Self-supervised learning (SSL) has emerged as a powerful paradigm for learning representations without labeled data. Most SSL approaches rely on strong, well-established, handcrafted data augmentations to generate diverse views for representation learning. However, designing such augmentations requires domainspecific knowledge and implicitly imposes representational invariances on the model, which can limit generalization. In this work, we propose an unsupervised representation learning method that replaces augmentations by generating views using orthonormal bases and overcomplete frames. We show that embeddings learned from orthonormal and overcomplete spaces reside on distinct manifolds, shaped by the geometric biases introduced by representing samples in different spaces. By jointly leveraging the complementary geometry of these distinct manifolds, our approach achieves superior performance without artificially increasing data diversity through strong augmentations. We demonstrate the effectiveness of our method on nine datasets across five temporal sequence tasks, where signalspecific characteristics make data augmentations particularly challenging. Without relying on augmentation-induced diversity, our method achieves performance gains of up to 15-20% over existing self-supervised approaches.

Top-down Bird's Eye View (BEV) maps are a popular perceptual representation for ground robot navigation due to their richness and flexibility for downstream

When data gathered from thereal world ispolluted, the absence of global information will damage the robust prediction capability of these algorithms. To address these problems, we propose a novel frameworknamed GLAFF.Withinthisframework,thetimestamps aremodeled individually to capture the global dependencies.

Language models are often evaluated with scalar metrics like accuracy, but such measures fail to capture how models internally represent ambiguity, especially when human annotators disagree. We propose a topological perspective to analyze how fine-tuned models encode ambiguity and more generally instances. Applied to RoBERTa-Large on the MD-Offense dataset, Mapper, a tool from topological data analysis, reveals that fine-tuning restructures embedding space into modular, non-convex regions aligned with model predictions, even for highly ambiguous cases. Over $98\%$ of connected components exhibit $\geq 90\%$ prediction purity, yet alignment with ground-truth labels drops in ambiguous data, surfacing a hidden tension between structural confidence and label uncertainty. Unlike traditional tools such as PCA or UMAP, Mapper captures this geometry directly uncovering decision regions, boundary collapses, and overconfident clusters. Our findings position Mapper as a powerful diagnostic tool for understanding how models resolve ambiguity. Beyond visualization, it also enables topological metrics that may inform proactive modeling strategies in subjective NLP tasks.

Vision-language models (VLMs) achieve remarkable performance through large-scale image-text pretraining. However, their reliance on labeled image datasets limits scalability and leaves vast amounts of unlabeled image data underutilized. To address this, we propose Unified Vision-Language Alignment for Zero-Label Enhancement (ViZer), an enhancement training framework that enables zero-label learning in image captioning, providing a practical starting point for broader zero-label adaptation in vision-language tasks. Unlike prior approaches that rely on human or synthetically annotated datasets, ViZer actively aligns vision and language representation features during training, enabling existing VLMs to generate improved captions without requiring text labels or full retraining. We demonstrate ViZer's advantage in qualitative evaluation, as automated caption metrics such as CIDEr and BERTScore often penalize details that are absent in reference captions. Applying ViZer on SmolVLM-Base and Qwen2-VL, we observe consistent qualitative improvements, producing captions that are more grounded and descriptive than their baseline.

Top-down Bird's Eye View (BEV) maps are a popular perceptual representation for ground robot navigation due to their richness and flexibility for downstream

