# Physics-Inspired Binary Neural Networks: Interpretable Compression with Theoretical Guarantees

arXiv: https://arxiv.org/abs/2502.01908 · HTML: https://mlsanity.com/paper/2502.01908/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 27 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Builds on (most cited first, 19 of 19)

- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [A White Paper on Neural Network Quantization](https://mlsanity.com/paper/2106.08295/) (2021)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [The Era of 1-bit LLMs: All Large Language Models are in 1.58 Bits](https://mlsanity.com/paper/2402.17764/) (2024)
- [Pruning and Quantization for Deep Neural Network Acceleration: A Survey](https://mlsanity.com/paper/2101.09671/) (2021)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [BitNet: Scaling 1-bit Transformers for Large Language Models](https://mlsanity.com/paper/2310.11453/) (2023)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds](https://mlsanity.com/paper/1808.10038/) (2018)
- [A Survey on Methods and Theories of Quantized Neural Networks](https://mlsanity.com/paper/1808.04752/) (2018)
- [ProxQuant: Quantized Neural Networks via Proximal Operators](https://mlsanity.com/paper/1810.00861/) (2018)
- [QMoE: Practical Sub-1-Bit Compression of Trillion-Parameter Models](https://mlsanity.com/paper/2310.16795/) (2023)
- [EEGdenoiseNet: A benchmark dataset for end-to-end deep learning solutions of EEG denoising](https://mlsanity.com/paper/2009.11662/) (2020)
- [Safeguarded Learned Convex Optimization](https://mlsanity.com/paper/2003.01880/) (2020)
- [Ada-LISTA: Learned Solvers Adaptive to Varying Models](https://mlsanity.com/paper/2001.08456/) (2020)
- [Hyperparameter Tuning is All You Need for LISTA](https://mlsanity.com/paper/2110.15900/) (2021)
- [Why Quantization Improves Generalization: NTK of Binary Weight Neural Networks](https://mlsanity.com/paper/2206.05916/) (2022)
- [Unlocking the Theory Behind Scaling 1-Bit Neural Networks](https://mlsanity.com/paper/2411.01663/) (2024)
- [One-Bit Quantization and Sparsification for Multiclass Linear Classification with Strong Regularization](https://mlsanity.com/paper/2402.10474/) (2024)

## Built on by (most cited first, 1 of 1)

- [When Can Depth Replace Precision? A Resource Theory of Quantized Neural Computation](https://mlsanity.com/paper/2607.23390/) (2026)

## Abstract (arXiv)

Why rely on dense neural networks and then blindly sparsify them when prior knowledge about the problem structure is already available? Many inverse problems admit algorithm-unrolled networks that naturally encode physics and sparsity. In this work, we propose a Physics-Inspired Binary Neural Network (PIBiNN) that combines two key components: (i) data-driven one-bit quantization with a single global scale, and (ii) problem-driven sparsity predefined by physics and requiring no updates during training. This design yields compression rates below one bit per weight by exploiting structural zeros, while preserving essential operator geometry. Unlike ternary or pruning-based schemes, our approach avoids ad-hoc sparsification, reduces metadata overhead, and aligns directly with the underlying task. Experiments suggest that PIBiNN achieves advantages in both memory efficiency and generalization compared to competitive baselines such as ternary and channel-wise quantization.