The shape of objects is an important source of visual information in a wide range of applications. One of the core challenges of shape quantification is to ensure that the extracted measurements remain invariant to transformations that preserve an object's intrinsic geometry, such as changing its size, orientation, and position in the image. In this work, we introduce ShapeEmbed, a self-supervised representation learning framework designed to encode the contour of objects in 2D images, represented as a Euclidean distance matrix, into a shape descriptor that is invariant to translation, scaling, rotation, reflection, and point indexing. Our approach overcomes the limitations of traditional shape descriptors while improving upon existing state-of-the-art autoencoder-based approaches. We demonstrate that the descriptors learned by our framework outperform their competitors in shape classification tasks on natural and biological images. We envision our approach to be of particular relevance to biological imaging applications.

Discrete diffusion models are a class of generative models that construct sequences by progressively denoising samples from a categorical noise distribution. Beyond their rapidly growing ability to generate coherent natural language, these models present a new and important opportunity to enforce sequence-level constraints, a capability that current autoregressive models cannot natively provide. This paper capitalizes on this opportunity by introducing Constrained Discrete Diffusion (CDD), a novel integration of differentiable constraint optimization within the diffusion process to ensure adherence to constraints, logic rules, or safety requirements for generated sequences. Unlike conventional text generators that often rely on post-hoc filtering or model retraining for controllable generation, CDD directly imposes constraints into the discrete diffusion sampling process, resulting in a training-free and effective approach. Experiments in toxicity-controlled text generation, property-constrained molecule design, and instruction-constrained text completion demonstrate that CDD achieves zero constraint violations in a diverse array of tasks while preserving fluency, novelty, and coherence, while outperforming autoregressive and existing discrete diffusion approaches.

Predicting the behavior of complex systems is critical in many scientific and engineering domains, and hinges on the model's ability to capture their underlying dynamics. Existing methods encode the intrinsic dynamics of high-dimensional observations through latent representations and predict autoregressively. However, these latent representations lose the inherent spatial structure of spatiotemporal dynamics, leading to the predictor's inability to effectively model spatial interactions and neglect emerging dynamics during long-term prediction. In this work, we propose SparseDiff, introducing a test-time adaptation strategy to dynamically update the encoding scheme to accommodate emergent spatiotemporal structures during the long-term evolution of the system.

Recent advancements have explored text-to-image diffusion models for synthesizing out-of-distribution (OOD) samples, substantially enhancing the performance of OOD detection. However, existing approaches typically rely on perturbing textconditioned embeddings, resulting in semantic instability and insufficient shift diversity, which limit generalization to realistic OOD. To address these challenges, we propose GOOD, a novel and flexible framework that directly guides diffusion sampling trajectories towards OOD regions using off-the-shelf in-distribution (ID) classifiers. GOOD incorporates dual-level guidance: (1) Image-level guidance based on the gradient of log partition to reduce input likelihood, drives samples toward low-density regions in pixel space.

Large language models (LLMs) have demonstrated remarkable reasoning capabilities in math and coding, often bolstered by post-training on the chain-of-thoughts (CoTs) generated by stronger models. However, existing strategies for curating such training data predominantly rely on heuristics, limiting generalizability and failing to capture subtleties underlying in data. To address these limitations, we leverage influence functions to systematically attribute LLMs' reasoning ability on math and coding to individual training examples, sequences, and tokens, enabling deeper insights into effective data characteristics. Our Influence-based Reasoning Attribution (Infra) uncovers nontrivial cross-domain effects across math and coding tasks: high-difficulty math examples improve both math and code reasoning, while low-difficulty code tasks most effectively benefit code reasoning. Based on these findings, we introduce a simple yet effective dataset reweighting strategy by flipping task difficulty, which doubles AIME24 accuracy from 10% to 20% and boosts LiveCodeBench accuracy from 33.8% to 35.3% for Qwen2.5-7B-Instruct. Moreover, our fine-grained attribution reveals that the sequence-level exploratory behaviors enhance reasoning performance in both math and code, and the tokenlevel influence patterns are distinct for math and code reasoning: the former prefers natural language logic connectors and the latter emphasizes structural syntax.

