Unsupervised Representation Learning

The dependence on expert annotation has long constituted the primary rate-limiting step in the application of artificial intelligence to biomedicine. While supervised learning drove the initial wave of clinical algorithms, a paradigm shift towards unsupervised and self-supervised learning (SSL) is currently unlocking the latent potential of biobank-scale datasets. By learning directly from the intrinsic structure of data - whether pixels in a magnetic resonance image (MRI), voxels in a volumetric scan, or tokens in a genomic sequence - these methods facilitate the discovery of novel phenotypes, the linkage of morphology to genetics, and the detection of anomalies without human bias. This article synthesises seminal and recent advances in "learning without labels," highlighting how unsupervised frameworks can derive heritable cardiac traits, predict spatial gene expression in histology, and detect pathologies with performance that rivals or exceeds supervised counterparts.

Unsupervised multi-view clustering (MVC) aims to partition data into meaningful groups by leveraging complementary information from multiple views without labels, yet a central challenge is to obtain a reliable shared structural signal to guide representation learning and cross-view alignment under view discrepancy and noise. Existing approaches often rely on magnitude-only affinities or early pseudo targets, which can be unstable when different views induce relations with comparable strengths but contradictory directional tendencies, thereby distorting the global spectral geometry and degrading clustering. In this paper, we propose Phase-Consistent Magnetic Spectral Learning for MVC: we derive a confidence-directed cross-view flow from anchor assignments, encode it as a phase term, and combine it with a nonnegative magnitude backbone to form a complex-valued magnetic affinity, extract a stable shared spectral signal via a Hermitian magnetic Laplacian, and use it as structured self-supervision to guide unsupervised multi-view representation learning and clustering. To obtain robust inputs for spectral extraction at scale, we construct a compact shared structure with anchor-based high-order consensus modeling and apply a lightweight refinement to suppress noisy or inconsistent relations. Experiments on ten public benchmarks show that our method achieves the best result on 22 of 30 dataset-metric combinations and ranks among the top two on 27 combinations, demonstrating strong and broadly consistent performance against classical and recent MVC baselines.

Integral Field Spectroscopy (IFS) surveys offer a unique new landscape in which to learn in both spatial and spectroscopic dimensions and could help uncover previously unknown insights into galaxy evolution. In this work, we demonstrate a new unsupervised deep learning framework using Convolutional Long-Short Term Memory Network Autoencoders to encode generalized feature representations across both spatial and spectroscopic dimensions spanning $19$ optical emission lines (3800A $< λ<$ 8000A) among a sample of $\sim 9000$ galaxies from the MaNGA IFS survey. As a demonstrative exercise, we assess our model on a sample of $290$ Active Galactic Nuclei (AGN) and highlight scientifically interesting characteristics of some highly anomalous AGN.

Unsupervised representations are widely assumed to be neutral with respect to sensitive attributes when those attributes are withheld from training. We show that this assumption is false. Using SOMtime, a topology-preserving representation method based on high-capacity Self-Organizing Maps, we demonstrate that sensitive attributes such as age and income emerge as dominant latent axes in purely unsupervised embeddings, even when explicitly excluded from the input. On two large-scale real-world datasets (the World Values Survey across five countries and the Census-Income dataset), SOMtime recovers monotonic orderings aligned with withheld sensitive attributes, achieving Spearman correlations of up to 0.85, whereas PCA and UMAP typically remain below 0.23 (with a single exception reaching 0.31), and against t-SNE and autoencoders which achieve at most 0.34. Furthermore, unsupervised segmentation of SOMtime embeddings produces demographically skewed clusters, demonstrating downstream fairness risks without any supervised task. These findings establish that fairness through unawareness fails at the representation level for ordinal sensitive attributes and that fairness auditing must extend to unsupervised components of machine learning pipelines. We have made the code available at~ https://github.com/JosephBingham/SOMtime

