Latent Representation

Current 3D-aware pretraining methods for embodied perception and manipulation are largely built on differentiable rendering frameworks, producing either fully implicit neural fields or fully explicit geometric primitives. Implicit representations, while expressive, lack explicit structural cues, whereas explicit ones preserve geometry but suffer from resolution limits and weak generalization. To address these limitations, we propose a novel pretraining framework that learns a hybrid representation-structural latent points. Specifically, we insert a point-wise latent variational autoencoder into the latent space of a point-cloud autoencoder, jointly regularizing point-wise features and coordinates toward a Gaussian prior. The resulting compact latent preserves coarse structural tendencies, which do not encode precise geometry but capture richer rough shape and semantic information, effectively combining the expressiveness of implicit representations with the structural priors of explicit ones. In addition, informed by shared design choices in prior work, we develop a streamlined, efficient 3DGS-based rendering pipeline that is deliberately kept lightweight, improving efficiency while leaving greater representational capacity to the front-end latent module. Extensive evaluations on RLBench, ManiSkill2, and a real-robot platform demonstrate consistent gains in task success, sample efficiency, and robustness to viewpoint and scene variations over strong baselines. Ablation studies further confirm that each component of our framework is critical to overall performance.

Despite the impressive results achieved by multimodal large language models (MLLMs), their training typically relies on jointly curated multimodal data, requiring substantial human effort to construct multi-way aligned datasets and thereby limiting scalability across domains. In this work, we explore training MLLMs by only leveraging multiple paired modalities as a surrogate for the full joint multimodal distribution. Specifically, we first provide a theoretical analysis of the conditions under which the representations are identifiable with only observing pairwise modalities. Building on this analysis, we propose a representation learning framework for aligning latent representations across modalities using only pairwise data. The framework consists of two stages: latent representation alignment and cross-modal recomposition. Specifically, in the first stage, we learn the shared latent space across modalities by both self-modal reconstruction and pair-wise contrastive learning. We also incorporate an inductive bias in the contrastive learning process by partially aligning and minimal latent specification. In stage two, we integrate the encoder of newly introduced modalities with the decoders of the pre-trained modalities to facilitate cross-modal transfer and generation. We evaluate our method by newly adding 3D point clouds and tactile modalities into pre-trained MLLMs with three modality pairs and show that, by learning an aligned latent representation space, our model achieves strong cross-modal performance.

Multimodal semantic segmentation benefits remote sensing analysis by combining complementary information from different sensor modalities. In real-world remote sensing applications, one or more modalities may be unavailable due to sensor failures, adverse atmospheric conditions, or data acquisition problems. Even with pretrained multimodal representations and existing fine-tuning or adaptation strategies, performance may remain limited because all modality availability scenarios are typically treated as equally informative during training. In this paper, we propose a novel training strategy that learns a scenario sampling distribution directly from the pretrained latent space. Instead of relying on uniform random modality dropout, the proposed method guides fine-tuning toward more informative modality availability scenarios. More specifically, we quantify the effect of each scenario independently based on the distortion it induces in the shared latent representation. We then capture scenario relations using a radial basis function kernel and derive refined scenario scores through a regularized kernel smoothing. These scores are then converted into a probability distribution during scenario sampling for fine-tuning. We evaluate this strategy on three remote sensing image sets, namely DSTL, Potsdam, and Hunan, using CBC-SLP, CBC, and CMX backbones. The experimental results with different image sets and backbones show that our method outperforms standard fine-tuning and LoRA-based adaptation. These findings suggest that the pretrained latent representation can serve as an effective basis for sampling during missing modality fine-tuning. Code is available at https://github.com/iremulku/Latent-Space-Guided-Scenario-Sampling

Deep learning models for medical image classification are susceptible to subgroup performance disparities across demographic attributes such as age, gender, and race. We identify a latent representational mechanism underlying these disparities: in transfer-learned models, the dominant penultimate-layer activation channel under positive predictions is co-activated by both disease-positive samples and privileged demographic groups (male, older patients), producing over-diagnosis; conversely, the dominant channel under negative predictions is co-activated by disadvantaged groups (female, younger patients), producing systematic under-diagnosis. To address this, we propose Neuron Incidence Redistribution (NIR), a lightweight regularization method that penalizes the variance of predicted-probability-weighted mean activations across penultimate-layer neurons, requiring no demographic labels at training time. On HAM10000, TPR disparity drops from 10.81% to 0.93% across age groups and from 12.04% to 0.74% across gender, with a marginal AUC improvement of 0.51 points. On Harvard OCT-RNFL, NIR reduces FPR disparity for race (from 15.68% to 10.66%) and age (from 12.69% to 1.80%), demonstrating that distributing latent disease evidence across the full penultimate layer is a principled and effective strategy for improving demographic fairness in medical AI.

Radiologist eye-tracking data provide a rich record of how experts search, compare, and accumulate evidence during image reading; yet, existing methods exploit this signal only partially, either as a static spatial prior or as an auxiliary prediction target decoupled from diagnosis. We propose GazeWorld, a medical imaging world model that treats the image as the world and the radiologist's fixation sequence as a trajectory through it. GazeWorld autoregressively predicts the latent representation of the next fixated patch from all previously visited ones, while a spatial-completion branch covers unvisited regions. At inference, GazeWorld generates a sequence of patch representations from the image alone without requiring real gaze data. Frozen GazeWorld features achieve state-of-the-art diagnostic accuracy across all nine supervised settings on CheXpert, RSNA Pneumonia, and SIIM-ACR Pneumothorax, as well as the highest zero-shot accuracy on all three benchmarks. On the GazeSearch benchmark, a generic decoder trained on the same frozen features outperforms the purpose-built LogitGaze-Med by over 16% in ScanMatch and 22% in SED, despite not being explicitly trained to predict gaze. GazeWorld demonstrates that modeling how experts read, not just what they conclude, offers a promising pretraining paradigm for medical imaging AI.

