Unsupervised Learning

Language models learn content and style jointly, making stylistic variation in their outputs difficult to identify and control. We study whether recurring styles in model responses can be discovered without supervision and explicitly controlled. We design an algorithm that learns to separate representations of content and style from language models' outputs and validate its effectiveness on math questions in a controlled setting. By applying this method to over 100K verified traces from nine distinct teacher models, we discover six recurring yet imbalanced styles. We then fine-tune smaller student models to follow these styles when explicitly conditioned on them, using importance weighting to balance the contribution of the styles represented in the corpus. This approach improves Pass@$k$ over standard fine-tuning on the same data across six math reasoning benchmarks, demonstrating that we can diversify the style of answers effectively. We confirm that this also results in strong correspondence between requested and realized styles. We find that style affects correctness: the probability of solving a problem depends on the style we condition on, and different problems benefit from different styles. In summary, our results show that stylistic variation in model-generated data can be discovered in an unsupervised way, and made explicit, providing a source of both control and improved reasoning performance.

We present TriO, a multi-modal unsupervised world model that predicts 4D occupancy, obstacle segmentation, flow and LiDAR. In contrast to prior work, TriO utilizes three distinct sensor modalities (camera, LiDAR, and RADAR) as both inputs and sources of self-supervision, eliminating the need for additional human annotations. Thanks to its novel supervision, the model is able to segment any occupancy from the drivable surface, overcoming the limitations of existing open-set methods in handling long-tail objects. TriO achieves state-of-the-art results in multiple 3D and 4D tasks, including occupancy, flow, and LiDAR prediction, as well as zero-shot road obstacle segmentation across multiple datasets such as Argoverse 2, and Spotting the Unexpected.

Text-based person search (TBPS) aims to retrieve images of a target person from a large image gallery based on a given natural language description. Most existing methods rely on supervised learning with manually annotated image-text pairs. In this paper, we explore unsupervised TBPS, with only unlabeled images. We propose GTR+, a two-stage generation-then-retrieval framework. In the generation stage, we introduce a tiered description generation framework designed to produce fine-grained and stylistically diverse textual descriptions through a three-tier sequential process. The base tier leverages an automated question-and-answer mechanism to generate basic visual attribute descriptions; the intermediate tier enhances fine-grained detail using an inter-sample contrastive mechanism; the advanced tier further enriches textual diversity via a stylized expansion mechanism. In the retrieval stage, to mitigate the impact of noisy pseudo texts, we develop an adaptive confidence-weighted retrieval learning framework. We model image-text pairs as clean or noisy using a Gaussian Mixture Model, calibrated by real-time image-text similarity and static text generation probability from the prior stage, yielding adaptive sample weights during training. Beyond that, we also contribute LargeFine-Person, a large-scale TBPS dataset with high-quality, fine-grained, and diverse textual annotations, enabling a practical and generalizable TBPS pre-training benchmark under unsupervised setting. Experiments on multiple TBPS benchmarks demonstrate the effectiveness and generalization of both GTR+ and LargeFine-Person. Code is available at: https://github.com/Flame-Chasers/GTR.

This position paper argues that the absence of labels does not imply the absence of human supervision in visual learning, and urges the research community to identify sources of supervision more explicitly. Many recent methods in computer vision build upon representations learned from large-scale unlabeled data, and are therefore grouped under the same umbrella term unsupervised.'' However, different data curation schemes and training objectives embed substantially different human priors on which models rely, and we argue that one unsupervised'' umbrella term is no longer capturing these distinctions. This ambiguity makes it harder to compare unsupervised learning research conducted under different assumptions, coinciding with a sharp decline in papers titled with ``unsupervised'' in flagship computer vision conferences since 2021, despite continued growth of the field. While we fully embrace pre-training as a strong foundation for modern computer vision, we advocate for a community-level effort toward greater conceptual clarity: authors are encouraged to disclose priors in data selection and learning objectives, and to specify which components of a learning pipeline depend on which assumptions. Standardized disclosure practices can improve academic communication, ensure fairer comparisons, and preserve methodological diversity in unsupervised learning.

