We propose UTSP, an Unsupervised Learning (UL) framework for solving the Travelling Salesman Problem (TSP). We train a Graph Neural Network (GNN) using a surrogate loss. The GNN outputs a heat map representing the probability for each edge to be part of the optimal path. We then apply local search to generate our final prediction based on the heat map. Our loss function consists of two parts: one pushes the model to find the shortest path and the other serves as a surrogate for the constraint that the route should form a Hamiltonian Cycle. Experimental results show that UTSP outperforms the existing data-driven TSP heuristics. Our approach is parameter efficient as well as data efficient: the model takes 10% of the number of parameters and 0.2% of training samples compared with Reinforcement Learning or Supervised Learning methods.

We propose UTSP, an Unsupervised Learning (UL) framework for solving the Travelling Salesman Problem (TSP). We train a Graph Neural Network (GNN) using a surrogate loss. The GNN outputs a heat map representing the probability for each edge to be part of the optimal path. We then apply local search to generate our final prediction based on the heat map. Our loss function consists of two parts: one pushes the model to find the shortest path and the other serves as a surrogate for the constraint that the route should form a Hamiltonian Cycle. Experimental results show that UTSP outperforms the existing data-driven TSP heuristics.Our approach is parameter efficient as well as data efficient: the model takes $\sim$ 10\% of the number of parameters and $\sim$ 0.2\% of training samples compared with Reinforcement Learning or Supervised Learning methods.

Experiments also suggest new intrinsic justifications, based on soundness, for popular heuristic tricks such as TV regularization and upsampling.

A.2 Gamma Correction For display, all linear HDR images I had their gamma adjusted using the following process: 1. Adjust exposure to set the white level to the p-th percentile ( p = 98) I I percentile(I, p) 2. Clamp between [0, 1] I clamp(I, 0, 1) 3. Apply gamma correction using the standard sRGB gamma curve: γRGB (I) = null 12 .92 We include additional qualitative results of the RENI model. Figure 3 demonstrates performance differences between RENI and SH at the environment completion task. RENI's prior on natural illumination enables significantly more Figure 7 shows one of RENI's failure cases. 2 Ground Truth Ground Truth 27 108 147 27 108 147 RENI SH SG RENI SH SG RENI SH SG RENI SH SG Heat maps with log-scale colour bars for ground truth and RENI are also shown. Heat maps with log-scale colour bars for ground truth and RENI are also shown.

Spatio-temporal data captures complex dynamics across both space and time, yet traditional visualizations are complex, require domain expertise and often fail to resonate with broader audiences. Here, we propose MapMuse, a storytelling-based framework for interpreting spatio-temporal datasets, transforming them into compelling, narrative-driven experiences. We utilize large language models and employ retrieval augmented generation (RAG) and agent-based techniques to generate comprehensive stories. Drawing on principles common in cinematic storytelling, we emphasize clarity, emotional connection, and audience-centric design. As a case study, we analyze a dataset of taxi trajectories. Two perspectives are presented: a captivating story based on a heat map that visualizes millions of taxi trip endpoints to uncover urban mobility patterns; and a detailed narrative following a single long taxi journey, enriched with city landmarks and temporal shifts. By portraying locations as characters and movement as plot, we argue that data storytelling drives insight, engagement, and action from spatio-temporal information. The case study illustrates how MapMuse can bridge the gap between data complexity and human understanding. The aim of this short paper is to provide a glimpse to the potential of the cinematic storytelling technique as an effective communication tool for spatio-temporal data, as well as to describe open problems and opportunities for future research.

A.2 Gamma Correction For display, all linear HDR images I had their gamma adjusted using the following process: 1. Adjust exposure to set the white level to the p-th percentile ( p = 98) I I percentile(I, p) 2. Clamp between [0, 1] I clamp(I, 0, 1) 3. Apply gamma correction using the standard sRGB gamma curve: γRGB (I) = null 12 .92 We include additional qualitative results of the RENI model. Figure 3 demonstrates performance differences between RENI and SH at the environment completion task. RENI's prior on natural illumination enables significantly more Figure 7 shows one of RENI's failure cases. 2 Ground Truth Ground Truth 27 108 147 27 108 147 RENI SH SG RENI SH SG RENI SH SG RENI SH SG Heat maps with log-scale colour bars for ground truth and RENI are also shown. Heat maps with log-scale colour bars for ground truth and RENI are also shown.

Example 1 Figure 1 shows a graph mapping. Edge mappings can be trivially inferred. Hence, the claim is proved. These four cases cover all possible situations and hence, the triangle inequality is established. From the triangle inequality, we can infer the lower bounds listed in lines 2 and 4 of Alg. 2. Hence, if Alg. 3 presents the pseudocode.

Active Feature Acquisition is an instance-wise, sequential decision making problem. The aim is to dynamically select which feature to measure based on current observations, independently for each test instance. Common approaches either use Reinforcement Learning, which experiences training difficulties, or greedily maximize the conditional mutual information of the label and unobserved features, which makes myopic acquisitions. To address these shortcomings, we introduce a latent variable model, trained in a supervised manner. Acquisitions are made by reasoning about the features across many possible unobserved realizations in a stochastic latent space. Extensive evaluation on a large range of synthetic and real datasets demonstrates that our approach reliably outperforms a diverse set of baselines.