Recent progress in Reinforcement Learning (RL) provides a principled approach to optimizing Vision-Language-Action (VLA) models, facilitating a shift from trajectory imitation to active learning in the task environment. Despite improvements in control precision, most RL optimizers remain task-specific, which reduces VLA models from generalist controllers to policies that overfit to a narrow set of tasks. In this study, we conduct an in-depth analysis of this phenomenon and highlight the importance of cross-task feature representations for improving the generalizability of VLA models. Motivated by this finding, we introduce DyGRO-VLA, a two-stage optimization framework that 1) effectively captures cross-task latent representations based on information-theoretic principles, and 2) dynamically refines policy optimization via a mixture-of-RL-residuals. DyGRO-VLA enables the RL optimizer to exploit task-relevant latent information while strategically mitigating adverse interference on the learned representations throughout the optimization process. We evaluate our approach on LIBERO, RoboTwin2 benchmarks, and further validate it on real world, demonstrating consistent improvements over strong baselines under multi-task training and distribution shift.

Learning meaningful latent representations from nonlinear fMRI data remains a fundamental challenge in neuroimaging analysis. Traditional independent component analysis, widely used due to its ability to estimate interpretable functional brain networks, relies on a linear mixing assumption for latent sources, limiting its ability to capture the inherently nonlinear and complex organization of brain dynamics. More recently, deep representation learning methods have emerged as promising alternatives for modeling nonlinear latent structure. However, many of these approaches have been evaluated primarily on simulated datasets or natural image benchmarks, with comparatively limited validation on real-world neuroimaging data such as fMRI. In this work, we are motivated by the $β$-TCVAE (Total Correlation Variational Autoencoder), a refinement of the $β$-VAE framework for learning latent representations without introducing additional hyperparameters during training. We adapt and modify this model to fMRI data for nonlinear source disentanglement, aiming to separate mixed spatial and temporal brain signals into interpretable components. We show that the $β$-TCVAE framework can recover meaningful nonlinear spatial components with biological relevance, including well-established intrinsic connectivity networks such as the default mode network. Furthermore, we evaluate the learned representations using functional network connectivity, showing that the latent structure captures coherent and interpretable brain organization patterns. This study provides a pilot investigation that bridges nonlinear representation learning and fMRI analysis.

Learning latent representations from complex data is central to modern machine learning, spanning temporal, multimodal, and partially observed systems. In such settings, representations are better understood as latent states capturing underlying system dynamics, rather than as mere compressed summaries of observations. Yet current approaches remain fragmented, relying on distinct -- and often implicit -- assumptions about what these states should represent. We argue that this fragmentation reflects a more fundamental limitation: latent representations are typically learned from underconstrained objectives that fail to specify the properties that meaningful latent states should satisfy. As a result, multiple representations can satisfy the same objective, leading to ambiguity in their structure and interpretation. While many of the underlying principles have been explored in isolation, their interactions have not been explicitly formalized. In this work, we propose constrained latent state modeling (CLSM) as a unifying perspective. We identify a set of core properties -- predictive sufficiency, minimality, temporal coherence, observation compatibility, invariance to nuisance factors, and structural constraints -- and show that they are intrinsically coupled through fundamental trade-offs. Revisiting major modeling families through this lens, we show that existing approaches can be interpreted as enforcing different subsets of constraints, thereby occupying distinct regions of a common design space. This perspective reframes persistent challenges such as lack of identifiability as consequences of underconstrained formulations, rather than isolated technical limitations. More broadly, CLSM provides a principled framework to make design choices explicit, to analyze trade-offs, and to guide the development of more interpretable, robust, and task-aligned latent state models.

In obstacle avoidance navigation of unmanned aerial vehicles (UAVs), variations in obstacle scale have received strangely less attention than obstacle number or density. Existing methods typically extract purely geometric features from single-frame depth observations. Such representations tend to neglect small obstacles and lose spatial context under occlusions caused by large obstacles, leading to noticeable degradation in environments with multi-scale obstacles. To address this issue, we propose CaMeRL, a Collision-aware and Memory-enhanced Reinforcement Learning framework for UAV navigation. The collision-aware latent representation encodes risk-sensitive depth cues to preserve fine-grained obstacle structures, thereby improving sensitivity to small obstacles. The temporal memory module integrates observations across frames, mitigating partial observability caused by large-obstacle occlusions. We evaluate CaMeRL with multi-scale obstacles, including ultra-small and extra-large obstacle settings. Results show that CaMeRL outperforms state-of-the-art baselines across all scales, with success rate gains of 0.48 and 0.28 in the ultra-small and extra-large settings, respectively. More importantly, CaMeRL achieves reliable navigation in cluttered outdoor environments.

