# Linear Readout of Object Manifolds

arXiv: https://arxiv.org/abs/1512.01834 · HTML: https://mlsanity.com/paper/1512.01834/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2015.

## Built on by (most cited first, 9 of 9)

- [On the geometry of generalization and memorization in deep neural networks](https://mlsanity.com/paper/2105.14602/) (2021)
- [Neural population geometry: An approach for understanding biological and artificial neural networks](https://mlsanity.com/paper/2104.07059/) (2021)
- [Neural Population Geometry Reveals the Role of Stochasticity in Robust Perception](https://mlsanity.com/paper/2111.06979/) (2021)
- [Linear Classification of Neural Manifolds with Correlated Variability](https://mlsanity.com/paper/2211.14961/) (2022)
- [Predicting and Enhancing the Fairness of DNNs with the Curvature of Perceptual Manifolds](https://mlsanity.com/paper/2303.12307/) (2023)
- [Random features and polynomial rules](https://mlsanity.com/paper/2402.10164/) (2024)
- [Contrastive Self-Supervised Learning As Neural Manifold Packing](https://mlsanity.com/paper/2506.13717/) (2025)
- [Soft-margin classification of object manifolds](https://mlsanity.com/paper/2203.07040/) (2022)
- [On the Dynamics & Transferability of Latent Generalization during Memorization](https://mlsanity.com/paper/2603.19865/) (2026)

## Abstract (arXiv)

Objects are represented in sensory systems by continuous manifolds due to sensitivity of neuronal responses to changes in physical features such as location, orientation, and intensity. What makes certain sensory representations better suited for invariant decoding of objects by downstream networks? We present a theory that characterizes the ability of a linear readout network, the perceptron, to classify objects from variable neural responses. We show how the readout perceptron capacity depends on the dimensionality, size, and shape of the object manifolds in its input neural representation.