GELD: A Unified Neural Model for Efficiently Solving Traveling Salesman Problems Across Different Scales

The Traveling Salesman Problem (TSP) is a well-known combinatorial optimization problem with broad real-world applications. Recent advancements in neural network-based TSP solvers have shown promising results. Nonetheless, these models often struggle to efficiently solve both small- and large-scale TSPs using the same set of pre-trained model parameters, limiting their practical utility. To address this issue, we introduce a novel neural TSP solver named GELD, built upon our proposed broad global assessment and refined local selection framework. Specifically, GELD integrates a lightweight Global-view Encoder (GE) with a heavyweight Local-view Decoder (LD) to enrich embedding representation while accelerating the decision-making process. Moreover, GE incorporates a novel low-complexity attention mechanism, allowing GELD to achieve low inference latency and scalability to larger-scale TSPs. Additionally, we propose a two-stage training strategy that utilizes training instances of different sizes to bolster GELD's generalization ability. Extensive experiments conducted on both synthetic and real-world datasets demonstrate that GELD outperforms seven state-of-the-art models considering both solution quality and inference speed. Furthermore, GELD can be employed as a post-processing method to significantly elevate the quality of the solutions derived by existing neural TSP solvers via spending affordable additional computing time. Notably, GELD is shown as capable of solving TSPs with up to 744,710 nodes, first-of-its-kind to solve this large size TSP without relying on divide-and-conquer strategies to the best of our knowledge.

Towards Minimizing Feature Drift in Model Merging: Layer-wise Task Vector Fusion for Adaptive Knowledge Integration

Multi-task model merging aims to consolidate knowledge from multiple fine-tuned task-specific experts into a unified model while minimizing performance degradation. Existing methods primarily approach this by minimizing differences between task-specific experts and the unified model, either from a parameter-level or a task-loss perspective. However, parameter-level methods exhibit a significant performance gap compared to the upper bound, while task-loss approaches entail costly secondary training procedures. In contrast, we observe that performance degradation closely correlates with feature drift, i.e., differences in feature representations of the same sample caused by model merging. Motivated by this observation, we propose Layer-wise Optimal Task Vector Merging (LOT Merging), a technique that explicitly minimizes feature drift between task-specific experts and the unified model in a layer-by-layer manner. LOT Merging can be formulated as a convex quadratic optimization problem, enabling us to analytically derive closed-form solutions for the parameters of linear and normalization layers. Consequently, LOT Merging achieves efficient model consolidation through basic matrix operations. Extensive experiments across vision and vision-language benchmarks demonstrate that LOT Merging significantly outperforms baseline methods, achieving improvements of up to 4.4% (ViT-B/32) over state-of-the-art approaches.

Two Causally Related Needles in a Video Haystack

Evaluating the video understanding capabilities of Video-Language Models (VLMs) remains a significant challenge. We propose a long-context video understanding benchmark, Causal2Needles, that assesses two crucial abilities insufficiently evaluated by existing benchmarks: (1) the ability to extract information from two separate locations in a long video and understand them jointly, and (2) the ability to model the world in terms of cause and effect in human behaviors. Specifically, Causal2Needles introduces 2-needle questions, which require extracting information from both the cause and effect human-behavior events in a long video and the associated narration text. To prevent textual bias, these questions comprise two complementary formats: one asking to identify the video clip containing the answer, and one asking for the textual description of an unrelated visual detail from that video clip. Our experiments reveal that models excelling in pre-existing benchmarks struggle with 2-needle visual grounding, and the model performance is negatively correlated with the distance between the two needles. These findings highlight critical limitations in current VLMs.