Community detection is a fundamental task in graph analytics that aims to identify cohesive groups of entities with similar behaviors or interests. Classic objective-driven methods struggle with complex graph structures, while deep-learning approaches improve performance at the expense of interpretability and rely on labeled data and training. Large language models (LLMs), with strong reasoning capabilities and world knowledge, are promising for interpretable, label-free community detection. To leverage these strengths, we propose LUCID, an LLM-guided, interpretable, training-free, and unsupervised community detection method. Inspired by phase-transition kinetics in natural systems, where complex structures emerge through initialization, merging, refinement, and selection, LUCID is designed as a four-stage pipeline. Within this pipeline, the LLM induces formal rules that translate implicit knowledge into explicit and interpretable logical structures. Specifically, (1) the Local-View Community Initialization stage encodes local graph structures using k-ego contexts and unsupervised node roles; (2) the Multi-factor Community Merge stage uses LLM-induced rules to iteratively merge local communities; (3) the Multi-grain Community Refinement stage applies LLM-induced coarse-to-fine rules in parallel to reduce boundary noise; and (4) the Global-view Community Selection stage identifies high-quality communities based on topological compactness and boundary clarity. Extensive experiments on real-world datasets demonstrate that LUCID, as an unsupervised approach, achieves state-of-the-art performance and consistently outperforms leading unsupervised and semi-supervised baselines.

A central aim of unsupervised learning is to uncover latent factors that explain dependencies among observations. Probabilistic models typically achieve this by introducing multiple latent variables linked through a graph of conditional relationships, with distributional parameters and their dependence learnt from data. Learning relies either on distributional choices that allow tractable belief propagation, or on approximations that scale poorly with model size and complexity. We build on the recently developed recognition-parametrised modelling paradigm to propose an alternative approach: RAMP, a method that implicitly defines latent structure by learning a flexible, nonlinear, amortised message-passing framework. We show that RAMP enables efficient likelihood-based recovery of latent-variable distributions within expressive nonlinear models acting on complex high-dimensional data.

Adaptive Mixture Independent Component Analysis (AMICA) is widely used in EEG research and has long been associated with strong empirical performance for blind source separation. Despite its impact, practical use has historically depended on a single Fortran implementation, accessed via the EEGLAB toolbox for MATLAB, limiting its accessibility for analytical pipelines not designed within the MATLAB ecosystem. Here we present AMICA-Python, a Python implementation of the AMICA algorithm, with a scikit-learn-conformant API designed for integration with existing scientific Python pipelines. The implementation follows the reference algorithm closely while adopting modern software engineering practices and an interface familiar to Python users. Additionally, we introduce an optional Anderson acceleration scheme that can dramatically reduce the time to convergence for this relatively slow algorithm. To evaluate numerical agreement and practical performance, we benchmarked AMICA-Python against the reference Fortran implementation on 14 open EEG recordings. After averaging 3 runs of each implementation on all 14 recordings, AMICA-Python closely matched the reference, with a median final normalized log-likelihoods of 11.572 for both the Fortran and Python implementations, and a negligible median relative absolute difference of only $1.07\times10^{-8}$ when normalized by the absolute Fortran value. Runtime was also competitive. Relative to the reference implementation, AMICA-Python was 17.7% faster, while the Anderson-accelerated variant was 34.1% faster. AMICA-Python reproduces the reference implementation to high numerical precision with competitive runtime, while making AMICA available through a more accessible and extensible Python interface.

A variety of self-supervised image clustering approaches are invented in the past years. However, all dominant approaches are exploitative: The direction of parameter updates is determined by known states (observed input samples and existing parameters). We propose an explorative self-supervised learning framework that steps out of this zone. We define a surprise score that measures how unlikely the model's output representation is, assuming that all pixels are i.i.d. random noise. Maximizing the surprise score forces the deep learning model to reject the random noise null hypothesis, or equivalently, to discover non-randomness from data. Also, we propose a fundamental assumption: a surprise score cannot, in general, be fully optimized by exploitative optimization approaches. Thus, we propose the converge-to-surprise scheme to optimize a model: an evolution-strategy (ES) outer loop, which maximizes the surprise score using the mutation-selection mechanism, paired with a periodic gradient-descent inner loop, which uses the surprising clusters already discovered by ES as surrogate targets. On simple image benchmarks, our framework trained from scratch achieves new state-of-the-art results in non-parametric self-supervised image clustering --- the strictest deep-clustering setting, where the number of classes is unknown during training.

Dependency parsing consists of finding a tree representation for a sequence. Unsupervised dependency parsing aims to develop parsing methods without a gold standard during model training. In human languages, an unsupervised parser can be evaluated because some gold standard is usually available or can be created. For other species, a gold standard is unknown. Thus one may conclude that it is impossible to determine the accuracy of an unsupervised parser and, consequently, dependency parsing is unfeasible in other species. However, here we apply recent advances in network science to demonstrate that the proportion of correct edges retrieved by a parser must be high for the sequences of vocalizations or gestures that non-human primates produce due to the fast decay of the sequence length distribution. In contrast, human language sequences lack that property. Therefore, evaluation without a gold standard is feasible in non-human primates but a hard problem in humans.

