# Technical note on: Zero-Training Feature-Space Alignment via Information Geometry

arXiv: https://arxiv.org/abs/2609.37302 · HTML: https://mlsanity.com/paper/2609.37302/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 26 references that are in the map.
- First posted on arXiv 29 Sep 2026.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2002.08546/) (2020)
- [Efficient Test-Time Model Adaptation without Forgetting](https://mlsanity.com/paper/2204.02610/) (2022)
- [Measuring Robustness to Natural Distribution Shifts in Image Classification](https://mlsanity.com/paper/2007.00644/) (2020)
- [Parameter-free Online Test-time Adaptation](https://mlsanity.com/paper/2201.05718/) (2022)
- [Efficient Test-Time Adaptation of Vision-Language Models](https://mlsanity.com/paper/2403.18293/) (2024)
- [Test-Time Model Adaptation with Only Forward Passes](https://mlsanity.com/paper/2404.01650/) (2024)
- [AdaNPC: Exploring Non-Parametric Classifier for Test-Time Adaptation](https://mlsanity.com/paper/2304.12566/) (2023)
- [Frustratingly Easy Test-Time Adaptation of Vision-Language Models](https://mlsanity.com/paper/2405.18330/) (2024)

## Abstract (arXiv)

Deep vision models often degrade under distribution shift. Test-time adaptation can improve robustness but typically requires iterative optimization, hyperparameter tuning, and multiple forward-backward passes. We propose Zero-Training Fisher Geometry Alignment (ZFGA), a closed-form method that improves robustness under covariate shift without modifying model parameters. ZFGA is based on the observation that distribution shifts distort feature-space geometry. It estimates the Fisher information matrix of the predictive distribution with respect to feature embeddings and applies a linear transformation that aligns test-feature Fisher geometry with a reference geometry computed from clean data. This provides a natural-gradient-inspired preconditioning step in feature space. We evaluate ZFGA on CIFAR-10-C and ImageNet-C using ResNet-50, DINO ViT-S/16, and CLIP ViT-B/32. ZFGA consistently improves over zero-shot inference across all three models, although it is not the strongest method for every model. Covariance whitening performs better on ResNet-50, while Fisher whitening is statistically indistinguishable from ZFGA on CLIP. Across six training-free and gradient-based alternatives (covariance whitening, Fisher whitening, TENT, T3A, LAME, and AdaNPC), ZFGA is the only method that does not substantially harm any of the three model families. The Fisher geometry distortion is also positively correlated with ZFGA gain (Pearson r = 0.366, p = 0.017), providing preliminary evidence that geometric misalignment contributes to robustness degradation. ZFGA requires only forward passes and matrix operations at inference time, offering a lightweight and deterministic alternative to optimization-based test-time adaptation.