We study the approval-based multi-winner election problem where \(n\) voters jointly decide a committee of \(k\) winners from \(m\) candidates. We focus on the axiom average justified representation (AJR) proposed by Fernández, Elkind, Lackner, García, Arias-Fisteus, Basanta-Val, and Skowron (2017). AJR postulates that every group of voters with a common preference should be sufficiently represented in that their average satisfaction should be no less than their Hare quota. Formally, for every group of \(\lceil \ell \cdot \tfrac{n}{k} \rceil\) voters with \(\ell\) common approved candidates, the average number of approved winners for this group should be at least \(\ell\). It is well-known that a winning committee satisfying AJR is not guaranteed to exist for all multi-winner election instances. In this paper, we study the likelihood of the existence of AJR under the Erdos–Rényi model. We consider the Erdos–Rényi model parameterized by \(p \in [0,1]\) that samples multi-winner election instances from the distribution where each voter approves each candidate with probability \(p\) (and the events that voters approve candidates are independent), and we provide a clean and complete characterization of the existence of AJR committees in the case where \(m\) is a constant and \(n\) tends to infinity. We show that there are two phase transition points \(p_1\) and \(p_2\) (with \(p_1 \le p_2\)) for the parameter \(p\) such that: 1) when \(p \lt p_1\) or \(p \gt p_2\), an AJR committee exists with probability \(1 - o(1)\), 2) when \(p_1 \lt p \lt p_2\), an AJR committee exists with probability \(o(1)\), and 3) when \(p = p_1\) or \(p = p_2\), the probability that an AJR committee exists is bounded away from both \(0\) and \(1\).

We characterize the maximum likelihood that two voting rule outcomes are different and that the winner of one voting rule is the loser of another (implying that they are {\em drastically different}) on positional scoring rules, Condorcet winner/loser, Copeland, Ranked Pairs, and STV (Single Transferable Vote) under any fixed number of alternatives. The most famous problem in this scope is strong Borda’s paradox, in which the winner of the plurality rule is the Condorcet loser. Under mild assumptions, we show that the maximum likelihood that different rules are drastically different is $\Theta(1)$ except for a few special cases, demonstrating the difference between these rules. We also prove that two scoring rules with linear independent scoring vectors have different winners with probability $\Theta(1)$, no matter how similar they are. Our analysis adopts the {\em smoothed social choice framework} \cite{xia2020smoothed} and can be applied to a variety of statistical models, including the standard impartial culture (IC).

T-cell receptor (TCR) recognition of antigens is fundamental to the adaptive immune response. With the expansion of experimental techniques, a substantial database of matched TCR-antigen pairs has emerged, presenting opportunities for computational prediction models. However, accurately forecasting the binding affinities of unseen antigen-TCR pairs remains a major challenge. Here, we present convolutional-self-attention TCR (CATCR), a novel framework tailored to enhance the prediction of epitope and TCR interactions. Our approach utilizes convolutional neural networks to extract peptide features from residue contact matrices, as generated by OpenFold, and a transformer to encode segment-based coded sequences. We introduce CATCR-D, a discriminator that can assess binding by analyzing the structural and sequence features of epitopes and CDR3-β regions. Additionally, the framework comprises CATCR-G, a generative module designed for CDR3-β sequences, which applies the pretrained encoder to deduce epitope characteristics and a transformer decoder for predicting matching CDR3-β sequences. CATCR-D achieved an AUROC of 0.89 on previously unseen epitope-TCR pairs and outperformed four benchmark models by a margin of 17.4%. CATCR-G has demonstrated high precision, recall and F1 scores, surpassing 95% in bidirectional encoder representations from transformers score assessments. Our results indicate that CATCR is an effective tool for predicting unseen epitope-TCR interactions. Incorporating structural insights enhances our understanding of the general rules governing TCR-epitope recognition significantly. The ability to predict TCRs for novel epitopes using structural and sequence information is promising, and broadening the repository of experimental TCR-epitope data could further improve the precision of epitope-TCR binding predictions.

