# Gradient-Momentum Coupling: A Parameter-Space Proxy for Learning Progress

arXiv: https://arxiv.org/abs/2605.05856 · HTML: https://mlsanity.com/paper/2605.05856/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 25 of its 41 references that are in the map.
- First posted on arXiv 7 May 2026.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 25 of 25)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Hindsight Experience Replay](https://mlsanity.com/paper/1707.01495/) (2017)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Exploration by Random Network Distillation](https://mlsanity.com/paper/1810.12894/) (2018)
- [Unifying Count-Based Exploration and Intrinsic Motivation](https://mlsanity.com/paper/1606.01868/) (2016)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Not All Samples Are Created Equal: Deep Learning with Importance Sampling](https://mlsanity.com/paper/1803.00942/) (2018)
- [Minigrid & Miniworld: Modular & Customizable Reinforcement Learning Environments for Goal-Oriented Tasks](https://mlsanity.com/paper/2306.13831/) (2023)
- [Large-Scale Study of Curiosity-Driven Learning](https://mlsanity.com/paper/1808.04355/) (2018)
- [Self-Supervised Exploration via Disagreement](https://mlsanity.com/paper/1906.04161/) (2019)
- [Count-Based Exploration with Neural Density Models](https://mlsanity.com/paper/1703.01310/) (2017)
- [Go-Explore: a New Approach for Hard-Exploration Problems](https://mlsanity.com/paper/1901.10995/) (2019)
- [Never Give Up: Learning Directed Exploration Strategies](https://mlsanity.com/paper/2002.06038/) (2020)
- [Teacher-Student Curriculum Learning](https://mlsanity.com/paper/1707.00183/) (2017)
- [Skew-Fit: State-Covering Self-Supervised Reinforcement Learning](https://mlsanity.com/paper/1903.03698/) (2019)
- [Stochastic Optimization with Importance Sampling](https://mlsanity.com/paper/1401.2753/) (2014)
- [Empirical Design in Reinforcement Learning](https://mlsanity.com/paper/2304.01315/) (2023)
- [CurES: From Gradient Analysis to Efficient Curriculum Learning for Reasoning LLMs](https://mlsanity.com/paper/2510.01037/) (2025)
- [Agent-Controller Representations: Principled Offline RL with Rich Exogenous Information](https://mlsanity.com/paper/2211.00164/) (2022)
- [Beyond Noisy-TVs: Noise-Robust Exploration Via Learning Progress Monitoring](https://mlsanity.com/paper/2509.25438/) (2025)

## Abstract (arXiv)

Measuring learning progress is at the core of curiosity-driven exploration, which rewards an agent for going where its model is still learning. However, the abstract notion of learning progress is not directly measurable, and existing methods often derive it from the prediction error in the output space. This paper proposes Gradient-Momentum Coupling (GMC), which measures how strongly a sample drives change in the parameter space, given by the normalized absolute product of its gradient with the momentum of previous gradients. Directions of change that persist across samples accumulate in momentum, while noise cancels out. In controlled experiments GMC allocates near uniform priority across tasks with varying levels of noise, where prediction error chases the noisiest, and orders learnable tasks by improvement speed rather than difficulty. On four MiniGrid MultiRoom tasks, substituting GMC for prediction error inside the Intrinsic Curiosity Module (ICM) recovers exploration ICM loses to unpredictable observations.