Ashish Khisti

We study channel simulation and distributed matching, two fundamental problems with several applications to machine learning, using a recently introduced generalization of the standard rejection sampling (RS) algorithm known as Ensemble Rejection Sampling (ERS). For channel simulation, we propose a new coding scheme based on ERS that achieves a near-optimal coding rate. In this process, we demonstrate that standard RS can also achieve a near-optimal coding rate and generalize the result of Braverman and Garg (2014) to the continuous alphabet setting. Next, as our main contribution, we present a distributed matching lemma for ERS, which serves as the rejection sampling counterpart to the Poisson Matching Lemma (PML) introduced by Li and Anantharam (2021). Our result also generalizes a recent work on importance matching lemma (Phan et al, 2024) and, to our knowledge, is the first result on distributed matching in the family of rejection sampling schemes where the matching probability is close to PML. We demonstrate the practical significance of our approach over prior works by applying it to distributed compression. The effectiveness of our proposed scheme is validated through experiments involving synthetic Gaussian sources and distributed image compression using the MNIST dataset.

In the context of lossy compression, Blau & Michaeli [1] adopt a mathematical notion of perceptual quality and define the information rate-distortion-perception function, generalizing the classical rate-distortion tradeoff. We consider the notion of universal representations in which one may fix a rate and an encoder then vary the decoder to achieve any point within a collection of distortion and perception constraints. We prove that the corresponding information-theoretic universal rate-distortion-perception function is operationally achievable in an approximate sense. Under MSE distortion, we show that the entire distortion-perception tradeoff of a Gaussian source can be achieved by a single encoder of the same rate asymptotically. We then characterize the achievable distortion-perception region for a fixed representation in the case of arbitrary distributions, and identify conditions under which the aforementioned results continue to hold approximately. Finally, we extend our notion of universality to the case where the rate is no longer fixed and additional bits can be sent at a second stage, generalizing the classical theory of successive refinement [2] with perception constraints. This motivates the study of practical constructions that are approximately universal across the RDP tradeoff, thereby alleviating the need to design a new encoder for each objective. We provide experimental results on MNIST and SVHN suggesting that on image compression tasks, the operational tradeoffs achieved by machine learning models with a fixed encoder suffer only a small penalty when compared to their variable encoder counterparts.

This survey article focuses on the emerging connections between machine learning and data compression. While the fundamental limits of classical (lossy) data compression are well-established through rate-distortion theory, recent advancements have uncovered new theoretical analyses and application areas inspired by machine learning. We review recent works on task-based and goal-oriented compression, rate-distortion-perception theory, and compression for estimation and inference. Deep learning-based approaches have provided natural, data-driven methods for compression. Accordingly, we survey recent efforts in applying deep learning techniques to task-based or goal-oriented compression, as well as image/video compression and transmission. Additionally, we discuss the potential use of large language models for text compression. Finally, we outline future research directions in this promising field.

A key operation in federated learning is the aggregation of gradient vectors generated by individual client nodes. We develop a method based on multiparty homomorphic encryption (MPHE) that enables the central node to compute this aggregate, while receiving only encrypted version of each individual gradients. Towards this end, we extend classical MPHE methods so that the decryption of the aggregate vector can be successful even when only a subset of client nodes are available. This is accomplished by introducing a secret-sharing step during the setup phase of MPHE when the public encryption key is generated. We develop conditions on the parameters of the MPHE scheme that guarantee correctness of decryption and (computational) security. We explain how our method can be extended to accommodate client nodes that do not participate during the setup phase. We also propose a compression scheme for gradient vectors at each client node that can be readily combined with our MPHE scheme and perform the associated convergence analysis. We discuss the advantages of our proposed scheme with other approaches based on secure multi-party computation. Finally we discuss a practical implementation of our system, compare the performance of our system with different approaches, and demonstrate that by suitably combining compression with encryption the overhead over baseline schemes is rather small.

This paper studies the rate-distortion-perception (RDP) tradeoff for a Gaussian vector source coding problem where the goal is to compress the multi-component source subject to distortion and perception constraints. Specifically, the RDP setting with either the Kullback-Leibler (KL) divergence or Wasserstein-2 metric as the perception loss function is examined, and it is shown that for Gaussian vector sources, jointly Gaussian reconstructions are optimal. We further demonstrate that the optimal tradeoff can be expressed as an optimization problem, which can be explicitly solved. An interesting property of the optimal solution is as follows. Without the perception constraint, the traditional reverse water-filling solution for characterizing the rate-distortion (RD) tradeoff of a Gaussian vector source states that the optimal rate allocated to each component depends on a constant, called the water level. If the variance of a specific component is below the water level, it is assigned a zero compression rate. However, with active distortion and perception constraints, we show that the optimal rates allocated to the different components are always positive. Moreover, the water levels that determine the optimal rate allocation for different components are unequal. We further treat the special case of perceptually perfect reconstruction and study its RDP function in the high-distortion and low-distortion regimes to obtain insight to the structure of the optimal solution.

