LLMs) deployment has become a critical concern in practical applications. While post-training quantization (PTQ) and structural pruning are established techniques for reducing memory footprint and inference latency, most existing PTQ approaches optimize quantization errors on a per-layer basis, overlooking how errors accumulate and propagate through the network, often resulting in suboptimal solutions. Traditional pipelines also tend to apply pruning and quantization in isolation or sequentially, further compounding sub-optimality. We introduce a novel end-to-end framework that addresses these limitations in two key ways. First, we propose a novel mixed-precision PTQ strategy that directly minimizes global error propagation across the entire model, rather than isolating layer-wise errors. Building on this, we develop a novel joint optimization approach that simultaneously learns structural pruning decisions and mixed-precision quantization policies within a unified search space. Extensive experiments show that, at ultra-low precisions (1-3 bits), our quantization method reduces WikiText perplexity by up to 21% compared to state-of-the-art (SoTA) weight-activation quantization baselines. Against leading weight-only quantization methods, it achieves up to 59% and 85% lower perplexity on WikiText and C4, respectively. Compared to the SoTA joint pruning-and-quantization techniques, our proposed method delivers superior perplexity and reasoning performance at ultra-low bits.

Hoang-Loc La, Truong-Thanh Le, Amir Taherkordi +1

UiT The Arctic University of Norway · University of Oslo, Norway

Mixed-Precision QuantizationLLM QuantizationLLM PruningLLM CompressionPost-Training QuantizationNeural Network Compression
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Jun 4, 2026

SPEAR: A System for Post-Quantization Error-Adaptive Recovery Enabling Efficient Low-Bit LLM Serving

Efficient large language model (LLM) serving is increasingly constrained by deployment cost. Quantization is a key technique for reducing serving cost, yet even state-of-the-art 4-bit quantizers exhibit a noticeable quality gap from FP16, particularly for smaller models where low-bit serving is most beneficial. We identify a fundamental cause of this gap: quantization error is highly input-dependent and varies substantially across tokens, while existing post-quantization compensation methods are static and apply identical corrections to all inputs. As a result, easy tokens are over-corrected while hard tokens remain under-corrected. We present SPEAR, a system for post-quantization error-adaptive recovery that improves low-bit LLM serving. SPEAR introduces lightweight Error Compensators (ECs) modulated by per-token gates and places them only at the most error-sensitive layers identified through a CKA-guided entropy-aware diagnostic. This focuses a small parameter budget where it is most effective. Efficient deployment of ECs presents several systems challenges, including additional computation, tensor-parallel synchronization caused by input-dependent gating, and latency instability across configurations. SPEAR addresses these issues through adaptive kernel-fusion dispatch, combining an epilogue-integrated peer-reduction kernel with P2P dual-write to fuse the post-EC computation into low-bit GEMMs, and an SLO-constrained EC-aware scheduler for predictable serving performance. Across challenging per-channel quantization settings, SPEAR recovers 56-75% of the perplexity gap between W4 and FP16 while adding less than 1% model memory overhead and maintaining latency comparable to a widely used 4-bit serving deployment.

Hongyuan Liu, Yawei Li, Zhiqiang Que +3

University of Electronic Science and Technology of China · University of Bristol · 3ETH Zurich

LLM QuantizationLLM ServingQuantization Error CompensationPost-Training QuantizationLow-Bit QuantizationNeural Network Quantization
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Jun 4, 2026

FAIR-Calib: Frontier-Aware Instability-Reweighted Calibration for Post-Training Quantization of Diffusion Large Language Models

Diffusion Large Language Models (dLLMs) refine tokens iteratively but commit them irreversibly, leading to a "stability lag" where early decisions remain fragile even after being written. We reveal that Post-Training Quantization (PTQ) error easily flips these borderline decisions at the write frontier, which are then permanently locked in and amplified. To address this, we propose Frontier-Aware Instability-Reweighted Calibration (FAIR-Calib), a two-stage PTQ framework for dLLMs. Stage I probes a full-precision teacher to estimate a position prior that combines frontier hits and masked-stage reliability. Stage II performs off-policy, layer-wise calibration by minimizing a reweighted hidden-state MSE, effectively prioritizing the protection of fragile frontier states without requiring expensive end-to-end diffusion rollouts. We further theoretically justify our weighted objective as a surrogate for output KL divergence. Empirically, FAIR-Calib consistently outperforms state-of-the-art baselines on LLaDA and Dream (W4A4), significantly reducing frontier decision flips and suppressing post-commit mismatches across diverse benchmarks.