While various works address reflective symmetry understanding in 3D data and images, pixel-level semantic left-right prediction of in-the-wild images remains challenging, due to certain difficulties including the lack of 3D information, occlusion, object pose variation, partiality, etc. In this work, we propose an unsupervised learning framework to tackle this challenge. Leveraging recent advances in vertex-wise semantic left-right understanding of 3D data, our unsupervised learning method jointly utilises 3D shape and image datasets to infer pixel-wise semantic left-right predictions in single-view images. In particular, we show that a medium-scale 3D shape dataset comprising mainly of human- and quadruped animal-like shapes, combined with diverse in-the-wild image data, are sufficient to achieve high-quality semantic left-right prediction in images, even for entirely unseen 3D object categories, such as cars or trains. Overall, our approach achieves superior performance in dense pixel-wise semantic left-right predictions on both rendered and in-the-wild image datasets when compared to existing state-of-the-art methods.

Combinatorial optimization (CO) problems are difficult because certifiable discrete structure induces exponential search. One needs to search over the set exponentially many candidates to certify optimality, however, the structural feasibility of a path, packing, or cover can be verified in polynomial time once supplied. In this study, we introduce Neural Certificate Pricing (NCP) that exploits this asymmetry under an unsupervised learning framework. A neural network is trained to predict certificate-level dual prices, while a structured recovery layer constructs the induced primal marginal. NCP can be viewed as amortized separation: instead of enumerating violated inequalities, it learns the residual prices through which their aggregate effect enters recovery. When the certificate-consistency condition holds, the recovered marginal is globally feasible, and a local theory shows that first-order errors in the predicted price induce only second-order loss in objective value. Across three classes of CO problems, NCP either outperforms state-of-the-art neural baselines by large margins or matches them at a fraction of the computation time, and shows stronger out-of-distribution generalization.

In this article we describe Cohort Organized Learning (CoOL), a method for clustering data without explicit distance or similarity computations. Herein, we will describe CoOL, derive the gradients determined by expectation maximization to train the networks, show how to monitor convergence during training and evaluate the clusters after training, and discuss a series of examples and use cases. We also discuss CoOL's limitations and future prospects on related tasks. Because CoOL uses neural networks to estimate the clusters, it can be used to cluster any data that can be made compatible and we illustrate this on vector data and images.

This paper explores unsupervised disentangled representation learning from a functional perspective. We define latent concepts as factors that influence observations through locally orthogonal directions, formalized as an orthogonality constraint on the Jacobian of the generative mapping. We prove that this condition yields identifiability of general nonlinear generative models, without requiring statistical independence or causal assumptions, provided the latent domain admits all combinations of factor values. Experiments with orthogonality-regularized normalizing flows empirically confirm the theory, demonstrate reliable recovery of ground-truth factors, and shed light on the success of VAEs. These findings challenge the prevailing impossibility claims for unsupervised disentanglement and provide a principled alternative foundation.

How can we learn the mapping between written words and their spoken counterparts in the absence of explicit textual supervision? We present a visually grounded method for building a vocabulary of spoken words using only images and their spoken descriptions. First, image captioning systems are used to build a vocabulary of written words representing salient visual concepts in the images. For each word, we then find utterances whose image captions contain that word. Then we use an unsupervised word discovery technique to align these utterances to locate instances of the target word. The result is spoken word segments that are linked to written words -- all accomplished without any text supervision. In spoken word retrieval and keyword spotting experiments, the proposed approach outperforms a strong neural baseline while being more interpretable. These results demonstrate the feasibility of the approach in English and motivate future work on low-resource languages without transcripts.

This paper addresses the missing-modality challenge in multi-modal learning by introducing Unsupervised Learning for Missing Modalities in Multi-Modal Learning (UL4M4), a flexible framework that imputes missing feature embeddings in a task-independent manner before supervised prediction. We propose modality-specific normalization and a novel partial-modality distance metric to enable fair clustering of incomplete observations, capturing cross-modal structures while preserving scale-invariance across varying dimensionalities and modality counts. Cluster centers from this unsupervised stage guide an iterative greedy imputation process for any missing modalities during training or inference, supporting arbitrary numbers of modalities and arbitrary missing patterns per sample. The imputation module is lightweight, uses frozen encoders, and decouples from the downstream task, allowing easy integration with any fusion/prediction architecture. Extensive experiments under diverse and highly incomplete regimes demonstrate UL4M4's robustness, achieving, to the best of our knowledge, the first consistent F1-Micro scores above 0.7 on challenging missing configurations even when more than 50% of modality slots are missing. Results are also stable across cluster sizes and significantly outperform state-of-the-art baselines. Code is available here: https://github.com/h-ismkhan/Multimodal-Learning-with-Missing-Modalities-via-Unsupervised-Learning.