We study certified runtime monitoring of past-time signal temporal logic (ptSTL) from visual observations under partial observability. The monitor must infer safety-relevant quantities from images and provide finite-sample guarantees, while being \emph{reusable}: once trained and calibrated, it should certify any formula in a target fragment without per-formula retraining. For fragments induced by a finite dictionary of temporal atoms, we prove that the \emph{semantic basis}, the vector of atom robustness scores, is the minimum prediction target within the class of monotone, 1-Lipschitz reusable interfaces: any formula is evaluated by a deterministic decoder derived from the parse tree, and a single conformal calibration pass certifies the entire fragment with no union bound. We also introduce a \emph{rolling prediction monitor} that predicts only current predicate values and reconstructs temporal history online; this is easier to learn but grows conservative at long horizons. On a pedestrian-crossroad benchmark, rolling achieves tighter certified bounds at short horizons while the semantic-basis monitor is up to 4-times tighter at long horizons. We validate the presented monitors on real-world Waymo driving data, where both monitors satisfy the conformal coverage guarantee empirically.

We construct a new kind of encoder, leveraging the expressive power of diffusion models. In a traditional variational autoencoder, the encoder and decoder jointly negotiate a latent representation of the input. This is made possible by the reparameterization trick, which simplifies training at the cost of restricting the encoder to a simple family of distributions. Replacing this encoder with a diffusion model requires rethinking how the decoder pressure can be transmitted back to the encoder, given that they tend to update their internal estimates of the latent in opposing directions. We solve this problem with an alternating training scheme, inspired by the expectation-maximization algorithm. Our method enables more reliable synchronization between encoder and decoder, while preserving the simple and efficient training objective of standard diffusion models.

Microbiome functions are encoded within the genes of the community-wide metagenome. A natural question is whether properties of a microbial community can be predicted just from knowing the raw DNA sequences of its members. In this work, we employ set-aggregated genome embeddings (SAGE) to predict community-level abundance profiles, exploiting the few-shot learning capabilities of genomic language models (GLMs). We benchmark this approach to show improved generalization on novel genomes compared to classical bioinformatics approaches. Model ablation shows that community-level latent representations directly result in improved performance. Lastly, we demonstrate the benefits of intermediate transformations between latent representations and demonstrate the differences between GLM embedding choices.

Latent representations learned by neural networks often exhibit semantic structure, where concept similarity is reflected by geometric proximity in embedding space. However, comparing such spaces across models remains difficult: changes in architecture, pretraining data, objective, or random seed can yield embeddings with similar content but incompatible geometry. This latent space alignment problem is central to interpretability, transfer and multimodal learning, federated systems, and semantic communication; however, progress remains limited by the lack of large-scale, model-diverse, and metadata-rich benchmarks. To address this gap, we introduce SEMASIA, a large-scale collection of latent representations extracted from approximately 1,700 pretrained vision models across eight standard image-classification benchmarks. SEMASIA pairs embeddings with structured metadata describing architectures, training regimes, pretraining sources, and model scale. We demonstrate three applications of the resource. First, we analyze the conceptual organization of individual latent spaces, showing consistent prototype-like clustering and hierarchical semantic neighborhoods across models and datasets. Second, we benchmark supervised alignment mappings between latent spaces using reconstruction error and downstream task performance. Third, we perform a large-scale regression analysis of how pretraining-data complexity, specialization, transfer learning, augmentation, and model scale relate to geometric and probing properties of embeddings. By coupling representational scale with standardized metadata, SEMASIA provides a reproducible foundation for studying latent geometry, evaluating alignment methods, and developing next-generation heterogeneous and interoperable AI systems.

Joint-Embedding Predictive Architectures (JEPAs) provide a simpleframework for learning world models by predicting future latent representations.However, JEPA training is subject to a bias-variance tradeoff.Without sufficient structural constraints, excessive representationalvariance causes the model to collapse to trivial solutions.The recent LeWorldModel (LeWM) shows that this issue can be alleviated bysimply constraining latent embeddings with an isotropic Gaussian prior.However, latent representations inherently lie on low-dimensional manifoldswithin a high-dimensional ambient space, and enforcing an isotropic Gaussianprior directly in this ambient space introduces an overly strong bias.In this work, we propose ame, which seeks a favorable operatingpoint on the bias-variance frontier by applying Gaussian constraints inmultiple random subspaces rather than in the originalembedding space.This design relaxes the global constraint while preserving itsanti-collapse effect, leading to a better balance between trainingstability and representation flexibility.Extensive experiments across fourcontinuous-control environments demonstrate that consistentlyoutperforms LeWM with very clear margins.Our method is simple yet effective, and serves as a strong baseline for future JEPA-based world model research.fdefinedeeemodeThe code is available at https://github.com/intcomp/Sub-JEPA.

Graph foundation models (GFMs) seek transferable representations across graph domains but are limited by structural heterogeneity and incompatible node feature spaces. We propose Structure-Centric Graph Foundation Models (SCGFM), which treat graph topology as the primary source of transferable knowledge. Modeling graphs as metric measure spaces, SCGFM introduces learnable geometric bases that define a shared structural coordinate system. Graphs are aligned to these bases via Gromov-Wasserstein distances, yielding structure-aligned latent representations that accommodate heterogeneous graph topologies. To address feature incompatibility, SCGFM employs a structure-aware feature re-encoding mechanism that unifies node representations without assuming a fixed feature dimensionality or requiring dataset-specific preprocessing. Experiments on graph- and node-level tasks demonstrate strong in-domain and cross-domain generalization, outperforming existing GFM approaches.

