Polly is the LLVM project's polyhedral loop nest optimizer. Recently, user-directed loop transformation pragmas were proposed based on LLVM/Clang and Polly. The search space exposed by the transformation pragmas is a tree, wherein each node represents a specific combination of loop transformations that can be applied to the code resulting from the parent node's loop transformations. We have developed a search algorithm based on Monte Carlo tree search (MCTS) to find the best combination of loop transformations. Our algorithm consists of two phases: exploring loop transformations at different depths of the tree to identify promising regions in the tree search space and exploiting those regions by performing a local search. Moreover, a restart mechanism is used to avoid the MCTS getting trapped in a local solution. The best and worst solutions are transferred from the previous phases of the restarts to leverage the search history. We compare our approach with random, greedy, and breadth-first search methods on PolyBench kernels and ECP proxy applications. Experimental results show that our MCTS algorithm finds pragma combinations with a speedup of 2.3x over Polly's heuristic optimizations on average.

From global pandemics to geopolitical turmoil, leaders in logistics, product allocation, procurement and operations are facing increasing difficulty with safeguarding their organizations against supply chain vulnerabilities. It is recommended to opt for forecasting against trending based benchmark because auditing a future forecast puts more focus on seasonality. The forecasting models provide with end-to-end, real time oversight of the entire supply chain, while utilizing predictive analytics and artificial intelligence to identify potential disruptions before they occur. By combining internal and external data points, coming up with an AI-enabled modelling engine can greatly reduce risk by helping retail companies proactively respond to supply and demand variability. This research paper puts focus on creating an ingenious way to tackle the impact of COVID19 on Supply chain, product allocation, trending and seasonality. Key words: Supply chain, covid-19, forecasting, coronavirus, manufacturing, seasonality, trending, retail.

Graph Neural Networks (GNNs) have been studied from the lens of expressive power and generalization. However, their optimization properties are less well understood. We take the first step towards analyzing GNN training by studying the gradient dynamics of GNNs. First, we analyze linearized GNNs and prove that despite the non-convexity of training, convergence to a global minimum at a linear rate is guaranteed under mild assumptions that we validate on real-world graphs. Second, we study what may affect the GNNs' training speed. Our results show that the training of GNNs is implicitly accelerated by skip connections, more depth, and/or a good label distribution. Empirical results confirm that our theoretical results for linearized GNNs align with the training behavior of nonlinear GNNs. Our results provide the first theoretical support for the success of GNNs with skip connections in terms of optimization, and suggest that deep GNNs with skip connections would be promising in practice.

Bayesian inference has the potential to improve deep neural networks (DNNs) by providing 1) uncertainty estimates for robust prediction and downstream decision-making, and 2) an objective function (the marginal likelihood) for hyperparameter selection [MacKay, 1992a; 1992b; 2003]. The recent success of deep learning [Krizhevsky et al., 2012; Vaswani et al., 2017; Schrittwieser et al., 2020] has renewed interest in large-scale Bayesian Neural Networks (BNNs) as well, with effort mainly focused on obtaining useful uncertainty estimates [Blundell et al., 2015; Kingma et al., 2015; Gal and Ghahramani, 2016]. Despite already providing usable uncertainty estimates, there is significant evidence that current approximations to the uncertainty on neural network weights can still be significantly improved [Hron et al., 2018; Foong et al., 2020]. The accuracy of the uncertainty approximation is also linked to the quality of the marginal likelihood estimate [Blei et al., 2017]. Since hyperparameter learning using the marginal likelihood fails for most common approximations [e.g., Blundell et al., 2015], the accuracy of the uncertainty estimates is also questionable. Damianou and Lawrence [2013] used Gaussian processes [Rasmussen and Williams, 2006] as layers to create a different Bayesian analogue to a DNN: the Deep Gaussian process (DGP). Gaussian processes (GPs) are a different representation of a single layer neural network, which is promising because it allows high-quality approximations to uncertainty [Titsias, 2009; Burt et al., 2019].

Uncertainty awareness is crucial to develop reliable machine learning models. In this work, we propose the Natural Posterior Network (NatPN) for fast and high-quality uncertainty estimation for any task where the target distribution belongs to the exponential family. Thus, NatPN finds application for both classification and general regression settings. Unlike many previous approaches, NatPN does not require out-of-distribution (OOD) data at training time. Instead, it leverages Normalizing Flows to fit a single density on a learned low-dimensional and task-dependent latent space. For any input sample, NatPN uses the predicted likelihood to perform a Bayesian update over the target distribution. Theoretically, NatPN assigns high uncertainty far away from training data. Empirically, our extensive experiments on calibration and OOD detection show that NatPN delivers highly competitive performance for classification, regression and count prediction tasks.