We introduce a theoretical framework for analyzing federated learning in a generative setting through a teacher-multiple interacting students scenario, in which each student receives a distinct realization of the data, either through a different noise corruption or by accessing a different subset, possibly of varying size. Using theoretical tools in equilibrium disordered system, we analytically show that interactions among students systematically enhance learning performance: highly noisy students require fewer samples to recover the underlying pattern, while low-noise students achieve a larger overlap with the ground-truth signal. We derive the optimal Bayesian conditions for teacher recovery as functions of the sample complexity, noise level, and interaction strength, and validate these predictions through numerical simulations. The resulting dynamics can be mapped onto equilibrium sampling in a Restricted Boltzmann Machine with a structured hidden layer, providing a principled theoretical understanding of how interactions improve distributed generative modeling.

Principal component analysis (PCA) is one of the most widely used unsupervised dimension reduction techniques. We study PCA for data from multiple related domains. Since principal components generally differ across domains, one way to obtain a shared low-rank embedding is to perform PCA on the pooled data. However, this approach can focus on spurious directions that exhibit high variation in only a few domains. To find a robust embedding that still explains most variance in unseen but similar domains, we propose instead to focus on shared directions of variation. To this end, we introduce Anchor PCA which trades off overall explained variance with agreement between the shared and domain-specific low-rank embeddings. Anchor PCA amounts to PCA on a modified target matrix and thus can be solved efficiently. Moreover, we show that Anchor PCA recovers a maximal invariant subspace and admits a minimax reconstruction interpretation under bounded domain-specific covariance inflations. On simulated and real-world gas sensor data with temporal drift, we demonstrate, respectively, that Anchor PCA recovers the maximally invariant subspace and yields embeddings that explain more variance on unseen domains than the pooling baseline and a worst-case alternative. Taken together, these findings establish Anchor PCA as a promising approach to robust unsupervised dimension reduction from multi-domain data.

The goal of single-channel source separation is to reconstruct $K$ sources given their mixture. In supervised settings where vast amounts of clean source data are available, this challenging, ill-posed problem has been addressed successfully by generative diffusion and flow-based prior models. However, access to such clean source samples is often limited, and even when available, supervised models are vulnerable to domain shifts. To bridge this gap, we present Separation via Unsupervised Remixing Flow (SURF), an unsupervised flow matching approach for source separation that learns directly from observed mixtures. This method relies on a novel combination of state-of-the-art supervised flow matching and regression-based self-supervised techniques. At a high level, starting from a teacher model, we utilize a "remixing" step to bootstrap the learning of a student flow model from the teacher's estimates. We provide insights into the objectives optimized by this approach and draw a novel connection to the Wake-Sleep algorithm. Empirical evaluations on image and audio benchmarks demonstrate that SURF establishes a new state-of-the-art, significantly outperforming existing unsupervised methods. See our demo page for examples. https://google.github.io/df-conformer/surf/

Sparse high-dimensional representations are conducive to uncovering nontrivial structures in unsupervised exploration of data. Such a representation can deal with the dense connectivity in graphs relevant to community detection problems. However, sparse high-dimensional representations are capable of doing more, including manifold tiling and feature learning. Conventional algorithms optimize in the space of computationally intractable completely positive matrices or relax the problem to the space of doubly nonnegative matrices that scale with sample size in a way rendering them impractical for large data sets. Some of these methods also impose a row sum constraint, such as double stochasticity. Row sum constraints have the added advantage of being shift-invariant, in the context of manifold tiling. Constraints on the row sum of output similarity matrices require nontrivial online learning rules. Addressing these needs, we propose a versatile online biologically plausible learning algorithm capable of learning sparse shift-invariant representations, useful for clustering, manifold tiling, or sparse coding, depending on the data structure.

Unsupervised learning methods -- topic modeling, partition-based and density-based clustering -- produce data groupings without human guidance, yet choosing and evaluating those groupings should not itself be unsupervised. We present \emph{SmartIterator}(SI), a visual analytics approach that treats the full sequence of grouping results across a parameter sweep as a first-class analytical object. For each method family, SI provides a structured six-phase workflow that guides the analyst through systematic exploration of grouping results -- from quality-metric overview through transition-stability assessment, membership-confidence evaluation, content and context inspection, and recurrent-archetype verification to an informed decision -- building cumulative understanding of data structure along the way. The workflows are operationalized through \emph{IteraScope}(IS), a coordinated visual display combining quality-metric charts with semantic color encoding, a 1D group embedding with Sankey-style transition flows and violin plots of membership confidence, a 2D group embedding with HDBSCAN-detected recurrent archetypes that highlights iterations capturing all persistent patterns, and domain-specific linked views for contextualized interpretation. We demonstrate the three workflows on: (1)~simulated social-media messages from the VAST Challenge 2011 (density-based clustering, validated against ground truth), (2)~EU population statistics across ${\sim}1\,500$ NUTS-3 regions (partition-based clustering), and (3)~30 years of IEEE VIS papers (NMF topic modeling). The workflows constitute the main contribution: they provide actionable, method-specific guidance for navigating parameter spaces, studying how data structure evolves across configurations, and grounding analytical understanding in domain context -- yielding knowledge about the data that no single ``best'' result can provide.

