Train to Stitch: Topology-Preserving Regularization for Interoperable Representations
The paper solves zero-shot stitching of autoencoders: enabling an encoder from one independently trained model to work with a decoder from another. The core idea is a training-time topological regularizer based on 0-dimensional persistent homology (MST edges) that preserves the input data's geometric skeleton in each latent space, so that after training only a lightweight affine map is needed. This matters for distributed and privacy-sensitive settings where encoders and decoders cannot be jointly optimized or share weights.
The paper presents a compelling training-time approach to interoperability. By adding a differentiable topological loss that aligns MST edge lengths between input and latent spaces, the authors consistently reduce stitching error across heterogeneous architectures and domains. However, the central theoretical guarantee is conditional on an unenforced bounded tree-stretch assumption, and some datasets show only modest gains over a plain affine connector.
The empirical gains are robust and multi-domain. On image compression the method improves stitched NMSE by 1-2 dB over direct affine alignment and far outperforms relative representations. The extension to quantized wireless CSI compression and to sketch-based image retrieval shows broad applicability. Most importantly, the geometric diagnostics in Section 4.4 directly validate the theoretical mechanism: topology-preserving training sharply reduces cross-model tree-metric discrepancy, correlating with downstream stitch quality.
The theory does not match the strength of the experiments. Theorem 3.1 gives a route to Euclidean near-isometry only under a bounded tree-stretch condition (Definition 1) that the loss does not enforce; the authors candidly treat it as a measurable diagnostic rather than a guarantee. Because the regularizer controls only MST edges, off-tree geometry remains unconstrained and latent embeddings are not uniquely determined. The sketch-retrieval task is also a conceptual stretch: it is cross-modal (sketch versus image) rather than same-data cross-architecture stitching, so the autoencoder framing is weakened. Finally, the relative-representation baseline is disadvantaged by requiring a dedicated decoder, making the comparison less direct.
There is also practical brittleness: the ablation in Section 4.5 shows that an overly large regularization weight $\lambda$ degrades reconstruction, signaling a tension between topology preservation and representational flexibility.
The evidence supports the core claims but with dataset-dependent nuance. Table 1 shows strong improvements on MNIST and CIFAR-10, yet the authors note that in Tiny-ImageNet the affine connector already captures most alignable structure, so topological regularization adds little. The comparison to relative representations is favorable, but that method operates in a similarity space with a specialized decoder, which the authors acknowledge. Notably missing is any comparison against other geometric regularizers surveyed in Section 2.2 (spectral, conformal, or graph-preserving autoencoders), leaving open whether the gains are specific to topological persistence or achievable by simpler geometric penalties.
Appendix B provides thorough hyperparameters, architectures, and training recipes for every dataset, and results are averaged over 5 independent random initializations. The calibration set size ($|D_T|=1000$) is clearly stated. Reproduction would nonetheless be nontrivial: the topological loss requires differentiable extraction of MST/persistence pairings on mini-batches, and the paper does not indicate whether code will be released. Without an official implementation, independently reproducing the persistence-based loss and its gradient flow is a significant barrier.
As large, powerful pre-trained models become more prevalent, there is growing interest in developing methods that allow different neural networks to be seamlessly combined with little or no direct communication between them. Take autoencoder-based data compression as an example: the ability to independently choose architectures and train encoder and decoder models, while still ensuring they work together, could fundamentally transform how such models are built, deployed, and updated. In this work, we introduce a novel approach that leverages topological regularization to align the latent spaces of two independently trained autoencoder models, entirely eliminating the need for coordination during training. We provide a conditional theoretical analysis showing how the structural agreement encouraged by our regularizer can translate into approximate geometric compatibility between independently learned representations. Reconstruction experiments validate this approach empirically, substantially narrowing the interoperability gap across multiple datasets.
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