Does vision-and-language (VL) training change the linguistic representations of language models in meaningful ways? Most results in the literature have shown inconsistent or marginal differences, both behaviorally and representationally. In this work, we start from the hypothesis that the domain in which VL training could have a significant effect is lexical-conceptual knowledge, in particular its taxonomic organization. Through comparing minimal pairs of text-only LMs and their VL-trained counterparts, we first show that the VL models often outperform their text-only counterparts on a text-only question-answering task that requires taxonomic understanding of concepts mentioned in the questions. Using an array of targeted behavioral and representational analyses, we show that the LMs and VLMs do not differ significantly in terms of their taxonomic knowledge itself, but they differ in how they represent questions that contain concepts in a taxonomic relation vs. a non-taxonomic relation. This implies that the taxonomic knowledge itself does not change substantially through additional VL training, but VL training does improve the deployment of this knowledge in the context of a specific task, even when the presentation of the task is purely linguistic.

Conformal prediction has been explored as a general and efficient way to provide uncertainty quantification for time series. However, current methods struggle to handle time series data with change points -- sudden shifts in the underlying data-generating process. In this paper, we propose a novel Conformal Prediction for Time-series with Change points (CPTC) algorithm, addressing this gap by integrating a model to predict the underlying state with online conformal prediction to model uncertainties in non-stationary time series. We prove CPTC's validity and improved adaptivity in the time series setting under minimum assumptions, and demonstrate CPTC's practical effectiveness on 6 synthetic and real-world datasets, showing improved validity and adaptivity compared to state-of-the-art baselines.

Effective modelling of uncertain information is crucial for quantifying uncertainty. Dempster-Shafer evidence (DSE) theory is a widely recognized approach for handling uncertain information. However, current methods often neglect the inherent a priori information within data during modelling, and imbalanced data lead to insufficient attention to key information in the model. To address these limitations, this paper presents a dynamic learning strategy based on nonuniform splitting mechanism and Hilbert space mapping. First, the framework uses a nonuniform splitting mechanism to dynamically adjust the weights of data subsets and combines the diffusion factor to effectively incorporate the data a priori information, thereby flexibly addressing uncertainty and conflict. Second, the conflict in the information fusion process is reduced by Hilbert space mapping. Experimental results on multiple tasks show that the proposed method significantly outperforms state-of-the-art methods and effectively improves the performance of classification and low-light image enhancement (LLIE) tasks. The code is available at https://anonymous.4open.science/r/Third-ED16.

Self-supervised learning (SSL) has emerged as a powerful paradigm for learning representations without labeled data, often by enforcing invariance to input transformations such as rotations or blurring. Recent studies have highlighted two pivotal properties for effective representations: (i) avoiding dimensional collapse-where the learned features occupy only a low-dimensional subspace, and (ii) enhancing uniformity of the induced distribution. In this work, we introduce T-REGS, a simple regularization framework for SSL based on the length of the Minimum Spanning Tree (MST) over the learned representation. We provide theoretical analysis demonstrating that T-REGS simultaneously mitigates dimensional collapse and promotes distribution uniformity on arbitrary compact Riemannian manifolds.

Federated Prompt Learning (FPL) enables communication-efficient adaptation by tuning lightweight prompts on top of frozen pre-trained models. Existing FPL methods typically rely on global information, which is only available after the second training round, to facilitate collaboration among client models. Therefore, they are inherently dependent on multi-round communication to fully exhibit their strengths. Moreover, existing one-shot federated learning methods typically focus on fitting seen tasks, but lack cross-task generalization. To bridge this gap, we propose the Global Prompt Refinement with Non-Interfering Attention Masking (GPR-NIAM) method for one-shot FPL.