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How can firms optimally negotiate bilateral contracts with each other in a financial network? Every firm seeks to maximize the utility it gains from its portfolio of contracts. We focus on mean-variance utilities, where each firm has its own beliefs about the expected returns of the contracts and the covariances between them (Markowitz, J. Finance 7(11), 1952). Instead of revealing these beliefs, a firm may adopt a different negotiating position, seeking better contract terms. We formulate a contract negotiation process by which such strategic behavior leads to a network of contracts. In our formulation, any subset of firms can be strategic. The negotiating positions of these firms can form Nash equilibria, where each firm's position is optimal given the others' positions. We give a polynomial-time algorithm to find the Nash equilibria, if they exist, and certify their nonexistence otherwise. We explore the implications of such equilibria on several model networks. These illustrate that firms' utilities can be sensitive to their negotiating position. We then propose trade deadlines as a mechanism to reduce the need for strategic behavior. At the deadline, each firm can unilaterally cancel some or all of its contracts, for a penalty. In our model networks, we show that trade deadlines can reduce the loss of utility from being honest. We empirically verify our insights using data on international trade between 46 large economies.

Uncertainty estimation for unlabeled data is crucial to active learning. With a deep neural network employed as the backbone model, the data selection process is highly challenging due to the potential over-confidence of the model inference. Existing methods resort to special learning fashions (e.g. adversarial) or auxiliary models to address this challenge. This tends to result in complex and inefficient pipelines, which would render the methods impractical. In this work, we propose a novel algorithm that leverages noise stability to estimate data uncertainty. The key idea is to measure the output derivation from the original observation when the model parameters are randomly perturbed by noise. We provide theoretical analyses by leveraging the small Gaussian noise theory and demonstrate that our method favors a subset with large and diverse gradients. Our method is generally applicable in various tasks, including computer vision, natural language processing, and structural data analysis. It achieves competitive performance compared against state-of-the-art active learning baselines.

Deep neural networks have achieved remarkable breakthroughs by leveraging multiple layers of data processing to extract hidden representations, albeit at the cost of large electronic computing power. To enhance energy efficiency and speed, the optical implementation of neural networks aims to harness the advantages of optical bandwidth and the energy efficiency of optical interconnections. In the absence of low-power optical nonlinearities, the challenge in the implementation of multilayer optical networks lies in realizing multiple optical layers without resorting to electronic components. In this study, we present a novel framework that uses multiple scattering that is capable of synthesizing programmable linear and nonlinear transformations concurrently at low optical power by leveraging the nonlinear relationship between the scattering potential, represented by data, and the scattered field. Theoretical and experimental investigations show that repeating the data by multiple scattering enables non-linear optical computing at low power continuous wave light. Moreover, we empirically found that scaling of this optical framework follows the power law as in state-of-the-art deep digital networks.

In many situations when people are assigned to coalitions, the utility of each person depends on the friends in her coalition. Additionally, in many situations, the size of each coalition should be bounded. This paper studies such coalition formation scenarios in both weighted and unweighted settings. Since finding a partition that maximizes the utilitarian social welfare is computationally hard, we provide a polynomial-time approximation algorithm. We also investigate the existence and the complexity of finding stable partitions. Namely, we show that the Contractual Strict Core (CSC) is never empty, but the Strict Core (SC) of some games is empty. Finding partitions that are in the CSC is computationally easy, but even deciding whether an SC of a given game exists is NP-hard. The analysis of the core is more involved. In the unweighted setting, we show that when the coalition size is bounded by 3 the core is never empty, and we present a polynomial time algorithm for finding a member of the core. However, for the weighted setting, the core may be empty, and we prove that deciding whether there exists a core is NP-hard.

The real-world data tends to be heavily imbalanced and severely skew the data-driven deep neural networks, which makes Long-Tailed Recognition (LTR) a massive challenging task. Existing LTR methods seldom train Vision Transformers (ViTs) with Long-Tailed (LT) data, while the off-the-shelf pretrain weight of ViTs always leads to unfair comparisons. In this paper, we systematically investigate the ViTs' performance in LTR and propose LiVT to train ViTs from scratch only with LT data. With the observation that ViTs suffer more severe LTR problems, we conduct Masked Generative Pretraining (MGP) to learn generalized features. With ample and solid evidence, we show that MGP is more robust than supervised manners. In addition, Binary Cross Entropy (BCE) loss, which shows conspicuous performance with ViTs, encounters predicaments in LTR. We further propose the balanced BCE to ameliorate it with strong theoretical groundings. Specially, we derive the unbiased extension of Sigmoid and compensate extra logit margins to deploy it. Our Bal-BCE contributes to the quick convergence of ViTs in just a few epochs. Extensive experiments demonstrate that with MGP and Bal-BCE, LiVT successfully trains ViTs well without any additional data and outperforms comparable state-of-the-art methods significantly, e.g., our ViT-B achieves 81.0% Top-1 accuracy in iNaturalist 2018 without bells and whistles. Code is available at //github.com/XuZhengzhuo/LiVT.

Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path in a large graph, neural networks allow learning from data to predict the most likely answer in more complex tasks such as image classification, which cannot be reduced to an exact algorithm. To get the best of both worlds, this thesis explores combining both concepts leading to more robust, better performing, more interpretable, more computationally efficient, and more data efficient architectures. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. When integrating an algorithm into a neural architecture, it is important that the algorithm is differentiable such that the architecture can be trained end-to-end and gradients can be propagated back through the algorithm in a meaningful way. To make algorithms differentiable, this thesis proposes a general method for continuously relaxing algorithms by perturbing variables and approximating the expectation value in closed form, i.e., without sampling. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable renderers, and differentiable logic gate networks. Finally, this thesis presents alternative training strategies for learning with algorithms.

Sequential recommendation aims to leverage users' historical behaviors to predict their next interaction. Existing works have not yet addressed two main challenges in sequential recommendation. First, user behaviors in their rich historical sequences are often implicit and noisy preference signals, they cannot sufficiently reflect users' actual preferences. In addition, users' dynamic preferences often change rapidly over time, and hence it is difficult to capture user patterns in their historical sequences. In this work, we propose a graph neural network model called SURGE (short for SeqUential Recommendation with Graph neural nEtworks) to address these two issues. Specifically, SURGE integrates different types of preferences in long-term user behaviors into clusters in the graph by re-constructing loose item sequences into tight item-item interest graphs based on metric learning. This helps explicitly distinguish users' core interests, by forming dense clusters in the interest graph. Then, we perform cluster-aware and query-aware graph convolutional propagation and graph pooling on the constructed graph. It dynamically fuses and extracts users' current activated core interests from noisy user behavior sequences. We conduct extensive experiments on both public and proprietary industrial datasets. Experimental results demonstrate significant performance gains of our proposed method compared to state-of-the-art methods. Further studies on sequence length confirm that our method can model long behavioral sequences effectively and efficiently.

Graph Neural Networks (GNNs) have proven to be useful for many different practical applications. However, many existing GNN models have implicitly assumed homophily among the nodes connected in the graph, and therefore have largely overlooked the important setting of heterophily, where most connected nodes are from different classes. In this work, we propose a novel framework called CPGNN that generalizes GNNs for graphs with either homophily or heterophily. The proposed framework incorporates an interpretable compatibility matrix for modeling the heterophily or homophily level in the graph, which can be learned in an end-to-end fashion, enabling it to go beyond the assumption of strong homophily. Theoretically, we show that replacing the compatibility matrix in our framework with the identity (which represents pure homophily) reduces to GCN. Our extensive experiments demonstrate the effectiveness of our approach in more realistic and challenging experimental settings with significantly less training data compared to previous works: CPGNN variants achieve state-of-the-art results in heterophily settings with or without contextual node features, while maintaining comparable performance in homophily settings.

It is important to detect anomalous inputs when deploying machine learning systems. The use of larger and more complex inputs in deep learning magnifies the difficulty of distinguishing between anomalous and in-distribution examples. At the same time, diverse image and text data are available in enormous quantities. We propose leveraging these data to improve deep anomaly detection by training anomaly detectors against an auxiliary dataset of outliers, an approach we call Outlier Exposure (OE). This enables anomaly detectors to generalize and detect unseen anomalies. In extensive experiments on natural language processing and small- and large-scale vision tasks, we find that Outlier Exposure significantly improves detection performance. We also observe that cutting-edge generative models trained on CIFAR-10 may assign higher likelihoods to SVHN images than to CIFAR-10 images; we use OE to mitigate this issue. We also analyze the flexibility and robustness of Outlier Exposure, and identify characteristics of the auxiliary dataset that improve performance.

We investigate the problem of automatically determining what type of shoe left an impression found at a crime scene. This recognition problem is made difficult by the variability in types of crime scene evidence (ranging from traces of dust or oil on hard surfaces to impressions made in soil) and the lack of comprehensive databases of shoe outsole tread patterns. We find that mid-level features extracted by pre-trained convolutional neural nets are surprisingly effective descriptors for this specialized domains. However, the choice of similarity measure for matching exemplars to a query image is essential to good performance. For matching multi-channel deep features, we propose the use of multi-channel normalized cross-correlation and analyze its effectiveness. Our proposed metric significantly improves performance in matching crime scene shoeprints to laboratory test impressions. We also show its effectiveness in other cross-domain image retrieval problems: matching facade images to segmentation labels and aerial photos to map images. Finally, we introduce a discriminatively trained variant and fine-tune our system through our proposed metric, obtaining state-of-the-art performance.