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Recent work introduced deep kernel processes as an entirely kernel-based alternative to NNs (Aitchison et al. 2020). Deep kernel processes flexibly learn good top-layer representations by alternately sampling the kernel from a distribution over positive semi-definite matrices and performing nonlinear transformations. A particular deep kernel process, the deep Wishart process (DWP), is of particular interest because its prior can be made equivalent to deep Gaussian process (DGP) priors for kernels that can be expressed entirely in terms of Gram matrices. However, inference in DWPs has not yet been possible due to the lack of sufficiently flexible distributions over positive semi-definite matrices. Here, we give a novel approach to obtaining flexible distributions over positive semi-definite matrices by generalising the Bartlett decomposition of the Wishart probability density. We use this new distribution to develop an approximate posterior for the DWP that includes dependency across layers. We develop a doubly-stochastic inducing-point inference scheme for the DWP and show experimentally that inference in the DWP can improve performance over doing inference in a DGP with the equivalent prior.

Until recently, applications of neural networks in machine learning have almost exclusively relied on real-valued networks. It was recently observed, however, that complex-valued neural networks (CVNNs) exhibit superior performance in applications in which the input is naturally complex-valued, such as MRI fingerprinting. While the mathematical theory of real-valued networks has, by now, reached some level of maturity, this is far from true for complex-valued networks. In this paper, we analyze the expressivity of complex-valued networks by providing explicit quantitative error bounds for approximating $C^n$ functions on compact subsets of $\mathbb{C}^d$ by complex-valued neural networks that employ the modReLU activation function, given by $\sigma(z) = \mathrm{ReLU}(|z| - 1) \, \mathrm{sgn} (z)$, which is one of the most popular complex activation functions used in practice. We show that the derived approximation rates are optimal (up to log factors) in the class of modReLU networks with weights of moderate growth.

PageRank is a fundamental property of graph and there have been plenty of PageRank algorithms. Generally, we consider undirected graph as a complicated directed graph. However, some properties of undirected graph, such as symmetry, are ignored when computing PageRank by existing algorithms. In this paper, we propose a parallel PageRank algorithm which is specially for undirected graph. We first demonstrate that the PageRank vector can be viewed as a linear combination of eigenvectors of probability transition matrix and the corresponding coefficients are the functions of eigenvalues. Then we introduce the Chebyshev polynomial approximation by which PageRank vector can be computed iteratively. Finally, we propose the parallel PageRank algorithm as the Chebyshev polynomial approximating algorithm(CPAA). Experimental results show that CPAA only takes 60% of iteration rounds of the power method and is at least 4 times faster than the power method.

Fine-tuned pre-trained language models (PLMs) have achieved awesome performance on almost all NLP tasks. By using additional prompts to fine-tune PLMs, we can further stimulate the rich knowledge distributed in PLMs to better serve downstream task. Prompt tuning has achieved promising results on some few-class classification tasks such as sentiment classification and natural language inference. However, manually designing lots of language prompts is cumbersome and fallible. For those auto-generated prompts, it is also expensive and time-consuming to verify their effectiveness in non-few-shot scenarios. Hence, it is challenging for prompt tuning to address many-class classification tasks. To this end, we propose prompt tuning with rules (PTR) for many-class text classification, and apply logic rules to construct prompts with several sub-prompts. In this way, PTR is able to encode prior knowledge of each class into prompt tuning. We conduct experiments on relation classification, a typical many-class classification task, and the results on benchmarks show that PTR can significantly and consistently outperform existing state-of-the-art baselines. This indicates that PTR is a promising approach to take advantage of PLMs for those complicated classification tasks.

Recent advances in Transformer models allow for unprecedented sequence lengths, due to linear space and time complexity. In the meantime, relative positional encoding (RPE) was proposed as beneficial for classical Transformers and consists in exploiting lags instead of absolute positions for inference. Still, RPE is not available for the recent linear-variants of the Transformer, because it requires the explicit computation of the attention matrix, which is precisely what is avoided by such methods. In this paper, we bridge this gap and present Stochastic Positional Encoding as a way to generate PE that can be used as a replacement to the classical additive (sinusoidal) PE and provably behaves like RPE. The main theoretical contribution is to make a connection between positional encoding and cross-covariance structures of correlated Gaussian processes. We illustrate the performance of our approach on the Long-Range Arena benchmark and on music generation.

