Counting hypergraph matchings up to uniqueness threshold

We study the problem of approximately counting matchings in hypergraphs of bounded maximum degree and maximum size of hyperedges. With an activity parameter $\lambda$, each matching $M$ is assigned a weight $\lambda^{|M|}$. The counting problem is formulated as computing a partition function that gives the sum of the weights of all matchings in a hypergraph. This problem unifies two extensively studied statistical physics models in approximate counting: the hardcore model (graph independent sets) and the monomer-dimer model (graph matchings). For this model, the critical activity $\lambda_c= \frac{d^d}{k (d-1)^{d+1}}$ is the threshold for the uniqueness of Gibbs measures on the infinite $(d+1)$-uniform $(k+1)$-regular hypertree. Consider hypergraphs of maximum degree at most $k+1$ and maximum size of hyperedges at most $d+1$. We show that when $\lambda < \lambda_c$, there is an FPTAS for computing the partition function; and when $\lambda = \lambda_c$, there is a PTAS for computing the log-partition function. These algorithms are based on the decay of correlation (strong spatial mixing) property of Gibbs distributions. When $\lambda > 2\lambda_c$, there is no PRAS for the partition function or the log-partition function unless NP$=$RP. Towards obtaining a sharp transition of computational complexity of approximate counting, we study the local convergence from a sequence of finite hypergraphs to the infinite lattice with specified symmetry. We show a surprising connection between the local convergence and the reversibility of a natural random walk. This leads us to a barrier for the hardness result: The non-uniqueness of infinite Gibbs measure is not realizable by any finite gadgets

SwinGNN: Rethinking Permutation Invariance in Diffusion Models for Graph Generation

Diffusion models based on permutation-equivariant networks can learn permutation-invariant distributions for graph data. However, in comparison to their non-invariant counterparts, we have found that these invariant models encounter greater learning challenges since 1) their effective target distributions exhibit more modes; 2) their optimal one-step denoising scores are the score functions of Gaussian mixtures with more components. Motivated by this analysis, we propose a non-invariant diffusion model, called $\textit{SwinGNN}$, which employs an efficient edge-to-edge 2-WL message passing network and utilizes shifted window based self-attention inspired by SwinTransformers. Further, through systematic ablations, we identify several critical training and sampling techniques that significantly improve the sample quality of graph generation. At last, we introduce a simple post-processing trick, $\textit{i.e.}$, randomly permuting the generated graphs, which provably converts any graph generative model to a permutation-invariant one. Extensive experiments on synthetic and real-world protein and molecule datasets show that our SwinGNN achieves state-of-the-art performances. Our code is released at https://github.com/qiyan98/SwinGNN

Decoupled Knowledge Distillation

State-of-the-art distillation methods are mainly based on distilling deep features from intermediate layers, while the significance of logit distillation is greatly overlooked. To provide a novel viewpoint to study logit distillation, we reformulate the classical KD loss into two parts, i.e., target class knowledge distillation (TCKD) and non-target class knowledge distillation (NCKD). We empirically investigate and prove the effects of the two parts: TCKD transfers knowledge concerning the "difficulty" of training samples, while NCKD is the prominent reason why logit distillation works. More importantly, we reveal that the classical KD loss is a coupled formulation, which (1) suppresses the effectiveness of NCKD and (2) limits the flexibility to balance these two parts. To address these issues, we present Decoupled Knowledge Distillation (DKD), enabling TCKD and NCKD to play their roles more efficiently and flexibly. Compared with complex feature-based methods, our DKD achieves comparable or even better results and has better training efficiency on CIFAR-100, ImageNet, and MS-COCO datasets for image classification and object detection tasks. This paper proves the great potential of logit distillation, and we hope it will be helpful for future research. The code is available at https://github.com/megvii-research/mdistiller.Comment: Accepted by CVPR2022, fix typ

Microbiological and Technological Insights on Anaerobic Digestion of Animal Manure: A Review

Anaerobic digestion of animal manure results in the production of renewable energy (biogas) and nutrient-rich biofertilizer. A further benefit of the technology is decreased greenhouse gas emissions that otherwise occur during manure storage. Since animal manure makes anaerobic digestion cost-efficient and further advance the technology for higher methane yields, it is of utmost importance to find strategies to improve bottlenecks such as the degradation of lignocellulose, e.g., in cattle manure, or to circumvent microbial inhibition by ammonia caused by the degradation of nitrogen compounds in, e.g., chicken, duck, or swine manure. This review summarizes the characteristics of different animal manures and provides insight into the underlying microbial mechanisms causing challenging problems with the anaerobic digestion process. A particular focus is put upon the retention time and organic loading rate in high-ammonia processes, which should be designed and optimized to support the microorganisms that tolerate high ammonia conditions, such as the syntrophic acetate oxidizing bacteria and the hydrogenotrophic methanogens. Furthermore, operating managements used to stabilize and increase the methane yield of animal manure, including supporting materials, the addition of trace elements, or the incorporation of ammonia removal technologies, are summarized. The review is finalized with a discussion of the research needed to outline conceivable operational methods for the anaerobic digestion process of animal manure to circumvent process instability and improve the process performance

Specialized Re-Ranking: A Novel Retrieval-Verification Framework for Cloth Changing Person Re-Identification

Cloth changing person re-identification(Re-ID) can work under more complicated scenarios with higher security than normal Re-ID and biometric techniques and is therefore extremely valuable in applications. Meanwhile, higher flexibility in appearance always leads to more similar-looking confusing images, which is the weakness of the widely used retrieval methods. In this work, we shed light on how to handle these similar images. Specifically, we propose a novel retrieval-verification framework. Given an image, the retrieval module can search for similar images quickly. Our proposed verification network will then compare the input image and the candidate images by contrasting those local details and give a similarity score. An innovative ranking strategy is also introduced to take a good balance between retrieval and verification results. Comprehensive experiments are conducted to show the effectiveness of our framework and its capability in improving the state-of-the-art methods remarkably on both synthetic and realistic datasets.Comment: Accepted by Pattern Recognitio

Curriculum Temperature for Knowledge Distillation

Most existing distillation methods ignore the flexible role of the temperature in the loss function and fix it as a hyper-parameter that can be decided by an inefficient grid search. In general, the temperature controls the discrepancy between two distributions and can faithfully determine the difficulty level of the distillation task. Keeping a constant temperature, i.e., a fixed level of task difficulty, is usually sub-optimal for a growing student during its progressive learning stages. In this paper, we propose a simple curriculum-based technique, termed Curriculum Temperature for Knowledge Distillation (CTKD), which controls the task difficulty level during the student's learning career through a dynamic and learnable temperature. Specifically, following an easy-to-hard curriculum, we gradually increase the distillation loss w.r.t. the temperature, leading to increased distillation difficulty in an adversarial manner. As an easy-to-use plug-in technique, CTKD can be seamlessly integrated into existing knowledge distillation frameworks and brings general improvements at a negligible additional computation cost. Extensive experiments on CIFAR-100, ImageNet-2012, and MS-COCO demonstrate the effectiveness of our method. Our code is available at https://github.com/zhengli97/CTKD.Comment: AAAI 202