Latent-Space Regularization

Next-token prediction leaves hidden-state trajectories largely unconstrained, while existing geometric regularizers primarily control the direction rather than the magnitude of trajectory deviations. We introduce ControlJEPA, a trajectory regularization framework based on a discrete-time Lyapunov contraction condition from practical Input-to-State Stability theory. Its Lyapunov Tube Loss penalizes violations of this condition on a normalized, scale-invariant measure of transversal deviation. When the contraction condition holds at every step, the hidden-state trajectory remains within an explicit tube around the reference secant. In the partial-ISS regime, we bound mean transversal energy, temporal variance, and average tube width using the Lyapunov loss and contraction parameters, with horizon-independent variance bounds under uniformly bounded violations. ControlJEPA requires no architectural modifications. Across six benchmarks and six model families, it consistently improves accuracy and data efficiency over standard fine-tuning and prior trajectory regularizers. The resulting smoother transversal profile also persists empirically during inference, when the regularizer is inactive. The code is publicly available at: https://github.com/t-khanusa/ControlJEPA

Learned world models for autonomous driving operate in unconstrained latent spaces, yet the physical systems they represent are governed by strict non-holonomic constraints: ground vehicles cannot realize instantaneous pure lateral motion. We study long-horizon latent rollout modeling for autonomous driving and ask whether rollout quality can be improved by assigning a motion-aware geometry to latent transitions, rather than by redesigning the predictor architecture. Starting from an unconstrained latent rollout baseline, we introduce Directional Pullback Regularization (DPR), a training time method that defines a kinematics-aware anisotropic Riemannian metric in decoded state space and pulls it back through the decoder Jacobian to the latent manifold. The resulting latent-space metric assigns higher cost to latent directions that decode to lateral vehicle motion, while preserving the original encoder-dynamics-decoder backbone. This yields a clean three-way comparison among an Unconstrained Latent Rollout model (ULR), an Euclidean Pullback Regularization ablation (EPR), and the full directional method (DPR). We evaluate all models on open-loop ego-motion rollout over a common 10-second test horizon, using training rollout lengths of 1, 3, 5, and 10 steps. Across all four training regimes, DPR achieves lower 10-second final displacement error than both ULR and EPR. The strongest relative accuracy gain appears for models trained with 3-step rollout supervision, where DPR reduces the 10-second final displacement error by approximately 44 percent relative to ULR. The strongest overall control-relevant tradeoff is obtained for longer rollout-trained models, especially at 10 steps, where DPR simultaneously improves displacement error, lateral motion consistency, and forward motion preservation relative to both ULR and EPR.

Model-based reinforcement learning (MBRL) achieves strong sample efficiency by planning within learned latent dynamics, yet its performance degrades substantially under unseen visual distractions such as background variations, lighting changes, or camera shifts. Unlike model-free RL, where encoder perturbations affect only single-step predictions, MBRL suffers from a two-level vulnerability: visual distractions first push encoder outputs out of distribution, and these errors then compound through recursive latent rollouts over the planning horizon. We propose visual generalization via latent-space consistency in model-based RL (VIGOR), a framework that enables zero-shot generalization to unseen visual distractions while retaining the sample efficiency of its MBRL backbone. VIGOR integrates three interdependent components: (i) asymmetric weak-to-strong augmentation, which pairs weak-only and weak-to-strong latent views within a single batch; (ii) dynamics-level consistency, which enforces augmentation-invariant transition predictions through direct latent regression; and (iii) encoder-level stabilization, which prevents encoder drift under the cross-augmentation supervision imposed by dynamics-level consistency. Evaluations on the DeepMind Control Suite (DMC) and Robosuite show that VIGOR outperforms state-of-the-art model-free and model-based baselines, surpassing the second-best baseline by 3.4% on DMC and 43.6% on Robosuite. Ablations further show that VIGOR's robustness is augmentation-agnostic: replacing the default augmentation with alternatives from distinct perturbation families preserves strong generalization, confirming that latent-space consistency, not the augmentation choice, drives robustness.

