# INST-Align: Implicit Neural Alignment for Spatial Transcriptomics via Canonical Expression Fields

arXiv: https://arxiv.org/abs/2604.12084 · HTML: https://mlsanity.com/paper/2604.12084/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 37 references that are in the map.
- First posted on arXiv 13 Apr 2026.

## Builds on (most cited first, 6 of 6)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Deep Implicit Optimization enables Robust Learnable Features for Deformable Image Registration](https://mlsanity.com/paper/2406.07361/) (2024)
- [SUICA: Learning Super-high Dimensional Sparse Implicit Neural Representations for Spatial Transcriptomics](https://mlsanity.com/paper/2412.01124/) (2024)

## Abstract (arXiv)

Spatial transcriptomics (ST) measures mRNA expression while preserving spatial organization, but multi-slice analysis faces two coupled difficulties: large non-rigid deformations across slices and inter-slice batch effects when alignment and integration are treated independently. We present INST-Align, an unsupervised pairwise framework that couples a coordinate-based deformation network with a shared Canonical Expression Field, an implicit neural representation mapping spatial coordinates to expression embeddings, for joint alignment and reconstruction. A two-phase training strategy first establishes a stable canonical embedding space and then jointly optimizes deformation and spatial-feature matching, enabling mutually constrained alignment and representation learning. Cross-slice parameter sharing of the canonical field regularizes ambiguous correspondences and absorbs batch variation. Across nine datasets, INST-Align achieves state-of-the-art mean OT Accuracy (0.702), NN Accuracy (0.719), and Chamfer distance, with Chamfer reductions of up to 94.9% on large-deformation sections relative to the strongest baseline. The framework also yields biologically meaningful spatial embeddings and coherent 3D tissue reconstruction. The code will be released after review phase.