Andrea J. Goldsmith

Alon Kipnis, Yonina C. Eldar, Andrea J. Goldsmith

Processing, storing and communicating information that originates as an analog signal involves conversion of this information to bits. This conversion can be described by the combined effect of sampling and quantization, as illustrated in Fig. 1. The digital representation is achieved by first sampling the analog signal so as to represent it by a set of discrete-time samples and then quantizing these samples to a finite number of bits. Traditionally, these two operations are considered separately. The sampler is designed to minimize information loss due to sampling based on characteristics of the continuous-time input. The quantizer is designed to represent the samples as accurately as possible, subject to a constraint on the number of bits that can be used in the representation. The goal of this article is to revisit this paradigm by illuminating the dependency between these two operations. In particular, we explore the requirements on the sampling system subject to constraints on the available number of bits for storing, communicating or processing the analog information.

Michal Yemini, Rajarshi Saha, Emre Ozfatura et al.

We present a semi-decentralized federated learning algorithm wherein clients collaborate by relaying their neighbors' local updates to a central parameter server (PS). At every communication round to the PS, each client computes a local consensus of the updates from its neighboring clients and eventually transmits a weighted average of its own update and those of its neighbors to the PS. We appropriately optimize these averaging weights to ensure that the global update at the PS is unbiased and to reduce the variance of the global update at the PS, consequently improving the rate of convergence. Numerical simulations substantiate our theoretical claims and demonstrate settings with intermittent connectivity between the clients and the PS, where our proposed algorithm shows an improved convergence rate and accuracy in comparison with the federated averaging algorithm.

Rajarshi Saha, Mohamed Seif, Michal Yemini et al.

This work considers the problem of Distributed Mean Estimation (DME) over networks with intermittent connectivity, where the goal is to learn a global statistic over the data samples localized across distributed nodes with the help of a central server. To mitigate the impact of intermittent links, nodes can collaborate with their neighbors to compute local consensus which they forward to the central server. In such a setup, the communications between any pair of nodes must satisfy local differential privacy constraints. We study the tradeoff between collaborative relaying and privacy leakage due to the additional data sharing among nodes and, subsequently, propose a novel differentially private collaborative algorithm for DME to achieve the optimal tradeoff. Finally, we present numerical simulations to substantiate our theoretical findings.

Mohamed Seif, Atsutse Kludze, Yasaman Ghasempour et al.

Explicit channel state information (CSI) feedback in IEEE~802.11 conveys \emph{transmit beamforming directions} by reporting quantized Givens rotation and phase angles that parametrize the right-singular subspace of the channel matrix. Because these angles encode fine-grained spatial signatures of the propagation environment, recent work have shown that plaintext CSI feedback can inadvertently reveal user activity, identity, and location to passive eavesdroppers. In this work, we introduce a standards-compatible \emph{differentially private (DP) quantization mechanism} that replaces deterministic angular quantization with an $\varepsilon$-DP stochastic quantizer applied directly to the Givens parameters of the transmit beamforming matrix. The mechanism preserves the 802.11 feedback structure, admits closed-form sensitivity bounds for the angular representation, and enables principled privacy calibration. Numerical simulations demonstrate strong privacy guarantees with minimal degradation in beamforming performance.

Liyan Xie, Muhammad Siddeek, Mohamed Seif et al.

Watermarking has become a key technique for proprietary language models, enabling the distinction between AI-generated and human-written text. However, in many real-world scenarios, LLM-generated content may undergo post-generation edits, such as human revisions or even spoofing attacks, making it critical to detect and localize such modifications. In this work, we introduce a new task: detecting post-generation edits locally made to watermarked LLM outputs. To this end, we propose a combinatorial pattern-based watermarking framework, which partitions the vocabulary into disjoint subsets and embeds the watermark by enforcing a deterministic combinatorial pattern over these subsets during generation. We accompany the combinatorial watermark with a global statistic that can be used to detect the watermark. Furthermore, we design lightweight local statistics to flag and localize potential edits. We introduce two task-specific evaluation metrics, Type-I error rate and detection accuracy, and evaluate our method on open-source LLMs across a variety of editing scenarios, demonstrating strong empirical performance in edit localization.

Rajarshi Saha, Mohamed Seif, Michal Yemini et al.