Haoyu Huang, Linlin Yang, Sheng Xu +5

National College for Excellent Engineers, Beihang University, Beijing, China · State Key Laboratory of Media Convergence and Communication, Communication University of China, Beijing, China · Independent researcher +4

LLM QuantizationDiffusion Model QuantizationLanguage Model CalibrationDiffusion Language ModelsPost-Training Quantization
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Jun 4, 2026

Value-and-Structure Alignment for Routing-Consistent Quantization of Mixture-of-Experts Models

Mixture-of-Experts (MoE) models scale foundation models efficiently by activating only a subset of experts for each token, but their large number of expert parameters still makes quantization essential for practical deployment. Unlike dense models, however, MoE models are sensitive to routing instability: small quantization-induced perturbations can change the top-kk expert selection, altering the computation path and degrading model quality. We propose Value-and-Structure Routing Alignment for Quantization (VSRAQ), a MoE-specific post-training quantization objective that preserves pre-quantization expert-selection behavior under quantization. VSRAQ combines two complementary objectives that jointly preserve expert-selection behavior: value alignment, which matches routing-relevant logits or scores, and structure alignment, which preserves expert ordering and top-kk decision boundaries. By maintaining routing consistency, VSRAQ reduces quantization-induced degradation without introducing any inference-time overhead and can be integrated into existing quantization frameworks. Experiments on recent MoE foundation models show that VSRAQ improves expert-selection consistency and consistently outperforms reconstruction-only and router-aware baselines.

Hancheol Park, Geonho Lee, Tairen Piao +1

Nota Inc., South Korea.

LLM QuantizationMixture-of-Experts QuantizationExpert RoutingMixture-of-Experts ModelsPost-Training QuantizationNeural Network Quantization
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Jun 3, 2026

Minimizing the Hidden Cost of Scales: Graph-Guided Ultra-Low-Bit Quantization for Large Language Models

Post-training quantization (PTQ) is critical for the efficient deployment of large language models (LLMs). Recent ultra-low-bit PTQ methods rely on rigid weight-saliency assumptions or position heuristics, introducing substantial hidden scaling overhead. We propose SAGE-PTQ (Saliency-Aware Graph-guided Efficient PTQ), a novel ultra-low-bit quantization framework for LLMs that minimizes hidden scaling cost. SAGE-PTQ separates salient and unsalient weights using distributional statistics, then models subsampled unsalient weights as a sparse graph to estimate the optimal number of groups per layer. SAGE-PTQ applies dual-mode quantization, assigning multi-bit precision to salient weights and binarizing unsalient weights. To reduce scaling overhead, SAGE-PTQ uses one per-channel scale for salient weights and one scalar per unsalient group. Finally, SAGE-PTQ implements adaptive saliency thresholding to select the optimal saliency ratio per matrix. SAGE-PTQ achieves 1.03 weight bits and only 0.004 scaling bits per matrix on average, outperforming state-of-the-art methods such as BiLLM and PB-LLM. On LLaMA-3-8B, SAGE-PTQ achieves 6.74 WikiText2 perplexity, compared to 55.8 for BiLLM, while using less than 50% of BiLLM's GPU memory. On LLaMA-2-70B, SAGE-PTQ provides 1.5x faster decoding on one NVIDIA L40 GPU, demonstrating practical inference efficiency.