PointArena: Probing Multimodal Grounding Through Language-Guided Pointing

Pointing serves as a fundamental and intuitive mechanism for grounding language within visual contexts, with applications spanning robotics, assistive technologies, and interactive AI systems. While recent multimodal models have started to support pointing capabilities, existing benchmarks typically focus only on referential object localization tasks. We introduce PointArena, a comprehensive platform for evaluating multimodal pointing across diverse reasoning scenarios. PointArena comprises three components: (1) Point-Bench, a curated dataset containing approximately 1,000 pointing tasks across five reasoning categories; (2) Point-Battle, an interactive, web-based arena facilitating blind, pairwise model comparisons, which has already gathered over 4,500 anonymized votes; and (3) Point-Act, a real-world robotic manipulation system allowing users to directly evaluate multimodal model pointing capabilities in practical settings. We conducted extensive evaluations of both state-of-the-art open-source and proprietary multimodal models. Results indicate that Molmo-72B consistently outperforms other models, though proprietary models increasingly demonstrate comparable performance. Additionally, we find that supervised training specifically targeting pointing tasks significantly enhances model performance. Across our multi-stage evaluation pipeline, we also observe strong correlations, underscoring the critical role of precise pointing capabilities in enabling multimodal models to effectively bridge abstract reasoning with concrete, real-world actions. Project page: https://pointarena.github.io/

Reach-Avoid-Stabilize Using Admissible Control Sets

Hamilton-Jacobi Reachability (HJR) analysis has been successfully used in many robotics and control tasks, and is especially effective in computing reach-avoid sets and control laws that enable an agent to reach a goal while satisfying state constraints. However, the original HJR formulation provides no guarantees of safety after a) the prescribed time horizon, or b) goal satisfaction. The reach-avoid-stabilize (RAS) problem has therefore gained a lot of focus: find the set of initial states (the RAS set), such that the trajectory can reach the target, and stabilize to some point of interest (POI) while avoiding obstacles. Solving RAS problems using HJR usually requires defining a new value function, whose zero sub-level set is the RAS set. The existing methods do not consider the problem when there are a series of targets to reach and/or obstacles to avoid. We propose a method that uses the idea of admissible control sets; we guarantee that the system will reach each target while avoiding obstacles as prescribed by the given time series. Moreover, we guarantee that the trajectory ultimately stabilizes to the POI. The proposed method provides an under-approximation of the RAS set, guaranteeing safety. Numerical examples are provided to validate the theory.

CAT Merging: A Training-Free Approach for Resolving Conflicts in Model Merging

Multi-task model merging offers a promising paradigm for integrating multiple expert models into a unified model without additional training. Existing state-of-the-art techniques, such as Task Arithmetic and its variants, merge models by accumulating task vectors -- the parameter differences between pretrained and finetuned models. However, task vector accumulation is often hindered by knowledge conflicts, leading to performance degradation. To address this challenge, we propose Conflict-Aware Task Merging (CAT Merging), a novel training-free framework that selectively trims conflict-prone components from the task vectors. CAT Merging introduces several parameter-specific strategies, including projection for linear weights and masking for scaling and shifting parameters in normalization layers. Extensive experiments on vision, language, and vision-language tasks demonstrate that CAT Merging effectively suppresses knowledge conflicts, achieving average accuracy improvements of up to 2.5% (ViT-B/32) and 2.0% (ViT-L/14) over state-of-the-art methods.

Solving Reach- and Stabilize-Avoid Problems Using Discounted Reachability

In this article, we consider the infinite-horizon reach-avoid (RA) and stabilize-avoid (SA) zero-sum game problems for general nonlinear continuous-time systems, where the goal is to find the set of states that can be controlled to reach or stabilize to a target set, without violating constraints even under the worst-case disturbance. Based on the Hamilton-Jacobi reachability method, we address the RA problem by designing a new Lipschitz continuous RA value function, whose zero sublevel set exactly characterizes the RA set. We establish that the associated Bellman backup operator is contractive and that the RA value function is the unique viscosity solution of a Hamilton-Jacobi variational inequality. Finally, we develop a two-step framework for the SA problem by integrating our RA strategies with a recently proposed Robust Control Lyapunov-Value Function, thereby ensuring both target reachability and long-term stability. We numerically verify our RA and SA frameworks on a 3D Dubins car system to demonstrate the efficacy of the proposed approach.

