Unpaired Joint Distribution Modeling via Multi-Scale Image Representations

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

Learning robust representations across extremely heterogeneous modalities remains a fundamental challenge in multi-modal vision. As a critical and profound instantiation of this challenge, high-resolution (HR) joint optical and synthetic aperture radar (SAR) pretraining seeks modality synergy to mutually enhance single-source representations; its potential is severely hindered by the Heterogeneity-Resolution Paradox: finer spatial scales drastically amplify the physical divergence between complex radar geometries and non-homologous optical textures. Consequently, migrating medium-resolution-oriented rigid alignment paradigms to HR scenarios triggers either severe feature suppression to force equivalence, or feature contamination driven by extreme epistemic uncertainty. Both extremes inevitably culminate in profound representation degradation and negative transfer. To overcome this bottleneck, we propose CoDe-MAE, pioneering a \textit{better synergy with less alignment} philosophy. First, Optical-anchored Knowledge Distillation (OKD) implicitly regularizes SAR's speckle noise by mapping it into a pure semantic manifold. Building on this, Conditioned Contrastive Learning (CCL) utilizes a gradient buffering mechanism to align shared consensus while safely preserving divergent physical signatures. Concurrently, Cross-Modal Degraded Reconstruction (CDR) deliberately strips non-homologous spectral pseudo-features, truncating the inherently ill-posed mapping to capture true structural invariants. Extensive analyses validate our theoretical claims. Pretrained on 1M samples, CoDe-MAE demonstrates remarkable data efficiency, successfully preventing representation degradation and establishing new state-of-the-art performance across diverse single- and bi-modal downstream tasks, substantially outperforming foundation models scaled on vastly larger datasets.

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.