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Towards Realistic Model Selection for Semi-supervised Learning
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Proposes SLAM, a validation-free model selection method for semi-supervised learning that combines labeled-data margin, spectral complexity, and local-consistency reweighting, with a PAC-style bound on excess error.
Problem
Model selection (early stopping, hyper-parameter selection) for semi-supervised learning is hard because labeled data is scarce, so splitting off a validation set hurts training and yields unreliable estimates; existing generalization measures are not tailored to SSL with pseudo-labels.
Approach
Uses the classification margin of labeled training data only, combined with the empirical spectral complexity (product of layer-wise spectral norms) and a KNN-based local-consistency reweighting of labeled points, in a margin-based PAC-Bayes style objective to select the model without any validation data.
Key results
- On CIFAR-10 with 40 labels under MixMatch, SLAM reaches 59.99% accuracy versus 62.97% for the test-set optimal model and 32.86% for EB-criterion.
- On CIFAR-100 with 400 labels under ReMixMatch, SLAM reaches 45.45% versus 45.96% for the optimal model, outperforming DEV, SND, MixVal and entropy baselines.
- SLAM outperforms the 10% and 20% validation-split strategies on CIFAR-10 with 250 and 4000 labels (e.g., 84.47% vs 72.60% for MixMatch with 250 labels).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| select checkpoints with SLAM instead of DEV | MixMatch · CIFAR-10, 40 labels | accuracy: 52.65 ± 4.30 -> 59.99 ± 2.79 | Helped |
| select checkpoints with SLAM instead of DEV | MixMatch · CIFAR-10, 250 labels | accuracy: 79.14 ± 8.02 -> 84.47 ± 0.87 | Helped |
| select checkpoints with SLAM instead of SND | ReMixMatch · CIFAR-10, 40 labels | accuracy: 89.92 ± 1.76 -> 89.79 ± 1.32 | Mixed |
| select checkpoints with SLAM instead of DEV | FixMatch · CIFAR-10, 40 labels | accuracy: 93.19 ± 0.97 -> 94.43 ± 0.73 | Helped |
| select checkpoints with SLAM instead of DEV | FixMatch · CIFAR-100, 400 labels | accuracy: 45.06 ± 2.48 -> 45.35 ± 1.74 | Helped |
| select checkpoints with SLAM instead of SND | FixMatch · CIFAR-100, 10000 labels | accuracy: 70.47 ± 0.10 -> 71.27 ± 0.59 | Helped |
| select checkpoints with SLAM instead of SND | MixMatch · Semi-Aves, 3959 labels | accuracy: 61.83 ± 0.76 -> 62.08 ± 0.84 | Helped |
| select checkpoints with SLAM instead of SND | FixMatch · Semi-Aves, 3959 labels | accuracy: 67.64 ± 0.21 -> 67.80 ± 0.03 | Helped |
| select checkpoints with SLAM rather than using a 10% validation split | MixMatch · CIFAR-10, 250 labels | accuracy: 68.64 ± 1.56 -> 84.47 ± 0.87 | Helped |
| select checkpoints with SLAM rather than using a 20% validation split | FixMatch · CIFAR-10, 250 labels | accuracy: 90.30 ± 2.06 -> 94.76 ± 0.73 | Helped |
Surprising findings
- Existing unsupervised model selection methods such as SND and MixVal can fail badly for poorly trained SSL models, e.g., FixMatch on CIFAR-10 with 40 labels, where MixVal gets 36.08% versus 94.50% for the optimal model.
Limitations
- The theoretical bound relies on a finite, nested hypothesis set and is largely asymptotic in the spectral complexity terms.
- The surrogate spectral complexity (product of layer-wise spectral norms) only approximates the full spectral complexity measure.
- Gains are smaller on some settings, and DEV is close on CIFAR-100 with stronger base models.
Experimental setup
Datasets: CIFAR-10 CIFAR-100 Semi-Aves
Benchmarks: CIFAR-10 CIFAR-100 Semi-Aves
Metrics: test accuracy of selected model excess error relative to test-set-optimal model
Baselines: EB-criterion DEV Entropy SND MixVal Validation split (10%/20%)
Builds on: Bartlett et al. spectral-normalized margin bound FixMatch MixMatch ReMixMatch DEV (density-reweighted cross-validation)
Closest papers by meaning
- CGMatch: A Different Perspective of Semi-supervised Learning (CVPR 2025 · similarity 0.89)
- Enhancing Semi-Supervised Learning via Representative and Diverse Sample Selection (NeurIPS 2024 · similarity 0.88)
- Revisiting Semi-Supervised Learning in the Era of Foundation Models (NeurIPS 2025 · similarity 0.86)
- Rethinking Confidence Scores and Thresholds in Pseudolabeling-based SSL (ICML 2025 · similarity 0.86)
- Erasing the Bias: Fine-Tuning Foundation Models for Semi-Supervised Learning (ICML 2024 · similarity 0.86)
- Unlocking the Potential of Unlabeled Data in Semi-Supervised Domain Generalization (CVPR 2025 · similarity 0.85)
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