Rayyan Abdalla, Amir Hussein, Min Wu +1

LLM QuantizationLLM Inference AccelerationWeight-Only QuantizationPost-Training QuantizationLow-Bit Quantization
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Jun 3, 2026

STaR-Quant: State-Time Consistent Post-Training Quantization for Diffusion Large Language Models

Diffusion large language models (DLLMs) have recently emerged as a promising alternative to autoregressive LLMs by generating text through iterative masked denoising with bidirectional context. However, their large model sizes and iterative denoising process introduce substantial memory and computational overhead, motivating post-training quantization for efficient deployment. In this paper, we identify two key challenges for low-bit DLLM quantization: state-dependent activation disparity and temporal error accumulation. Masked and unmasked tokens exhibit different activation distributions within each denoising step, while quantization errors can accumulate across steps during iterative decoding. To address these challenges, we propose STaR-Quant, a state-time consistent PTQ framework for DLLMs. STaR-Quant introduces State-Guided Activation Transformation (SGAT) to assign masked and unmasked tokens to different activation transformation spaces with a unified static weight-side transformation. It further introduces Temporal Attention Compensation (TAC) to correct the quantized attention representation via a lightweight block-diagonal affine mapping. Experiments on representative DLLMs demonstrate that STaR-Quant consistently improves low-bit weight-activation quantization over strong PTQ baselines, while delivering up to 1.69x speedup and 3.14x memory saving over FP16 deployment.

Xin Yan, Aqiang Wang, Zhenglin Wan +2

School of Artificial Intelligence, Beijing Normal University, Beijing, China · Department of Computer Science, National University of Singapore, Singapore · Centre for Frontier AI Research, Agency for Science, Technology and Research (A*STAR), Singapore

LLM QuantizationDiffusion Model QuantizationActivation QuantizationDiffusion Language ModelsPost-Training Quantization
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Jun 3, 2026

QuBLAST: A Framework for Quantizing Large Language Models with Block-Level Compression Approach and Activation Scaling Strategy

LLMs have become the state-of-the-art algorithms for solving NLP tasks. However, they typically come at huge computational and memory costs, thus making them difficult to deploy on embedded systems. Toward this, state-of-the-art methods typically employ uniform post-training quantization (PTQ) across attention blocks of the network, hence overlooking the potential of applying different quantization levels in the same network. They also employ complex operations to mitigate the negative impact of activation outliers, hence incurring high computational overheads. Moreover, they have not considered evaluation using emerging LLMs with non-conventional attention architectures (e.g., state-space models), which pose different challenges in applying quantization. To address these limitations, we propose QuBLAST, a novel PTQ methodology that employs block-level compression approach with activation scaling strategy for LLMs. Block-level compression approach enables mixed-precision quantization across blocks of the network, while activation scaling strategy efficiently mitigates the negative impact of activation outliers. Specifically, QuBLAST first analyzes the sensitivity of different attention blocks in the pre-trained model through the cross-entropy loss analysis. QuBLAST leverages this sensitivity analysis to determine the weight quantization level for each attention block in the model. Furthermore, QuBLAST employs the activation scaling map for each block to control the range of activation values and mitigate the negative impact of activation outliers, thereby enabling better quantization results. Experimental results show that, QuBLAST reduces model sizes by 40%-45.2% across different model architectures (i.e., Qwen3-8B, Llama3-8B, Mistral v0.1-8B, and Falcon H1R-7B), while maintaining the performance within 5% perplexity increase for the WikiText-2 and WikiText-103 datasets.

Pasindu Wickramasinghe, Achyuta Muthuvelan, Rachmad Vidya Wicaksana Putra +2

eBRAIN Lab, Division of Engineering, New York University (NYU) Abu Dhabi, United Arab Emirates

Mixed-Precision QuantizationLLM QuantizationPost-Training QuantizationNeural Network Quantization
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Jun 3, 2026

MorphoQuant: Modality-Aware Quantization for Omni-modal Large Language Models

Conventional Post-Training Quantization (PTQ) methods struggle with 4-bit Omni-modal Large Language Models (OLLMs) due to the extreme distribution heterogeneity and disparate outlier patterns across modalities. To address this, we propose MorphoQuant, a modality-aware PTQ framework engineered to preserve cross-modal morphology and mitigate outlier loss. Specifically, we introduce Distribution-Aware Bias Compensation (DABC), which selectively absorbs long-tailed outliers into channel-wise biases. This mechanism safeguards outlier magnitudes while maintaining high-precision discretization for dense inliers, thereby preserving accurate discretization across diverse modal distribution. Complementing this, we propose Morphology-Directed Quantization Function Optimization (MDQFO) to co-optimize the quantization grid with the bias mask, ensuring fine-grained alignment across modalities. Extensive evaluations on Qwen2.5-Omni across benchmarks like MMMU and Video-MME demonstrate our approach's superiority. Notably, our W4A4 model achieves 76.63% on ScienceQA, significantly outperforming SOTA W4A4 methods and surprisingly surpassing the W4A16 baseline, which fully demonstrates the exceptional accuracy-efficiency trade-off of our framework.

