We explore a feed-forward approach for decomposing a video into layers, where each layer contains an object of interest along with its associated shadows, reflections, and other visual effects. This problem is challenging since associated effects vary widely with the 3D geometry and lighting conditions in the scene, and ground-truth labels for visual effects are difficult (and in some cases impractical) to collect. We take a self-supervised approach and train a neural network to produce a foreground image and alpha matte from a rough object segmentation mask under a reconstruction and sparsity loss. Under reconstruction loss, the layer decomposition problem is underdetermined: many combinations of layers may reconstruct the input video.Inspired by the game theory concept of focal points---or \emph{Schelling points}---we pose the problem as a coordination game, where each player (network) predicts the effects for a single object without knowledge of the other players' choices. The players learn to converge on the ``natural'' layer decomposition in order to maximize the likelihood of their choices aligning with the other players'. We train the network to play this game with itself, and show how to design the rules of this game so that the focal point lies at the correct layer decomposition. We demonstrate feed-forward results on a challenging synthetic dataset, then show that pretraining on this dataset significantly reduces optimization time for real videos.

Diffusion models have recently motivated great success in many generation tasks like object removal. Nevertheless, existing image decomposition methods struggle to disentangle semi-transparent or transparent layer occlusions due to mask prior dependencies, static object assumptions, and the lack of datasets. In this paper, we delve into a novel task: Layer-Wise Decomposition of Alpha-Composited Images, aiming to recover constituent layers from single overlapped images under the condition of semi-transparent/transparent alpha layer non-linear occlusion. To address challenges in layer ambiguity, generalization, and data scarcity, we first introduce AlphaBlend, the first large-scale and high-quality dataset for transparent and semi-transparent layer decomposition, supporting six real-world subtasks (e.g., translucent flare removal, semi-transparent cell decomposition, glassware decomposition). Building on this dataset, we present DiffDecompose, a diffusion Transformer-based framework that learns the posterior over possible layer decompositions conditioned on the input image, semantic prompts, and blending type. Rather than regressing alpha mattes directly, DiffDecompose performs In-Context Decomposition, enabling the model to predict one or multiple layers without per-layer supervision, and introduces Layer Position Encoding Cloning to maintain pixel-level correspondence across layers. Extensive experiments on the proposed AlphaBlend dataset and public LOGO dataset verify the effectiveness of DiffDecompose. The code and dataset will be available upon paper acceptance. Our code will be available at: https://github.com/Wangzt1121/DiffDecompose.

We explore a feed-forward approach for decomposing a video into layers, where each layer contains an object of interest along with its associated shadows, reflections, and other visual effects. This problem is challenging since associated effects vary widely with the 3D geometry and lighting conditions in the scene, and ground-truth labels for visual effects are difficult (and in some cases impractical) to collect. We take a self-supervised approach and train a neural network to produce a foreground image and alpha matte from a rough object segmentation mask under a reconstruction and sparsity loss. Under reconstruction loss, the layer decomposition problem is underdetermined: many combinations of layers may reconstruct the input video.Inspired by the game theory concept of focal points---or \emph{Schelling points}---we pose the problem as a coordination game, where each player (network) predicts the effects for a single object without knowledge of the other players' choices. The players learn to converge on the natural'' layer decomposition in order to maximize the likelihood of their choices aligning with the other players'.

We study a generalization of the standard approval-based model of participatory budgeting (PB), in which voters are providing approval ballots over a set of predefined projects and -- in addition to a global budget limit, there are several groupings of the projects, each group with its own budget limit. We study the computational complexity of identifying project bundles that maximize voter satisfaction while respecting all budget limits. We show that the problem is generally intractable and describe efficient exact algorithms for several special cases, including instances with only few groups and instances where the group structure is close to be hierarchical, as well as efficient approximation algorithms. Our results could allow, e.g., municipalities to hold richer PB processes that are thematically and geographically inclusive.

We analyze a new property of directed acyclic graphs (DAGs), called layerwidth, arising from a class of DAGs proposed by Eiter and Lukasiewicz. This class of DAGs permits certain problems of structural model-based causality and explanation to be tractably solved. In this paper, we first address an open question raised by Eiter and Lukasiewicz - the computational complexity of deciding whether a given graph has a bounded layerwidth. After proving that this problem is NP-complete, we proceed by proving numerous important properties of layerwidth that are helpful in efficiently computing the optimal layerwidth. Finally, we compare this new DAG property to two other important DAG properties: treewidth and bandwidth.