GAN-based image restoration inverts the generative process to repair images corrupted by known degradations. Existing unsupervised methods must be carefully tuned for each task and degradation level. In this work, we make StyleGAN image restoration robust: a single set of hyperparameters works across a wide range of degradation levels. This makes it possible to handle combinations of several degradations, without the need to retune. Our proposed approach relies on a 3-phase progressive latent space extension and a conservative optimizer, which avoids the need for any additional regularization terms. Extensive experiments demonstrate robustness on inpainting, upsampling, denoising, and deartifacting at varying degradations levels, outperforming other StyleGAN-based inversion techniques. Our approach also favorably compares to diffusion-based restoration by yielding much more realistic inversion results. Code is available at //lvsn.github.io/RobustUnsupervised/.
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Multidimensional scaling (MDS) is a widely used approach to representing high-dimensional, dependent data. MDS works by assigning each observation a location on a low-dimensional geometric manifold, with distance on the manifold representing similarity. We propose a Bayesian approach to multidimensional scaling when the low-dimensional manifold is hyperbolic. Using hyperbolic space facilitates representing tree-like structures common in many settings (e.g. text or genetic data with hierarchical structure). A Bayesian approach provides regularization that minimizes the impact of measurement error in the observed data and assesses uncertainty. We also propose a case-control likelihood approximation that allows for efficient sampling from the posterior distribution in larger data settings, reducing computational complexity from approximately $O(n^2)$ to $O(n)$. We evaluate the proposed method against state-of-the-art alternatives using simulations, canonical reference datasets, Indian village network data, and human gene expression data.
The visual object category reports of artificial neural networks (ANNs) are notoriously sensitive to tiny, adversarial image perturbations. Because human category reports (aka human percepts) are thought to be insensitive to those same small-norm perturbations -- and locally stable in general -- this argues that ANNs are incomplete scientific models of human visual perception. Consistent with this, we show that when small-norm image perturbations are generated by standard ANN models, human object category percepts are indeed highly stable. However, in this very same "human-presumed-stable" regime, we find that robustified ANNs reliably discover low-norm image perturbations that strongly disrupt human percepts. These previously undetectable human perceptual disruptions are massive in amplitude, approaching the same level of sensitivity seen in robustified ANNs. Further, we show that robustified ANNs support precise perceptual state interventions: they guide the construction of low-norm image perturbations that strongly alter human category percepts toward specific prescribed percepts. These observations suggest that for arbitrary starting points in image space, there exists a set of nearby "wormholes", each leading the subject from their current category perceptual state into a semantically very different state. Moreover, contemporary ANN models of biological visual processing are now accurate enough to consistently guide us to those portals.
Centrality measures for simple graphs are well-defined and several main-memory algorithms exist for each. Simple graphs are not adequate for modeling complex data sets with multiple entities and relationships. Multilayer networks (MLNs) have been shown to be better suited, but there are very few algorithms for centrality computation directly on MLNs. They are converted (aggregated or collapsed) to simple graphs using Boolean AND or OR operators to compute centrality, which is not only inefficient but incurs a loss of structure and semantics. In this paper, we propose algorithms that compute closeness centrality on an MLN directly using a novel decoupling-based approach. Individual results of layers (or simple graphs) of an MLN are used and a composition function developed to compute the centrality for the MLN. The challenge is to do this accurately and efficiently. However, since these algorithms do not have complete information of the MLN, computing a global measure such as closeness centrality is a challenge. Hence, these algorithms rely on heuristics derived from intuition. The advantage is that this approach lends itself to parallelism and is more efficient compared to the traditional approach. We present two heuristics for composition and experimentally validate accuracy and efficiency on a large number of synthetic and real-world graphs with diverse characteristics.
Offline change point detection seeks to identify points in a time series where the data generating process changes. This problem is well studied for univariate i.i.d. data, but becomes challenging with increasing dimension and temporal dependence. For the at most one change point problem, we propose the use of a conceptor matrix to learn the characteristic dynamics of a specified training window in a time series. The associated random recurrent neural network acts as a featurizer of the data, and change points are identified from a univariate quantification of the distance between the featurization and the space spanned by a representative conceptor matrix. This model agnostic method can suggest potential locations of interest that warrant further study. We prove that, under mild assumptions, the method provides a consistent estimate of the true change point, and quantile estimates for statistics are produced via a moving block bootstrap of the original data. The method is tested on simulations from several classes of processes, and we evaluate performance with clustering metrics, graphical methods, and observed Type 1 error control. We apply our method to publicly available neural data from rats experiencing bouts of non-REM sleep prior to exploration of a radial maze.
Knowledge distillation (KD) has received much attention due to its success in compressing networks to allow for their deployment in resource-constrained systems. While the problem of adversarial robustness has been studied before in the KD setting, previous works overlook what we term the relative calibration of the student network with respect to its teacher in terms of soft confidences. In particular, we focus on two crucial questions with regard to a teacher-student pair: (i) do the teacher and student disagree at points close to correctly classified dataset examples, and (ii) is the distilled student as confident as the teacher around dataset examples? These are critical questions when considering the deployment of a smaller student network trained from a robust teacher within a safety-critical setting. To address these questions, we introduce a faithful imitation framework to discuss the relative calibration of confidences and provide empirical and certified methods to evaluate the relative calibration of a student w.r.t. its teacher. Further, to verifiably align the relative calibration incentives of the student to those of its teacher, we introduce faithful distillation. Our experiments on the MNIST, Fashion-MNIST and CIFAR-10 datasets demonstrate the need for such an analysis and the advantages of the increased verifiability of faithful distillation over alternative adversarial distillation methods.