Scintillation detectors with excellent timing resolution enable more precise localization of radiation sources in positron emission tomography, leading to substantial improvements in diagnostic capability for diseases such as cancer and dementia. At the extreme timing precision required for such applications at the picosecond scale, detector performance is governed by the microscopic dynamics of scintillation photons generated within the detector and their subsequent detection processes. However, detector signals have conventionally been treated only as collective responses of many photons due to structural constraints inherent to photodetectors. In this study, we overcome this fundamental limitation using deep learning, enabling direct access to the timing information of individual photons. The proposed method estimates photon-by-photon arrival times directly from detector waveforms without requiring any modification to the detector structure; the method operates on an event-by-event basis without ground-truth labels by integrating an unsupervised learning framework with a physically informed detector-response model. Through comprehensive validation combining Monte Carlo simulation and experimental measurements across various detector configurations, we experimentally demonstrate improved timing resolution, visualized depth-of-interaction-dependent photon transport, and classified Cherenkov and scintillation photons based on the estimated photon-level timing information using a unified deep learning-based framework. These results provide experimental access to photon dynamics, bridging the gap between theoretical modeling and experimental observation, and they open a new data-driven pathway for discovery in detector physics and optimization.

Generative models, from diffusion models to large language models, achieve remarkable performance but at a cost in training data orders of magnitude larger than what biological learners require. An alternative paradigm has emerged in which networks are trained to predict their \emph{own} latent representations of related views or masked regions, as in data2vec and JEPA -- an idea related to predictive-coding accounts of the cortex. Despite strong empirical results, the theoretical understanding of these methods remains limited. Central questions include: by how much does latent prediction actually improve data efficiency? Is there a benefit to stacking such methods into multi-scale hierarchies? We answer both using as data a tractable probabilistic context-free grammar that captures the compositional structure of natural language and images. Such a grammar generates strings of visible tokens by recursively applying production rules along a tree of hidden symbols of depth $L$. For such data, supervised or token-level SSL require a number of samples \emph{exponential} in $L$ to recover the latent tree; we prove that latent prediction achieves this with a number of samples \emph{constant} in $L$, up to logarithmic factors. We confirm this bound with (i) a hierarchical clustering algorithm, (ii) an end-to-end neural network whose predictor-clusterer modules predict their own latents at each level via gradient descent, and (iii) the first sample-complexity analysis of data2vec, which we show implicitly performs hierarchical latent prediction. This suggests that explicit stacking such as H-JEPA is largely redundant.

In point clouds, noise directly perturbs point coordinates that encode both spatial location and geometry, making one-to-one correspondence construction more challenging than in images. Existing methods impose statistical mappings across noisy variants via noise or optimal transport, but suffer from correspondence ambiguity. In this work, we propose Self-Induced Mirror-Point Consistency (SIMPC) to learn deterministic correspondences between points and the underlying surface in an unsupervised manner. For each noisy point, SIMPC generates a mirror-point on the opposite side of the underlying surface, guided by geometric priors during the denoising process. By encouraging consistency between the denoising targets of the original point and its mirror counterpart, SIMPC effectively localizes the position of underlying surface. Extensive experiments on synthetic and real-world datasets demonstrate that SIMPC significantly outperforms state-of-the-art unsupervised methods and surpasses several strong supervised counterparts.

Many learning problems require uncovering a hidden ordering that reveals structure in unordered data, such as monotonicity in sorting or spatial continuity in jigsaw reconstruction. In these settings, permutations can be learned as latent operators by optimizing objectives defined directly on the reordered output, often without access to ground-truth orderings. Differentiable relaxations such as Gumbel-Sinkhorn make this approach practical by approximating permutation matrices with doubly stochastic matrices. However, learning from structure without supervision induces a non-uniform uncertainty: some assignments become confident early, while others remain ambiguous. Existing methods control this process using a single global temperature, forcing all assignments to sharpen or diffuse simultaneously and leading to instability at scale. We introduce an entropy-adaptive formulation of Gumbel-Sinkhorn that locally modulates temperature based on assignment uncertainty. This allows confident assignments to discretize early while preserving exploration where uncertainty remains. Across sorting and jigsaw reconstruction tasks and in routing-style settings, adaptive entropy control improves training stability and final permutation quality relative to fixed-temperature baselines, particularly as problem size and assignment ambiguity increase.