Imitation learning for robotic tasks has relied primarily on policies trained only on successful demonstrations, although failures are unavoidable during human data collection. Many existing approaches for exploiting failure data require additional data processing or iterative policy updates through autonomous rollouts, making it difficult to directly and stably utilize failure data accumulated during data collection. In this work, we propose a method that learns latent representations of success-failure discrepancies and incorporates them into the attention mechanism. During inference, an appropriate latent mode is selected from the initial observation to improve action stability. Furthermore, we introduce a post-training metric that quantifies the attention discrepancy between each failure sample and successful demonstrations to select failure data. Simulation results show that the proposed method improves task success rates when trained with failure data and that the proposed metric identifies failure samples that are beneficial for learning when combined with successful demonstrations. These results suggest that the proposed method can support more efficient use of collected demonstrations in robotic data collection pipelines.

Decades of cognitive science establish that humans navigate environments by forming cognitive maps, defined as allocentric and topology-preserving representations of 3D space. While modern Vision-Language Models (VLMs) demonstrate emergent spatial reasoning from 2D egocentric inputs, it remains unclear whether they construct an analogous 3D internal representation. In this paper, we demonstrate that current VLMs do possess a latent topological map of 3D scenes, but it is heavily overshadowed by non-geometric visual semantics, such as color and shape. By isolating this spatial subspace through cross-scene linear feature extraction, we extract a clean spatial subspace that causally controls the model's spatial outputs. We mathematically shape this latent representation and prove its correspondence to the Laplacian eigenmaps of the scene's 3D Gaussian-kernel graph, converging to the physical 3D space in the continuous limit. Motivated by this geometric identification, we further introduce a mathematically principled latent regularization method for VLMs, based on Dirichlet energy. Applying this single-term regularizer to a minimal 500-step supervised VLM fine-tuning (SFT) on simple synthetic data yields significant improvements on real-world spatial benchmarks, outperforming standard SFT and competitive baselines by up to 12.1% in spatial tasks involving scene topology understanding. Source code is available at https://github.com/pittisl/vlm-latent-shaping

Despite extensive research into mitigating distribution shifts, many existing algorithms yield inconsistent performance, often failing to outperform baseline Empirical Risk Minimization (ERM) across diverse scenarios and necessitating newer algorithms which can handle scenarios where existing algorithms currently underperform. Furthermore, high algorithmic complexity frequently limits interpretability and offers only an indirect means of addressing spurious correlations. We propose eXplaining to Learn (eX2L): an interpretable, explanation-based framework that decorrelates confounding features from a classifier's latent representations during training. eX2L achieves this by penalizing the similarity between Grad-CAM activation maps generated by a primary label classifier and those from a concurrently trained confounder classifier. On the rigorous Spawrious Many-to-Many Hard Challenge synthetic data benchmark, eX2L achieves an average accuracy (AA) of 82.24% +/- 3.87% and a worst-group accuracy (WGA) of 66.31% +/- 8.73%, outperforming the current state-of-the-art (SOTA) by 5.49% and 10.90%, respectively. Beyond its competitive performance, eX2L demonstrates that functional domain invariance can be enforced by explicitly decoupling label and nuisance attributes at the group level.

Aerodynamic surrogate models are increasingly used to replace repeated high-fidelity CFD evaluations in many-query design settings, but current approaches still face two important limitations: they often scale poorly to the very large fields arising in realistic 3D aerodynamics, and they rarely produce latent representations that are directly useful for analysis and design. We introduce AeroJEPA, a Joint-Embedding Predictive Architecture for aerodynamic field modeling that addresses both issues. Rather than predicting the full flow field directly from geometry, AeroJEPA predicts a target latent representation of the flow from a context latent representation of the geometry and operating conditions, and optionally reconstructs the field through a continuous implicit decoder. This formulation decouples latent prediction from field resolution while encouraging the latent space to organize semantically. We evaluate AeroJEPA on two complementary datasets: HiLiftAeroML, which stresses the method in a high-fidelity regime with extremely large boundary-layer fields, and SuperWing, which tests large-scale generalization and latent-space optimization over a broad family of transonic wings. Across these benchmarks, AeroJEPA is competitive as a continuous surrogate for aerodynamic fields, scales naturally to high-resolution outputs, and learns context and predicted latents that encode geometry and aerodynamic quantities not used directly as supervision. We further show that the resulting latent space supports controlled interpolation, linear probing, concept-vector arithmetic, and a constrained design latent-optimization experiment. These results suggest that predictive latent learning is a promising direction for scalable and design-meaningful aerodynamic surrogate modeling.

With the rapid development of cloud computing and Web services, Quality of Service (QoS) has become a key criterion for service selection and recommendation. Tensor latent feature analysis provides an effective way to model multidimensional QoS data, and most existing QoS prediction methods are mainly based on Canonical Polyadic (CP) decomposition or Tucker decomposition. However, constrained by their inherent structural properties, these methods cannot accurately capture the complex and dynamic dependencies in user-service interactions, which limits their prediction performance. To address this issue, this paper proposes a dynamic QoS prediction framework based on the Biased Nonnegative Block Term Tensor Decomposition Model, termed BNBT. Specifically, the proposed framework is developed from three aspects: (1) block term tensor decomposition is employed to enhance the representation capability of latent feature learning; (2) linear bias terms are incorporated to further improve prediction accuracy; and (3) a tensor-oriented single-element-dependent nonnegative multiplicative update algorithm, called SLF-NMUT, is designed for efficient parameter estimation. Extensive experiments on real-world QoS datasets demonstrate that the proposed BNBT framework consistently outperforms several state-of-the-art QoS prediction methods in terms of prediction accuracy.

