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URLOST: Unsupervised Representation Learning without Stationarity or Topology
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Proposes URLOST, which clusters signal dimensions via density-adjusted spectral clustering on mutual information, aligns clusters with a self-organizing layer, and trains a masked autoencoder, enabling representation learning on data without known stationarity or topology.
Problem
Self-supervised representation learning typically assumes data has known stationarity and domain topology (e.g., image grids), which fails for irregular, non-stationary high-dimensional signals such as foveated vision, V1 neural recordings, and gene expression.
Approach
Recover a coarse topology from pairwise mutual information between signal dimensions via density-adjusted spectral clustering, then align the resulting irregular clusters with a learnable non-shared self-organizing layer before a standard masked autoencoder with a ViT backbone.
Key results
- URLOST MAE reaches 86.4% on Permuted CIFAR-10 and 85.4% on Foveated CIFAR-10 linear probing, while pixel-level MAE gets 56.7% and 48.5% and SimCLR (ResNet-18) gets 47.9% and 38.0%.
- On V1 response decoding, URLOST MAE achieves 78.75% versus 75.64% for beta-VAE, 73.9% for raw signal, and 70.6% for MAE.
- On TCGA pan-cancer classification, URLOST MAE achieves 94.90% versus 94.15% for beta-VAE, 91.7% for raw signal, and 90.6% for MAE.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use similar-dimension clusters as masking units instead of randomly aggregating dimensions (ablation) | URLOST MAE · Permuted CIFAR-10 | probing accuracy: 55.7% -> 86.4% | Helped |
| use similar-dimension clusters as masking units instead of individual dimensions (ablation) | URLOST MAE · Foveated CIFAR-10 | probing accuracy: 48.5% -> 85.4% | Helped |
| use similar-dimension clusters as masking units instead of randomly aggregating dimensions (ablation) | URLOST MAE · TCGA Gene | probing accuracy: 91.7% -> 94.9% | Helped |
| use similar-dimension clusters as masking units instead of individual dimensions (ablation) | URLOST MAE · V1 Response | probing accuracy: 64.8% -> 78.8% | Helped |
| use a non-shared self-organizing projection instead of a shared projection (ablation) | URLOST MAE · Locally-Permuted CIFAR-10 | linear probing accuracy: 81.4 % -> 87.6 % | Helped |
| use a non-shared self-organizing projection instead of a shared projection (ablation) | URLOST MAE · Permuted CIFAR-10 | linear probing accuracy: 80.7 % -> 86.4 % | Helped |
| use density-adjusted spectral clustering instead of uniform-density spectral clustering (ablation) | URLOST MAE · Foveated CIFAR-10 | linear probing accuracy: 82.7 % -> 85.4 % | Helped |
| set α=0.5 and β=2 instead of α=1.0 and β=2 (ablation) | URLOST MAE · Foveated CIFAR-10 | evaluation accuracy: 81.62 % -> 85.43 % | Helped |
| set α=0.5 and β=2 instead of α=0 and β=0 (ablation) | URLOST MAE · Foveated CIFAR-10 | evaluation accuracy: 82.74 % -> 85.43 % | Helped |
Surprising findings
- On standard CIFAR-10, SimCLR with ResNet-18 (90.7%) and MAE with ViT patches (88.3%) outperform URLOST-style clustering inputs, so the gains are confined to non-stationary/non-topological settings.
- Clustering on the mutual information graph of 10,000-dimensional data takes about 130 minutes, indicating quadratic scaling limits for very high-dimensional inputs.
Limitations
- Clustering and mutual information are computed separately from MAE training and scale quadratically, infeasible for d > 10,000 with current implementation.
- Cluster generation is not learned end-to-end with the representation model.
- Evaluated only on relatively small natural science datasets; hyperparameters (cluster count, density parameters) need per-dataset grid search.
Experimental setup
Datasets: CIFAR-10 Foveated CIFAR-10 Permuted CIFAR-10 Locally-Permuted CIFAR-10 V1 neural response dataset TCGA miRNA pan-cancer dataset
Benchmarks: CIFAR-10 Permuted CIFAR-10 Foveated CIFAR-10 V1 response decoding TCGA pan-cancer classification
Metrics: linear probing accuracy decoding accuracy classification accuracy (5-fold CV)
Baselines: MAE SimCLR beta-VAE Vision GNN (ViG) ResNet-18
Builds on: masked autoencoder SimCLR beta-VAE Vision Transformer FlexiViT
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