W e present Spanning Tree Autoregressive (STAR) modeling, which can incorporate prior knowledge of images, such as center bias and locality, to maintain sampling performance while also providing sufficiently flexible sequence orders to accommodate image editing at inference. Approaches that expose randomly permuted sequence orders to conventional autoregressive (AR) models in visual generation for bidirectional context either suffer from a decline in performance or compromise the flexibility in sequence order choice at inference. Instead, STAR utilizes traversal orders of uniform spanning trees sampled in a lattice defined by the positions of image patches. Traversal orders are obtained through breadth-first search, allowing us to efficiently construct a spanning tree whose traversal order ensures that the connected partial observation of the image appears as a prefix in the sequence through rejection sampling. Through the tailored yet structured randomized strategy compared to random permutation, STAR preserves the capability of postfix completion while maintaining sampling performance without any significant changes to the model architecture widely adopted in the language AR modeling.

We thank all reviewers for their valuable comments. We address the concerns raised by them below. The idea of using imitation learning to make approximate decisions is not new. The author needs to provide a wall-clock time cost comparison of different methods. We will include them in the final verision.

This paper introduces GraphOmni, a comprehensive benchmark designed to evaluate the reasoning capabilities of LLMs on graph-theoretic tasks articulated in natural language. GraphOmni encompasses diverse graph types, serialization formats, and prompting schemes, significantly exceeding prior efforts in both scope and depth. Through extensive systematic evaluation, we identify critical interactions among these dimensions, demonstrating their substantial impact on model performance. Our experiments reveal that state-of-the-art models like Claude-3.5 and o4-mini consistently outperform other models, yet even these leading models exhibit substantial room for improvement. Performance variability is evident depending on the specific combinations of factors we considered, underscoring the necessity of comprehensive evaluations across these interconnected dimensions. Additionally, we observe distinct impacts of serialization and prompting strategies between open-source and closed-source models, encouraging the development of tailored approaches. Motivated by the findings, we also propose a reinforcement learning-inspired framework that adaptively selects the optimal factors influencing LLM reasoning capabilities. This flexible and extendable benchmark not only deepens our understanding of LLM performance on structured tasks but also provides a robust foundation for advancing research in LLM-based graph reasoning. The code and datasets are available at https://github.com/GAI-Community/GraphOmni.

Building on VeriX (Verified eXplainability, arXiv:2212.01051), a system for producing optimal verified explanations for machine learning model outputs, we present VeriX+, which significantly improves both the size and the generation time of verified explanations. We introduce a bound propagation-based sensitivity technique to improve the size, and a binary search-based traversal with confidence ranking for improving time -- the two techniques are orthogonal and can be used independently or together. We also show how to adapt the QuickXplain (Junker 2004) algorithm to our setting to provide a trade-off between size and time. Experimental evaluations on standard benchmarks demonstrate significant improvements on both metrics, e.g., a size reduction of 38% on the GTSRB dataset and a time reduction of 90% on MNIST. We also explore applications of our verified explanations and show that explanation size is a useful proxy for both incorrectness detection and out-of-distribution detection.

We study a fundamental NP-hard motion coordination problem for multi-robot/multi-agent systems: We are given a graph $G$ and set of agents, where each agent has a given directed path in $G$. Each agent is initially located on the first vertex of its path. At each time step an agent can move to the next vertex on its path, provided that the vertex is not occupied by another agent. The goal is to find a sequence of such moves along the given paths so that each reaches its target, or to report that no such sequence exists. The problem models guidepath-based transport systems, which is a pertinent abstraction for traffic in a variety of contemporary applications, ranging from train networks or Automated Guided Vehicles (AGVs) in factories, through computer game animations, to qubit transport in quantum computing. It also arises as a sub-problem in the more general multi-robot motion-planning problem. We provide a fine-grained tractability analysis of the problem by considering new assumptions and identifying minimal values of key parameters for which the problem remains NP-hard. Our analysis identifies a critical parameter called vertex multiplicity (VM), defined as the maximum number of paths passing through the same vertex. We show that a prevalent variant of the problem, which is equivalent to Sequential Resource Allocation (concerning deadlock prevention for concurrent processes), is NP-hard even when VM is 3. On the positive side, for VM $\le$ 2 we give an efficient algorithm that iteratively resolves cycles of blocking relations among agents. We also present a variant that is NP-hard when the VM is 2 even when $G$ is a 2D grid and each path lies in a single grid row or column. By studying highly distilled yet NP-hard variants, we deepen the understanding of what makes the problem intractable and thereby guide the search for efficient solutions under practical assumptions.

Modern neural networks require long training to reach decent performance on massive datasets. One common approach to speed up training is model parallelization, where large neural networks are split across multiple devices. However, different device placements of the same neural network lead to different training times. Most of the existing device placement solutions treat the problem as sequential decision-making by traversing neural network graphs and assigning their neurons to different devices. This work studies the impact of graph traversal order on device placement. In particular, we empirically study how different graph traversal order leads to different device placement, which in turn affects the training execution time. Our experiment results show that the best graph traversal order depends on the type of neural networks and their computation graphs features. In this work, we also provide recommendations on choosing graph traversal order in device placement for various neural network families to improve the training time in model parallelization.

We present Placeto, a reinforcement learning (RL) approach to efficiently find device placements for distributed neural network training. Unlike prior approaches that only find a device placement for a specific computation graph, Placeto can learn generalizable device placement policies that can be applied to any graph. We propose two key ideas in our approach: (1) we represent the policy as performing iterative placement improvements, rather than outputting a placement in one shot; (2) we use graph embeddings to capture relevant information about the structure of the computation graph, without relying on node labels for indexing. These ideas allow Placeto to train efficiently and generalize to unseen graphs. Our experiments show that Placeto requires up to 6.1x fewer training steps to find placements that are on par with or better than the best placements found by prior approaches. Moreover, Placeto is able to learn a generalizable placement policy for any given family of graphs, which can then be used without any retraining to predict optimized placements for unseen graphs from the same family. This eliminates the large overhead incurred by prior RL approaches whose lack of generalizability necessitates re-training from scratch every time a new graph is to be placed.