Regulating the latent space to an isotropic Gaussian distribution provides a stable and information-maximized landscape for world model planning. However, the latent space property and successful planning remain disconnected. We first study this by comparing SIGReg and VISReg, two regularization loss functions with the same distribution target but different properties. Compared with SIGReg, VISReg has more flexibility in controlling the weights of center, scale, and shape regularization, and a larger batch size brings a finer distribution approximation. We find that the former, despite being beneficial in self-supervised learning (SSL), does not help the planning, whereas the latter improves the planning success on out-of-domain (OOD) datasets. This motivates a deep understanding of the factors that correlate with the success rate. Unlike the previous metrics focusing on the encoded latent only, we propose the Veracity-Influence-Sobriety score (VIScore), a metric that quantifies the reachability and capacity of a predictor given the encoded feature, and the hallucination of the searching-based planner. Compared with straightness, physical-state probing, and empowerment, we show that, with the measurement covering encoder, predictor, and planner, VIScore explains the success rate better than the others, as reflected by a strong Spearman correlation. Specifically, VIScore consistently achieves a Spearman correlation over 0.75 on both seen and unseen models and datasets on the cross-task success rate pool. Moreover, VIScore is the only metric that has a calibration error below the constant fit across all testing scenarios, showcasing the importance of these three aspects in planning success. We hope this metric can help future studies on world model design and diagnosis.

Latent world models enable efficient planning by predicting future states in a compact representation space, but their performance depends critically on the quality of the learned latent distribution. LeWorldModel (LeWM) regularizes its latents toward an isotropic Gaussian using the Epps-Pulley (EP) objective. We show that the corrective gradients of EP rapidly vanish for isolated tail samples, leaving heavy-tailed deviations insufficiently controlled. To address this limitation, we propose QQWorld, which replaces EP with a quantile-quantile matching objective that directly aligns projected latent samples with rank-matched Gaussian quantiles, thereby maintaining effective corrective gradients in the tails. We further develop cross-batch QQ, which enlarges the effective ranking pool using detached samples from previous batches, and characterize its bias-variance trade-off. Across four control environments, QQWorld effectively improves the average planning success rate of LeWM, while consistently yielding better Gaussian alignment and thinner latent tails.

Recent work on LeWorldModel (LeWM) has shown that the Sketched Isotropic Gaussian Regularizer (SIGReg) enables stable end-to-end world-model learning from pixels by regularizing the latent marginal distribution toward an isotropic Gaussian, thereby preventing representation collapse. While effective and elegant in single-task settings, this recipe does not extend reliably to multi-task training, leading to substantially worse downstream behavior-cloning performance. In this paper, we show that marginal Gaussianization compresses the separation between task-dependent latent clusters relative to within-cluster variation. This compression introduces representation aliasing across tasks and states, and makes the learned representations highly sensitive to small visual perturbations. To address this problem, we apply SIGReg to temporally centered residuals rather than to the latent marginal distribution. This surrogate target places no direct regularization pressure on the separation among cluster centers, removes the requirement that the full latent follow a single isotropic Gaussian, and retains the anti-collapse effect of SIGReg. On the LIBERO benchmark, our method improves downstream success on the long-horizon suite by 1.7x and raises the average success rate across four suites from 53.2% to 73.6%. Without external pretraining, it slightly outperforms Diffusion Policy trained from scratch and approaches the performance of large-scale pretrained policy baselines. These results reveal a structural incompatibility between marginal Gaussian priors and multi-task latent structure, and provide a simple route toward stable and scalable end-to-end multi-task world-model learning.

Joint-Embedding Predictive Architectures (JEPAs) are the dominant design for latent world models, yet they are usually justified by empirical performance rather than a normative principle. We show that the choice of anti-collapse regulariser determines whether a JEPA's training objective, a prediction loss plus a weighted embedding regulariser, is a valid Active Inference (AIF) variational free energy. We organise four non-contrastive regularisers (VICReg, LogDet, PairDist, and SIGReg) into an entropy-estimator hierarchy indexed by a prior-miscalibration gap, and show that the gap's sign, whether the estimator bounds the latent entropy from above or below, decides whether the AIF surprise bound survives: VICReg and LogDet are unsafe upper bounds, PairDist a safe lower bound, and SIGReg eliminates the gap. We then prove a correspondence theorem: under the standard constant-noise encoder model and successful SIGReg enforcement (isotropic-Gaussian embeddings), the gap vanishes, the objective becomes an exact information bottleneck, the surprise bound is preserved, and the latent goal cost becomes an exact proxy for AIF pragmatic value, whereas VICReg leaves an irreducible second-order anisotropy term. We extend the correspondence to multi-step expected free energy, ensemble epistemic value, and a learned-policy regime, and we identify the one AIF term no current JEPA world model computes: the state-epistemic value, a future-state coverage signal. The predictions differ in kind, not degree, and are stated here as theoretical consequences left for empirical test in separate work; full proofs are in Appendix A, and the algebraic core of every result is machine-verified in Lean 4 (Appendix D).

