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.
Figures & tables
Figure 1: Overview of the INST-Align pipeline. Phase 1 learns a shared canonical expression field fθ as an implicit neural representation that maps spatial coordinates to embedding vectors and reconstructs gene expression profiles. Phase 2 jointly optimizes a non-rigid deformation network and feature-guided spatial matching within the shared field, enabling mutually reinforcing alignment and representation learning under smoothness regularization.
DLPFC
MERFISH Brain
Metric
Method
D1
D2
D3
MB2
MB7
MB11
ST
MH
ME
Mean
OT Acc ↑
Raw
.745
.887
.673
.013
.050
.209
.860
.051
.116
.400
PASTE
.859
.904
.806
.267
.726
.349
.882
.674
.031
.611
STalign
.866
.905
.808
.022
.046
.143
.861
.051
.112
.424
Spateo
.864
.884
.818
.343
.750
.298
.860
.681
.723
.691
ICP
.829
.888
.829
.251
.709
.347
.852
.689
.710
.678
Table 1: D1–D3: DLPFC samples; MB2/MB7/MB11: MERFISH Brain sections; ST: STARMap; MH: MERFISH Hypothalamus; ME: MouseEmbryo. Spatial alignment results across nine datasets. Best in bold , second-best underlined . “–” indicates method not available or no alignment.
DLPFC Samp. 1
DLPFC Samp. 2
DLPFC Samp. 3
MouseEmbryo
Mean
Method
ARI
NMI
ARI
NMI
ARI
NMI
ARI
NMI
ARI
NMI
PCA
.298
.385
.205
.364
.208
.340
.128
.215
.210
.326
Seurat
.237
.372
.285
.287
.253
.397
.078
.220
.213
.319
STAligner
.273
.474
.463
.556
.293
.491
.356
.552
.346
.518
GraphST
.431
.641
.490
.589
.618
.724
.266
.516
.451
.618
SPIRAL
.558
.652
.359
.484
.356
.478
.192
.355
.366
.492
Table 2: Embedding quality (ARI / NMI) via mclust clustering. Each is from the target slice. Baselines include STAligner [ 14 ] , GraphST [ 15 ] , SPIRAL [ 36 ] , and Seurat [ 37 ] .
Figure 2: Qualitative results. (a) MouseEmbryo after rigid ICP pre-alignment; (b) INST-Align non-rigid alignment on the same pair; (c) 3D reconstruction of DLPFC Sample 3 from consecutively aligned slices, colored by cortical layer.
Alignment
Embedding
Variant
OT Acc ↑
Chamfer ↓
ARI ↑
NMI ↑
Full (Ours)
.810
0.36
.334
.450
w/o Phase 1 (pretrain)
.813
0.47
.045
.079
w/o Phase 2 (joint opt.)
.807
0.56
.295
.434
w/o Jacobian reg.
.805
0.49
.287
.400
Table 3: Ablation study on DLPFC Sample 1. Each row removes one component from the full model.