Multi-rater medical image segmentation captures the inherent ambiguity of clinical interpretation, where diagnostic boundaries vary across experts and imaging devices. Existing approaches often reduce this diversity to consensus labels or treat rater differences as noise, resulting in overconfident and poorly calibrated models. We propose a harmonized probabilistic framework that disentangles acquisition artifacts from genuine annotator variability through adaptive feature conditioning and frequency-domain personalization. A lightweight Harmonizer Network implicitly models scanner-specific artifacts and performs dynamic feature modulation to standardize latent representations, ensuring that uncertainty reflects anatomy rather than noise. To represent rater-specific styles, we introduce a novel High-Frequency Prompt Modules that operate in the spectral domain to encode annotator-dependent boundary precision and textural sensitivity. These prompts adaptively modulate harmonized features to produce personalized yet anatomically consistent segmentations. Furthermore, a Generalized Energy Distance based regularization aligns the generative distribution with empirical annotation variability, promoting diversity where experts disagree and consensus where they converge. Experiments on LIDC-IDRI and NPC-170 show SOTA aggregated and individualized segmentation, with notable GED reductions and improved Dice scores, especially on noisy cases. Beyond accuracy, the model exhibits clinically meaningful uncertainty. Confidence rises in agreement regions and declines in ambiguous areas, supporting its use as a reliable and interpretable tool for multi-expert clinical workflows.

We introduce a framework for learning latent representations of 4D objects which are descriptive, faithfully capturing object geometry and appearance; compressive, aiding in downstream efficiency; and accessible, requiring minimal input, i.e., an unstructured dynamic point cloud, to construct. Specifically, Velox trains an encoder to compress spatiotemporal color point clouds into a set of dynamic shape tokens. These tokens are supervised using two complementary decoders: a 4D surface decoder, which models the time-varying surface distribution capturing the geometry; and a Gaussian decoder, which maps the tokens to 3D Gaussians, helping learn appearance. To demonstrate the utility of our representation, we evaluate it across three downstream tasks -- video-to-4D generation, 3D tracking, and cloth simulation via image-to-4D generation -- and observe strong performances in all settings.

We propose HeadsUp, a scalable feed-forward method for reconstructing high-quality 3D Gaussian heads from large-scale multi-camera setups. Our method employs an efficient encoder-decoder architecture that compresses input views into a compact latent representation. This latent representation is then decoded into a set of UV-parameterized 3D Gaussians anchored to a neutral head template. This UV representation decouples the number of 3D Gaussians from the number and resolution of input images, enabling training with many high-resolution input views. We train and evaluate our model on an internal dataset with more than 10,000 subjects, which is an order of magnitude larger than existing multi-view human head datasets. HeadsUp achieves state-of-the-art reconstruction quality and generalizes to novel identities without test-time optimization. We extensively analyze the scaling behavior of our model across identities, views, and model capacity, revealing practical insights for quality-compute trade-offs. Finally, we highlight the strength of our latent space by showcasing two downstream applications: generating novel 3D identities and animating the 3D heads with expression blendshapes.

Self-supervised learning (SSL) excels at finding general-purpose latent representations from complex data, yet lacks a unifying theoretical framework that explains the diverse existing methods and guides the design of new ones. We cast SSL as latent distribution matching (LDM): learning representations that maximize their log-probability under an assumed latent model (alignment), while maximizing latent entropy to prevent collapse (uniformity). This view unifies independent component analysis with contrastive, non-contrastive, and predictive SSL methods, including stop gradient approaches. Leveraging LDM, we derive a nonlinear, sampling-free Bayesian filtering model with a Kalman-based predictor for high-dimensional timeseries. We further prove that predictive LDM yields identifiable latent representations under mild assumptions, even with nonlinear predictors. Overall, LDM clarifies the assumptions behind established SSL methods and provides principled guidance for developing new approaches.

Self-supervised learning has achieved remarkable empirical success in learning robust representations without explicit labels, most recently demonstrated within the framework of Joint-Embedding Predictive Architectures (JEPA). However, a fundamental question remains: what analytical principles drive these encoders toward specific distributional states? In this paper, we demonstrate that the preference for normal distributions in self-supervised encoders is a direct consequence of the Information Bottleneck (IB) principle. By recasting the IB objective as a rate-distortion problem over the predictive manifold, we provide a theoretical basis for why optimal, target-neutral, latent representations should tend towards isotropic Gaussian states. Under this framework, we show that latent representations correspond to soft clustering of inputs sharing similar predictive distributions, organized within a natural simplex structure. This perspective unifies a wide range of existing supervised and less-supervised objectives and provides a principled explanation for commonly used regularization schemes. Furthermore, we derive practical loss objectives that approximate this structure and demonstrate their effectiveness on standard benchmarks. Ultimately, our framework offers a geometric lens to understanding representation collapse and it establishes a mathematical system for regularization strategies to be used to ensure high-entropy, informative embeddings in modern self-supervised models.