Safety alignment of text-to-image (T2I) diffusion models aims to suppress harmful generations while preserving utility on benign prompts. Recent methods often appear to deliver high safety with high utility, but this conclusion rests largely on coarse global utility metrics (e.g., FID, CLIPScore) that are insensitive to fine-grained semantic correctness, creating an illusion of high utility. We show that when utility is measured with structured evaluation, this illusion breaks: on TIFA (Text-to-Image Faithfulness evaluation with Question Answering), safety-aligned models suffer substantial drops in semantic fidelity, including failures in object counts, attributes, and relationships. To diagnose the source of this gap, we analyze the text-encoder prompt embedding space and uncover semantic collapse, a contraction of embedding spread coupled with distortion of inter-prompt similarity structure, which strongly correlates with structured utility loss. Guided by this insight, we propose StructureAware Geometric Regularization (SAGE), a safety alignment objective that explicitly preserves embedding spread and inter-prompt relational structure during adaptation. Our method restores structured utility (TIFA +5.0% over prior state-of-the-art) while maintaining strong safety performance and competitive coarse-grained utility scores. Our source code and trained models are available at https://adeelyousaf.github.io/SAGE_ECCV26_Project_Page/.

A central difficulty in training Joint-Embedding Predictive Architectures (JEPAs) is preventing representation collapse. LeJEPA addresses this by enforcing an isotropic Gaussian target on the embeddings via Sketched Isotropic Gaussian Regularization (SIGReg). This target is in tension with the manifold hypothesis, which expects embeddings to concentrate on a low-dimensional subset of the ambient space. We propose UR-JEPA, which targets a uniformly $n$-rectifiable measure of local tangent dimension $n$ at small scales, realized through a Gaussian-kernel smoothed Carleson-type square function $\mathcal{L}^{\text{CGLT}}$, with a complementary Jones $β$-number formulation. On Inet10, UR-JEPA($\mathcal{L}^{\text{CGLT}}$) attains $0.9141 \pm 0.0014$ for a $+0.83$,pp gain over LeJEPA($\mathcal{L}^{\text{SIGReg}}$) with $\sim 30\%$ lower seed standard deviation; on matched-recipe Galaxy10~SDSS, a single-seed ImageNet-$100$ run, and a $3$-seed EuroSAT remote-sensing run, the two methods lie in the same peak-accuracy band at convergence, with UR-JEPA retaining its lower-seed-variance signature. On EuroSAT the in-domain pair is competitive at $96.0$ to $96.1\%$ with large remote-sensing foundation-model transfer at a $25\times$ smaller backbone. The distinction is geometric: direct visualization of the projector output distribution shows that on all four datasets UR--JEPA($\mathcal{L}^{\text{CGLT}}$) produces a global PCA spectrum with a $4$ to $5$ order-of-magnitude drop at index $\sim 20$ to $25$ out of $D = 32$, while LeJEPA's spectrum is near-flat (top-to-bottom ratio at most $3.6$). Per-dimension marginals are simultaneously near-Gaussian for both methods (mean Shapiro-Wilk $W \in [0.992, 0.996]$) as a Diaconis-Freedman consequence. At matched accuracy the two regularizers therefore yield structurally distinct projected representations.

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.

Semi-supervised learning has emerged as a powerful paradigm for leveraging large amounts of unlabeled data to improve the performance of machine learning models when labeled data are scarce. Among existing approaches, methods derived from FixMatch have achieved state-of-the-art results in image classification by combining weak and strong data augmentations with confidence-based pseudo-labeling. Despite their strong empirical performance, these methods typically struggle with two critical bottlenecks: majority classes tend to dominate the learning process, which is amplified by incorrect pseudo-labels, leading to biased models. Furthermore, noisy early pseudo-labels prevent the model from forming clear decision boundaries, requiring prolonged training to learn informative representation. In this paper, we introduce a paradigm shift from conventional logical output threshold base, toward an explicit shaping of geometric representations. Our approach is inspired by the recently proposed Latent-Euclidean Joint-Embedding Predictive Architectures (LeJEPA), a theoretically grounded framework asserting that meaningful representations should exhibit an isotropic Gaussian structure in latent space. Building on this principle, we propose a new training objective that combines the classical semi-supervised loss used in FlexMatch, an adaptive extension of FixMatch, with a latent-space regularization term derived from LeJEPA. Our proposed approach, encourages well-structured representations while preserving the advantages of pseudo-labeling strategies. Through extensive experiments on CIFAR-100, STL-10 and Tiny-ImageNet, we demonstrate that the proposed method consistently outperforms existing baselines. In addition, our method significantly accelerates the convergence, drastically reducing the overall computational cost compared to standard FixMatch-based pipelines.

