Besides proportionality, in another parallel line of research, envy-freeness and its relaxations, namely envy-free up to one item (EF1) and envy-free up to any item (EFX), are also widely studied. It was shown in [35] and [11] for goods and chores, respectively, that an EF1 allocation exists for the monotone combinatorial functions. However, the existence of EFX allocations is still unknown even with additive functions. Therefore, approximation algorithms were proposed in [2, 42] for additive functions and in [39, 16] for subadditive functions. We refer the readers to [3] for a detailed survey on fair allocation of indivisible items.

Reconstructing the 3D articulated shape of an animal from a single in-the-wild image is a challenging task. We propose LEPARD, a learning-based framework that discovers semantically meaningful 3D parts and reconstructs 3D shapes in a part-based manner. This is advantageous as 3D parts are robust to pose variations due to articulations and their shape is typically simpler than the overall shape of the object. In our framework, the parts are explicitly represented as parameterized primitive surfaces with global and local deformations in 3D that deform to match the image evidence. We propose a kinematics-inspired optimization to guide each transformation of the primitive deformation given 2D evidence. Similar to recent approaches, LEPARD is only trained using off-the-shelf deep features from DINO and does not require any form of 2D or 3D annotations. Experiments on 3D animal shape reconstruction, demonstrate significant improvement over existing alternatives in terms of both the overall reconstruction performance as well as the ability to discover semantically meaningful and consistent parts.

Conventional diffusion models often rely on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative trajectories, and results in costly inference for diffusion models. To address these limitations, we introduce Neural Flow Diffusion Models (NFDM), a novel framework that enhances diffusion models by supporting a broader range of forward processes beyond the standard linear Gaussian. We also propose a novel parameterization technique for learning the forward process. Our framework provides an end-to-end, simulation-free optimization objective, effectively minimizing a variational upper bound on the negative log-likelihood. Experimental results demonstrate NFDM's strong performance, evidenced by state-of-the-art likelihoods across a range of image generation tasks. Furthermore, we investigate NFDM's capacity for learning generative dynamics with specific characteristics, such as deterministic straight lines trajectories, and demonstrate how the framework can be adopted for learning bridges between two distributions. The results underscores NFDM's versatility and its potential for a wide range of applications.

Many few-shot segmentation (FSS) methods use cross attention to fuse support foreground (FG) into query features, regardless of the quadratic complexity. A recent advance Mamba can also well capture intra-sequence dependencies, yet the complexity is only linear. Hence, we aim to devise a cross (attention-like) Mamba to capture inter-sequence dependencies for FSS. A simple idea is to scan on support features to selectively compress them into the hidden state, which is then used as the initial hidden state to sequentially scan query features. Nevertheless, it suffers from (1) support forgetting issue: query features will also gradually be compressed when scanning on them, so the support features in hidden state keep reducing, and many query pixels cannot fuse sufficient support features; (2) intra-class gap issue: query FG is essentially more similar to itself rather than to support FG, i.e., query may prefer not to fuse support features but their own ones from the hidden state, yet the success of FSS relies on the effective use of support information. To tackle them, we design a hybrid Mamba network (HMNet), including (1) a support recapped Mamba to periodically recap the support features when scanning query, so the hidden state can always contain rich support information; (2) a query intercepted Mamba to forbid the mutual interactions among query pixels, and encourage them to fuse more support features from the hidden state. Consequently, the support information is better utilized, leading to better performance. Extensive experiments have been conducted on two public benchmarks, showing the superiority of HMNet. The code is available at https://github.com/Sam1224/HMNet.

S1.1 WebVision1k It contains 2.4M web images collected from Google and Flickr, which share the same 1k category names with ImageNet1k [1]. For each example, we use all available description, title, and tag in its metadata for raw text preparation. Besides, we follow [2, 3] to use the subset of WebVision-Google500 for ablation studies in consideration of lower GPU resource and time consumption without losing generalization. It contains 0.48M images from Google with randomly chosen 500 categories. The testing set of ImageNet1k and its subset ImageNet500 are involved as well for evaluation. S1.2 NUS-WIDE (Web) It contains 0.26M web images from Flickr with 5k unique user tags. Each example is manually annotated with multiple labels within 81 concepts that are filtered out of the 5k tags.

This paper considers the problem of inferring the behaviors of multiple interacting experts by estimating their reward functions and constraints where the distributed demonstrated trajectories are sequentially revealed to a group of learners. We formulate the problem as a distributed online bi-level optimization problem where the outer-level problem is to estimate the reward functions and the inner-level problem is to learn the constraints and corresponding policies. We propose a novel "multi-agent behavior inference from distributed and streaming demonstrations" (MA-BIRDS) algorithm that allows the learners to solve the outer-level and innerlevel problems in a single loop through intermittent communications.

We introduce IMP-MARL, an open-source suite of multi-agent reinforcement learning (MARL) environments for large-scale Infrastructure Management Planning (IMP), offering a platform for benchmarking the scalability of cooperative MARL methods in real-world engineering applications. In IMP, a multi-component engineering system is subject to a risk of failure due to its components' damage condition. Specifically, each agent plans inspections and repairs for a specific system component, aiming to minimise maintenance costs while cooperating to minimise system failure risk. With IMP-MARL, we release several environments including one related to offshore wind structural systems, in an effort to meet today's needs to improve management strategies to support sustainable and reliable energy systems. Supported by IMP practical engineering environments featuring up to 100 agents, we conduct a benchmark campaign, where the scalability and performance of state-of-the-art cooperative MARL methods are compared against expert-based heuristic policies. The results reveal that centralised training with decentralised execution methods scale better with the number of agents than fully centralised or decentralised RL approaches, while also outperforming expert-based heuristic policies in most IMP environments. Based on our findings, we additionally outline remaining cooperation and scalability challenges that future MARL methods should still address. Through IMP-MARL, we encourage the implementation of new environments and the further development of MARL methods.

The knowledge of protein interactions is crucial but challenging for drug discovery applications. This work focuses on protein interface prediction, which aims to determine whether a pair of residues from different proteins interact. Existing data-driven methods have made significant progress in effectively learning protein structures. Nevertheless, they overlook the conformational changes (i.e., flexibility) within proteins upon binding, leading to poor generalization ability. In this paper, we regard the protein flexibility as an attack on the trained model and aim to defend against it for improved generalization. To fulfill this purpose, we propose ATProt, an adversarial training framework for protein representations to robustly defend against the attack of protein flexibility. ATProt can theoretically guarantee protein representation stability under complicated protein flexibility. Experiments on various benchmarks demonstrate that ATProt consistently improves the performance for protein interface prediction. Moreover, our method demonstrates broad applicability, performing the best even when provided with testing structures from structure prediction models like ESMFold and AlphaFold2.