Fractionally supervised classification (FSC) offers a flexible framework for combining labeled and unlabeled data in model-based classification, but existing formulations assume simple random sampling. In many applications, however, the retained observation is an extreme order statistic from a set rather than a randomly selected unit. This is particularly appealing when the target population is rare, since maxima nomination sampling (NS) can enrich the sample with the most informative observations, as in screening, environmental monitoring, repeated testing, and reliability studies. Under such designs, the likelihood function changes fundamentally, and the usual FSC EM construction is no longer valid. We develop FSC for nominated samples by introducing a latent representation that accounts for both the class membership of the observed maximum and the latent composition of the remaining units in the set. The resulting method yields a proper EM algorithm and a coherent weighted-likelihood FSC procedure for NS data. We present the methodology in general form, illustrate it for a rare-event contamination normal mixtures, and show through simulation that it substantially improves on the misspecified alternative by ignoring the extra rank information of such data. A real-data analysis demonstrates its practical value.

A central problem in unsupervised domain adaptation is determining what to transfer from labeled source domains to an unlabeled target domain. To handle high-dimensional observations (e.g., images), a line of approaches use deep learning to learn latent representations of the observations, which facilitate knowledge transfer in the latent space. However, existing approaches often rely on restrictive assumptions to establish identifiability of the joint distribution in the target domain, such as independent latent variables or invariant label distributions, limiting their real-world applicability. In this work, we propose a general domain adaptation framework that learns compact latent representations to capture distribution shifts relative to the prediction task and address the fundamental question of what representations should be learned and transferred. Notably, we first demonstrate that learning representations based on all the predictive information, i.e., the label's Markov blanket in terms of the learned representations, is often underspecified in general settings. Instead, we show that, interestingly, general domain adaptation can be achieved by partitioning the representations of Markov blanket into those of the label's parents, children, and spouses. Moreover, its identifiability guarantee can be established. Building on these theoretical insights, we develop a practical, nonparametric approach for domain adaptation in a general setting, which can handle different types of distribution shifts.

Neural networks can be trained to learn task-relevant representations from data. Understanding how these networks make decisions falls within the Explainable AI (XAI) domain. This paper proposes to study an XAI topic: analysing, visualising and understanding the unknown organisation of network representations, particularly those a speaker recognition network learns from utterances, for recognising speaker identity. Past studies have employed algorithms (e.g. K-means) to analyse the different ways in which network representations can be naturally grouped into clusters, i.e. to analyse different flat clustering phenomena within the space defined by those representations. In contrast, this work applies two algorithms -- Single-Linkage Clustering (SLINK) and Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) -- to analyse the different ways in which representations from the speaker recognition network can form clusters with hierarchical relationships, i.e., to analyse different hierarchical clustering phenomena within the representation space of the speaker recognition network. Furthermore, an algorithm called Hierarchical Cluster-Class Matching (HCCM) is designed to semantically interpret one of the above hierarchical clustering phenomena analysed using SLINK. Given the clusters representing this phenomenon, HCCM identifies which ones best match individual semantic classes related to gender and nationality (e.g.\ male, female, Ireland, UK) and and-logic conjunctions of these classes (e.g.\ female and Ireland). The Liebig score metric is also proposed within HCCM to quantify the matching quality of each cluster-class pair and diagnose the factor that limits each match.

Text-to-Image generation has seen significant advancements in output realism with the advent of diffusion models. However, diffusion models encounter difficulties when tasked with generating multiple objects, frequently resulting in hallucinations where certain entities are omitted. While existing solutions typically focus on optimizing latent representations within diffusion models, the relevance of the initial generation seed is typically underestimated. While using various seeds in multiple iterations can improve results, this method also significantly increases time and energy costs. To address this challenge, we introduce HEaD+ (Hallucination Early Detection +), a novel approach designed to identify incorrect generations early in the diffusion process. The HEaD+ framework integrates cross-attention maps and textual information with a novel input, the Predicted Final Image. The objective is to assess whether to proceed with the current generation or restart it with a different seed, thereby exploring multiple-generation seeds while conserving time. HEaD+ is trained on the newly created InsideGen dataset of 45,000 generated images, each containing prompts with up to seven objects. Our findings demonstrate a 6-8% increase in the likelihood of achieving a complete generation (i.e., an image accurately representing all specified subjects) with four objects when applying HEaD+ alongside existing models. Additionally, HEaD+ reduces generation times by up to 32% when aiming for a complete image, enhancing the efficiency of generating complete and accurate object representations relative to leading models. Moreover, we propose an integrated localization module that predicts object centroid positions and verifies pairwise spatial relations (if requested by the users) at an intermediate timestep, gating generation together with object presence to further improve relation-consistent outcomes.

Chain-of-Thought (CoT) reasoning significantly elevates the complex problem-solving capabilities of multimodal large language models (MLLMs). However, adapting CoT to vision typically discretizes signals to fit LLM inputs, causing early semantic collapse and discarding fine-grained details. While external tools can mitigate this, they introduce a rigid bottleneck, confining reasoning to predefined operations. Although recent latent reasoning paradigms internalize visual states to overcome these limitations, optimizing the resulting hybrid discrete-continuous action space remains challenging. In this work, we propose HyLaR (Hybrid Latent Reasoning), a framework that seamlessly interleaves discrete text generation with continuous visual latent representations. Specifically, following an initial cold-start supervised fine-tuning (SFT), we introduce DePO (Decoupled Policy Optimization) to enable effective reinforcement learning within this hybrid space. DePO decomposes the policy gradient objective, applying independent trust-region constraints to the textual and latent components, alongside an exact closed-form von Mises-Fisher (vMF) KL regularizer. Extensive experiments demonstrate that HyLaR outperforms standard MLLMs and state-of-the-art latent reasoning approaches across fine-grained perception and general multimodal understanding benchmarks. Code is available at https://github.com/EthenCheng/HyLaR.

