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Data depth is a powerful nonparametric tool originally proposed to rank multivariate data from center outward. In this context, one of the most archetypical depth notions is Tukey's halfspace depth. In the last few decades notions of depth have also been proposed for functional data. However, Tukey's depth cannot be extended to handle functional data because of its degeneracy. Here, we propose a new halfspace depth for functional data which avoids degeneracy by regularization. The halfspace projection directions are constrained to have a small reproducing kernel Hilbert space norm. Desirable theoretical properties of the proposed depth, such as isometry invariance, maximality at center, monotonicity relative to a deepest point, upper semi-continuity, and consistency are established. Moreover, the regularized halfspace depth can rank functional data with varying emphasis in shape or magnitude, depending on the regularization. A new outlier detection approach is also proposed, which is capable of detecting both shape and magnitude outliers. It is applicable to trajectories in L2, a very general space of functions that include non-smooth trajectories. Based on extensive numerical studies, our methods are shown to perform well in terms of detecting outliers of different types. Three real data examples showcase the proposed depth notion.

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Structured data in the form of tabular datasets contain features that are distinct and discrete, with varying individual and relative importances to the target. Combinations of one or more features may be more predictive and meaningful than simple individual feature contributions. R's mixed effect linear models library allows users to provide such interactive feature combinations in the model design. However, given many features and possible interactions to select from, model selection becomes an exponentially difficult task. We aim to automate the model selection process for predictions on tabular datasets incorporating feature interactions while keeping computational costs small. The framework includes two distinct approaches for feature selection: a Priority-based Random Grid Search and a Greedy Search method. The Priority-based approach efficiently explores feature combinations using prior probabilities to guide the search. The Greedy method builds the solution iteratively by adding or removing features based on their impact. Experiments on synthetic demonstrate the ability to effectively capture predictive feature combinations.

Smart contracts are computer programs running on blockchains to automate the transaction execution between users. The absence of contract specifications poses a real challenge to the correctness verification of smart contracts. Program invariants are properties that are always preserved throughout the execution, which characterize an important aspect of the program behaviors. In this paper, we propose a novel invariant generation framework, INVCON+, for Solidity smart contracts. INVCON+ extends the existing invariant detector, InvCon, to automatically produce verified contract invariants based on both dynamic inference and static verification. Unlike INVCON+, InvCon only produces likely invariants, which have a high probability to hold, yet are still not verified against the contract code. Particularly, INVCON+ is able to infer more expressive invariants that capture richer semantic relations of contract code. We evaluate INVCON+ on 361 ERC20 and 10 ERC721 real-world contracts, as well as common ERC20 vulnerability benchmarks. The experimental results indicate that INVCON+ efficiently produces high-quality invariant specifications, which can be used to secure smart contracts from common vulnerabilities.

Most modern computing tasks have digital electronic input and output data. Due to these constraints imposed by real-world use cases of computer systems, any analog computing accelerator, whether analog electronic or optical, must perform an analog-to-digital conversion on its input data and a subsequent digital-to-analog conversion on its output data. The energy and latency costs incurred by data conversion place performance limits on analog computing accelerators. To avoid this overhead, analog hardware must replace the full functionality of traditional digital electronic computer hardware. This is not currently possible for optical computing accelerators due to limitations in gain, input-output isolation, and information storage in optical hardware. This article presents a case study that profiles 27 benchmarks for an analog optical Fourier transform and convolution accelerator which we designed and built. The case study shows that an ideal optical Fourier transform and convolution accelerator can produce an average speedup of 9.4 times and a median speedup of 1.9 times for the set of benchmarks. The optical Fourier transform and convolution accelerator only produces significant speedup for pure Fourier transform (45.3 times) and convolution (159.4 times) applications.

Neural networks efficiently encode learned information within their parameters. Consequently, many tasks can be unified by treating neural networks themselves as input data. When doing so, recent studies demonstrated the importance of accounting for the symmetries and geometry of parameter spaces. However, those works developed architectures tailored to specific networks such as MLPs and CNNs without normalization layers, and generalizing such architectures to other types of networks can be challenging. In this work, we overcome these challenges by building new metanetworks - neural networks that take weights from other neural networks as input. Put simply, we carefully build graphs representing the input neural networks and process the graphs using graph neural networks. Our approach, Graph Metanetworks (GMNs), generalizes to neural architectures where competing methods struggle, such as multi-head attention layers, normalization layers, convolutional layers, ResNet blocks, and group-equivariant linear layers. We prove that GMNs are expressive and equivariant to parameter permutation symmetries that leave the input neural network functions unchanged. We validate the effectiveness of our method on several metanetwork tasks over diverse neural network architectures.

In many real-world problems, there is a limited set of training data, but an abundance of unlabeled data. We propose a new method, Generative Posterior Networks (GPNs), that uses unlabeled data to estimate epistemic uncertainty in high-dimensional problems. A GPN is a generative model that, given a prior distribution over functions, approximates the posterior distribution directly by regularizing the network towards samples from the prior. We prove theoretically that our method indeed approximates the Bayesian posterior and show empirically that it improves epistemic uncertainty estimation and scalability over competing methods.