Graph convolutional networks (GCNs) can successfully learn the graph signal representation by graph convolution. The graph convolution depends on the graph filter, which contains the topological dependency of data and propagates data features. However, the estimation errors in the propagation matrix (e.g., the adjacency matrix) can have a significant impact on graph filters and GCNs. In this paper, we study the effect of a probabilistic graph error model on the performance of the GCNs. We prove that the adjacency matrix under the error model is bounded by a function of graph size and error probability. We further analytically specify the upper bound of a normalized adjacency matrix with self-loop added. Finally, we illustrate the error bounds by running experiments on a synthetic dataset and study the sensitivity of a simple GCN under this probabilistic error model on accuracy.
Graph Neural Networks (GNNs) have been successfully used in many problems involving graph-structured data, achieving state-of-the-art performance. GNNs typically employ a message-passing scheme, in which every node aggregates information from its neighbors using a permutation-invariant aggregation function. Standard well-examined choices such as the mean or sum aggregation functions have limited capabilities, as they are not able to capture interactions among neighbors. In this work, we formalize these interactions using an information-theoretic framework that notably includes synergistic information. Driven by this definition, we introduce the Graph Ordering Attention (GOAT) layer, a novel GNN component that captures interactions between nodes in a neighborhood. This is achieved by learning local node orderings via an attention mechanism and processing the ordered representations using a recurrent neural network aggregator. This design allows us to make use of a permutation-sensitive aggregator while maintaining the permutation-equivariance of the proposed GOAT layer. The GOAT model demonstrates its increased performance in modeling graph metrics that capture complex information, such as the betweenness centrality and the effective size of a node. In practical use-cases, its superior modeling capability is confirmed through its success in several real-world node classification benchmarks.
This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. With the framelet system, we can decompose the graph feature into low-pass and high-pass frequencies as extracted features for network training, which then defines a framelet-based graph convolution. The framelet decomposition naturally induces a graph pooling strategy by aggregating the graph feature into low-pass and high-pass spectra, which considers both the feature values and geometry of the graph data and conserves the total information. The graph neural networks with the proposed framelet convolution and pooling achieve state-of-the-art performance in many types of node and graph prediction tasks. Moreover, we propose shrinkage as a new activation for the framelet convolution, which thresholds the high-frequency information at different scales. Compared to ReLU, shrinkage in framelet convolution improves the graph neural network model in terms of denoising and signal compression: noises in both node and structure can be significantly reduced by accurately cutting off the high-pass coefficients from framelet decomposition, and the signal can be compressed to less than half its original size with the prediction performance well preserved.
Knowledge graph (KG) embedding encodes the entities and relations from a KG into low-dimensional vector spaces to support various applications such as KG completion, question answering, and recommender systems. In real world, knowledge graphs (KGs) are dynamic and evolve over time with addition or deletion of triples. However, most existing models focus on embedding static KGs while neglecting dynamics. To adapt to the changes in a KG, these models need to be re-trained on the whole KG with a high time cost. In this paper, to tackle the aforementioned problem, we propose a new context-aware Dynamic Knowledge Graph Embedding (DKGE) method which supports the embedding learning in an online fashion. DKGE introduces two different representations (i.e., knowledge embedding and contextual element embedding) for each entity and each relation, in the joint modeling of entities and relations as well as their contexts, by employing two attentive graph convolutional networks, a gate strategy, and translation operations. This effectively helps limit the impacts of a KG update in certain regions, not in the entire graph, so that DKGE can rapidly acquire the updated KG embedding by a proposed online learning algorithm. Furthermore, DKGE can also learn KG embedding from scratch. Experiments on the tasks of link prediction and question answering in a dynamic environment demonstrate the effectiveness and efficiency of DKGE.
Link prediction for knowledge graphs is the task of predicting missing relationships between entities. Previous work on link prediction has focused on shallow, fast models which can scale to large knowledge graphs. However, these models learn less expressive features than deep, multi-layer models -- which potentially limits performance. In this work, we introduce ConvE, a multi-layer convolutional network model for link prediction, and report state-of-the-art results for several established datasets. We also show that the model is highly parameter efficient, yielding the same performance as DistMult and R-GCN with 8x and 17x fewer parameters. Analysis of our model suggests that it is particularly effective at modelling nodes with high indegree -- which are common in highly-connected, complex knowledge graphs such as Freebase and YAGO3. In addition, it has been noted that the WN18 and FB15k datasets suffer from test set leakage, due to inverse relations from the training set being present in the test set -- however, the extent of this issue has so far not been quantified. We find this problem to be severe: a simple rule-based model can achieve state-of-the-art results on both WN18 and FB15k. To ensure that models are evaluated on datasets where simply exploiting inverse relations cannot yield competitive results, we investigate and validate several commonly used datasets -- deriving robust variants where necessary. We then perform experiments on these robust datasets for our own and several previously proposed models, and find that ConvE achieves state-of-the-art Mean Reciprocal Rank across all datasets.
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