# Learning Array Signal Topologies as Conditional Neural Manifolds

arXiv: https://arxiv.org/abs/2609.18616 · HTML: https://mlsanity.com/paper/2609.18616/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 28 references that are in the map.
- First posted on arXiv 16 Sep 2026.

## Builds on (most cited first, 7 of 7)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [Deep Networks for Direction-of-Arrival Estimation in Low SNR](https://mlsanity.com/paper/2011.08848/) (2020)
- [DA-MUSIC: Data-Driven DoA Estimation via Deep Augmented MUSIC Algorithm](https://mlsanity.com/paper/2109.10581/) (2021)
- [Image Generation with a Sphere Encoder](https://mlsanity.com/paper/2602.15030/) (2026)
- [SubspaceNet: Deep Learning-Aided Subspace Methods for DoA Estimation](https://mlsanity.com/paper/2306.02271/) (2023)
- [Three more Decades in Array Signal Processing Research: An Optimization and Structure Exploitation Perspective](https://mlsanity.com/paper/2210.15012/) (2022)

## Abstract (arXiv)

Subspace methods such as multiple signal classification (MUSIC) achieve super-resolution direction of arrival (DoA) estimation by exploiting the orthogonality between the array manifold and the noise subspace of the measurements. Their accuracy therefore depends on the assumed manifold and degrades under model mismatch, while parameters not identifiable from the spatial manifold cannot be recovered. In this work, we propose the conditional neural manifold (CNM), which replaces the fixed manifold with an observation-conditioned mapping from source parameters to steering vectors. An encoder maps the snapshots to a latent scene representation that conditions a zero-initialized neural field over the parameter space. The manifold is learned without steering-vector supervision by shaping the resulting MUSIC landscape. Since the correction acts on the manifold rather than on the estimator, it can be used by other manifold-based methods without modification. The CNM restores resolution under array imperfections, colored noise, correlated sources, and near-field propagation, and resolves the angle-frequency ambiguity inherent to the nominal spatial manifold.