In this paper, we build a lightweight convolution neural network M-SOSAnet that combines efficiency and accuracy for edge devices. Just as DenseNet connects each layer to every other layer in the neural network. Although dense connection can effectively keep information between the middle layers, the increasing input channels by dense connection leads to resource consumption, which greatly increases the amount of parameters and is inefficient. MobileNet series use depthwise separable convolutions, which reduces the amount of calculation and parameters, but will reduce the accuracy. ESPnetv2 uses group pointwise and depthwise dilated separable convolution to learn representation from a large receptive field with fewer flops and parameters but will get a little accuracy decrease. In order to solve these problems, we propose two module: 1. Mobile SOSA Module 2. Downsampling Block with scoring mechanism, and also introduce the attention mechanism. Compare to some past methods, our model M-SOSAnet has lower flops, higher accuracy, maintains the similar amount of parameters. We evaluated model in the areas of image classification, and semantic segmentation to prove that our methods have better performance.

We study 3D shape modeling from a single image and make contributions to it in three aspects. First, we present Pix3D, a large-scale benchmark of diverse image-shape pairs with pixel-level 2D-3D alignment. Pix3D has wide applications in shape-related tasks including reconstruction, retrieval, viewpoint estimation, etc. Building such a large-scale dataset, however, is highly challenging; existing datasets either contain only synthetic data, or lack precise alignment between 2D images and 3D shapes, or only have a small number of images. Second, we calibrate the evaluation criteria for 3D shape reconstruction through behavioral studies, and use them to objectively and systematically benchmark cutting-edge reconstruction algorithms on Pix3D. Third, we design a novel model that simultaneously performs 3D reconstruction and pose estimation; our multi-task learning approach achieves state-of-the-art performance on both tasks.

From a single image, humans are able to perceive the full 3D shape of an object by exploiting learned shape priors from everyday life. Contemporary single-image 3D reconstruction algorithms aim to solve this task in a similar fashion, but often end up with priors that are highly biased by training classes. Here we present an algorithm, Generalizable Reconstruction (GenRe), designed to capture more generic, class-agnostic shape priors. We achieve this with an inference network and training procedure that combine 2.5D representations of visible surfaces (depth and silhouette), spherical shape representations of both visible and non-visible surfaces, and 3D voxel-based representations, in a principled manner that exploits the causal structure of how 3D shapes give rise to 2D images. Experiments demonstrate that GenRe performs well on single-view shape reconstruction, and generalizes to diverse novel objects from categories not seen during training.

Recent progress in deep generative models has led to tremendous breakthroughs in image generation. While being able to synthesize photorealistic images, existing models lack an understanding of our underlying 3D world. Different from previous works built on 2D datasets and models, we present a new generative model, Visual Object Networks (VONs), synthesizing natural images of objects with a disentangled 3D representation. Inspired by classic graphics rendering pipelines, we unravel the image formation process into three conditionally independent factors---shape, viewpoint, and texture---and present an end-to-end adversarial learning framework that jointly models 3D shape and 2D texture. Our model first learns to synthesize 3D shapes that are indistinguishable from real shapes. It then renders the object's 2.5D sketches (i.e., silhouette and depth map) from its shape under a sampled viewpoint. Finally, it learns to add realistic textures to these 2.5D sketches to generate realistic images. The VON not only generates images that are more realistic than the state-of-the-art 2D image synthesis methods but also enables many 3D operations such as changing the viewpoint of a generated image, shape and texture editing, linear interpolation in texture and shape space, and transferring appearance across different objects and viewpoints.

We study the problem of 3D object generation. We propose a novel framework, namely 3D Generative Adversarial Network (3D-GAN), which generates 3D objects from a probabilistic space by leveraging recent advances in volumetric convolutional networks and generative adversarial nets. The benefits of our model are three-fold: first, the use of an adversarial criterion, instead of traditional heuristic criteria, enables the generator to capture object structure implicitly and to synthesize high-quality 3D objects; second, the generator establishes a mapping from a low-dimensional probabilistic space to the space of 3D objects, so that we can sample objects without a reference image or CAD models, and explore the 3D object manifold; third, the adversarial discriminator provides a powerful 3D shape descriptor which, learned without supervision, has wide applications in 3D object recognition. Experiments demonstrate that our method generates high-quality 3D objects, and our unsupervisedly learned features achieve impressive performance on 3D object recognition, comparable with those of supervised learning methods.