# Intelligence Inertia: Physical Isomorphism and Applications

arXiv: https://arxiv.org/abs/2603.22347 · HTML: https://mlsanity.com/paper/2603.22347/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 77 references that are in the map.
- First posted on arXiv 22 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [An Empirical Model of Large-Batch Training](https://mlsanity.com/paper/1812.06162/) (2018)
- [A disciplined approach to neural network hyper-parameters: Part 1 -- learning rate, batch size, momentum, and weight decay](https://mlsanity.com/paper/1803.09820/) (2018)
- [Revisiting Natural Gradient for Deep Networks](https://mlsanity.com/paper/1301.3584/) (2013)
- [On the Measure of Intelligence](https://mlsanity.com/paper/1911.01547/) (2019)
- [A Survey of Label-noise Representation Learning: Past, Present and Future](https://mlsanity.com/paper/2011.04406/) (2020)
- [Machine Learning and Variational Algorithms for Lattice Field Theory](https://mlsanity.com/paper/2106.01975/) (2021)

## Abstract (arXiv)

Classical frameworks like Fisher Information approximate the cost of neural adaptation only in low-density regimes, failing to explain the explosive computational overhead incurred during deep structural reconfiguration. To address this, we introduce Intelligence Inertia, a property derived from the fundamental non-commutativity between rules and states ([hatS, hatR] = iD). Rather than claiming a new fundamental physical law, we establish a heuristic mathematical isomorphism between deep learning dynamics and Minkowski spacetime. Acting as an textiteffective theory for high-dimensional tensor evolution, we derive a non-linear cost formula mirroring the Lorentz factor, predicting a relativistic J-shaped inflation curve -- a computational wall where classical approximations fail. We validate this framework via three experiments: (1) adjudicating the J-curve divergence under high-entropy noise, (2) mapping the optimal geodesic for architecture evolution, and (3) deploying an inertia-aware scheduler wrapper that prevents catastrophic forgetting. Adopting this isomorphism yields an exact quantitative metric for structural resistance, advancing the stability and efficiency of intelligent agents.