Yue Wu, Changyuan Wang, Zixuan Wang +2

LLM Quantization4-Bit QuantizationMultimodal Large Language ModelsActivation QuantizationPost-Training Quantization
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Jun 2, 2026

Recover-LoRA for Aggressive Quantization: Reclaiming Accuracy in 2-Bit Language Models via Low-Rank Adaptation with Knowledge Distillation on Synthetic Data

Aggressive weight quantization to 2-bit precision offers substantial throughput and memory gains for large language model (LLM) inference, but typically incurs severe accuracy degradation. These gains are particularly relevant for edge and on-device deployment, where memory capacity and bandwidth are primary constraints. In this work, we extend Recover-LoRA -- a lightweight, data-free accuracy recovery method originally developed for general model weight corruption -- to the setting of ultra-low-bit quantization. We propose a selective mixed-precision strategy in which only gate and up projection layers of the MLP are quantized to 2-bit (W2), while all other linear layers remain at higher precision, yielding a mixed-precision GateUp configuration. We demonstrate via roofline analysis across three model families (4B--20B) and two hardware platforms that a W4/W2-GateUp deployment (4-bit base with 2-bit gate/up) delivers 7.5--23.3% TPS improvement over uniform W4 depending on model and context length, while confining quantization error to a predictable subset of layers. We then apply Recover-LoRA -- training low-rank adapters on the quantized layers via logit distillation with synthetic data -- to recover accuracy lost from 2-bit quantization of the gate and up layers. In a case study on Qwen3-4B, Recover-LoRA achieves 80--95% accuracy recovery on 9 of 12 benchmarks, using only 10k synthetic training samples and no labeled data. We further demonstrate that synthetic data performs comparably to curated labeled data for distillation-based recovery, and that recovery generalizes to out-of-distribution evaluation tasks. Our results present Recover-LoRA as a practical post-quantization accuracy recovery tool for aggressive weight compression in deployment settings.

Devleena Das, Rajeev Patwari, Elliott Delaye +1

Advanced Micro Devices, Inc. (AMD)

Mixed-Precision QuantizationLLM QuantizationLow-Rank AdaptationPost-Training QuantizationLow-Bit Quantization
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Jun 2, 2026

Perplexity Can Miss SAE Feature Damage Under Quantization

Quantization is a standard path to deploying large language models, and quantized models are typically judged acceptable when perplexity or downstream accuracy remains close to the full-precision original. But behavioral parity need not imply feature fidelity: the sparse-autoencoder (SAE) features used to interpret a full-precision model may change after weight rounding. We test this directly by using a frozen SAE as a fixed measurement basis, encoding full-precision and round-to-nearest (RTN) quantized activations on identical tokens, and measuring per-feature survival by Pearson correlation across bit-widths from INT8 to INT4 on Pythia-70M and Gemma-2-2B. Our central finding is that perplexity can miss feature damage: on Gemma-2-2B, INT7 improves perplexity while degrading 18.7% of active SAE features, and under sliding-window evaluation INT6 also improves perplexity while only 51.3% of active features survive. Feature survival is graded rather than cliff-like, with 62.4% of active Pythia features and 51.3% of active Gemma features surviving at INT6; most non-surviving features are blurred rather than fully damaged. Survival is also predictable from full-precision feature statistics alone, with cross-validated AUC 0.92--0.97 and peak activation as the strongest marginal predictor. Finally, RTN quantization and matched-perplexity magnitude pruning damage strongly overlapping feature sets, with Jaccard overlap 0.79--0.86 and damage-score Spearman correlation 0.98. These results show that behavioral metrics alone are insufficient evidence that full-precision interpretability findings transfer to quantized models, motivating feature-level audits of compression.