Multimodal variational autoencoders (VAEs) have emerged as a powerful framework for survival risk modeling in multiple myeloma by integrating heterogeneous omics and clinical data. However, when trained under survival supervision, standard latent regularization strategies often fail to preserve prognostically relevant variation, leading to unstable or overly constrained representations. Despite numerous proposed variants, it remains unclear which aspects of latent design fundamentally govern performance in this setting. In this work, we conduct a controlled investigation of latent modeling choices for multimodal survival prediction within a unified extension of the MyeVAE framework. By systematically isolating regularization scale, posterior geometry, and latent space structure under identical architectures and optimization protocols, we show that survival-driven training is primarily sensitive to the magnitude and structure of latent regularization rather than the specific divergence formulation. In particular, moderate relaxation of KL regularization consistently improves survival discrimination, while alternative divergence mechanisms such as MMD and HSIC provide limited benefit without appropriate scaling. We further demonstrate that structuring the latent space can improve alignment between learned representations and survival risk gradients. A hybrid continuous--discrete formulation based on Gumbel--Softmax enhances global risk ordering in the continuous latent subspace, even though stable discrete subtype discovery does not emerge under survival supervision. Guided by these findings, we instantiate a robust multimodal survival model, termed MO-RiskVAE, which consistently improves risk stratification over the original MyeVAE without introducing additional supervision or complex training heuristics.

Latent diffusion models have emerged as the dominant framework for high-fidelity and efficient image generation, owing to their ability to learn diffusion processes in compact latent spaces. However, while previous research has focused primarily on reconstruction accuracy and semantic alignment of the latent space, we observe that another critical factor, robustness to sampling perturbations, also plays a crucial role in determining generation quality. Through empirical and theoretical analyses, we show that the commonly used $β$-VAE-based tokenizers in latent diffusion models, tend to produce overly compact latent manifolds that are highly sensitive to stochastic perturbations during diffusion sampling, leading to visual degradation. To address this issue, we propose a simple yet effective solution that constructs a latent space robust to sampling perturbations while maintaining strong reconstruction fidelity. This is achieved by introducing a Variance Expansion loss that counteracts variance collapse and leverages the adversarial interplay between reconstruction and variance expansion to achieve an adaptive balance that preserves reconstruction accuracy while improving robustness to stochastic sampling. Extensive experiments demonstrate that our approach consistently enhances generation quality across different latent diffusion architectures, confirming that robustness in latent space is a key missing ingredient for stable and faithful diffusion sampling.

We study a simple unsupervised regularization scheme for autoencoders called Manifold-Matching (MMAE): we align the pairwise distances in the latent space to those of the input data space by minimizing mean squared error. Because alignment occurs on pairwise distances rather than coordinates, it can also be extended to a lower-dimensional representation of the data, adding flexibility to the method. We find that this regularization outperforms similar methods on metrics based on preservation of nearest-neighbor distances and persistent homology-based measures. We also observe that MMAE provides a scalable approximation of Multi-Dimensional Scaling (MDS).

Medical image segmentation models are typically optimised with voxel-wise losses that constrain predictions only in the output space. This leaves latent feature representations largely unconstrained, potentially limiting generalisation. We propose {SegReg}, a latent-space regularisation framework that operates on feature maps of U-Net models to encourage structured embeddings while remaining fully compatible with standard segmentation losses. Integrated with the nnU-Net framework, we evaluate SegReg on prostate, cardiac, and hippocampus segmentation and demonstrate consistent improvements in domain generalisation. Furthermore, we show that explicit latent regularisation improves continual learning by reducing task drift and enhancing forward transfer across sequential tasks without adding memory or any extra parameters. These results highlight latent-space regularisation as a practical approach for building more generalisable and continual-learning-ready models.