This paper proposes a new reconstruction loss for unsupervised training of representations. This loss extends auto-encoders via a pretext task that uses the marginal distribution of features. The reviewers were unanimous in their decision to accept this paper.

Here we summarize all our model assumptions and highlight what are learned from data. Model assumptions: The choice of coordinates: we choose which set of coordinate we want to learn and design coordinate-aware VAE accordingly. This is important from an interpretability perspective. Take the Acrobot as an example, the set of generalized coordinates that describes the time evolution of the system is not unique (see Figure 5 in [1] for another choice of generalized coordinates.) Because of this non-uniqueness, without specifying which set of coordinates we want to learn will let the model lose interpretability.

This is not obvious since recent work has applied Hamiltonian/Lagrangian to general latent spaces as opposed to rigid body systems.

Self-training and contrastive learning have emerged as leading techniques for incorporating unlabeled data, both under distribution shift (unsupervised domain adaptation) and when it is absent (semi-supervised learning). However, despite the popularity and compatibility of these techniques, their efficacy in combination remains surprisingly unexplored. In this paper, we first undertake a systematic empirical investigation of this combination, finding (i) that in domain adaptation settings, self-training and contrastive learning offer significant complementary gains; and (ii) that in semi-supervised learning settings, surprisingly, the benefits are not synergistic. Across eight distribution shift datasets (e.g., BREEDs, WILDS), we demonstrate that the combined method obtains 3-8% higher accuracy than either approach independently. Finally, we theoretically analyze these techniques in a simplified model of distribution shift demonstrating scenarios under which the features produced by contrastive learning can yield a good initialization for self-training to further amplify gains and achieve optimal performance, even when either method alone would fail.

The paper discusses how to solve semi-supervised learning with multi-layer graphs. For single-layer graphs, this is achieved by label regression regularized by Laplacian matrix. For multi-layer, the paper argues that it should use a power mean Laplacian instead of the plain additive sum of Laplacians in each layer. This generalizes prior work including using the harmonic means. Some theoretical discussions follow under the assumptions from Multilayer Stochastic Block Model (MSBM), showing that specificity and robustness trade-offs can be achieved by adjusting the power parameter.

We study the task of semi-supervised learning on multilayer graphs by taking into account both labeled and unlabeled observations together with the information encoded by each individual graph layer. We propose a regularizer based on the generalized matrix mean, which is a one-parameter family of matrix means that includes the arithmetic, geometric and harmonic means as particular cases. We analyze it in expectation under a Multilayer Stochastic Block Model and verify numerically that it outperforms state of the art methods. Moreover, we introduce a matrix-free numerical scheme based on contour integral quadratures and Krylov subspace solvers that scales to large sparse multilayer graphs.

This paper makes a contribution toward the theory of semi-supervised learning for graph classification, as well as an efficient algorithm for computing the proposed classifier. This is an interesting problem and the reviewers agree the contribution is at least incremental. I suggest the authors carefully revise the paper to address reviewer concerns to get the maximum impact.

It seems trivial to extend the Triplet Mutual Information [1] and its code [2]. The contribution of the proposed method is not clear. Please explain the difference between your work and [1] about Triplet Mutual Information. For the comparison, how were the parameters of other methods tuned? 4. Deformable template matching is an existing technology. Please explain the difference between your work and [3, 4] separately.

Unlabeled data learning has attracted considerable attention recently. However, it is still elusive to extract the expected high-level semantic feature with mere unsupervised learning. In the meantime, semi-supervised learning (SSL) demonstrates a promising future in leveraging few samples. In this paper, we combine both to propose an Unsupervised Semantic Aggregation and Deformable Template Matching (USADTM) framework for SSL, which strives to improve the classification performance with few labeled data and then reduce the cost in data annotating. Specifically, unsupervised semantic aggregation based on Triplet Mutual Information (T-MI) loss is explored to generate semantic labels for unlabeled data. Then the semantic labels are aligned to the actual class by the supervision of labeled data. Furthermore, a feature pool that stores the labeled samples is dynamically updated to assign proxy labels for unlabeled data, which are used as targets for cross-entropy minimization. Extensive experiments and analysis across four standard semisupervised learning benchmarks validate that USADTM achieves top performance (e.g., 90.46% accuracy on CIFAR-10 with 40 labels and 95.20% accuracy with 250 labels).

The reviewers found the usage of the deformable templates here interesting and this work will be useful to a large part of the NeurIPS community.