When to Align, When to Predict: A Phase Diagram for Multimodal Learning

Cross-modal alignment (CA) and cross-modal prediction (CP) are the dominant paradigms for multimodal representation learning, yet there is no systematic understanding of when each succeeds, when each fails, and when cross-modal training helps at all -- a gap that leaves practitioners, especially in scientific domains like biomedicine or astrophysics, with heterogeneous instruments and multiple levels of organization and measurement, unable to diagnose why standard methods underperform the best single modality. We develop a unified linear framework that addresses both questions. Under a spiked signal-plus-noise model with structured cross-modal nuisance correlation, we derive separation ratios for both objectives that expose complementary failure modes: alignment whitens each modality and fails when nuisance is strongly correlated across views; prediction encodes whatever is cross-predictable through a one-sided whitening, with recovery governed by source-modality quality. The resulting phase diagram partitions multimodal problems into four regimes: Both, CA only, CP only, and Neither. We present a data-driven procedure to locate real-world datasets in this diagram using a small labeled subsample, identifying the preferred objective and prediction direction before any cross-modal training. Experiments on synthetic data, stereo-vision benchmarks, image-caption pairs, and real astrophysical data validate the predictions in the nonlinear regime, including the Neither regime where cross-modal training is actively harmful. Our framework lets practitioners diagnose their multimodal problem and choose the right objective before committing to training. Code to reproduce the results is available at https://github.com/IlayMalinyak/mm_align_vs_pred.

A Geometric View of Counterfactual Behavior: Interaction of Boundary Proximity and Local Support

Counterfactual explanations seek small, semantically meaningful changes to an input that alter a model's prediction, and are widely used to interpret and audit machine learning systems. In modern vision, language, and multimodal systems, pretrained encoders map inputs to representation spaces, and downstream classifier heads impose decision boundaries within those spaces. As a result, the feasibility and distance of nearby counterfactuals depend on boundary placement relative to the data. Yet models with similar predictive performance can differ substantially in whether such changes are achievable and how far representations must move. This work examines this variation using a standardized local search probe across several pretrained encoders and linear classifier heads. Results show that despite similar predictive performance, models differ substantially in their counterfactual behavior. Under fixed representations, varying only the classifier head alters counterfactual outcomes while leaving predictive performance largely unchanged. This variation is explained by the interaction of decision-boundary proximity and local data support, which jointly determine whether prediction changes are both feasible and lie in regions supported by the data, and can also improve counterfactual search within fixed models. Together, these findings identify counterfactual behavior as a distinct dimension beyond predictive performance and show that it can be altered without changing accuracy, with implications for model selection, robustness, and the reliability of counterfactual methods.

VISReg: Variance-Invariance-Sketching Regularization for JEPA training

Self-supervised learning methods prevent embedding collapse via modeling heuristics or explicit regularization of the embedding space. Among the latter, VICReg decomposes regularization into variance and covariance objectives, offering flexibility and interpretability. However, covariance captures only second-order statistics -- encouraging decorrelation but failing to enforce the full distributional shape needed for stable training. Sketching-based methods such as SIGReg address this by aligning embeddings to an isotropic Gaussian, but lack flexibility and suffer from vanishing gradients under collapse. We propose Variance-Invariance-Sketching Regularization (VISReg), which replaces covariance with a Sliced-Wasserstein-based sketching objective that enforces full distributional shape, while retaining a variance term for scale control. By decoupling scale and shape, VISReg combines VICReg's flexibility with the distributional rigor of sketching methods, providing robust gradients even under collapse. We show that VISReg scales linearly, outperforms existing regularization on low-quality datasets, and is resilient to long-tailed and low-rank regimes. Pre-trained on ImageNet-1K, VISReg achieves state-of-the-art performance on out-of-distribution datasets. Pre-trained on ImageNet-22K, it matches DINOv2's OOD performance despite the latter using 10x more data (LVD-142M). Project and code: https://haiyuwu.github.io/visreg.

When Does LeJEPA Learn a World Model?

A representation that scrambles the true degrees of freedom of the world cannot support reliable planning or compositional generalization. We prove that LeJEPA (alignment plus Gaussian regularization) linearly recovers the world's latent variables from nonlinear observations, a property known as linear identifiability, in a broad class of worlds where latents evolve under stationary, additive-noise transitions. Our main result is that among all such worlds, the Gaussian is the unique latent distribution for which this guarantee holds. The forward direction rests on a spectral decomposition in which each degree of nonlinearity is strictly penalized by alignment, making the linear map the optimum; the converse rules out every non-Gaussian alternative. We further prove an approximate identifiability result where the guarantee degrades gracefully, and show that linear, orthogonal identifiability enables optimal latent-space planning. We validate the theory with experiments ranging from 2D examples to 1024-dimensional latents, including distributional ablations and pixel-based robotic control. Our theory turns an empirically successful recipe into a mathematical guarantee, providing the foundation for building World Models that provably recover the structure of the world.

stable-worldmodel: A Platform for Reproducible World Modeling Research and Evaluation

World models are central to building agents that can reason, plan, and generalize beyond their training data. However, research on world models is currently fragmented, with disparate codebases, data pipelines, and evaluation protocols hindering reproducibility and fair comparison. Current practice is further limited by three key bottlenecks: fragile one-off codebases, slow video data loading, and the lack of standardized generalization benchmarks. We present stable-worldmodel (swm), an open-source platform for standardized and reproducible world modeling research and evaluation. It delivers (1) a high-performance Lance-based data layer with native support and conversion tools for MP4, HDF5, and LeRobot datasets, (2) clean, well-tested implementations of modern world model baselines and planning solvers, and (3) a broad suite of environments and tasks extended with controllable visual, geometric, and physical factors of variation for systematic in-silico evaluation of dynamics understanding, control performance, representation quality, and out-of-distribution generalization. By unifying the full pipeline under a single, scalable framework, \texttt{swm} dramatically reduces research overhead and accelerates trustworthy progress toward reliable world models.