Evan Duan

University of Michigan

LLM QuantizationLLM InterpretabilitySparse AutoencodersPost-Training Quantization
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Jun 1, 2026

Qift: Shift-Friendly No-Zero W2 Post-Training Quantization for Rotated W2A4/KV4 LLM Inference

Two-bit weight quantization is attractive for memory-efficient LLM inference, but the standard W2 level set {-2,-1,0,+1} often collapses under aggressive W2A4/KV4 settings. We study the scalar level-set geometry of two-bit weights in a Hadamard-rotated quantization pipeline. Conventional asymmetric W2 substantially improves over the standard level set, indicating that W2A4 failure is not only a bit-width problem but also a reconstruction-level problem. Across all 224 linear modules in each of LLaMA-2-7B and LLaMA-3.1-8B, pretrained weights are already nearly zero-centered, while Hadamard rotation primarily Gaussianizes their standardized shape: excess kurtosis and Q-Q error drop by orders of magnitude. Based on this approximate zero-centered Gaussian-like source model, we propose Qift, a fixed no-zero W2 level set for rotated W2A4/KV4 inference. The main level set is {+/-0.5, +/-1.5}, equivalently {+/-1, +/-3} under a half-scale reparameterization; a power-of-two variant uses {+/-1, +/-4} for sign-and-shift decoded weight application. Qift redesigns the fixed two-bit code-to-level mapping and is training-free, learned-codebook-free, group-grid-free, and zero-point-free, retaining the standard per-channel scale. A scale-invariant ratio analysis identifies an effective inner/outer centroid ratio range of 0.25 to 0.33, explaining why mirror no-zero (MNZ), Lloyd, NF2, and PoT-MNZ perform well while {+/-1, +/-2} does not. On both models, the no-zero level sets consistently improve pure W2A4 perplexity, L-layer mixed W2/W4 perplexity, downstream accuracy, and GPTQ residual behavior over the standard W2 level set. At L=16 mixed precision, they substantially narrow the gap to W3A4 while keeping half of the transformer layers at two-bit precision, giving a simple, source-aware, and deployment-friendly alternative to more complex learned W2 codebooks.

Chi-Wei Huang, Chia-Chi Tsai

National Cheng Kung University

LLM QuantizationRotation-Based QuantizationPost-Training QuantizationLow-Bit QuantizationQuantization
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Jun 1, 2026

Massive Spikes in LLMs are Bias Vectors: Mechanistic Uncovering and Spike-Free Quantization

Massive activation spikes in Large Language Models (LLMs) severely degrade quantization by stretching dynamic ranges. While prior hypotheses characterize these as high-level scalar biases, we argue that they are merely the scalar intermediates of rigid, structural vector biases in the spike-carrying tokens. We show that these tokens converge to constant vectors after normalization that drive the attention sink and value-state drain mechanisms. We geometrically substantiate this by analyzing the coordination of projection weights: WKW_K contrastively amplifies the vector, WQW_Q aligns semantic tokens toward it, and WVW_V projects it into the spectral null-space. Furthermore, we reveal that the model actively preserves these structural biases against Rotary Positional Embedding (RoPE) perturbations by localizing them in "zones of rotational stability" utilizing low-frequency bands and coherent channel pairs. Leveraging this, we propose INSERTQUANT, a post-training quantization (PTQ) framework that clamps spikes and restores their function via pre-computed template vectors. This renders activations strictly spike-free, enabling robust low-bit quantization with high fidelity. INSERTQUANT achieves parity with state-of-the-art per-tensor quantization methods on LLMs and uniquely generalizes beyond text to other modalities such as ViTs.

Yung-Chin Chen, Chung Peng Lee, Ze-Wei Liou +1

Princeton University, NJ, USA · EnCharge AI, CA, USA

LLM QuantizationActivation OutliersActivation QuantizationAttention SinksPost-Training Quantization
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May 31, 2026

GPTQ-intrinsic LoRA: A Near-optimal Algorithm for Low-precision Quantization with Low-rank Adaptation

