# Mind the Phase: Effective Rank and Representation Health in Legged Locomotion

arXiv: https://arxiv.org/abs/2609.06958 · HTML: https://mlsanity.com/paper/2609.06958/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 26 of its 32 references that are in the map.
- First posted on arXiv 7 Sep 2026.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 26 of 26)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Learning Quadrupedal Locomotion over Challenging Terrain](https://mlsanity.com/paper/2010.11251/) (2020)
- [Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning](https://mlsanity.com/paper/2109.11978/) (2021)
- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [Orbit: A Unified Simulation Framework for Interactive Robot Learning Environments](https://mlsanity.com/paper/2301.04195/) (2023)
- [Understanding plasticity in neural networks](https://mlsanity.com/paper/2303.01486/) (2023)
- [Extreme Parkour with Legged Robots](https://mlsanity.com/paper/2309.14341/) (2023)
- [The Low-Rank Simplicity Bias in Deep Networks](https://mlsanity.com/paper/2103.10427/) (2021)
- [Implicit Under-Parameterization Inhibits Data-Efficient Deep Reinforcement Learning](https://mlsanity.com/paper/2010.14498/) (2020)
- [Loss of Plasticity in Continual Deep Reinforcement Learning](https://mlsanity.com/paper/2303.07507/) (2023)
- [Sim-to-Real Learning of All Common Bipedal Gaits via Periodic Reward Composition](https://mlsanity.com/paper/2011.01387/) (2020)
- [Continual Backprop: Stochastic Gradient Descent with Persistent Randomness](https://mlsanity.com/paper/2108.06325/) (2021)
- [SimBa: Simplicity Bias for Scaling Up Parameters in Deep Reinforcement Learning](https://mlsanity.com/paper/2410.09754/) (2024)
- [Transient Non-Stationarity and Generalisation in Deep Reinforcement Learning](https://mlsanity.com/paper/2006.05826/) (2020)
- [Depthwise Hyperparameter Transfer in Residual Networks: Dynamics and Scaling Limit](https://mlsanity.com/paper/2309.16620/) (2023)
- [Regularizing Action Policies for Smooth Control with Reinforcement Learning](https://mlsanity.com/paper/2012.06644/) (2020)
- [1000 Layer Networks for Self-Supervised RL: Scaling Depth Can Enable New Goal-Reaching Capabilities](https://mlsanity.com/paper/2503.14858/) (2025)
- [Hyperspherical Normalization for Scalable Deep Reinforcement Learning](https://mlsanity.com/paper/2502.15280/) (2025)
- [Learning Smooth Humanoid Locomotion through Lipschitz-Constrained Policies](https://mlsanity.com/paper/2410.11825/) (2024)
- [No Representation, No Trust: Connecting Representation, Collapse, and Trust Issues in PPO](https://mlsanity.com/paper/2405.00662/) (2024)
- [Stabilize Deep ResNet with A Sharp Scaling Factor τ](https://mlsanity.com/paper/1903.07120/) (2019)
- [High-Performance Reinforcement Learning on Spot: Optimizing Simulation Parameters with Distributional Measures](https://mlsanity.com/paper/2504.17857/) (2025)
- [FlashSAC: Fast and Stable Off-Policy Reinforcement Learning for High-Dimensional Robot Control](https://mlsanity.com/paper/2604.04539/) (2026)
- [Learning Smooth Time-Varying Linear Policies with an Action Jacobian Penalty](https://mlsanity.com/paper/2602.18312/) (2026)
- [SLowRL: Safe Low-Rank Adaptation Reinforcement Learning for Locomotion](https://mlsanity.com/paper/2603.17092/) (2026)

## Abstract (arXiv)

Reinforcement learning has become the leading paradigm in legged locomotion, enabling complex behaviors from backflips to parkour through massively parallel simulation. Under PPO's non-stationarity, shallow networks remain the de facto architecture, supported by carefully staged curricula and environments, yet the representations these policies learn stay poorly understood, leaving no training-time signal of how they will behave on hardware. In this work, we empirically study locomotion policies through the effective rank of the policy Jacobian and show that conditioning rank on the gait phase exposes architectural structure that global rank averages away. In particular, we find that standard architectural choices, namely layer normalization and residual connections, allocate roughly two more dimensions of effective rank to swing than to stance, which is fully absent in vanilla MLPs. Building on this, we propose a simple recipe that turns these representational signatures into smoother, more reliable sim-to-real transfer. In practice, this results in roughly 3x lower joint jitter that holds from simulation onto a physical Spot, suggesting that representation health is an effective training-time lens to track sim-to-real smoothness.