# Punching Above Precision: Small Quantized Model Distillation with Learnable Regularizer

arXiv: https://arxiv.org/abs/2509.20854 · HTML: https://mlsanity.com/paper/2509.20854/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 26 of its 36 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Placed in

- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 26 of 26)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Paying More Attention to Attention: Improving the Performance of Convolutional Neural Networks via Attention Transfer](https://mlsanity.com/paper/1612.03928/) (2016)
- [YOLOX: Exceeding YOLO Series in 2021](https://mlsanity.com/paper/2107.08430/) (2021)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [Channel-wise Knowledge Distillation for Dense Prediction](https://mlsanity.com/paper/2011.13256/) (2020)
- [Learning to Quantize Deep Networks by Optimizing Quantization Intervals with Task Loss](https://mlsanity.com/paper/1808.05779/) (2018)
- [Rethinking Soft Labels for Knowledge Distillation: A Bias-Variance Tradeoff Perspective](https://mlsanity.com/paper/2102.00650/) (2021)
- [Apprentice: Using Knowledge Distillation Techniques To Improve Low-Precision Network Accuracy](https://mlsanity.com/paper/1711.05852/) (2017)
- [Towards Effective Low-bitwidth Convolutional Neural Networks](https://mlsanity.com/paper/1711.00205/) (2017)
- [Adaptive Multi-Teacher Multi-level Knowledge Distillation](https://mlsanity.com/paper/2103.04062/) (2021)
- [Towards Cross-Tokenizer Distillation: the Universal Logit Distillation Loss for LLMs](https://mlsanity.com/paper/2402.12030/) (2024)
- [MQBench: Towards Reproducible and Deployable Model Quantization Benchmark](https://mlsanity.com/paper/2111.03759/) (2021)
- [Confidence-Aware Multi-Teacher Knowledge Distillation](https://mlsanity.com/paper/2201.00007/) (2021)
- [Dynamic Knowledge Distillation for Pre-trained Language Models](https://mlsanity.com/paper/2109.11295/) (2021)
- [Collaborative Multi-Teacher Knowledge Distillation for Learning Low Bit-width Deep Neural Networks](https://mlsanity.com/paper/2210.16103/) (2022)
- [Q-VDiT: Towards Accurate Quantization and Distillation of Video-Generation Diffusion Transformers](https://mlsanity.com/paper/2505.22167/) (2025)
- [Stochastic Precision Ensemble: Self-Knowledge Distillation for Quantized Deep Neural Networks](https://mlsanity.com/paper/2009.14502/) (2020)
- [Quantized Feature Distillation for Network Quantization](https://mlsanity.com/paper/2307.10638/) (2023)
- [Poster: Self-Supervised Quantization-Aware Knowledge Distillation](https://mlsanity.com/paper/2309.13220/) (2023)

## Built on by (most cited first, 2 of 2)

- [Gated Relational Alignment via Confidence-based Distillation for Efficient VLMs](https://mlsanity.com/paper/2601.22709/) (2026)
- [Decoder-Free Distillation for Quantized Image Restoration](https://mlsanity.com/paper/2603.09624/) (2026)

## Abstract (arXiv)

Quantization-aware training (QAT) combined with knowledge distillation (KD) is a promising strategy for compressing Artificial Intelligence (AI) models for deployment on resource-constrained hardware. However, existing QAT-KD methods often struggle to balance task-specific (TS) and distillation losses due to heterogeneous gradient magnitudes, especially under low-bit quantization. We propose Game of Regularizer (GoR), a novel learnable regularization method that adaptively balances TS and KD objectives using only two trainable parameters for dynamic loss weighting. GoR reduces conflict between supervision signals, improves convergence, and boosts the performance of small quantized models (SQMs). Experiments on image classification, object detection (OD), and large language model (LLM) compression show that GoR consistently outperforms state-of-the-art QAT-KD methods. On low-power edge devices, it delivers faster inference while maintaining full-precision accuracy. We also introduce QAT-EKD-GoR, an ensemble distillation framework that uses multiple heterogeneous teacher models. Under optimal conditions, the proposed EKD-GoR can outperform full-precision models, providing a robust solution for real-world deployment.