# Tunneling the Loss Landscape: Bypassing Memorization with Monte Carlo Parameter Swapping

arXiv: https://arxiv.org/abs/2608.01833 · HTML: https://mlsanity.com/paper/2608.01833/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 34 references that are in the map.
- First posted on arXiv 3 Aug 2026.

## Builds on (most cited first, 17 of 17)

- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [Empirical Analysis of the Hessian of Over-Parametrized Neural Networks](https://mlsanity.com/paper/1706.04454/) (2017)
- [Towards Understanding Grokking: An Effective Theory of Representation Learning](https://mlsanity.com/paper/2205.10343/) (2022)
- [Grokking as the Transition from Lazy to Rich Training Dynamics](https://mlsanity.com/paper/2310.06110/) (2023)
- [The Slingshot Mechanism: An Empirical Study of Adaptive Optimizers and the Grokking Phenomenon](https://mlsanity.com/paper/2206.04817/) (2022)
- [A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks](https://mlsanity.com/paper/2303.11873/) (2023)
- [Deep Networks Always Grok and Here is Why](https://mlsanity.com/paper/2402.15555/) (2024)
- [Grokking at the Edge of Numerical Stability](https://mlsanity.com/paper/2501.04697/) (2025)
- [End-to-End Kernel Learning with Supervised Convolutional Kernel Networks](https://mlsanity.com/paper/1605.06265/) (2016)
- [Is Grokking a Computational Glass Relaxation?](https://mlsanity.com/paper/2505.11411/) (2025)
- [High-entropy Advantage in Neural Networks' Generalizability](https://mlsanity.com/paper/2503.13145/) (2025)
- [Bias of Stochastic Gradient Descent or the Architecture: Disentangling the Effects of Overparameterization of Neural Networks](https://mlsanity.com/paper/2407.03848/) (2024)

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

- [An Exploratory Replica-Overlap Probe of the Grokking Transition](https://mlsanity.com/paper/2609.25634/) (2026)

## Abstract (arXiv)

Grokking is a striking phenomenon in neural network training, where a model can undergo a prolonged period of pure memorization before abrupt generalization. While previous works have attempted to interpret it through classical machine learning mechanisms like weight norm, recent research draws an analogy from statistical physics, framing grokking as a form of computational glass relaxation. This theory defines the initial memorization as a result of `fast cooling' where the training loss is reduced so quickly that a glass state is formed, followed by a `slow relaxation' towards final generalization. Although providing a unifying framework for representative grokking theories, this perspective has remained largely at the theoretical on macroscopic level without direct empirical validation on training dynamics. Here we introduce a three-component framework to directly characterize the training dynamics via parameter mobility (PM), and two representative measurements from glassy dynamics: replica correlation (RC) and fractal dimension (FD). We demonstrate that standard optimization presents clear signatures of glass dynamics and inherently traps the grokking network in a kinetic arrested memorization state with a collapsed mobility, strong history dependence, and channel-like motions. This quantitative agreement motivates us to introduce State-Aware Monte Carlo Parameter Swapping (SAM-Swap), an optimization plug-in that can accelerate generalization, inspired by swap Monte Carlo algorithm widely used in glass dynamics. Comparing SAM-Swap, weight decay, and Gaussian gradient noise, we find that accelerated generalization is consistently associated with random exploration in the parameter space, similar to diffusion in physics.