We consider the problem of privately estimating the mean of vectors distributed across different nodes of an unreliable wireless network, where communications between nodes can fail intermittently. We adopt a semi-decentralized setup, wherein to mitigate the impact of intermittently connected links, nodes can collaborate with their neighbors to compute a local consensus, which they relay to a central server. In such a setting, the communications between any pair of nodes must ensure that the privacy of the nodes is rigorously maintained to prevent unauthorized information leakage. We study the tradeoff between collaborative relaying and privacy leakage due to the data sharing among nodes and, subsequently, propose PriCER: Private Collaborative Estimation via Relaying -- a differentially private collaborative algorithm for mean estimation to optimize this tradeoff. The privacy guarantees of PriCER arise (i) implicitly, by exploiting the inherent stochasticity of the flaky network connections, and (ii) explicitly, by adding Gaussian perturbations to the estimates exchanged by the nodes. Local and central privacy guarantees are provided against eavesdroppers who can observe different signals, such as the communications amongst nodes during local consensus and (possibly multiple) transmissions from the relays to the central server. We substantiate our theoretical findings with numerical simulations. Our implementation is available at https://github.com/rajarshisaha95/private-collaborative-relaying.

Rajarshi Saha, Mert Pilanci, Andrea J. Goldsmith

We study first-order optimization algorithms under the constraint that the descent direction is quantized using a pre-specified budget of $R$-bits per dimension, where $R \in (0 ,\infty)$. We propose computationally efficient optimization algorithms with convergence rates matching the information-theoretic performance lower bounds for: (i) Smooth and Strongly-Convex objectives with access to an Exact Gradient oracle, as well as (ii) General Convex and Non-Smooth objectives with access to a Noisy Subgradient oracle. The crux of these algorithms is a polynomial complexity source coding scheme that embeds a vector into a random subspace before quantizing it. These embeddings are such that with high probability, their projection along any of the canonical directions of the transform space is small. As a consequence, quantizing these embeddings followed by an inverse transform to the original space yields a source coding method with optimal covering efficiency while utilizing just $R$-bits per dimension. Our algorithms guarantee optimality for arbitrary values of the bit-budget $R$, which includes both the sub-linear budget regime ($R < 1$), as well as the high-budget regime ($R \geq 1$), while requiring $O\left(n^2\right)$ multiplications, where $n$ is the dimension. We also propose an efficient relaxation of this coding scheme using Hadamard subspaces that requires a near-linear time, i.e., $O\left(n \log n\right)$ additions.Furthermore, we show that the utility of our proposed embeddings can be extended to significantly improve the performance of gradient sparsification schemes. Numerical simulations validate our theoretical claims. Our implementations are available at https://github.com/rajarshisaha95/DistOptConstrComm.

Mohamed Seif, Yuqi Nie, Andrea J. Goldsmith et al.

Collaborative inference among multiple wireless edge devices has the potential to significantly enhance Artificial Intelligence (AI) applications, particularly for sensing and computer vision. This approach typically involves a three-stage process: a) data acquisition through sensing, b) feature extraction, and c) feature encoding for transmission. However, transmitting the extracted features poses a significant privacy risk, as sensitive personal data can be exposed during the process. To address this challenge, we propose a novel privacy-preserving collaborative inference mechanism, wherein each edge device in the network secures the privacy of extracted features before transmitting them to a central server for inference. Our approach is designed to achieve two primary objectives: 1) reducing communication overhead and 2) ensuring strict privacy guarantees during feature transmission, while maintaining effective inference performance. Additionally, we introduce an over-the-air pooling scheme specifically designed for classification tasks, which provides formal guarantees on the privacy of transmitted features and establishes a lower bound on classification accuracy.

Antti Koskela, Mohamed Seif, Andrea J. Goldsmith

We investigate privacy-preserving spectral clustering for community detection within stochastic block models (SBMs). Specifically, we focus on edge differential privacy (DP) and propose private algorithms for community recovery. Our work explores the fundamental trade-offs between the privacy budget and the accurate recovery of community labels. Furthermore, we establish information-theoretic conditions that guarantee the accuracy of our methods, providing theoretical assurances for successful community recovery under edge DP.

Mohamed Seif, Malcolm Egan, Andrea J. Goldsmith et al.

