# Formal Algorithms for Model Efficiency

arXiv: https://arxiv.org/abs/2508.14000 · HTML: https://mlsanity.com/paper/2508.14000/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 23 references that are in the map.
- First posted on arXiv 19 Aug 2025.

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

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [MnasNet: Platform-Aware Neural Architecture Search for Mobile](https://mlsanity.com/paper/1807.11626/) (2018)
- [Once-for-All: Train One Network and Specialize it for Efficient Deployment](https://mlsanity.com/paper/1908.09791/) (2019)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [Be Your Own Teacher: Improve the Performance of Convolutional Neural Networks via Self Distillation](https://mlsanity.com/paper/1905.08094/) (2019)
- [Deep Learning with Limited Numerical Precision](https://mlsanity.com/paper/1502.02551/) (2015)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [A Survey of Model Compression and Acceleration for Deep Neural Networks](https://mlsanity.com/paper/1710.09282/) (2017)
- [Depth-Adaptive Transformer](https://mlsanity.com/paper/1910.10073/) (2019)
- [Predicting Parameters in Deep Learning](https://mlsanity.com/paper/1306.0543/) (2013)
- [Compressing Deep Convolutional Networks using Vector Quantization](https://mlsanity.com/paper/1412.6115/) (2014)
- [NewsRecLib: A PyTorch-Lightning Library for Neural News Recommendation](https://mlsanity.com/paper/2310.01146/) (2023)

## Abstract (arXiv)

We introduce the Knob-Meter-Rule (KMR) framework, a unified formalism for representing and reasoning about model efficiency techniques in deep learning. By abstracting diverse methods, including pruning, quantization, knowledge distillation, and parameter-efficient architectures, into a consistent set of controllable knobs, deterministic rules, and measurable meters, KMR provides a mathematically precise and modular perspective on efficiency optimization. The framework enables systematic composition of multiple techniques, flexible policy-driven application, and iterative budgeted optimization through the Budgeted-KMR algorithm. We demonstrate how well-known efficiency methods can be instantiated as KMR triples and present concise algorithmic templates for each. The framework highlights underlying relationships between methods, facilitates hybrid pipelines, and lays the foundation for future research in automated policy learning, dynamic adaptation, and theoretical analysis of cost-quality trade-offs. Overall, KMR offers both a conceptual and practical tool for unifying and advancing model efficiency research.