# Pruning-induced phases in fully-connected neural networks: the eumentia, the dementia, and the amentia

arXiv: https://arxiv.org/abs/2603.12316 · HTML: https://mlsanity.com/paper/2603.12316/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 42 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [To prune, or not to prune: exploring the efficacy of pruning for model compression](https://mlsanity.com/paper/1710.01878/) (2017)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [Gradient Descent Finds Global Minima of Deep Neural Networks](https://mlsanity.com/paper/1811.03804/) (2018)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [Rigging the Lottery: Making All Tickets Winners](https://mlsanity.com/paper/1911.11134/) (2019)
- [ShortGPT: Layers in Large Language Models are More Redundant Than You Expect](https://mlsanity.com/paper/2403.03853/) (2024)
- [The Unreasonable Ineffectiveness of the Deeper Layers](https://mlsanity.com/paper/2403.17887/) (2024)
- [A Constructive Prediction of the Generalization Error Across Scales](https://mlsanity.com/paper/1909.12673/) (2019)
- [Proving the Lottery Ticket Hypothesis: Pruning is All You Need](https://mlsanity.com/paper/2002.00585/) (2020)
- [Spectrum Dependent Learning Curves in Kernel Regression and Wide Neural Networks](https://mlsanity.com/paper/2002.02561/) (2020)
- [How Sparse Can We Prune A Deep Network: A Fundamental Limit Perspective](https://mlsanity.com/paper/2306.05857/) (2023)

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

- [A Hamiltonian-Inspired Local-Operator Ansatz for Slimming Large Language Models](https://mlsanity.com/paper/2605.25344/) (2026)

## Abstract (arXiv)

Modern neural networks are heavily overparameterized, and pruning, which removes redundant neurons or connections, has emerged as a key approach to compressing them without sacrificing performance. However, while practical pruning methods are well developed, whether pruning induces sharp phase transitions in the neural networks and, if so, to what universality class they belong, remain open questions. To address this, we study fully-connected neural networks trained on MNIST, independently varying the dropout (i.e., removing neurons) rate at both the training and evaluation stages to map the phase diagram. We identify three distinct phases: eumentia (the network learns), dementia (the network has forgotten), and amentia (the network cannot learn), sharply distinguished by the power-law scaling of the cross-entropy loss with the training dataset size. {In the eumentia phase, the algebraic decay of the loss, as documented in the machine learning literature as neural scaling laws, is from the perspective of statistical mechanics the hallmark of quasi-long-range order.} We demonstrate that the transition between the eumentia and dementia phases is accompanied by scale invariance, with a diverging length scale that exhibits hallmarks of a Berezinskii-Kosterlitz-Thouless-like transition; the phase structure is robust across different network widths and depths. Our results establish that dropout-induced pruning provides a concrete setting in which neural network behavior can be understood through the lens of statistical mechanics.