AI-based sensing at wireless edge devices has the potential to significantly enhance Artificial Intelligence (AI) applications, particularly for vision and perception tasks such as in autonomous driving and environmental monitoring. AI systems rely both on efficient model learning and inference. In the inference phase, features extracted from sensing data are utilized for prediction tasks (e.g., classification or regression). In edge networks, sensors and model servers are often not co-located, which requires communication of features. As sensitive personal data can be reconstructed by an adversary, transformation of the features are required to reduce the risk of privacy violations. While differential privacy mechanisms provide a means of protecting finite datasets, protection of individual features has not been addressed. In this paper, we propose a novel framework for privacy-preserving AI-based sensing, where devices apply transformations of extracted features before transmission to a model server.

Mohamed Seif, Antti Koskela, H. Vincent Poor et al.

We study the problem of spectral graph clustering under edge differential privacy (DP). Specifically, we develop three mechanisms: (i) graph perturbation via randomized edge flipping combined with adjacency matrix shuffling, which enforces edge privacy while preserving key spectral properties of the graph. Importantly, shuffling considerably amplifies the guarantees: whereas flipping edges with a fixed probability alone provides only a constant epsilon edge DP guarantee as the number of nodes grows, the shuffled mechanism achieves (epsilon, delta) edge DP with parameters that tend to zero as the number of nodes increase; (ii) private graph projection with additive Gaussian noise in a lower-dimensional space to reduce dimensionality and computational complexity; and (iii) a noisy power iteration method that distributes Gaussian noise across iterations to ensure edge DP while maintaining convergence. Our analysis provides rigorous privacy guarantees and a precise characterization of the misclassification error rate. Experiments on synthetic and real-world networks validate our theoretical analysis and illustrate the practical privacy-utility trade-offs.

Michal Yemini, Rajarshi Saha, Emre Ozfatura et al.

Intermittent connectivity of clients to the parameter server (PS) is a major bottleneck in federated edge learning frameworks. The lack of constant connectivity induces a large generalization gap, especially when the local data distribution amongst clients exhibits heterogeneity. To overcome intermittent communication outages between clients and the central PS, we introduce the concept of collaborative relaying wherein the participating clients relay their neighbors' local updates to the PS in order to boost the participation of clients with poor connectivity to the PS. We propose a semi-decentralized federated learning framework in which at every communication round, each client initially computes a local consensus of a subset of its neighboring clients' updates, and eventually transmits to the PS a weighted average of its own update and those of its neighbors'. We appropriately optimize these local consensus weights to ensure that the global update at the PS is unbiased with minimal variance - consequently improving the convergence rate. Numerical evaluations on the CIFAR-10 dataset demonstrate that our collaborative relaying approach outperforms federated averaging-based benchmarks for learning over intermittently-connected networks such as when the clients communicate over millimeter wave channels with intermittent blockages.

Rajarshi Saha, Mert Pilanci, Andrea J. Goldsmith

High-dimensional models often have a large memory footprint and must be quantized after training before being deployed on resource-constrained edge devices for inference tasks. In this work, we develop an information-theoretic framework for the problem of quantizing a linear regressor learned from training data $(\mathbf{X}, \mathbf{y})$, for some underlying statistical relationship $\mathbf{y} = \mathbf{X}\boldsymbolθ + \mathbf{v}$. The learned model, which is an estimate of the latent parameter $\boldsymbolθ \in \mathbb{R}^d$, is constrained to be representable using only $Bd$ bits, where $B \in (0, \infty)$ is a pre-specified budget and $d$ is the dimension. We derive an information-theoretic lower bound for the minimax risk under this setting and propose a matching upper bound using randomized embedding-based algorithms which is tight up to constant factors. The lower and upper bounds together characterize the minimum threshold bit-budget required to achieve a performance risk comparable to the unquantized setting. We also propose randomized Hadamard embeddings that are computationally efficient and are optimal up to a mild logarithmic factor of the lower bound. Our model quantization strategy can be generalized and we show its efficacy by extending the method and upper-bounds to two-layer ReLU neural networks for non-linear regression. Numerical simulations show the improved performance of our proposed scheme as well as its closeness to the lower bound.

