Authors: Lei Wang, Syuan-Hao Li, Yongsheng Gao, Piotr Koniusz
Abstract
Aligning structured data is a fundamental problem in computer vision and machine learning, underlying tasks such as time series analysis, human action recognition, and visual representation learning. Existing alignment methods, including Dynamic Time Warping (DTW) and its differentiable variants, rely on deterministic similarity measures and are therefore sensitive to heterogeneous and noisy features. In this work, we introduce uncertainty-aware alignment, a probabilistic framework that models pairwise correspondences with heteroscedastic uncertainty and performs structured matching along alignment paths. Our formulation, uncertainty-DTW (uDTW), assigns each correspondence a Normal distribution and parametrizes each alignment path by a Maximum Likelihood Estimate objective consisting of (i) a precision-weighted matching term that suppresses unreliable features, and (ii) a log-variance regularization that prevents degenerate solutions. This yields a probabilistic alignment mechanism that is robust to noise and interpretable, as uncertainty directly reflects the reliability of matches. We further generalize this framework from temporal sequences to tokenized visual representations, enabling structured matching over sets of visual tokens. The learned uncertainty can be interpreted as a reverse-attention: semantically relevant regions exhibit low uncertainty and dominate the alignment, while ambiguous/noisy regions have high uncertainty. This provides a connection between alignment, attention, and uncertainty modeling. We evaluate the proposed framework across diverse domains. The results demonstrate consistent improvements over state-of-the-art methods and show that learned uncertainty correlates with semantic importance. These findings establish uncertainty-aware alignment as a general, robust, and interpretable framework for learning from structured data.
Unified visual tokenization faces a fundamental trade-off between high-fidelity pixel reconstruction (spatial equivariance) and semantic abstraction (conceptual invariance). We attribute this conflict to Manifold Misalignment: naive joint optimization induces opposing gradients, creating a zero-sum game between reconstruction and perception. To address this, we propose MUSE, a framework based on Topological Orthogonality. By treating Structure as an orthogonal bridge, MUSE decouples optimization within Transformers: structural gradients refine attention topology, while semantic gradients update feature values. This turns destructive interference into Mutual Reinforcement. Experiments show that MUSE breaks the trade-off, achieving state-of-the-art generation quality (gFID 3.08) and surpassing its teacher InternViT-300M in linear probing (85.2% vs. 82.5%), demonstrating that structurally aligned reconstruction can enhance semantic perception. Code is available at https://github.com/PanqiYang1/MUSE.
This paper proposes the Distribution-Alignment Bridge (DAB), a framework that reconceptualizes text-to-video retrieval as a distribution alignment task rather than traditional deterministic point matching. By modeling both text and video embeddings as Gaussian distributions defined by mean and variance, DAB explicitly accounts for modality-specific uncertainty. We employ a deterministic, diffusion-inspired bridge to iteratively refine text distributions toward their target video distributions through a truncated refinement process. This approach unifies probabilistic embedding and distributional transformation into a cohesive, end-to-end trainable system. To optimize cross-modal similarity, we introduce a distribution-aware contrastive loss based on Kullback-Leibler divergence. Extensive evaluations on MSR-VTT, MSVD, and VATEX benchmarks confirm that DAB significantly outperforms existing probabilistic and diffusion-based baselines, while providing calibrated uncertainty-aware ranking through bridge-induced distributional margins.
Neural networks encode inputs as high-dimensional vectors, known as representations, that capture how models process data by encoding task-relevant structure and semantics. Representation alignment refers to the degree to which different models, layers, or training conditions produce similar representations for the same inputs, with important implications for model interpretation, selection, and robustness analysis. Existing approaches to measure alignment primarily rely on geometric properties, such as neighborhood and cluster similarity, offering limited insight into the global organization of representations. In this work, we present TopoAlign, a topology-aware framework for visually comparing model representations from a structural perspective. Leveraging mapper graphs from topological data analysis, TopoAlign jointly analyzes graphs constructed from representations of shared inputs across different models or layers. The framework supports a top-down comparative workflow: it first performs global structure alignment via joint force-directed optimization to produce coordinated graph layouts; it then identifies local correspondences through automated detection of structurally matching regions, visualized with Bubble Sets; and finally it enables fine-grained pattern inspection through motif-based queries and membrane-inspired visualizations. We demonstrate TopoAlign through case studies on language and multimodal models, complemented by expert feedback. Our results show that TopoAlign provides meaningful insights into representation structure and alignment from a topological perspective.