We define a new filtration called the Steinhaus filtration built from a single cover based on a generalized Steinhaus distance, a generalization of Jaccard distance. The homology persistence module of a Steinhaus filtration with infinitely many cover elements may not be $q$-tame, even when the covers are in a totally bounded space. While this may pose a challenge to derive stability results, we show that the Steinhaus filtration is stable when the cover is finite. We show that while the \v{C}ech and Steinhaus filtrations are not isomorphic in general, they are isomorphic for a finite point set in dimension one. Furthermore, the VR filtration completely determines the $1$-skeleton of the Steinhaus filtration in arbitrary dimension. We then develop a language and theory for stable paths within the Steinhaus filtration. We demonstrate how the framework can be applied to several applications where a standard metric may not be defined but a cover is readily available. We introduce a new perspective for modeling recommendation system datasets. As an example, we look at a movies dataset and we find the stable paths identified in our framework represent a sequence of movies constituting a gentle transition and ordering from one genre to another. For explainable machine learning, we apply the Mapper algorithm for model induction by building a filtration from a single Mapper complex, and provide explanations in the form of stable paths between subpopulations. For illustration, we build a Mapper complex from a supervised machine learning model trained on the FashionMNIST dataset. Stable paths in the Steinhaus filtration provide improved explanations of relationships between subpopulations of images.

Classical unsupervised learning methods like clustering and linear dimensionality reduction parametrize large-scale geometry when it is discrete or linear, while more modern methods from manifold learning find low dimensional representation or infer local geometry by constructing a graph on the input data. More recently, topological data analysis popularized the use of simplicial complexes to represent data topology with two main methodologies: topological inference with geometric complexes and large-scale topology visualization with Mapper graphs -- central to these is the nerve construction from topology, which builds a simplicial complex given a cover of a space by subsets. While successful, these have limitations: geometric complexes scale poorly with data size, and Mapper graphs can be hard to tune and only contain low dimensional information. In this paper, we propose to study the problem of learning covers in its own right, and from the perspective of optimization. We describe a method for learning topologically-faithful covers of geometric datasets, and show that the simplicial complexes thus obtained can outperform standard topological inference approaches in terms of size, and Mapper-type algorithms in terms of representation of large-scale topology.

Enhancing low-resolution, low-frame-rate videos to high-resolution, high-frame-rate quality is essential for a seamless user experience, motivating advancements in Continuous Spatial-Temporal Video Super Resolution (C-STVSR). While prior methods employ Implicit Neural Representation (INR) for continuous encoding, they often struggle to capture the complexity of video data, relying on simple coordinate concatenation and pre-trained optical flow network for motion representation. Interestingly, we find that adding position encoding, contrary to common observations, does not improve-and even degrade performance. This issue becomes particularly pronounced when combined with pre-trained optical flow networks, which can limit the model's flexibility. To address these issues, we propose BF-STVSR, a C-STVSR framework with two key modules tailored to better represent spatial and temporal characteristics of video: 1) B-spline Mapper for smooth temporal interpolation, and 2) Fourier Mapper for capturing dominant spatial frequencies. Our approach achieves state-of-the-art PSNR and SSIM performance, showing enhanced spatial details and natural temporal consistency.

Referring Expression Comprehension (REC), which aims to ground a local visual region via natural language, is a task that heavily relies on multimodal alignment. Most existing methods utilize powerful pre-trained models to transfer visual/linguistic knowledge by full fine-tuning. However, full fine-tuning the entire backbone not only breaks the rich prior knowledge embedded in the pre-training, but also incurs significant computational costs. Motivated by the recent emergence of Parameter-Efficient Transfer Learning (PETL) methods, we aim to solve the REC task in an effective and efficient manner. Directly applying these PETL methods to the REC task is inappropriate, as they lack the specific-domain abilities for precise local visual perception and visual-language alignment. Therefore, we propose a novel framework of Multimodal Prior-guided Parameter Efficient Tuning, namely MaPPER. Specifically, MaPPER comprises Dynamic Prior Adapters guided by an aligned prior, and Local Convolution Adapters to extract precise local semantics for better visual perception. Moreover, the Prior-Guided Text module is proposed to further utilize the prior for facilitating the cross-modal alignment. Experimental results on three widely-used benchmarks demonstrate that MaPPER achieves the best accuracy compared to the full fine-tuning and other PETL methods with only 1.41% tunable backbone parameters. Our code is available at https://github.com/liuting20/MaPPER.