Coded computing has emerged as a promising framework for tackling significant challenges in large-scale distributed computing, including the presence of slow, faulty, or compromised servers. In this approach, each worker node processes a combination of the data, rather than the raw data itself. The final result then is decoded from the collective outputs of the worker nodes. However, there is a significant gap between current coded computing approaches and the broader landscape of general distributed computing, particularly when it comes to machine learning workloads. To bridge this gap, we propose a novel foundation for coded computing, integrating the principles of learning theory, and developing a framework that seamlessly adapts with machine learning applications. In this framework, the objective is to find the encoder and decoder functions that minimize the loss function, defined as the mean squared error between the estimated and true values. Facilitating the search for the optimum decoding and functions, we show that the loss function can be upper-bounded by the summation of two terms: the generalization error of the decoding function and the training error of the encoding function. Focusing on the second-order Sobolev space, we then derive the optimal encoder and decoder.

We propose an efficient encrypted policy synthesis to develop privacy-preserving model-based reinforcement learning. We first demonstrate that the relative-entropy-regularized reinforcement learning framework offers a computationally convenient linear and ``min-free'' structure for value iteration, enabling a direct and efficient integration of fully homomorphic encryption with bootstrapping into policy synthesis. Convergence and error bounds are analyzed as encrypted policy synthesis propagates errors under the presence of encryption-induced errors including quantization and bootstrapping. Theoretical analysis is validated by numerical simulations. Results demonstrate the effectiveness of the RERL framework in integrating FHE for encrypted policy synthesis.

In the past years, predictive process monitoring (PPM) techniques based on artificial neural networks have evolved as a method to monitor the future behavior of business processes. Existing approaches mostly focus on interpreting the processes as sequences, so-called traces, and feeding them to neural architectures designed to operate on sequential data such as recurrent neural networks (RNNs) or transformers. In this study, we investigate an alternative way to perform PPM: by transforming each process in its directly-follows-graph (DFG) representation we are able to apply graph neural networks (GNNs) for the prediction tasks. By this, we aim to develop models that are more suitable for complex processes that are long and contain an abundance of loops. In particular, we present different ways to create DFG representations depending on the particular GNN we use. The tested GNNs range from classical node-based to novel edge-based architectures. Further, we investigate the possibility of using multi-graphs. By these steps, we aim to design graph representations that minimize the information loss when transforming traces into graphs.

Coded computing has demonstrated promising results in addressing straggler resiliency in distributed computing systems. However, most coded computing schemes are designed for exact computation, requiring the number of responding servers to exceed a certain recovery threshold. Additionally, these schemes are tailored for highly structured functions. Recently, new coded computing schemes for general computing functions, where exact computation is replaced with approximate computation, have emerged. In these schemes, the availability of additional results corresponds to more accurate estimation of computational tasks. This flexibility introduces new questions that need to be addressed. This paper addresses the practically important scenario in the context of general coded computing, where each server may become a straggler with a probability $p$, independently from others. We theoretically analyze the approximation error of two existing general coded computing schemes: Berrut Approximate Coded Computing (BACC) and Learning Theoretic Coded Computing (LeTCC). Under the probabilistic straggler configuration, we demonstrate that the average approximation error for BACC and LeTCC converge to zero with the rate of at least $\mathcal{O}(\log^3_{\frac{1}{p}}(N)\cdot{N^{-3}})$ and $\mathcal{O}(\log^4_{\frac{1}{p}}(N)\cdot{N^{-2}})$, respectively. This is perhaps surprising, as earlier results does not indicate a convergence when the number of stragglers scales with the total number of servers $N$. However, in this case, despite the average number of stragglers being $Np$, the independence of servers in becoming stragglers allows the approximation error to converge to zero. These theoretical results are validated through experiments on various computing functions, including deep neural networks.