Graph convolution is the core of most Graph Neural Networks (GNNs) and usually approximated by message passing between direct (one-hop) neighbors. In this work, we remove the restriction of using only the direct neighbors by introducing a powerful, yet spatially localized graph convolution: Graph diffusion convolution (GDC). GDC leverages generalized graph diffusion, examples of which are the heat kernel and personalized PageRank. It alleviates the problem of noisy and often arbitrarily defined edges in real graphs. We show that GDC is closely related to spectral-based models and thus combines the strengths of both spatial (message passing) and spectral methods. We demonstrate that replacing message passing with graph diffusion convolution consistently leads to significant performance improvements across a wide range of models on both supervised and unsupervised tasks and a variety of datasets. Furthermore, GDC is not limited to GNNs but can trivially be combined with any graph-based model or algorithm (e.g. spectral clustering) without requiring any changes to the latter or affecting its computational complexity. Our implementation is available online.

This paper proposes a new generative adversarial network for pose transfer, i.e., transferring the pose of a given person to a target pose. The generator of the network comprises a sequence of Pose-Attentional Transfer Blocks that each transfers certain regions it attends to, generating the person image progressively. Compared with those in previous works, our generated person images possess better appearance consistency and shape consistency with the input images, thus significantly more realistic-looking. The efficacy and efficiency of the proposed network are validated both qualitatively and quantitatively on Market-1501 and DeepFashion. Furthermore, the proposed architecture can generate training images for person re-identification, alleviating data insufficiency. Codes and models are available at: //github.com/tengteng95/Pose-Transfer.git.

In order to avoid the curse of dimensionality, frequently encountered in Big Data analysis, there was a vast development in the field of linear and nonlinear dimension reduction techniques in recent years. These techniques (sometimes referred to as manifold learning) assume that the scattered input data is lying on a lower dimensional manifold, thus the high dimensionality problem can be overcome by learning the lower dimensionality behavior. However, in real life applications, data is often very noisy. In this work, we propose a method to approximate $\mathcal{M}$ a $d$-dimensional $C^{m+1}$ smooth submanifold of $\mathbb{R}^n$ ($d \ll n$) based upon noisy scattered data points (i.e., a data cloud). We assume that the data points are located "near" the lower dimensional manifold and suggest a non-linear moving least-squares projection on an approximating $d$-dimensional manifold. Under some mild assumptions, the resulting approximant is shown to be infinitely smooth and of high approximation order (i.e., $O(h^{m+1})$, where $h$ is the fill distance and $m$ is the degree of the local polynomial approximation). The method presented here assumes no analytic knowledge of the approximated manifold and the approximation algorithm is linear in the large dimension $n$. Furthermore, the approximating manifold can serve as a framework to perform operations directly on the high dimensional data in a computationally efficient manner. This way, the preparatory step of dimension reduction, which induces distortions to the data, can be avoided altogether.

A fundamental computation for statistical inference and accurate decision-making is to compute the marginal probabilities or most probable states of task-relevant variables. Probabilistic graphical models can efficiently represent the structure of such complex data, but performing these inferences is generally difficult. Message-passing algorithms, such as belief propagation, are a natural way to disseminate evidence amongst correlated variables while exploiting the graph structure, but these algorithms can struggle when the conditional dependency graphs contain loops. Here we use Graph Neural Networks (GNNs) to learn a message-passing algorithm that solves these inference tasks. We first show that the architecture of GNNs is well-matched to inference tasks. We then demonstrate the efficacy of this inference approach by training GNNs on a collection of graphical models and showing that they substantially outperform belief propagation on loopy graphs. Our message-passing algorithms generalize out of the training set to larger graphs and graphs with different structure.

Modeling and generating graphs is fundamental for studying networks in biology, engineering, and social sciences. However, modeling complex distributions over graphs and then efficiently sampling from these distributions is challenging due to the non-unique, high-dimensional nature of graphs and the complex, non-local dependencies that exist between edges in a given graph. Here we propose GraphRNN, a deep autoregressive model that addresses the above challenges and approximates any distribution of graphs with minimal assumptions about their structure. GraphRNN learns to generate graphs by training on a representative set of graphs and decomposes the graph generation process into a sequence of node and edge formations, conditioned on the graph structure generated so far. In order to quantitatively evaluate the performance of GraphRNN, we introduce a benchmark suite of datasets, baselines and novel evaluation metrics based on Maximum Mean Discrepancy, which measure distances between sets of graphs. Our experiments show that GraphRNN significantly outperforms all baselines, learning to generate diverse graphs that match the structural characteristics of a target set, while also scaling to graphs 50 times larger than previous deep models.