Hypergraph Neural Networks (HyGNNs) have demonstrated remarkable success in modeling higher-order relationships among entities. However, their performance often degrades on heterophilic hypergraphs, where nodes connected by the same hyperedge tend to have dissimilar semantic representations or belong to different classes. While several HyGNNs, including our prior work BHyGNN, have been proposed to address heterophily, their reliance on labeled data significantly limits their applicability in real-world scenarios where annotations are scarce or costly. To overcome this limitation, we introduce BHyGNN+, a self-supervised learning framework that extends BHyGNN for representation learning on heterophilic hypergraphs without requiring ground-truth labels. The core idea of BHyGNN+ is hypergraph duality, a structural transformation where the roles of nodes and hyperedges are interchanged. By contrasting augmented views of a hypergraph against its dual using cosine similarity, our framework captures essential structural patterns in a fully unsupervised manner. Notably, this duality-based formulation eliminates the need for negative samples, a common requirement in existing hypergraph contrastive learning methods that is often difficult to satisfy in practice. Extensive experiments on eleven benchmark datasets demonstrate that BHyGNN+ consistently outperforms state-of-the-art supervised and self-supervised baselines on both heterophilic and homophilic hypergraphs. Our results validate the effectiveness of leveraging hypergraph duality for self-supervised learning and establish a new paradigm for representation learning on challenging, unlabeled hypergraphs.

As unsupervised pretraining becomes increasingly ubiquitous in reinforcement learning, a more thorough theoretical understanding of these methods becomes of equal importance to their empirical success. We focus on the setting of unsupervised learning via interaction, where the forward-backward (FB) representation learning serves as a prototypical and popular example. In this paper, we shed light on FB by formally contextualizing the method within a broader class of recent methods that use regression to obtain a low-rank approximation of a successor measure ratio. Our analysis clarifies when FB representations can exist and how the low-rank approximation converges in practice. Building upon the theory, we propose a variant of FB that is both more amenable to theoretical understanding and simpler to optimize in practice. Experiments in didactic settings, as well as in $10$ state-based and image-based continuous control domains, demonstrate that our method converges to desired representations with $10^5 \times$ smaller errors than FB, achieving $+24\%$ improved zero-shot performance on average. We also demonstrate that zero-shot policies inferred by our algorithm provide an efficient initialization if the user prefers further fine-tuning on downstream tasks. Our project website is available at https://chongyi-zheng.github.io/onestep-fb.

A prevailing paradigm in modern representation learning is the map-first approach, in which a representation map is learned from reconstruction, embedding, or task objectives. At the optimum, when the learned map accurately recovers a global coordinate chart, it should exhibit three structural properties whose geometric meaning can be illustrated through a face-editing example: Commutativity requires that changing pose and then expression gives the same result as applying them in the reverse order; Time Coherence requires that the same variation along one coordinate induces the same expression change across faces; Common-Reference requires that all faces are organized relative to a common reference face. However, small approximation errors in the learned map need not translate into small errors in these structural properties, and can therefore disrupt the global organization of the representation. Based on this observation, we consider the converse of the map-first formulation and ask whether a global representation can instead emerge by directly learning these properties. We represent variations along individual coordinates through vector fields defined in the ambient space and introduce a non-contraction condition preventing one transformation from destroying directions associated with the others. We derive an unsupervised objective that learns these structural properties and establish theoretical results connecting its minimization to tangent-space recovery. Experiments on controlled manifolds validate the predicted tangent-space recovery and global structure, while an autoencoder baseline shows that small map-first errors can still produce substantial violations of the targeted properties.