Context: Students often misunderstand programming problem descriptions. This can lead them to solve the wrong problem, which creates frustration, obstructs learning, and imperils grades. Researchers have found that students can be made to better understand the problem by writing examples before they start programming. These examples are checked against correct and wrong implementations -- analogous to mutation testing -- provided by course staff. Doing so results in better student understanding of the problem as well as better test suites to accompany the program, both of which are desirable educational outcomes. Inquiry: Producing mutant implementations requires care. If there are too many, or they are too obscure, students will end up spending a lot of time on an unproductive task and also become frustrated. Instead, we want a small number of mutants that each correspond to common problem misconceptions. This paper presents a workflow with partial automation to produce mutants of this form which, notably, are not those produced by mutation-testing tools. Approach: We comb through student tests that fail a correct implementation. The student misconceptions are embedded in these failures. We then use methods to semantically cluster these failures. These clusters are then translated into conceptual mutants. These can then be run against student data to determine whether we they are better than prior methods. Some of these processes also enjoy automation. Knowledge: We find that student misconceptions illustrated by failing tests can be operationalized by the above process. The resulting mutants do much better at identifying student misconceptions. Grounding: Our findings are grounded in a manual analysis of student examples and a quantitative evaluation of both our clustering techniques and our process for making conceptual mutants. The clustering evaluation compares against a ground truth using standard cluster-correspondence measures, while the mutant evaluation examines how conceptual mutants perform against student data. Importance: Our work contributes a workflow, with some automation, to reduce the cost and increase the effectiveness of generating conceptually interesting mutants. Such mutants can both improve learning outcomes and reduce student frustration, leading to better educational outcomes. In the process, we also identify a variation of mutation testing not commonly discussed in the software literature.

Invariant risk minimization (IRM) has recently emerged as a promising alternative for domain generalization. Nevertheless, the loss function is difficult to optimize for nonlinear classifiers and the original optimization objective could fail when pseudo-invariant features and geometric skews exist. Inspired by IRM, in this paper we propose a novel formulation for domain generalization, dubbed invariant information bottleneck (IIB). IIB aims at minimizing invariant risks for nonlinear classifiers and simultaneously mitigating the impact of pseudo-invariant features and geometric skews. Specifically, we first present a novel formulation for invariant causal prediction via mutual information. Then we adopt the variational formulation of the mutual information to develop a tractable loss function for nonlinear classifiers. To overcome the failure modes of IRM, we propose to minimize the mutual information between the inputs and the corresponding representations. IIB significantly outperforms IRM on synthetic datasets, where the pseudo-invariant features and geometric skews occur, showing the effectiveness of proposed formulation in overcoming failure modes of IRM. Furthermore, experiments on DomainBed show that IIB outperforms $13$ baselines by $0.9\%$ on average across $7$ real datasets.

Data augmentation has been widely used to improve generalizability of machine learning models. However, comparatively little work studies data augmentation for graphs. This is largely due to the complex, non-Euclidean structure of graphs, which limits possible manipulation operations. Augmentation operations commonly used in vision and language have no analogs for graphs. Our work studies graph data augmentation for graph neural networks (GNNs) in the context of improving semi-supervised node-classification. We discuss practical and theoretical motivations, considerations and strategies for graph data augmentation. Our work shows that neural edge predictors can effectively encode class-homophilic structure to promote intra-class edges and demote inter-class edges in given graph structure, and our main contribution introduces the GAug graph data augmentation framework, which leverages these insights to improve performance in GNN-based node classification via edge prediction. Extensive experiments on multiple benchmarks show that augmentation via GAug improves performance across GNN architectures and datasets.

We present a new method to learn video representations from large-scale unlabeled video data. Ideally, this representation will be generic and transferable, directly usable for new tasks such as action recognition and zero or few-shot learning. We formulate unsupervised representation learning as a multi-modal, multi-task learning problem, where the representations are shared across different modalities via distillation. Further, we introduce the concept of loss function evolution by using an evolutionary search algorithm to automatically find optimal combination of loss functions capturing many (self-supervised) tasks and modalities. Thirdly, we propose an unsupervised representation evaluation metric using distribution matching to a large unlabeled dataset as a prior constraint, based on Zipf's law. This unsupervised constraint, which is not guided by any labeling, produces similar results to weakly-supervised, task-specific ones. The proposed unsupervised representation learning results in a single RGB network and outperforms previous methods. Notably, it is also more effective than several label-based methods (e.g., ImageNet), with the exception of large, fully labeled video datasets.

In this paper, we propose a conceptually simple and geometrically interpretable objective function, i.e. additive margin Softmax (AM-Softmax), for deep face verification. In general, the face verification task can be viewed as a metric learning problem, so learning large-margin face features whose intra-class variation is small and inter-class difference is large is of great importance in order to achieve good performance. Recently, Large-margin Softmax and Angular Softmax have been proposed to incorporate the angular margin in a multiplicative manner. In this work, we introduce a novel additive angular margin for the Softmax loss, which is intuitively appealing and more interpretable than the existing works. We also emphasize and discuss the importance of feature normalization in the paper. Most importantly, our experiments on LFW BLUFR and MegaFace show that our additive margin softmax loss consistently performs better than the current state-of-the-art methods using the same network architecture and training dataset. Our code has also been made available at //github.com/happynear/AMSoftmax

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