Post-training quantization is widely used for compressing large neural networks, but aggressive low-bit quantization can significantly degrade model quality. A common remedy is to augment the quantized weights with a low-rank correction, leading to approximations of the form W≈Q+LRW\approx Q+LR. In this paper, we study this low-precision plus low-rank representation through the layer-wise reconstruction objective ∥XW−X(Q+LR)∥F2\|XW-X(Q+LR)\|_F^2, where XX is a calibration matrix. We establish, to our knowledge, the first information-theoretic lower bounds for this problem under finite-alphabet and bounded low-rank compensation constraints. We then propose GPTQ-intrinsic LoRA, a training-free algorithm that incorporates the low-rank correction directly into a GPTQ-style quantization pass by appropriately augmenting the calibration Hessian. For the choice L=VrL=V_r, where VrV_r contains the top right singular vectors of XX, we prove layer-wise reconstruction error bounds in which the usual GPTQ dependence on ∥X∥F2\|X\|_F^2 is replaced by the rank-rr residual ∥X−Xr∥F2\|X-X_r\|_F^2, up to regularization terms. Under natural structural assumptions, these bounds match the information-theoretic lower bounds in their dominant scaling, up to constants and mild factors. We also introduce Bid-Up, a fixed-grid quantization refinement step that can be alternated with optimal low-rank compensation with guaranteed non-increasing layer-wise reconstruction error. Experiments on Qwen3 language models and DeiT vision transformers show that GPTQ-intrinsic LoRA improves over GPTQ and GPTQ followed by low-rank compensation, with additional gains from refinement loops.

Shihao Zhang, Rayan Saab

Department of Mathematics, University of California San Diego

LLM QuantizationLow-Rank AdaptationLow-Rank CompressionPost-Training QuantizationLow-Bit QuantizationNeural Network Quantization
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May 31, 2026

Boundary-Protection W8A8 HiFloat8 Quantization for Large-Scale Text-to-Video Diffusion Transformers

We present a post-training quantization (PTQ) approach for Wan2.1-T2V-14B, a 14-billion-parameter text-to-video diffusion transformer, targeting the W8A8 HiFloat8 (HiF8) format on Ascend 910B NPUs. A central challenge in quantizing video DiT models is the heterogeneous activation distribution across transformer blocks: boundary blocks (the first and last few blocks) exhibit fundamentally different statistical properties from middle blocks, making uniform quantization ineffective. We conduct a systematic per-block activation analysis across all 40 WanAttentionBlocks and use the findings to motivate a boundary-protection strategy that retains the first two and last three blocks in BF16 while quantizing the remaining 35 blocks with W8A8 HiF8. The proposed PTQ method matches or marginally exceeds the BF16 baseline on all five VBench dimensions evaluated, indicating no measurable accuracy loss within the 5-prompt evaluation set. An ablation study over four protection configurations confirms that full boundary protection yields the highest average VBench score, validating the data-driven block selection. We additionally investigate quantization-aware training (QAT) as a complementary fine-tuning stage and analyze the conditions under which it fails to outperform plain PTQ on single-card hardware.

Yiming Zhao

University of Chinese Academy of Sciences Beijing, China

Video Diffusion ModelsDiffusion Model QuantizationT2V GenerationPost-Training QuantizationNeural Network Quantization
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May 30, 2026

Collaborative Few-Step Distillation and Low-Bit Quantization for Wan2.2 Dual-Expert Video Diffusion Models

Large video diffusion models achieve strong visual quality but remain expensive to deploy because each sample requires many denoising steps and a large resident parameter footprint. This paper studies a deployment-oriented compression pipeline for Wan2.2-T2V-A14B by combining few-step distribution-matching distillation with low-bit quantization. The pipeline follows the model's dual-expert denoising route, calibrates the high-noise and low-noise branches separately, protects sensitive entrance layers, and uses HiF4-style low-bit representation to improve dynamic-range coverage. Quantization is calibrated on the distilled few-step student rather than on the original long-step trajectory, reducing activation-distribution mismatch during inference. The proposed co-design keeps the quantized model close to the same-step full-precision model and surpasses the original full-precision baseline at 8 and 20 steps on average. The 20-step setting gives the best quality-efficiency trade-off in the tested configurations.