Michal Yemini, Stephanie Gil, Andrea J. Goldsmith

We consider a centralized detection problem where sensors experience noisy measurements and intermittent connectivity to a centralized fusion center. The sensors collaborate locally within predefined sensor clusters and fuse their noisy sensor data to reach a common local estimate of the detected event in each cluster. The connectivity of each sensor cluster is intermittent and depends on the available communication opportunities of the sensors to the fusion center. Upon receiving the estimates from all the connected sensor clusters the fusion center fuses the received estimates to make a final determination regarding the occurrence of the event across the deployment area. We refer to this hybrid communication scheme as a \emph{cloud-cluster} architecture. We propose a method for optimizing the decision rule for each cluster and analyzing the expected detection performance resulting from our hybrid scheme. Our method is tractable and addresses the high computational complexity caused by heterogeneous sensors' and clusters' detection quality, heterogeneity in their communication opportunities, and non-convexity of the loss function. Our analysis shows that clustering the sensors provides resilience to noise in the case of low sensor communication probability with the cloud. For larger clusters, a steep improvement in detection performance is possible even for a low communication probability by using our cloud-cluster architecture.

Nir Shlezinger, Nariman Farsad, Yonina C. Eldar et al.

We present an introduction to model-based machine learning for communication systems. We begin by reviewing existing strategies for combining model-based algorithms and machine learning from a high level perspective, and compare them to the conventional deep learning approach which utilizes established deep neural network (DNN) architectures trained in an end-to-end manner. Then, we focus on symbol detection, which is one of the fundamental tasks of communication receivers. We show how the different strategies of conventional deep architectures, deep unfolding, and DNN-aided hybrid algorithms, can be applied to this problem. The last two approaches constitute a middle ground between purely model-based and solely DNN-based receivers. By focusing on this specific task, we highlight the advantages and drawbacks of each strategy, and present guidelines to facilitate the design of future model-based deep learning systems for communications.

Nir Shlezinger, Nariman Farsad, Yonina C. Eldar et al.

The design of methods for inference from time sequences has traditionally relied on statistical models that describe the relation between a latent desired sequence and the observed one. A broad family of model-based algorithms have been derived to carry out inference at controllable complexity using recursive computations over the factor graph representing the underlying distribution. An alternative model-agnostic approach utilizes machine learning (ML) methods. Here we propose a framework that combines model-based algorithms and data-driven ML tools for stationary time sequences. In the proposed approach, neural networks are developed to separately learn specific components of a factor graph describing the distribution of the time sequence, rather than the complete inference task. By exploiting stationary properties of this distribution, the resulting approach can be applied to sequences of varying temporal duration. Learned factor graph can be realized using compact neural networks that are trainable using small training sets, or alternatively, be used to improve upon existing deep inference systems. We present an inference algorithm based on learned stationary factor graphs, which learns to implement the sum-product scheme from labeled data, and can be applied to sequences of different lengths. Our experimental results demonstrate the ability of the proposed learned factor graphs to learn to carry out accurate inference from small training sets for sleep stage detection using the Sleep-EDF dataset, as well as for symbol detection in digital communications with unknown channels.

Nariman Farsad, Nir Shlezinger, Andrea J. Goldsmith et al.

The design of symbol detectors in digital communication systems has traditionally relied on statistical channel models that describe the relation between the transmitted symbols and the observed signal at the receiver. Here we review a data-driven framework to symbol detection design which combines machine learning (ML) and model-based algorithms. In this hybrid approach, well-known channel-model-based algorithms such as the Viterbi method, BCJR detection, and multiple-input multiple-output (MIMO) soft interference cancellation (SIC) are augmented with ML-based algorithms to remove their channel-model-dependence, allowing the receiver to learn to implement these algorithms solely from data. The resulting data-driven receivers are most suitable for systems where the underlying channel models are poorly understood, highly complex, or do not well-capture the underlying physics. Our approach is unique in that it only replaces the channel-model-based computations with dedicated neural networks that can be trained from a small amount of data, while keeping the general algorithm intact. Our results demonstrate that these techniques can yield near-optimal performance of model-based algorithms without knowing the exact channel input-output statistical relationship and in the presence of channel state information uncertainty.

Nir Shlezinger, Nariman Farsad, Yonina C. Eldar et al.

