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This paper studies MapReduce-based heterogeneous coded distributed computing (CDC) where, besides different computing capabilities at workers, input files to be accessed by computing jobs have nonuniform popularity. We propose a file placement strategy that can handle an arbitrary number of input files. Furthermore, we design a nested coded shuffling strategy that can efficiently manage the nonuniformity of file popularity to maximize the coded multicasting opportunity. We then formulate the joint optimization of the proposed file placement and nested shuffling design variables to optimize the proposed CDC scheme. To reduce the high computational complexity in solving the resulting mixed-integer linear programming (MILP) problem, we propose a simple two-file-group-based file placement approach to obtain an approximate solution. Numerical results show that the optimized CDC scheme outperforms other alternatives. Also, the proposed two-file-group-based approach achieves nearly the same performance as the conventional branch-and-cut method in solving the MILP problem but with substantially lower computational complexity that is scalable over the number of files and workers. For computing jobs with aggregate target functions that commonly appear in machine learning applications, we propose a heterogeneous compressed CDC (C-CDC) scheme to further improve the shuffling efficiency. The C-CDC scheme uses a local data aggregation technique to compress the data to be shuffled for the shuffling load reduction. We again optimize the proposed C-CDC scheme and explore the two-file-group-based low-complexity approach for an approximate solution. Numerical results show the proposed C-CDC scheme provides a considerable shuffling load reduction over the CDC scheme, and also, the two-file-group-based file placement approach maintains good performance.

In order to understand the in-context learning phenomenon, recent works have adopted a stylized experimental framework and demonstrated that Transformers can learn gradient-based learning algorithms for various classes of real-valued functions. However, the limitations of Transformers in implementing learning algorithms, and their ability to learn other forms of algorithms are not well understood. Additionally, the degree to which these capabilities are confined to attention-based models is unclear. Furthermore, it remains to be seen whether the insights derived from these stylized settings can be extrapolated to pretrained Large Language Models (LLMs). In this work, we take a step towards answering these questions by demonstrating the following: (a) On a test-bed with a variety of Boolean function classes, we find that Transformers can nearly match the optimal learning algorithm for 'simpler' tasks, while their performance deteriorates on more 'complex' tasks. Additionally, we find that certain attention-free models perform (almost) identically to Transformers on a range of tasks. (b) When provided a teaching sequence, i.e. a set of examples that uniquely identifies a function in a class, we show that Transformers learn more sample-efficiently. Interestingly, our results show that Transformers can learn to implement two distinct algorithms to solve a single task, and can adaptively select the more sample-efficient algorithm depending on the sequence of in-context examples. (c) Lastly, we show that extant LLMs, e.g. LLaMA-2, GPT-4, can compete with nearest-neighbor baselines on prediction tasks that are guaranteed to not be in their training set.

Multiway data analysis aims to uncover patterns in data structured as multi-indexed arrays, and the covariance of such data plays a crucial role in various machine learning applications. However, the intrinsically high dimension of multiway covariance presents significant challenges. To address these challenges, factorized covariance models have been proposed that rely on a separability assumption: the multiway covariance can be accurately expressed as a sum of Kronecker products of mode-wise covariances. This paper is concerned with the accuracy of such separable models for representing multiway covariances. We reduce the question of whether a given covariance can be represented as a separable multiway covariance to an equivalent question about separability of quantum states. Based on this equivalence, we establish that generic multiway covariances tend to be not separable. Moreover, we show that determining the best separable approximation of a generic covariance is NP-hard. Our results suggest that factorized covariance models might not accurately approximate covariance, without additional assumptions ensuring separability. To balance these negative results, we propose an iterative Frank-Wolfe algorithm for computing Kronecker-separable covariance approximations with some additional side information. We establish an oracle complexity bound and empirically observe its consistent convergence to a separable limit point, often close to the ``best'' separable approximation. These results suggest that practical methods may be able to find a Kronecker-separable approximation of covariances, despite the worst-case NP hardness results.

We investigate a novel modeling approach for end-to-end neural network training using hidden Markov models (HMM) where the transition probabilities between hidden states are modeled and learned explicitly. Most contemporary sequence-to-sequence models allow for from-scratch training by summing over all possible label segmentations in a given topology. In our approach there are explicit, learnable probabilities for transitions between segments as opposed to a blank label that implicitly encodes duration statistics. We implement a GPU-based forward-backward algorithm that enables the simultaneous training of label and transition probabilities. We investigate recognition results and additionally Viterbi alignments of our models. We find that while the transition model training does not improve recognition performance, it has a positive impact on the alignment quality. The generated alignments are shown to be viable targets in state-of-the-art Viterbi trainings.

Photonic computing promises faster and more energy-efficient deep neural network (DNN) inference than traditional digital hardware. Advances in photonic computing can have profound impacts on applications such as autonomous driving and defect detection that depend on fast, accurate and energy efficient execution of image segmentation models. In this paper, we investigate image segmentation on photonic accelerators to explore: a) the types of image segmentation DNN architectures that are best suited for photonic accelerators, and b) the throughput and energy efficiency of executing the different image segmentation models on photonic accelerators, along with the trade-offs involved therein. Specifically, we demonstrate that certain segmentation models exhibit negligible loss in accuracy (compared to digital float32 models) when executed on photonic accelerators, and explore the empirical reasoning for their robustness. We also discuss techniques for recovering accuracy in the case of models that do not perform well. Further, we compare throughput (inferences-per-second) and energy consumption estimates for different image segmentation workloads on photonic accelerators. We discuss the challenges and potential optimizations that can help improve the application of photonic accelerators to such computer vision tasks.

The discrete logarithm problem is a fundamental challenge in number theory with significant implications for cryptographic protocols. In this paper, we investigate the limitations of gradient-based methods for learning the parity bit of the discrete logarithm in finite cyclic groups of prime order. Our main result, supported by theoretical analysis and empirical verification, reveals the concentration of the gradient of the loss function around a fixed point, independent of the logarithm's base used. This concentration property leads to a restricted ability to learn the parity bit efficiently using gradient-based methods, irrespective of the complexity of the network architecture being trained. Our proof relies on Boas-Bellman inequality in inner product spaces and it involves establishing approximate orthogonality of discrete logarithm's parity bit functions through the spectral norm of certain matrices. Empirical experiments using a neural network-based approach further verify the limitations of gradient-based learning, demonstrating the decreasing success rate in predicting the parity bit as the group order increases.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.

Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as the graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many studies on extending deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks, graph recurrent neural networks, graph attention networks, graph generative networks, spatial-temporal graph convolutional networks, and hybrid forms of GNNs) are summarized, and key applications in power systems such as fault diagnosis, power prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.

This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from -- or the same as -- the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.

We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.