# Deep Feature Space: A Geometrical Perspective

arXiv: https://arxiv.org/abs/2007.00062 · HTML: https://mlsanity.com/paper/2007.00062/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2020.

## Built on by (most cited first, 10 of 10)

- [A Geometric Perspective towards Neural Calibration via Sensitivity Decomposition](https://mlsanity.com/paper/2110.14577/) (2021)
- [Event Quality Score (EQS): Assessing the Realism of Simulated Event Camera Streams via Distances in Latent Space](https://mlsanity.com/paper/2504.12515/) (2025)
- [Real-Time Monocular Human Depth Estimation and Segmentation on Embedded Systems](https://mlsanity.com/paper/2108.10506/) (2021)
- [Do Neural Network Weights account for Classes Centers?](https://mlsanity.com/paper/2104.07004/) (2021)
- [Graph Your Own Prompt](https://mlsanity.com/paper/2509.23373/) (2025)
- [Tilt and Average : Geometric Adjustment of the Last Layer for Recalibration](https://mlsanity.com/paper/2406.10017/) (2024)
- [Spiking Neural Network Feature Discrimination Boosts Modality Fusion](https://mlsanity.com/paper/2502.10423/) (2025)
- [Minimizing Chebyshev Prototype Risk Magically Mitigates the Perils of Overfitting](https://mlsanity.com/paper/2404.07083/) (2024)
- [ReLU Networks as Random Functions: Their Distribution in Probability Space](https://mlsanity.com/paper/2503.22082/) (2025)
- [Visual Place Recognition for Large-Scale UAV Applications](https://mlsanity.com/paper/2507.15089/) (2025)

## Abstract (arXiv)

One of the most prominent attributes of Neural Networks (NNs) constitutes their capability of learning to extract robust and descriptive features from high dimensional data, like images. Hence, such an ability renders their exploitation as feature extractors particularly frequent in an abundant of modern reasoning systems. Their application scope mainly includes complex cascade tasks, like multi-modal recognition and deep Reinforcement Learning (RL). However, NNs induce implicit biases that are difficult to avoid or to deal with and are not met in traditional image descriptors. Moreover, the lack of knowledge for describing the intra-layer properties -- and thus their general behavior -- restricts the further applicability of the extracted features. With the paper at hand, a novel way of visualizing and understanding the vector space before the NNs' output layer is presented, aiming to enlighten the deep feature vectors' properties under classification tasks. Main attention is paid to the nature of overfitting in the feature space and its adverse effect on further exploitation. We present the findings that can be derived from our model's formulation, and we evaluate them on realistic recognition scenarios, proving its prominence by improving the obtained results.