A common setting for scientific inference is the ability to sample from a high-fidelity forward model (simulation) without having an explicit probability density of the data. We propose a simulation-based maximum likelihood deconvolution approach in this setting called OmniFold. Deep learning enables this approach to be naturally unbinned and (variable-, and) high-dimensional. In contrast to model parameter estimation, the goal of deconvolution is to remove detector distortions in order to enable a variety of down-stream inference tasks. Our approach is the deep learning generalization of the common Richardson-Lucy approach that is also called Iterative Bayesian Unfolding in particle physics. We show how OmniFold can not only remove detector distortions, but it can also account for noise processes and acceptance effects.

In many applications, it is desirable that a classifier not only makes accurate predictions, but also outputs calibrated probabilities. However, many existing classifiers, especially deep neural network classifiers, tend not to be calibrated. Post-hoc calibration is a technique to recalibrate a model, and its goal is to learn a calibration map. Existing approaches mostly focus on constructing calibration maps with low calibration errors. Contrary to these methods, we study post-hoc calibration for multi-class classification under constraints, as a calibrator with a low calibration error does not necessarily mean it is useful in practice. In this paper, we introduce two practical constraints to be taken into consideration. We then present Meta-Cal, which is built from a base calibrator and a ranking model. Under some mild assumptions, two high-probability bounds are given with respect to these constraints. Empirical results on CIFAR-10, CIFAR-100 and ImageNet and a range of popular network architectures show our proposed method significantly outperforms the current state of the art for post-hoc multi-class classification calibration.

The key challenge in cross-modal retrieval is to find similarities between objects represented with different modalities, such as image and text. However, each modality embeddings stem from non-related feature spaces, which causes the notorious 'heterogeneity gap'. Currently, many cross-modal systems try to bridge the gap with self-attention. However, self-attention has been widely criticized for its quadratic complexity, which prevents many real-life applications. In response to this, we propose T-EMDE - a neural density estimator inspired by the recently introduced Efficient Manifold Density Estimator (EMDE) from the area of recommender systems. EMDE operates on sketches - representations especially suitable for multimodal operations. However, EMDE is non-differentiable and ingests precomputed, static embeddings. With T-EMDE we introduce a trainable version of EMDE which allows full end-to-end training. In contrast to self-attention, the complexity of our solution is linear to the number of tokens/segments. As such, T-EMDE is a drop-in replacement for the self-attention module, with beneficial influence on both speed and metric performance in cross-modal settings. It facilitates communication between modalities, as each global text/image representation is expressed with a standardized sketch histogram which represents the same manifold structures irrespective of the underlying modality. We evaluate T-EMDE by introducing it into two recent cross-modal SOTA models and achieving new state-of-the-art results on multiple datasets and decreasing model latency by up to 20%.

Describing visual content in a natural-language utterance is an emerging interdisciplinary problem, which lies at the intersection of computer vision (CV) and natural language processing (NLP) ((1)). As a sentence-level short image caption ((2, 3, 4)) has a limited descriptive capacity, (5) introduce a paragraphlevel caption method that aims to generate a detailed and coherent paragraph for describing an image in a finer manner. Recent advances in image paragraph generation focus on building different types of hierarchical recurrent neural network (HRNN), e.g., LSTM ((6)), to generate the visual paragraphs. For HRNN, the high-level RNN recursively produces a sequence of sentence-level topic vectors given the image features as the input, while the low-level RNN is subsequently adopted to decode each topic vector into an output sentence. By modeling each sentence and coupling the sentences into one paragraph, these hierarchical architectures often outperform the flat models ((5)). To improve the performance and generate more diverse paragraphs, advanced methods, extending the HRNN based on generative adversarial network (GAN) ((7)) or variational auto-encoders (VAE) ((8)), are proposed by (9) and (10).

Restricted Boltzmann machines (RBM) and deep Boltzmann machines (DBM) are important models in machine learning, and recently found numerous applications in quantum many-body physics. We show that there are fundamental connections between them and tensor networks. In particular, we demonstrate that any RBM and DBM can be exactly represented as a two-dimensional tensor network. This representation gives an understanding of the expressive power of RBM and DBM using entanglement structures of the tensor networks, also provides an efficient tensor network contraction algorithm for the computing partition function of RBM and DBM. Using numerical experiments, we demonstrate that the proposed algorithm is much more accurate than the state-of-the-art machine learning methods in estimating the partition function of restricted Boltzmann machines and deep Boltzmann machines, and have potential applications in training deep Boltzmann machines for general machine learning tasks.