Many important schemes in signal processing and communications, ranging from the BCJR algorithm to the Kalman filter, are instances of factor graph methods. This family of algorithms is based on recursive message passing-based computations carried out over graphical models, representing a factorization of the underlying statistics. Consequently, in order to implement these algorithms, one must have accurate knowledge of the statistical model of the considered signals. In this work we propose to implement factor graph methods in a data-driven manner. In particular, we propose to use machine learning (ML) tools to learn the factor graph, instead of the overall system task, which in turn is used for inference by message passing over the learned graph. We apply the proposed approach to learn the factor graph representing a finite-memory channel, demonstrating the resulting ability to implement BCJR detection in a data-driven fashion. We demonstrate that the proposed system, referred to as BCJRNet, learns to implement the BCJR algorithm from a small training set, and that the resulting receiver exhibits improved robustness to inaccurate training compared to the conventional channel-model-based receiver operating under the same level of uncertainty. Our results indicate that by utilizing ML tools to learn factor graphs from labeled data, one can implement a broad range of model-based algorithms, which traditionally require full knowledge of the underlying statistics, in a data-driven fashion.

Yun Liao, Nariman Farsad, Nir Shlezinger et al.

This paper proposes to use a deep neural network (DNN)-based symbol detector for mmWave systems such that CSI acquisition can be bypassed. In particular, we consider a sliding bidirectional recurrent neural network (BRNN) architecture that is suitable for the long memory length of typical mmWave channels. The performance of the DNN detector is evaluated in comparison to that of the Viterbi detector. The results show that the performance of the DNN detector is close to that of the optimal Viterbi detector with perfect CSI, and that it outperforms the Viterbi algorithm with CSI estimation error. Further experiments show that the DNN detector is robust to a wide range of noise levels and varying channel conditions, and that a pretrained detector can be reliably applied to different mmWave channel realizations with minimal overhead.

Nir Shlezinger, Nariman Farsad, Yonina C. Eldar et al.

Symbol detection plays an important role in the implementation of digital receivers. In this work, we propose ViterbiNet, which is a data-driven symbol detector that does not require channel state information (CSI). ViterbiNet is obtained by integrating deep neural networks (DNNs) into the Viterbi algorithm. We identify the specific parts of the Viterbi algorithm that are channel-model-based, and design a DNN to implement only those computations, leaving the rest of the algorithm structure intact. We then propose a meta-learning based approach to train ViterbiNet online based on recent decisions, allowing the receiver to track dynamic channel conditions without requiring new training samples for every coherence block. Our numerical evaluations demonstrate that the performance of ViterbiNet, which is ignorant of the CSI, approaches that of the CSI-based Viterbi algorithm, and is capable of tracking time-varying channels without needing instantaneous CSI or additional training data. Moreover, unlike conventional Viterbi detection, ViterbiNet is robust to CSI uncertainty, and it can be reliably implemented in complex channel models with constrained computational burden. More broadly, our results demonstrate the conceptual benefit of designing communication systems to that integrate DNNs into established algorithms.

Yuxin Chen, Changho Suh, Andrea J. Goldsmith

This paper is concerned with jointly recovering $n$ node-variables $\left\{ x_{i}\right\}_{1\leq i\leq n}$ from a collection of pairwise difference measurements. Imagine we acquire a few observations taking the form of $x_{i}-x_{j}$; the observation pattern is represented by a measurement graph $\mathcal{G}$ with an edge set $\mathcal{E}$ such that $x_{i}-x_{j}$ is observed if and only if $(i,j)\in\mathcal{E}$. To account for noisy measurements in a general manner, we model the data acquisition process by a set of channels with given input/output transition measures. Employing information-theoretic tools applied to channel decoding problems, we develop a \emph{unified} framework to characterize the fundamental recovery criterion, which accommodates general graph structures, alphabet sizes, and channel transition measures. In particular, our results isolate a family of \emph{minimum} \emph{channel divergence measures} to characterize the degree of measurement corruption, which together with the size of the minimum cut of $\mathcal{G}$ dictates the feasibility of exact information recovery. For various homogeneous graphs, the recovery condition depends almost only on the edge sparsity of the measurement graph irrespective of other graphical metrics; alternatively, the minimum sample complexity required for these graphs scales like \[ \text{minimum sample complexity }\asymp\frac{n\log n}{\mathsf{Hel}_{1/2}^{\min}} \] for certain information metric $\mathsf{Hel}_{1/2}^{\min}$ defined in the main text, as long as the alphabet size is not super-polynomial in $n$. We apply our general theory to three concrete applications, including the stochastic block model, the outlier model, and the haplotype assembly problem. Our theory leads to order-wise tight recovery conditions for all these scenarios.