We study how large language models recall relational knowledge during text generation, with a focus on identifying latent representations suitable for relation classification via linear probes. Prior work shows how attention heads and MLPs interact to resolve subject, predicate, and object, but it remains unclear which representations support faithful linear relation classification and why some relation types are easier to capture linearly than others. We systematically evaluate different latent representations derived from attention head and MLP contributions, showing that per-head attention contributions to the residual stream are comparatively strong features for linear relation classification. Feature attribution analyses of the trained probes, as well as characteristics of the different relation types, reveal clear correlations between probe accuracy and relation specificity, entity connectedness, and how distributed the signal on which the probe relies is across attention heads. Finally, we show how token-level feature attribution of probe predictions can be used to reveal probe behavior in further detail.

Incomplete Multi-View Clustering (IMVC) faces the challenge of learning discriminative representations from fragmentary observations while maintaining robustness against missing views. However, prevalent Euclidean-based methods suffer from a geometric mismatch when modeling real-world data with intrinsic hierarchies, leading to semantic blurring where representations drift towards spatially proximal but semantically distinct neighbors. To bridge this gap, we propose HERL, a Hyperbolic Enhanced Representation Learning framework for IMVC. Operating within the Poincaré ball, HERL constructs a structure-aware latent space to enhance representation learning. Specifically, we design a dual-constraint hyperbolic contrastive mechanism optimizing: an angular-based loss to preserve semantic identity via directional alignment, and a distance-based loss to enforce hierarchical compactness. Furthermore, a hyperbolic prototype head is introduced to rectify global structural drift by aligning cross-view hierarchy-aware prototype distributions. Consequently, HERL disentangles fine-grained semantic correlations to sharpen cluster boundaries and imposes geometric constraints to rectify the data recovery process. Extensive experimental results demonstrate that HERL consistently outperforms state-of-the-art approaches.

Predicting the relative value of any given chess piece in a position remains an open challenge, as a piece's contribution depends on its spatial relationships with every other piece on the board. We demonstrate that incorporating the state of the full chess board via latent position representations derived using a CNN-based autoencoder significantly improves accuracy for MLP-based piece value prediction architectures. Using a dataset of over 12 million piece-value pairs gathered from Grandmaster-level games, with ground-truth labels generated by Stockfish 17, our enhanced piece value predictor significantly outperforms context-independent MLP-based systems, reducing validation mean absolute error by 16% and predicting relative piece value within approximately 0.65 pawns. More generally, our findings suggest that encoding the full problem state as context provides useful inductive bias for predicting the contribution of any individual component.

We propose a multimodal, physically grounded approach for metric-scale amodal object reconstruction and pose estimation under severe hand occlusion. Unlike prior occlusion-aware 3D generation methods that rely only on vision, we leverage physical interaction signals: proprioception provides the posed hand geometry, and multi-contact touch constrains where the object surface must lie, reducing ambiguity in occluded regions. We represent object structure as a pose-aware, camera-aligned signed distance field (SDF) and learn a compact latent space with a Structure-VAE. In this latent space, we train a conditional flow-matching diffusion model, pretraining on vision-only images and finetuning on occluded manipulation scenes while conditioning on visible RGB evidence, occluder/visibility masks, the hand latent representation, and tactile information. Crucially, we incorporate physics-based objectives and differentiable decoder-guidance during finetuning and inference to reduce hand--object interpenetration and to align the reconstructed surface with contact observations. Because our method produces a metric, physically consistent structure estimate, it integrates naturally into existing two-stage reconstruction pipelines, where a downstream module refines geometry and predicts appearance. Experiments in simulation show that adding proprioception and touch substantially improves completion under occlusion and yields physically plausible reconstructions at correct real-world scale compared to vision-only baselines; we further validate transfer by deploying the model on a real humanoid robot with an end-effector different from those used during training.

Synthetic hyperspectral image (HSI) generation is essential for large-scale simulation, algorithm development, and mission design, yet traditional radiative transfer models remain computationally expensive and proposed emulation methods are often limited to spectrum-level outputs. In this work, we propose a latent representation-based framework for hyperspectral emulation that learns a probabilistic latent representation of hyperspectral data. The proposed approach supports both spectrum-level and spatial-spectral emulation and can be trained either in a direct one-step formulation or in a two-step strategy that couples variational autoencoder (VAE) pretraining with parameter-to-latent mapping. Experiments on PROSAIL-simulated vegetation data and Sentinel-3 OLCI imagery demonstrate that the method outperforms classical regression-based emulators in reconstruction accuracy, spectral fidelity, and robustness to real-world spatial variability. We further show that emulated HSIs preserve performance in downstream biophysical parameter retrieval, highlighting the practical relevance of emulated data for remote sensing applications.