Enhancing Vision-Language Compositional Understanding with Multimodal Synthetic Data

Despite impressive advancements in various multimodal tasks, vision-language models (VLMs) still struggle with compositional understanding due to limited exposure to training samples that contain subtle variations within paired examples. With advances in multimodal generative models, a natural solution is to generate synthetic samples with subtle variations for training VLMs. However, generating and training on synthetic samples with subtle variations presents two challenges: difficulty in accurately creating precise variations and inconsistency in cross-modal alignment quality. To address these challenges, we propose SVD-GT (Subtle Variation Data Generation and Training), which integrates image feature injection into a text-to-image generative model to enhance the quality of synthetic variations and employs an adaptive margin loss to differentiate samples using adaptive margins, which help filter out potentially incorrect synthetic samples and focus the learning on informative hard samples. Evaluations on four compositional understanding benchmarks demonstrate that SVD-GT significantly improves the compositionality of VLMs, boosting the average accuracy of CLIP by over 8% across all benchmarks and outperforming state-of-the-art methods by 2% on three benchmarks.

Task Arithmetic in Trust Region: A Training-Free Model Merging Approach to Navigate Knowledge Conflicts

Multi-task model merging offers an efficient solution for integrating knowledge from multiple fine-tuned models, mitigating the significant computational and storage demands associated with multi-task training. As a key technique in this field, Task Arithmetic (TA) defines task vectors by subtracting the pre-trained model ($\theta_{\text{pre}}$) from the fine-tuned task models in parameter space, then adjusting the weight between these task vectors and $\theta_{\text{pre}}$ to balance task-generalized and task-specific knowledge. Despite the promising performance of TA, conflicts can arise among the task vectors, particularly when different tasks require distinct model adaptations. In this paper, we formally define this issue as knowledge conflicts, characterized by the performance degradation of one task after merging with a model fine-tuned for another task. Through in-depth analysis, we show that these conflicts stem primarily from the components of task vectors that align with the gradient of task-specific losses at $\theta_{\text{pre}}$. To address this, we propose Task Arithmetic in Trust Region (TATR), which defines the trust region as dimensions in the model parameter space that cause only small changes (corresponding to the task vector components with gradient orthogonal direction) in the task-specific losses. Restricting parameter merging within this trust region, TATR can effectively alleviate knowledge conflicts. Moreover, TATR serves as both an independent approach and a plug-and-play module compatible with a wide range of TA-based methods. Extensive empirical evaluations on eight distinct datasets robustly demonstrate that TATR improves the multi-task performance of several TA-based model merging methods by an observable margin.

SPHERE: A Hierarchical Evaluation on Spatial Perception and Reasoning for Vision-Language Models

Current vision-language models may incorporate single-dimensional spatial cues, such as depth, object boundary, and basic spatial directions (e.g. left, right, front, back), yet often lack the multi-dimensional spatial reasoning necessary for human-like understanding and real-world applications. To address this gap, we develop SPHERE (Spatial Perception and Hierarchical Evaluation of REasoning), a hierarchical evaluation framework with a new human-annotated dataset to pinpoint model strengths and weaknesses, advancing from single-skill tasks to multi-skill tasks, and ultimately to complex reasoning tasks that require the integration of multiple spatial and visual cues with logical reasoning. Benchmark evaluation of state-of-the-art open-source models reveal significant shortcomings, especially in the abilities to understand distance and proximity, to reason from both allocentric and egocentric viewpoints, and to perform complex reasoning in a physical context. This work underscores the need for more advanced approaches to spatial understanding and reasoning, paving the way for improvements in vision-language models and their alignment with human-like spatial capabilities. The dataset will be open-sourced upon publication.