This paper investigates a novel lossy compression framework operating under logarithmic loss, designed to handle situations where the reconstruction distribution diverges from the source distribution. This framework is especially relevant for applications that require joint compression and retrieval, and in scenarios involving distributional shifts due to processing. We show that the proposed formulation extends the classical minimum entropy coupling framework by integrating a bottleneck, allowing for a controlled degree of stochasticity in the coupling. We explore the decomposition of the Minimum Entropy Coupling with Bottleneck (MEC-B) into two distinct optimization problems: Entropy-Bounded Information Maximization (EBIM) for the encoder, and Minimum Entropy Coupling (MEC) for the decoder. Through extensive analysis, we provide a greedy algorithm for EBIM with guaranteed performance, and characterize the optimal solution near functional mappings, yielding significant theoretical insights into the structural complexity of this problem. Furthermore, we illustrate the practical application of MEC-B through experiments in Markov Coding Games (MCGs) under rate limits. These games simulate a communication scenario within a Markov Decision Process, where an agent must transmit a compressed message from a sender to a receiver through its actions. Our experiments highlight the trade-offs between MDP rewards and receiver accuracy across various compression rates, showcasing the efficacy of our method compared to conventional compression baseline.

This paper studies the rate-distortion-perception (RDP) tradeoff for a memoryless source model in the asymptotic limit of large block-lengths. The perception measure is based on a divergence between the distributions of the source and reconstruction sequences conditioned on the encoder output, first proposed by Mentzer et al. We consider the case when there is no shared randomness between the encoder and the decoder and derive, for the case of discrete memoryless sources, a single-letter characterization of the RDP function. This is in contrast to the marginal-distribution metric case (introduced by Blau and Michaeli), whose RDP characterization remains open when there is no shared randomness. The achievability scheme is based on lossy source coding with a posterior reference map. For the case of continuous valued sources under the squared error distortion measure and the squared quadratic Wasserstein perception measure, we also derive a single-letter characterization and show that the decoder can be restricted to a noise-adding mechanism. Interestingly, the RDP function characterized for the case of zero perception loss coincides with that of the marginal metric and further zero perception loss can be achieved with a 3-dB penalty in minimum distortion. Finally we specialize to the case of Gaussian sources, and derive the RDP function for Gaussian vector case and propose a reverse water-filling type solution. We also partially characterize the RDP function for a mixture of Gaussian vector sources.

Parameter-Efficient Fine-Tuning (PEFT) has risen as an innovative training strategy that updates only a select few model parameters, significantly lowering both computational and memory demands. PEFT also helps to decrease data transfer in federated learning settings, where communication depends on the size of updates. In this work, we explore the constraints of previous studies that integrate a well-known PEFT method named LoRA with federated fine-tuning, then introduce RoLoRA, a robust federated fine-tuning framework that utilizes an alternating minimization approach for LoRA, providing greater robustness against decreasing fine-tuning parameters and increasing data heterogeneity. Our results indicate that RoLoRA not only presents the communication benefits but also substantially enhances the robustness and effectiveness in multiple federated fine-tuning scenarios.

This paper studies the transmission of a stream of data packets through a multi-hop multi-link communication network. The source generate sequential source packets and transmits them through a network to a destination. Each intermediary node is allowed to perform any processing operation in order to successfully forward the message to the destination. Each link connecting two nodes is subject to an adversarial packet erasure channel, where the number of erasures is limited. The destination must recover each source packet within a delay deadline, otherwise that packet is considered lost. The particular case when each hop consists of only one link has been studied by Domanovitz et. al in [1]. We extend this work to the multi-link scenario by multiplexing multiple copies of streaming codes in [1] and optimizing the rate using a linear programming framework. We also demonstrate how our framework can be naturally extended when there is a different propagation delay on each link. Numerical results demonstrate that our proposed approach provides significant improvements over baseline schemes.We further demonstrate that our proposed scheme also provides improved audio quality over baseline schemes in experiments involving Gilbert-Elliott channels.

In the context of prediction-as-a-service, concerns about the privacy of the data and the model have been brought up and tackled via secure inference protocols. These protocols are built up by using single or multiple cryptographic tools designed under a variety of different security assumptions. In this paper, we introduce SECO, a secure inference protocol that enables a user holding an input data vector and multiple server nodes deployed with a split neural network model to collaboratively compute the prediction, without compromising either party's data privacy. We extend prior work on secure inference that requires the entire neural network model to be located on a single server node, to a multi-server hierarchy, where the user communicates to a gateway server node, which in turn communicates to remote server nodes. The inference task is split across the server nodes and must be performed over an encrypted copy of the data vector. We adopt multiparty homomorphic encryption and multiparty garbled circuit schemes, making the system secure against dishonest majority of semi-honest servers as well as protecting the partial model structure from the user. We evaluate SECO on multiple models, achieving the reduction of computation and communication cost for the user, making the protocol applicable to user's devices with limited resources.