# Ordinal Neural Collapse as a Representation Prior for Visual Navigation

arXiv: https://arxiv.org/abs/2606.26839 · HTML: https://mlsanity.com/paper/2606.26839/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 37 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Builds on (most cited first, 30 of 31)

- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [CURL: Contrastive Unsupervised Representations for Reinforcement Learning](https://mlsanity.com/paper/2004.04136/) (2020)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [R3M: A Universal Visual Representation for Robot Manipulation](https://mlsanity.com/paper/2203.12601/) (2022)
- [End-to-end Driving via Conditional Imitation Learning](https://mlsanity.com/paper/1710.02410/) (2017)
- [Learning Invariant Representations for Reinforcement Learning without Reconstruction](https://mlsanity.com/paper/2006.10742/) (2020)
- [Joint 2D-3D-Semantic Data for Indoor Scene Understanding](https://mlsanity.com/paper/1702.01105/) (2017)
- [Decoupling Representation Learning from Reinforcement Learning](https://mlsanity.com/paper/2009.08319/) (2020)
- [NoMaD: Goal Masked Diffusion Policies for Navigation and Exploration](https://mlsanity.com/paper/2310.07896/) (2023)
- [A Geometric Analysis of Neural Collapse with Unconstrained Features](https://mlsanity.com/paper/2105.02375/) (2021)
- [ViNT: A Foundation Model for Visual Navigation](https://mlsanity.com/paper/2306.14846/) (2023)
- [Where are we in the search for an Artificial Visual Cortex for Embodied Intelligence?](https://mlsanity.com/paper/2303.18240/) (2023)
- [Learning to Navigate in Complex Environments](https://mlsanity.com/paper/1611.03673/) (2016)
- [Exploring Deep Neural Networks via Layer-Peeled Model: Minority Collapse in Imbalanced Training](https://mlsanity.com/paper/2101.12699/) (2021)
- [Socially Compliant Navigation Dataset (SCAND): A Large-Scale Dataset of Demonstrations for Social Navigation](https://mlsanity.com/paper/2203.15041/) (2022)
- [Rapid Exploration for Open-World Navigation with Latent Goal Models](https://mlsanity.com/paper/2104.05859/) (2021)
- [On the Role of Neural Collapse in Transfer Learning](https://mlsanity.com/paper/2112.15121/) (2021)
- [Inducing Neural Collapse in Imbalanced Learning: Do We Really Need a Learnable Classifier at the End of Deep Neural Network?](https://mlsanity.com/paper/2203.09081/) (2022)
- [On the Optimization Landscape of Neural Collapse under MSE Loss: Global Optimality with Unconstrained Features](https://mlsanity.com/paper/2203.01238/) (2022)
- [SACSoN: Scalable Autonomous Control for Social Navigation](https://mlsanity.com/paper/2306.01874/) (2023)
- [Deep Visual MPC-Policy Learning for Navigation](https://mlsanity.com/paper/1903.02749/) (2019)
- [Learning Navigational Visual Representations with Semantic Map Supervision](https://mlsanity.com/paper/2307.12335/) (2023)
- [Neural Collapse for Unconstrained Feature Model under Cross-entropy Loss with Imbalanced Data](https://mlsanity.com/paper/2309.09725/) (2023)
- [NaviDiffusor: Cost-Guided Diffusion Model for Visual Navigation](https://mlsanity.com/paper/2504.10003/) (2025)
- [Prior Does Matter: Visual Navigation via Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2504.10041/) (2025)
- [Understanding and Improving Transfer Learning of Deep Models via Neural Collapse](https://mlsanity.com/paper/2212.12206/) (2022)
- [Control-oriented Clustering of Visual Latent Representation](https://mlsanity.com/paper/2410.05063/) (2024)

## Abstract (arXiv)

Learning robust navigation policies directly from visual observations remains a fundamental challenge in vision-based robotic navigation. In end-to-end imitation learning approaches, the visual encoder and action decoder are jointly optimized using a single action loss, which provides only an indirect supervisory signal to the encoder. This indirect supervision frequently results in the encoder learning ambiguous, action-agnostic representations. The problem is further complicated by substantial variations in scene structure and appearance across diverse environments, as well as the prevalence of visual distractors inherent to real-world navigation settings. Such action-agnostic features cause the navigation policy to produce inconsistent actions at ambiguous decision points, leading to navigation failure. To overcome these limitations, we propose ORION (Ordinal Neural Collapse for Visual Navigation), a method that explicitly organizes the encoder's representation space according to the ordinal structure of navigation actions. In the context of goal-directed navigation, ego-centric control categories from Far Left to Far Right exhibit a natural ordinal relationship in which neighboring classes share similar visual contexts, while semantically opposing classes differ substantially in appearance. We encourage class representations to be arranged sequentially along a single discriminative axis, while suppressing off-axis variance within each class. The pretrained encoder is then integrated into a diffusion-based navigation framework, and the full pipeline is fine-tuned end-to-end. Extensive experiments in both simulation and real-world settings show that ORION consistently outperforms end-to-end and neural collapse baselines in navigation success rate and goal progress, with notable gains in visually challenging scenarios such as complex multi-way intersections.