The Linear Centroids Hypothesis: How Deep Network Features Represent Data

Identifying and understanding the features that a deep network (DN) extracts from its inputs to produce its outputs is a focal point of interpretability research. The Linear Representation Hypothesis (LRH) identifies features in terms of the linear directions formed by the inputs in a DN's latent space. However, the LRH is limited as it abstracts away from individual components (e.g., neurons and layers), is susceptible to identifying spurious features, and cannot be applied across sub-components (e.g., multiple layers). In this paper, we introduce the Linear Centroids Hypothesis (LCH) as a new framework for identifying the features of a DN. The LCH posits that features correspond to linear directions of centroids, which are vector summarizations of the functional behavior of a DN in a local region of its input space. Interpretability studies under the LCH can leverage existing LRH tools, such as sparse autoencoders, by applying them to the DN's centroids rather than to its latent activations. We demonstrate that doing so yields sparser feature dictionaries for DINO vision transformers, which also perform better on downstream tasks. The LCH also inspires novel approaches to interpretability; for example, LCH can readily identify circuits in GPT2-Large. For code to study the LCH https://github.com/ThomasWalker1/LinearCentroidsHypothesis .

Post-Hoc Guidance for Consistency Models by Joint Flow Distribution Learning

Classifier-free Guidance (CFG) lets practitioners trade-off fidelity against diversity in Diffusion Models (DMs). The practicality of CFG is however hindered by DMs sampling cost. On the other hand, Consistency Models (CMs) generate images in one or a few steps, but existing guidance methods require knowledge distillation from a separate DM teacher, limiting CFG to Consistency Distillation (CD) methods. We propose Joint Flow Distribution Learning (JFDL), a lightweight alignment method enabling guidance in a pre-trained CM. With a pre-trained CM as an ordinary differential equation (ODE) solver, we verify with normality tests that the variance-exploding noise implied by the velocity fields from unconditional and conditional distributions is Gaussian. In practice, JFDL equips CMs with the familiar adjustable guidance knob, yielding guided images with similar characteristics to CFG. Applied to an original Consistency Trained (CT) CM that could only do conditional sampling, JFDL unlocks guided generation and reduces FID on both CIFAR-10 and ImageNet 64x64 datasets. This is the first time that CMs are able to receive effective guidance post-hoc without a DM teacher, thus, bridging a key gap in current methods for CMs.

Hierarchical Planning with Latent World Models

Model predictive control (MPC) with learned world models has emerged as a promising paradigm for embodied control, particularly for its ability to generalize zero-shot when deployed in new environments. However, learned world models often struggle with long-horizon control due to the accumulation of prediction errors and the exponentially growing search space. In this work, we address these challenges by learning latent world models at multiple temporal scales and performing hierarchical planning across these scales, enabling long-horizon reasoning while substantially reducing inference-time planning complexity. Our approach serves as a modular planning abstraction that applies across diverse latent world-model architectures and domains. We demonstrate that this hierarchical approach enables zero-shot control on real-world non-greedy robotic tasks, achieving a 70% success rate on pick-&-place using only a final goal specification, compared to 0% for a single-level world model. In addition, across physics-based simulated environments including push manipulation and maze navigation, hierarchical planning achieves higher success while requiring up to 4x less planning-time compute.

Temporal Straightening for Latent Planning

Learning good representations is essential for latent planning with world models. While pretrained visual encoders produce strong semantic visual features, they are not tailored to planning and contain information irrelevant -- or even detrimental -- to planning. Inspired by the perceptual straightening hypothesis in human visual processing, we introduce temporal straightening to improve representation learning for latent planning. Using a curvature regularizer that encourages locally straightened latent trajectories, we jointly learn an encoder and a predictor. We show that reducing curvature this way makes the Euclidean distance in latent space a better proxy for the geodesic distance and improves the conditioning of the planning objective. We demonstrate empirically that temporal straightening makes gradient-based planning more stable and yields significantly higher success rates across a suite of goal-reaching tasks.

Semantic Tube Prediction: Beating LLM Data Efficiency with JEPA

Large Language Models (LLMs) obey consistent scaling laws -- empirical power-law fits that predict how loss decreases with compute, data, and parameters. While predictive, these laws are descriptive rather than prescriptive: they characterize typical training, not optimal training. Surprisingly few works have successfully challenged the data-efficiency bounds implied by these laws -- which is our primary focus. To that end, we introduce the Geodesic Hypothesis, positing that token sequences trace geodesics on a smooth semantic manifold and are therefore locally linear. Building on this principle, we propose a novel Semantic Tube Prediction (STP) task, a JEPA-style regularizer that confines hidden-state trajectories to a tubular neighborhood of the geodesic. STP generalizes JEPA to language without requiring explicit multi-view augmentations. We show this constraint improves signal-to-noise ratio, and consequently preserves diversity by preventing trajectory collisions during inference. Empirically, STP allows LLMs to match baseline accuracy with 16$\times$ less training data on the NL-RX-SYNTH dataset, directly violating the data term of Chinchilla-style scaling laws and demonstrating that principled geometric priors can surpass brute-force scaling. Code is available at https://github.com/galilai-group/llm-jepa#stp.