Coded computing has emerged as a promising framework for tackling significant challenges in large-scale distributed computing, including the presence of slow, faulty, or compromised servers. In this approach, each worker node processes a combination of the data, rather than the raw data itself. The final result then is decoded from the collective outputs of the worker nodes. However, there is a significant gap between current coded computing approaches and the broader landscape of general distributed computing, particularly when it comes to machine learning workloads. To bridge this gap, we propose a novel foundation for coded computing, integrating the principles of learning theory, and developing a new framework that seamlessly adapts with machine learning applications. In this framework, the objective is to find the encoder and decoder functions that minimize the loss function, defined as the mean squared error between the estimated and true values. Facilitating the search for the optimum decoding and functions, we show that the loss function can be upper-bounded by the summation of two terms: the generalization error of the decoding function and the training error of the encoding function. Focusing on the second-order Sobolev space, we then derive the optimal encoder and decoder. We show that in the proposed solution, the mean squared error of the estimation decays with the rate of $O(S^4 N^{-3})$ and $O(S^{\frac{8}{5}}N^{\frac{-3}{5}})$ in noiseless and noisy computation settings, respectively, where $N$ is the number of worker nodes with at most $S$ slow servers (stragglers). Finally, we evaluate the proposed scheme on inference tasks for various machine learning models and demonstrate that the proposed framework outperforms the state-of-the-art in terms of accuracy and rate of convergence.

Subword tokenization is a key part of many NLP pipelines. However, little is known about why some tokenizer and hyperparameter combinations lead to better downstream model performance than others. We propose that good tokenizers lead to \emph{efficient} channel usage, where the channel is the means by which some input is conveyed to the model and efficiency can be quantified in information-theoretic terms as the ratio of the Shannon entropy to the maximum possible entropy of the token distribution. Yet, an optimal encoding according to Shannon entropy assigns extremely long codes to low-frequency tokens and very short codes to high-frequency tokens. Defining efficiency in terms of R\'enyi entropy, on the other hand, penalizes distributions with either very high or very low-frequency tokens. In machine translation, we find that across multiple tokenizers, the R\'enyi entropy with $\alpha = 2.5$ has a very strong correlation with \textsc{Bleu}: $0.78$ in comparison to just $-0.32$ for compressed length.

In this paper, we consider high-dimensional stationary processes where a new observation is generated from a compressed version of past observations. The specific evolution is modeled by an encoder-decoder structure. We estimate the evolution with an encoder-decoder neural network and give upper bounds for the expected forecast error under specific structural and sparsity assumptions. The results are shown separately for conditions either on the absolutely regular mixing coefficients or the functional dependence measure of the observed process. In a quantitative simulation we discuss the behavior of the network estimator under different model assumptions. We corroborate our theory by a real data example where we consider forecasting temperature data.

This paper presents a generative approach to speech enhancement based on a recurrent variational autoencoder (RVAE). The deep generative speech model is trained using clean speech signals only, and it is combined with a nonnegative matrix factorization noise model for speech enhancement. We propose a variational expectation-maximization algorithm where the encoder of the RVAE is fine-tuned at test time, to approximate the distribution of the latent variables given the noisy speech observations. Compared with previous approaches based on feed-forward fully-connected architectures, the proposed recurrent deep generative speech model induces a posterior temporal dynamic over the latent variables, which is shown to improve the speech enhancement results.

In the field of machine learning, it is still a critical issue to identify and supervise the learned representation without manually intervention or intuition assistance to extract useful knowledge or serve for the latter tasks in machine learning. In this work, we focus on supervising the influential factors extracted by the variational autoencoder(VAE). The VAE is proposed to learn independent low dimension representation while facing the problem that sometimes pre-set factors are ignored. We argue that the mutual information of the input and each learned factor of the representation plays a necessary indicator. We find the VAE objective inclines to induce mutual information sparsity in factor dimension over the data intrinsic dimension and results in some non-influential factors whose function on data reconstruction could be ignored. We show mutual information also influences the lower bound of VAE's reconstruction error and latter classification task. To make such indicator applicable, we design an algorithm on calculating the mutual information for VAE and prove its consistency. Experimental results on Mnist, CelebA and Deap datasets show that mutual information can help determine influential factors, of which some are interpretable and can be used to further generation and classification tasks, and help discover the variant that connects with emotion on Deap dataset.