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  1. Low-capacity scenarios have become increasingly important in the technology of the In- ternet of Things (IoT) and the next generation of wireless networks. Such scenarios require efficient and reliable transmission over channels with an extremely small capacity. Within these constraints, the state-of-the-art coding techniques may not be directly applicable. More- over, the prior work on the finite-length analysis of optimal channel coding provides inaccurate predictions of the limits in the low-capacity regime. In this paper, we study channel coding at low capacity from two perspectives: fundamental limits at finite length and code construc- tions. We first specify what a low-capacity regime means. We then characterize finite-length fundamental limits of channel coding in the low-capacity regime for various types of channels, including binary erasure channels (BECs), binary symmetric channels (BSCs), and additive white Gaussian noise (AWGN) channels. From the code construction perspective, we charac- terize the optimal number of repetitions for transmission over binary memoryless symmetric (BMS) channels, in terms of the code blocklength and the underlying channel capacity, such that the capacity loss due to the repetition is negligible. Furthermore, it is shown that capacity- achieving polar codes naturally adopt the aforementioned optimal number of repetitions. 
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    Free, publicly-accessible full text available August 16, 2024
  2. Autoencoders are a popular model in many branches of machine learning and lossy data com- pression. However, their fundamental limits, the performance of gradient methods and the features learnt during optimization remain poorly under- stood, even in the two-layer setting. In fact, earlier work has considered either linear autoencoders or specific training regimes (leading to vanish- ing or diverging compression rates). Our paper addresses this gap by focusing on non-linear two- layer autoencoders trained in the challenging pro- portional regime in which the input dimension scales linearly with the size of the representation. Our results characterize the minimizers of the pop- ulation risk, and show that such minimizers are achieved by gradient methods; their structure is also unveiled, thus leading to a concise descrip- tion of the features obtained via training. For the special case of a sign activation function, our analysis establishes the fundamental limits for the lossy compression of Gaussian sources via (shal- low) autoencoders. Finally, while the results are proved for Gaussian data, numerical simulations on standard datasets display the universality of the theoretical predictions. 
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    Free, publicly-accessible full text available July 12, 2024
  3. Recent advances in text-to-image generative models provide the ability to generate high-quality images from short text descriptions. These foundation models, when pre-trained on billion-scale datasets, are effective for various downstream tasks with little or no further training. A natural question to ask is how such models may be adapted for image compression. We investigate several techniques in which the pre-trained models can be directly used to implement compression schemes targeting novel low rate regimes. We show how text descriptions can be used in conjunction with side information to generate high-fidelity reconstructions that preserve both semantics and spatial structure of the original. We demonstrate that at very low bit-rates, our method can significantly improve upon learned compressors in terms of perceptual and semantic fidelity, despite no end-to-end training. 
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    Free, publicly-accessible full text available July 4, 2024
  4. Free, publicly-accessible full text available June 25, 2024
  5. One of the primary challenges in large-scale distributed learning stems from stringent communication constraints. While several recent works address this challenge for static optimization problems, sequential decision-making under uncertainty has remained much less explored in this regard. Motivated by this gap, we introduce a new linear stochastic bandit formulation over a bit-constrained channel. Specifically, in our setup, an agent interacting with an environment transmits encoded estimates of an unknown model parameter to a server over a communication channel of finite capacity. The goal of the server is to take actions based on these estimates to minimize cumulative regret. To this end, we develop a novel and general algorithmic framework that hinges on two main components: (i) an adaptive encoding mechanism that exploits statistical concentration bounds, and (ii) a decision-making principle based on confidence sets that account for encoding errors. As our main result, we prove that when the unknown model is d-dimensional, a channel capacity of O(d) bits suffices to achieve order-optimal regret. We also establish that for the simpler unstructured multi-armed bandit problem, 1 bit channel capacity is sufficient for achieving optimal regret bounds. 
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    Free, publicly-accessible full text available June 6, 2024
  6. One of the primary challenges in large-scale distributed learning stems from stringent communication constraints. While several recent works address this challenge for static optimization problems, sequential decision-making under uncertainty has remained much less explored in this regard. Motivated by this gap, we introduce a new linear stochastic bandit formulation over a bit-constrained channel. Specifically, in our setup, an agent interacting with an environment transmits encoded estimates of an unknown model parameter to a server over a communication channel of finite capacity. The goal of the server is to take actions based on these estimates to minimize cumulative regret. To this end, we develop a novel and general algorithmic framework that hinges on two main components:(i) an adaptive encoding mechanism that exploits statistical concentration bounds, and (ii) a decision-making principle based on confidence sets that account for encoding errors. As our main result, we prove that when the unknown model is -dimensional, a channel capacity of bits suffices to achieve order-optimal regret. We also establish that for the simpler unstructured multi-armed bandit problem, bit channel capacity is sufficient for achieving optimal regret bounds. 
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  7. One of the primary challenges in large-scale distributed learning stems from stringent communication constraints. While several recent works address this challenge for static optimization problems, sequential decision-making under uncertainty has remained much less explored in this regard. Motivated by this gap, we introduce a new linear stochastic bandit formulation over a bit-constrained channel. Specifically, in our setup, an agent interacting with an environment transmits encoded estimates of an unknown model parameter to a server over a communication channel of finite capacity. The goal of the server is to take actions based on these estimates to minimize cumulative regret. To this end, we develop a novel and general algorithmic framework that hinges on two main components: (i) an adaptive encoding mechanism that exploits statistical concentration bounds, and (ii) a decision-making principle based on confidence sets that account for encoding errors. As our main result, we prove that when the unknown model is d-dimensional, a channel capacity of O(d) bits suffices to achieve order-optimal regret. We also establish that for the simpler unstructured multi-armed bandit problem, 1 bit channel capacity is sufficient for achieving optimal regret bounds. Keywords: Linear Bandits, Distributed Learning, Communication Constraints 
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  8. Federated learning is a distributed framework according to which a model is trained over a set of devices, while keeping data localized. This framework faces several systems-oriented challenges which include (i) communication bottleneck since a large number of devices upload their local updates to a parameter server, and (ii) scalability as the federated network consists of millions of devices. Due to these systems challenges as well as issues related to statistical heterogeneity of data and privacy concerns, designing a provably efficient federated learning method is of significant importance yet it remains challenging. In this paper, we present FedPAQ, a communication-efficient Federated Learning method with Periodic Averaging and Quantization. FedPAQ relies on three key features:(1) periodic averaging where models are updated locally at devices and only periodically averaged at the server;(2) partial device participation where only a fraction of devices participate in each round of the training; and (3) quantized message-passing where the edge nodes quantize their updates before uploading to the parameter server. These features address the communications and scalability challenges in federated learning. We also show that FedPAQ achieves near-optimal theoretical guarantees for strongly convex and non-convex loss functions and empirically demonstrate the communication-computation tradeoff provided by our method. 
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  9. Low-capacity scenarios have become increasingly important in the technology of Internet of Things (IoT) and the next generation of mobile networks. Such scenarios require efficient and reliable transmission of information over channels with an extremely small capacity. Within these constraints, the performance of state-of-the-art coding techniques is far from optimal in terms of either rate or complexity. Moreover, the current non-asymptotic laws of optimal channel coding provide inaccurate predictions for coding in the low-capacity regime. In this paper, we provide the first comprehensive study of channel coding in the low-capacity regime. We will investigate the fundamental non-asymptotic limits for channel coding as well as challenges that must be overcome for efficient code design in low-capacity scenarios. 
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