Tau positron emission tomography supports Alzheimer's disease staging but is difficult to scale because of tracer, scanner, and radiation constraints. Synthesis from structural MRI is therefore attractive, but it is a particularly difficult setting. T1-weighted and FLAIR MRI provide anatomy and disease correlated morphology, but they do not directly measure Tau-PET relevant signal. We introduce SFL-Net, a multi-input synthesis framework that predicts Tau-PET from T1-weighted and FLAIR MRI. SFL-Net factorizes the latent representation into shared, T1-specific, FLAIR-specific, and complementary pathways and preserves anatomical detail through latent structural conditioning rather than direct encoder-decoder connections. We evaluated SFL-Net and baseline models using 605 training and 83 validation subjects from ADNI-3 and OASIS-3 datasets. Evaluation included raw image fidelity, standardized uptake value ratio agreement, high uptake overlap, regional Bland-Altman bias, braak derived stage agreement, non-inferiority sensitivity analysis, and latent component Shapley attribution. SFL-Net performed competitively on both clinically relevant and reconstruction metrics, while also delivering explicit source level auditability that conventional UNet derived models lack.

A popular approach to post-training control of large language models (LLMs) is the steering of intermediate latent representations. Namely, identify a well-chosen direction depending on the task at hand and perturbs representations along this direction at inference time. While many propositions exist to pick this direction, considerably less is understood about how to choose the magnitude of the move, whereas its importance is clear: too little and the intended behavior does not emerge, too much and the model's performance degrades beyond repair. In this work, we propose the first theoretical analysis of steering strength. We characterize its effect on next token probability, presence of a concept, and cross-entropy, deriving precise qualitative laws governing these quantities. Our analysis reveals surprising behaviors, including non-monotonic effects of steering strength. We validate our theoretical predictions empirically on eleven language models, ranging from a small GPT architecture to modern models.

Generative modeling frameworks have emerged as an effective approach to capture high-dimensional image distributions from large datasets without requiring domain-specific knowledge, a capability essential for disease progression modeling. Recent generative approaches have attempted to capture progression by mapping images to a latent space and guiding representations to generate follow-up images from previous time points. However, these methods impose constraints on distribution learning, resulting in latent spaces with limited controllability for generating follow-up images without paired subject-specific longitudinal guidance. In order to enable controlled movements in the latent representational space and generate progression images from a previous time-point image without subject-specific guidance, we introduce a conditionable Diffusion Auto-encoder framework that forms a compact latent space capturing high-level semantics and providing means to control generation. Our approach leverages this latent space to condition and apply controlled shifts to the representations of previous time-point images by isolating progression and subject identity information for generating follow-up images. The shifts are implicitly guided by correlating with progression attributes and constraining to Alzheimer's disease specific regions, without paired longitudinal guidance. We validate the generations through image quality metrics, volumetric progression analysis, and downstream tasks in Alzheimer's disease datasets from different sources. This demonstrates the effectiveness of our approach for Alzheimer's progression modeling and longitudinal image generation.

Recent progress in large-scale robotic datasets and vision-language models (VLMs) has advanced research on vision-language-action (VLA) models. However, existing VLA models still face two fundamental challenges: (i) producing precise low-level actions from high-dimensional observations, (ii) bridging domain gaps across heterogeneous data sources, including diverse robot embodiments and human demonstrations. Existing methods often encode latent variables from either visual dynamics or robotic actions to guide policy learning, but they fail to fully exploit the complementary multi-modal knowledge present in large-scale, heterogeneous datasets. In this work, we present X Robotic Model 1 (XR-1), a novel framework for versatile and scalable VLA learning across diverse robots, tasks, and environments. XR-1 introduces the \emph{Unified Vision-Motion Codes (UVMC)}, a discrete latent representation learned via a dual-branch VQ-VAE that jointly encodes visual dynamics and robotic motion. UVMC addresses these challenges by (i) serving as an intermediate representation between the observations and actions, and (ii) aligning multimodal dynamic information from heterogeneous data sources to capture complementary knowledge. To effectively exploit UVMC, we propose a three-stage training paradigm: (i) self-supervised UVMC learning, (ii) UVMC-guided pretraining on large-scale cross-embodiment robotic datasets, and (iii) task-specific post-training. We validate XR-1 through extensive real-world experiments with more than 14,000 rollouts on six different robot embodiments, spanning over 120 diverse manipulation tasks. XR-1 consistently outperforms state-of-the-art baselines such as $π_{0.5}$, $π_0$, RDT, UniVLA, and GR00T-N1.5 while demonstrating strong generalization to novel objects, background variations, distractors, and illumination changes. Our project is at https://xr-1-vla.github.io/.

Large Language Models (LLMs) face significant computational challenges when processing long contexts due to the quadratic complexity of self-attention. While soft context compression methods, which map input text to smaller latent representations, have shown promise, their real-world adoption is limited. Existing techniques typically compress the context as a single unit, which leads to quadratic compression complexity and an inability to reuse computations across queries with overlapping contexts. In this work, we introduce CompLLM, a soft compression technique designed for practical deployment. Instead of processing the context holistically, CompLLM divides it into segments and compresses each one independently. This simple design choice yields three critical properties: efficiency, as the compression step scales linearly with the context length; scalability, enabling models trained on short sequences (e.g., 1k tokens) to generalize to contexts of 100k tokens; and reusability, allowing compressed segments to be cached and reused across different queries. Our experiments show that with a 2x compression rate, at high context lengths CompLLM speeds up Time To First Token (TTFT) by up to 4x and reduces the KV cache size by 50%. Furthermore, CompLLM achieves performance comparable to that obtained with the uncompressed context, and even surpasses it on very long sequences, demonstrating its effectiveness and practical utility.