Thank you all for the helpful reviews. "and the goal is to figure out what type of object each pixel corresponds to" [Forouzan, 2015]. As suggested, we will run and report experiments on more networks, for a more comprehensive picture of our algorithm. We will focus more on the real-world networks. Segmentation-11 details... See above section on experiments .

We study the decomposability and the subdifferential of the tensor nuclear norm. Both concepts are well understood and widely applied in matrices but remain unclear for higher-order tensors. We show that the tensor nuclear norm admits a full decomposability over specific subspaces and determine the largest possible subspaces that allow the full decomposability. We derive novel inclusions of the subdifferential of the tensor nuclear norm and study its subgradients in a variety of subspaces of interest. All the results hold for tensors of an arbitrary order. As an immediate application, we establish the statistical performance of the tensor robust principal component analysis, the first such result for tensors of an arbitrary order.

Neural Information Processing Systems http://nips.cc/

--Large-scale itinerary planning is a variant of the traveling salesman problem, aiming to determine an optimal path that maximizes the collected points of interest (POIs) scores while minimizing travel time and cost, subject to travel duration constraints. This paper analyzes the decomposability of large-scale itinerary planning, proving that strict decomposability is difficult to satisfy, and introduces a weak decomposability definition based on a necessary condition, deriving the corresponding graph structures that fulfill this property. With decomposability guaranteed, we propose a novel multi-objective cooperative coevolutionary algorithm for large-scale itinerary planning, addressing the challenges of component imbalance and interactions. Specifically, we design a dynamic decomposition strategy based on the normalized fitness within each component, define optimization potential considering component scale and contribution, and develop a computational resource allocation strategy. Finally, we evaluate the proposed algorithm on a set of real-world datasets. Comparative experiments with state-of-the-art multi-objective itinerary planning algorithms demonstrate the superiority of our approach, with performance advantages increasing as the problem scale grows. Itinerary planning is a class of the orienteering problem, where a traveler aims to determine an optimal route within a city under given duration constraints, selecting a subset of points of interest (POIs) to maximize the total collected score [1]. It can be seen as a variant of the traveling salesman problem (TSP) and a combination of the knapsack problem and TSP [2]. As a real-world application, itinerary planning not only seeks to maximize the overall travel experience, i.e., the total collected score, but also considers objectives such as minimizing travel time and cost. This work is partly supported by the Natural Science Foundation of Jiangsu Province (Grant No. BK20230419), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 23KJB520018) and the National Natural Science Foundation of China (Grant No. U23B2058). Wenjian Luo is with the School of Computer Science and Technology, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, Guangdong, China.

The paper provides a unified framework analysis on the model selection consistency with geometrically decomposable penalties. As special cases of this framework, it also derives the consistency results of some machine learning examples. This paper deals with very interesting topic in the sense that; while the model consistencies have been already derived'individually' by several works, there has been a recent trend to provide a unified framework on statistical guarantee for more different types of M-estimator for the future. Nevertheless, my major concern on this paper is its clarity; it is not clearly written, and explanation is somehow terse. They are briefly described only in Introduction, not in Section 2 where authors introduce a geometrically decomposability.

Probabilistic circuits are a unifying representation of functions as computation graphs of weighted sums and products. Their primary application is in probabilistic modeling, where circuits with non-negative weights (monotone circuits) can be used to represent and learn density/mass functions, with tractable marginal inference. Recently, it was proposed to instead represent densities as the square of the circuit function (squared circuits); this allows the use of negative weights while retaining tractability, and can be exponentially more compact than monotone circuits. Unfortunately, we show the reverse also holds, meaning that monotone circuits and squared circuits are incomparable in general. This raises the question of whether we can reconcile, and indeed improve upon the two modeling approaches. We answer in the positive by proposing InceptionPCs, a novel type of circuit that naturally encompasses both monotone circuits and squared circuits as special cases, and employs complex parameters. Empirically, we validate that InceptionPCs can outperform both monotone and squared circuits on image datasets.

Vision-language models, such as CLIP, have shown promising Out-of-Distribution (OoD) generalization under various types of distribution shifts. Recent studies attempted to investigate the leading cause of this capability. In this work, we follow the same path, but focus on a specific type of OoD data - images with novel compositions of attribute-object pairs - and study whether such models can successfully classify those images into composition classes. We carefully designed an authentic image test dataset called ImageNet-AO, consisting of attributes for objects that are unlikely encountered in the CLIP training sets. We found that CLIPs trained with large datasets such as OpenAI CLIP, LAION-400M, and LAION-2B show orders-of-magnitude improvement in effective compositional OoD generalization compared to both supervised models and CLIPs trained with smaller datasets, such as CC-12M and YFCC-15M. Our results provide evidence that the scale and diversity of training data and language supervision play a key role in unlocking the compositional generalization abilities of vision-language models.

We analyze the statistical performance of a recently proposed convex tensor decomposition algorithm. Conventionally tensor decomposition has been formulated as non-convex optimization problems, which hindered the analysis of their performance. We show under some conditions that the mean squared error of the convex method scales linearly with the quantity we call the normalized rank of the true tensor. The current analysis naturally extends the analysis of convex low-rank matrix estimation to tensors. Furthermore, we show through numerical experiments that our theory can precisely predict the scaling behaviour in practice.

Computing the MAP assignment in graphical models is generally intractable. As a result, for discrete graphical models, the MAP problem is often approximated using linear programming relaxations. Much research has focused on characterizing when these LP relaxations are tight, and while they are relatively well-understood in the discrete case, only a few results are known for their continuous analog. In this work, we use graph covers to provide necessary and sufficient conditions for continuous MAP relaxations to be tight. We use this characterization to give simple proofs that the relaxation is tight for log-concave decomposable and logsupermodular decomposable models. We conclude by exploring the relationship between these two seemingly distinct classes of functions and providing specific conditions under which the MAP relaxation can and cannot be tight.