Many novel unsupervised feature selection methods are proposed each year, yet their empirical evaluation is limited to supervised and unsupervised evaluation metrics computed on selected datasets, along with comparisons to existing methods. However, in the absence of an established evaluation baseline, it is difficult to determine the value added to the existing literature by each of these methods, and how effective their underlying approaches are. We propose using random feature selection as a baseline for evaluating the unsupervised feature selection methods. We empirically show that many of the state-of-the-art methods in unsupervised feature selection are outperformed by random feature selection in both performance and efficiency. Accordingly, we emphasize on the strict requirement of considering random feature selection as a baseline in the development process of novel unsupervised feature selection methods to ensure a consistent improvement over random feature selection.

Biological visual systems learn from limited experience, unlike deep learning models that rely on millions of training images. What learning principles make this possible? We tested whether efficient coding, the idea that neural representations capture the statistical structure of natural inputs, can build a hierarchy of human-aligned visual features from limited data. We developed an unsupervised learning procedure in which each layer of a deep network compresses its inputs onto the dominant modes of variation in natural images, using only local statistics and no labels, tasks, or backpropagation. This unsupervised procedure yields features that progress from edges and colors to textures and shapes. The features of this deep efficient coding model are readily recognized by human observers and are predictive of image-evoked fMRI responses in human visual cortex. Furthermore, a hybrid learning procedure that combines efficient coding with supervised fine-tuning yields better brain alignment in low-data settings and more rapid category learning. These findings suggest that efficient coding may shape representations across the entire visual hierarchy and help explain the data efficiency of biological vision.

Non-contrastive self-supervised learning (SSL) is an effective framework for predictive representation learning, but popular (and in practice effective) methods such as SimSiam, BYOL, I-JEPA or DINO, which rely on a form of self-distillation to train a teacher-student network, remain poorly understood as they typically do not minimize a well-defined objective. We analyze the dynamics of a variant of the Joint Embedding Predictive Architecture (JEPA) using a regularized linear regressor to predict the learned representations of two views of the data from one another, and fully characterize its stability: non-collapsed stable equilibria align with leading nonlinear canonical correlation subspaces, while collapsed equilibria may also be stable attractors. Motivated by this result, we introduce PEIRA, a non-contrastive SSL method with an explicit objective defined through the trace of the optimal linear regressor. We show that its only stable equilibria are nontrivial global minimizers and recover the same canonical correlation subspaces, with regularization selecting the effective dimension. Experiments on ImageNet-1K and CIFAR-10 show PEIRA is competitive with VICReg and LeJEPA baselines, and qualitative empirical results support the theory.

Unsupervised outlier detection is attractive because it eliminates the need for labeled data. Moreover, forming multi-model ensembles can improve detection robustness. However, composing an ensemble without labeled data is challenging. Naively composed ensembles can suffer from ensemble saturation, where redundant or unreliable detection models degrade performance and incur unnecessary computation. We propose MetaEns, an automatic unsupervised framework for selecting ensembles of outlier detection models. Using labeled meta-datasets, MetaEns learns a model that predicts marginal ensemble gains, estimating the expected improvement from adding a candidate model to a partially constructed ensemble. At test time, this learned signal is combined with a submodular-inspired proxy objective that enforces diminishing returns through diversity-aware discounting and family-level risk regularization, thereby enabling greedy sequential selection with adaptive early stopping. As a result, MetaEns constructs compact, high-quality ensembles without access to ground-truth labels. Experiments on 39 real-world datasets show that MetaEns consistently outperforms state-of-the-art unsupervised selectors and ensemble baselines, achieving higher average precision while using fewer models.

Given a generalist model, learning a task-relevant specialist representation is fundamental for downstream applications. Identifiability, the asymptotic guarantee of recovering the ground-truth representation, is critical because it sets the ultimate limit of any model, even with infinite data and computation. We study this problem in a completely nonparametric setting, without relying on interventions, parametric forms, or structural constraints. We first prove that the structure between time steps and tasks is identifiable in a fully unsupervised manner, even when sequences lack strict temporal dependence and may exhibit disconnections, and task assignments can follow arbitrarily complex and interleaving structures. We then prove that, within each time step, the task-relevant latent representation can be disentangled from the irrelevant part under a simple sparsity regularization, without any additional information or parametric constraints. Together, these results establish a hierarchical foundation: task structure is identifiable across time steps, and task-relevant latent representations are identifiable within each step. To our knowledge, each result provides a first general nonparametric identifiability guarantee, and together they mark a step toward provably moving from generalist to specialist models.

