# High-Dimensional Learning Dynamics of Quantized Models with Straight-Through Estimator

arXiv: https://arxiv.org/abs/2510.10693 · HTML: https://mlsanity.com/paper/2510.10693/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 71 references that are in the map.
- First posted on arXiv 12 Oct 2025.

## Builds on (most cited first, 30 of 54)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [Pruning and Quantization for Deep Neural Network Acceleration: A Survey](https://mlsanity.com/paper/2101.09671/) (2021)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [Learning curves of generic features maps for realistic datasets with a teacher-student model](https://mlsanity.com/paper/2102.08127/) (2021)
- [Deep Learning with Low Precision by Half-wave Gaussian Quantization](https://mlsanity.com/paper/1702.00953/) (2017)
- [The Gaussian equivalence of generative models for learning with shallow neural networks](https://mlsanity.com/paper/2006.14709/) (2020)
- [Dynamics of stochastic gradient descent for two-layer neural networks in the teacher-student setup](https://mlsanity.com/paper/1906.08632/) (2019)
- [PAC-Bayes Compression Bounds So Tight That They Can Explain Generalization](https://mlsanity.com/paper/2211.13609/) (2022)
- [Training Quantized Nets: A Deeper Understanding](https://mlsanity.com/paper/1706.02379/) (2017)
- [Universality of empirical risk minimization](https://mlsanity.com/paper/2202.08832/) (2022)
- [Universal Approximation of Functions on Sets](https://mlsanity.com/paper/2107.01959/) (2021)
- [Phase diagram of Stochastic Gradient Descent in high-dimensional two-layer neural networks](https://mlsanity.com/paper/2202.00293/) (2022)
- [Optimize Weight Rounding via Signed Gradient Descent for the Quantization of LLMs](https://mlsanity.com/paper/2309.05516/) (2023)
- [Quantization Error Propagation: Revisiting Layer-Wise Post-Training Quantization](https://mlsanity.com/paper/2504.09629/) (2025)
- [Rao-Blackwellizing the Straight-Through Gumbel-Softmax Gradient Estimator](https://mlsanity.com/paper/2010.04838/) (2020)
- [Bridging Discrete and Backpropagation: Straight-Through and Beyond](https://mlsanity.com/paper/2304.08612/) (2023)
- [Universality laws for Gaussian mixtures in generalized linear models](https://mlsanity.com/paper/2302.08933/) (2023)
- [Learning strides in convolutional neural networks](https://mlsanity.com/paper/2202.01653/) (2022)

## Built on by (most cited first, 4 of 4)

- [More Than Bits: Multi-Envelope Double Binary Factorization for Extreme Quantization](https://mlsanity.com/paper/2512.24545/) (2025)
- [Improving Generalization by Permutation Routing Across Model Copies](https://mlsanity.com/paper/2605.09256/) (2026)
- [Signs Beat Floats: Low-Rank Double-Binary Adaptation for On-Device Fine-Tuning](https://mlsanity.com/paper/2605.24058/) (2026)
- [Neural Network Quantization by Learning Low-Loss Subspaces](https://mlsanity.com/paper/2606.25087/) (2026)

## Abstract (arXiv)

Quantized neural network training optimizes a discrete, non-differentiable objective. The straight-through estimator (STE) enables backpropagation through surrogate gradients and is widely used. While previous studies have primarily focused on the properties of surrogate gradients and their convergence, the influence of quantization hyperparameters, such as bit width and quantization range, on learning dynamics remains largely unexplored. We theoretically show that in the high-dimensional limit, STE dynamics converge to a deterministic ordinary differential equation. This reveals that STE training exhibits a plateau followed by a sharp drop in generalization error, with plateau length depending on the quantization range. A fixed-point analysis quantifies the asymptotic deviation from the unquantized linear model. We also extend analytical techniques for stochastic gradient descent to nonlinear transformations of weights and inputs.