Jinyang Du, Shenghao Jin, Ziqian Xu +5

SenseTime

Video Diffusion ModelsDiffusion Model QuantizationDiffusion Model DistillationFew-Step Diffusion SamplingPost-Training QuantizationLow-Bit Quantization+1
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May 30, 2026

ScaleSweep: Accurate NVFP4 Post-Training Quantization of LLMs via Block Scale Initialization

NVFP4 is a recently introduced hardware-supported FP4 format that improves the fidelity of 4-bit quantization through fine-grained block scales. However, existing NVFP4 scale initialization methods still primarily rely on AbsMax initialization, which leaves a noticeable gap to the optimal solution. To address this, we propose ScaleSweep, a simple and efficient scale optimization method that sweeps over feasible block scale candidates and selects the candidate that minimizes a target objective. We further provide a theoretical analysis of NVFP4 quantization and derive both lower and upper bounds for the required sweep range under mean square error (MSE) and weighted mean square error (WMSE) between the original tensor and the quantized reconstructed tensor. The proposed bounds substantially reduce the sweep space while preserving the optimal candidate, enabling negligible overhead compared with the baseline quantization operators. Experiments on Llama and Qwen models demonstrate that ScaleSweep consistently improves quantization performance over existing initialization methods and further narrows the gap to full precision. In particular, under aggressive end-to-end quantization of weights, activations, KV cache, and query states, ScaleSweep preserves more than 93% of the full-precision performance.

Li Lin, Xiaojun Wan

Wangxuan Institute of Computer Technology, Peking University

LLM Quantization4-Bit QuantizationActivation QuantizationPost-Training QuantizationNeural Network Quantization
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May 30, 2026

ProjQ: Project-and-Quantize for Adapter-Aware LLM Compression

Post-Training Quantization (PTQ) and Low-Rank Adaptation (LoRA) constitute the standard pipeline for efficient Large Language Model (LLM) deployment. However, applying them sequentially poses a problem: PTQ often leaves behind random noise that is spread out (across the model's weights) in a way LoRA can't easily fix, meaning that LoRA ends up wasting its limited capacity trying to fix uncorrectable noise instead of improving task performance. In this paper, we propose ProjQ, a novel framework for constraining quantization noise to the low-rank manifold via orthogonal subspace projection. We derive an efficient alternating algorithm that shapes the quantization noise into a low-rank structure, effectively offloading dominant error components to the subsequent adapter while minimizing the residual error in the orthogonal "uncorrectable" subspace. Our theoretical analysis demonstrates that ProjQ preserves strictly greater model plasticity for downstream tasks compared to standard PTQ. Extensive experiments on LLaMA-2, Qwen2.5 and Qwen3 confirm that ProjQ consistently outperforms existing methods in both quantization error compensation and downstream task fine-tuning, achieving up to 2×2\times lower evaluation loss for compensation and matching the performance of standard 4-bit baselines on language modeling tasks with only 3 bits. The code is available on https://github.com/yy9301/ProjQ .

Wenya Yu, Chao Zhang, Li Wang +2

School of Mathematics and Statistics, Central South University, Changsha, China · Department of Computer Science, Central South University, Changsha, China · CRAN, Université de Lorraine, CNRS, Nancy, France +1

LLM QuantizationPost-Training QuantizationLow-Bit QuantizationNeural Network Quantization
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May 29, 2026

Quantized Reasoning Models Think They Need to Think Longer, but They Do Not

Post-training quantization (PTQ) is widely used to deploy large language models efficiently, but its effect on reasoning models is not well understood. Across math, coding, and science QA, we find that aggressive PTQ reduces accuracy while increasing chain-of-thought (CoT) length. Surprisingly, we show that in up to 52% of the quantized models' failures, models reach the right answer in intermediate reasoning steps but do not output it as a final answer. To understand why quantization leads to this increase in overthinking errors, we measure the token-level KL divergence between quantized and full-precision output distributions. Positions with high KL divergence correlate strongly with high next-token entropy, and at these positions quantized models disproportionately sample overthinking markers such as "wait", "but", and "alternatively". We show that simply introducing a training-free logit penalty on a curated set of overthinking markers can reduce CoT length by 12--23% while preserving or improving accuracy across 5 models (1.5B-32B parameters), 3 quantization methods, and 5 benchmarks, yielding a favorable Pareto frontier of accuracy against reasoning cost compared to penalizing other token sets. Overthinking errors produced by quantized models are particularly reduced by up to 58%.

Sanae Lotfi, Polina Kirichenko, Steven Li +1

1FAIR at Meta · 2Meta AI

Logit AdjustmentOverthinking in Language ModelsCoT ReasoningEfficient Language Model ReasoningPost-Training QuantizationLLM Reasoning+1
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