Legal documents pose substantial challenges for unsupervised knowledge discovery due to specialized domain terminology, multi-scale document lengths, and scarce expert annotations. This paper introduces Topic-Graph Spherical Fusion (TGSF), a dual-manifold representation learning framework for unsupervised legal document clustering that unifies dense topic-semantic discovery and relational graph embeddings on a joint unit hypersphere. Instantiating dense topic discovery via Top2Vec and biased second-order random walks via Node2Vec, TGSF constructs a connected multi-relational document-topic graph combining multi-topic centroid bridges with temperature-sharpened semantic k-Nearest Neighbor (k-NN) document edges, guaranteeing a single connected component. The resulting L2-normalized semantic and graph representations are fused via modality-weighted concatenation onto a joint unit hypersphere prior to KMeans partitioning, decomposing squared chordal distance into a convex combination of semantic and structural cosine similarities. Evaluations across three legal benchmarks (ACORD, CUAD, and LEDGAR) show that TGSF outperforms semantic-only, structural-only, Latent Dirichlet Allocation (LDA), Non-Negative Matrix Factorization (NMF), and TF-IDF baselines. Across 216 factorial grid configurations and 240 Bayesian TPE and Multi-Objective NSGA-II Pareto optimization trials per dataset (720 trials total), TGSF improves Normalized Mutual Information (NMI) from 0.606 to 0.653 on LEDGAR (ARI = 0.425), 0.228 to 0.284 on ACORD (ARI = 0.260), and 0.535 to 0.570 on CUAD (ARI = 0.282). Functional ANOVA and Pareto frontier diagnostics further characterize hyperparameter sensitivity for reproducible legal text mining.

A local-valley (LV) centered approach to assessing the quality of sampling from Restricted Boltzmann Machines (RBMs) was applied to the latest generation of the D-Wave quantum annealer. D-Wave and Gibbs samples from a classically trained RBM were obtained at conditions relevant to the contrastive-divergence-based RBM learning. The samples were compared for the number of the LVs to which they belonged and the energy of the corresponding local minima. No significant (desirable) increase in the number of the LVs has been achieved by decreasing the D-Wave annealing time. At any training epoch, the states sampled by the D-Wave belonged to a somewhat higher number of LVs than in the Gibbs sampling. However, many of those LVs found by the two techniques differed. For high-probability sampled states, the two techniques were (unfavorably) less complementary and more overlapping. Nevertheless, many potentially "important" local minima, i.e., those having intermediate, even if not high, probability values, were found by only one of the two sampling techniques while missed by the other. The two techniques overlapped less at later than earlier training epochs, which is precisely the stage of the training when modest improvements to the sampling quality could make meaningful differences for the RBM trainability. The results of this work may explain the failure of previous investigations to achieve substantial (or any) improvement when using D-Wave-based sampling. However, the results reveal some potential for improvement, e.g., using a combined classical-quantum approach.

Unsupervised anomaly detection (UAD) aims to detect anomalies without labeled data, a necessity in many machine learning applications where anomalous samples are rare or not available. Most state-of-the-art methods fall into two categories: reconstruction-based approaches, which often reconstruct anomalies too well, and decoupled representation learning with density estimators, which can suffer from suboptimal feature spaces. While some recent methods attempt to couple feature learning and anomaly detection, they often rely on surrogate objectives, restrict kernel choices, or introduce approximations that limit their expressiveness and robustness. To address this challenge, we propose a novel method that couples representation learning the exact One-Class SVM (OCSVM) optimization problem, through a custom loss formulation that directly aligns latent features with the OCSVM decision boundary. The model is evaluated on two tasks: a benchmark based on MNIST-C, and a challenging brain MRI lesion detection task. Unlike most methods that focus on large, hyperintense lesions at the image level, our approach succeeds to target small, non-hyperintense lesions, while we evaluate voxel-wise metrics, addressing a more clinically relevant scenario. Both experiments evaluate a form of robustness to domain shifts, including corruption types in MNIST-C and texture or population age variations in MRI. Results demonstrate performance and robustness of our proposed model, highlighting its potential for general UAD and real-world medical imaging applications. The source code is available at https://github.com/Nicolas-Pinon/uad\_ocsvm\_guided\_repr\_learning.