Exploratory analysis of high-dimensional data rarely stops at a single embedding. In practice, analysts rerun dimensionality reduction after changing preprocessing, subsets, or hyperparameters, and standard nonlinear methods can quickly become the bottleneck. We introduce FastUMAP (Bipartite Manifold Approximation and Projection), a landmark-based method designed for this repeated-use setting. FastUMAP builds a sparse point-landmark fuzzy graph, computes a Nystrom spectral warm start from the induced landmark affinity, and then refines all sample coordinates with a UMAP-style objective on the bipartite graph. The landmark ratio r = m/n provides a direct way to trade runtime against fidelity. On 9 benchmark datasets spanning 178 to 70,000 samples, FastUMAP has the lowest runtime on 7 datasets in our reported default-implementation comparison on one workstation. On MNIST and Fashion-MNIST (n=70000), it runs in about 4.6 seconds, compared with about 73--75 seconds for Barnes--Hut t-SNE, while reaching 91.4% mean kNN accuracy versus 94.6% for the strongest accuracy baseline. FastUMAP is therefore best viewed as a fast option for repeated exploratory embedding, rather than as a replacement for accuracy-first methods.

Techniques for concept extraction, such as sparse autoencoders and transcoders, aim to extract high-level symbolic concepts from low-level nonsymbolic representations. When these extracted concepts are used for downstream tasks such as model steering and unlearning, it is essential to understand their guarantees, or lack thereof. In this work, we present a unified theoretical framework for unsupervised concept extraction, in which we frame the task of concept extraction as identifying a generative model. We present a general meta-theorem for identifiability, which reduces the problem of establishing identifiability guarantees to the problem of characterizing the intersection of two sets. As we demonstrate on a range of widely-used approaches, this meta-theorem substantially simplifies the task of proving such guarantees, thus paving the way for the development of new, principled approaches for concept extraction.

Supervised No Free Lunch Theorems (NFLTs) are well studied, yet unsupervised NFLTs remain underexplored. For elliptical distributions, we prove that there exist two equally optimal, scientifically meaningful bump-hunting strategies that are exact opposites, with no universal winner. Specifically, peeling $k$ orthogonal dimensions from $\mathbb{R}^d$ ($d \ge k$), retaining an inter-quantile region of probability $1-α$ per peeled dimension, maximizes total variance and Frobenius norm when the $k$ smallest principal components (called pettiest components) are selected, and minimizes them when the selected dimensions are the $k$ leading principal components. These optima inspire PRIM-based bump-hunting algorithms either by minimizing variance or by minimizing volume, thereby motivating an NFLT. We test our results on the Fashion-MNIST database, showing that peeling the largest principal components captures multiplicity, while peeling the smallest principal components isolates popular styles.

Sketch techniques have been extensively studied in recent years and are especially well-suited to data streaming scenarios, where the sketch summary is updated quickly and compactly. However, it is challenging to recover the current state from these summaries in a way that is accurate, fast, and real. In this paper, we seek a solution that reconciles this tension, aiming for near-perfect recovery with lightweight computational procedures. Focusing on linear sketching problems of the form $\boldsymbolΦf \rightarrow f$, our study proceeds in three stages. First, we dissect existing techniques and show the root cause of the sketching dilemma: an orthogonal information loss. Second, we examine how generative priors can be leveraged to bridge the information gap. Third, we propose FLORE, a novel generative sketching framework that embraces these analyses to achieve the best of all worlds. More importantly, FLORE can be trained without access to ground-truth data. Comprehensive evaluations demonstrate FLORE's ability to provide high-quality recovery, and support summary with low computing overhead, outperforming previous methods by up to 1000 times in error reduction and 100 times in processing speed compared to learning-based solutions.

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 \textit{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

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.

The unsupervised discovery of features that are both semantically meaningful and stable across runs remains a central challenge in representation learning. We introduce entropy-ordered flows (EOFlows), a normalizing flow (NF) framework that augments standard maximum likelihood training with an orthogonality regularizer on the decoder Jacobian. The regularizer is rooted in Independent Mechanism Analysis and encourages geometric disentanglement, and a stochastic estimator makes it tractable at image scale (CelebA at $D=2352$ and $12288$). Learned features form near-orthogonal curvilinear coordinates and can be ordered by their $\textit{explained (manifold) entropy}$ after training, analogous to the ranking by explained variance in PCA, which turns EOFlows into a non-linear generalization of PCA. EOFlows identify an order of magnitude more stable features than existing methods, and these features emerge in distinguishable categories (global, local, and generic) and support tentative semantic interpretations. The local features have strikingly sparse support in pixel space, although our method never enforces this. Retaining only the most important, i.e. highest entropy, features turns the bijective flow into an autoencoder with adjustable bottleneck, rivaling the rate-distortion performance of dedicated autoencoders.

Joint-embedding self-supervised learning (SSL), the key paradigm for unsupervised representation learning from visual data, learns from invariances between semantically-related data pairs. We study the one-to-many mapping problem in SSL, where each datum may be mapped to multiple valid targets. This arises when data pairs come from naturally occurring generative processes, e.g., successive video frames. We show that existing methods struggle to flexibly capture this conditional uncertainty. As a remedy, we introduce a latent variable to account for this uncertainty and derive a variational lower bound on the mutual information between paired embeddings. Our derivation yields a simple regularization term for standard SSL objectives. The resulting method, which we call AdaSSL, applies to both contrastive and distillation-based SSL objectives, and we empirically show its versatility in causal representation learning, fine-grained image understanding, and world modeling on videos.

A central problem in self-supervised learning is preventing representation collapse. Most methods avoid it through global mechanisms, such as contrastive expansion, variance constraints, decorrelating dimensions, or enforcing certain output distributions. In this work, we study a different design: short-range repulsion. We introduce Hypersolid, a self-supervised objective that combines view alignment with local collision avoidance. Our method induces a latent geometry of compact, semantically aligned neighborhoods with low anisotropy. This geometry is especially effective for unsupervised clustering and fine-grained separation, although it comes at the cost of weaker transferability.

In unsupervised learning, the training data for deep learning does not come with any labels, thus forcing the algorithm to discover hidden patterns in the data for discerning useful information. This, in principle, could be a powerful tool in identifying topological order since topology does not always manifest in obvious physical ways (e.g., topological superconductivity) for its decisive confirmation. The problem, however, is that unsupervised learning is a difficult challenge, necessitating huge computing resources, which may not always work. In the current work, we combine unsupervised and supervised learning to establish that unlabeled (simulated) data in the Majorana splitting in realistic short disordered nanowires may enable not only a distinction between topological' and trivial', but also where their crossover happens in the relevant parameter space. This may be a useful tool in identifying topology in experimental Majorana nanowires.

Large Language Models (LLMs) often produce inconsistent answers when faced with different phrasings of the same prompt. In this paper, we propose Flip-Flop Consistency ($F^2C$), an unsupervised training method that improves robustness to such perturbations. $F^2C$ is composed of two key components. The first, Consensus Cross-Entropy (CCE), uses a majority vote across prompt variations to create a hard pseudo-label. The second is a representation alignment loss that pulls lower-confidence and non-majority predictors toward the consensus established by high-confidence, majority-voting variations. We evaluate our method on 11 datasets spanning four NLP tasks, with 4-15 prompt variations per dataset. On average, $F^2C$ raises observed agreement by 11.62%, improves mean $F_1$ by 8.94%, and reduces performance variance across formats by 3.29%. In out-of-domain evaluations, $F^2C$ generalizes effectively, increasing $\overline{F_1}$ and agreement while decreasing variance across most source-target pairs. Finally, when trained on only a subset of prompt perturbations and evaluated on held-out formats, $F^2C$ consistently improves both performance and agreement while reducing variance. These findings highlight $F^2C$ as an effective unsupervised method for enhancing LLM consistency, performance, and generalization under prompt perturbations. Code is available at https://github.com/ParsaHejabi/Flip-Flop-Consistency-Unsupervised-Training-for-Robustness-to-Prompt-Perturbations-in-LLMs.

Unsupervised feature selection is critical for improving clustering performance in high-dimensional data, where irrelevant features can obscure meaningful structure. In this work, we propose the Minkowski weighted $k$-means++, a novel initialisation strategy for the Minkowski Weighted $k$-means. Our initialisation selects centroids probabilistically using feature relevance estimates derived from the data itself. Building on this, we propose two new feature selection algorithms, FS-MWK++, which aggregates feature weights across a range of Minkowski exponents identifying stable and informative features, and SFS-MWK++, a scalable variant based on subsampling. We support our approach with a theoretical analysis, demonstrating that, under explicit assumptions on noise features and cluster structure, relevant features are assigned consistently higher weights than noise features across a range of Minkowski exponents. Our software can be found at https://github.com/xzhang4-ops1/FSMWK.