Large Language Models (LLMs), pre-trained on massive text corpora, exhibit remarkable human-level language understanding, reasoning, and decision-making abilities. However, they tend to memorize unwanted information, such as private or copyrighted content, raising significant privacy and legal concerns. Unlearning has emerged as a promising solution, but existing methods face a significant challenge of over-forgetting. This issue arises because they indiscriminately suppress the generation of all the tokens in forget samples, leading to a substantial loss of model utility. To overcome this challenge, we introduce the Targeted Information Forgetting (TIF) framework, which consists of (1) a flexible targeted information identifier designed to differentiate between unwanted words (UW) and general words (GW) in the forget samples, and (2) a novel Targeted Preference Optimization approach that leverages Logit Preference Loss to unlearn unwanted information associated with UW and Preservation Loss to retain general information in GW, effectively improving the unlearning process while mitigating utility degradation. Extensive experiments on the TOFU and MUSE benchmarks demonstrate that the proposed TIF framework enhances unlearning effectiveness while preserving model utility and achieving state-of-the-art results.

In geographical image segmentation, performance is often constrained by the limited availability of training data and a lack of generalizability, particularly for segmenting mobility infrastructure such as roads, sidewalks, and crosswalks. Vision foundation models like the Segment Anything Model (SAM), pre-trained on millions of natural images, have demonstrated impressive zero-shot segmentation performance, providing a potential solution. However, SAM struggles with geographical images, such as aerial and satellite imagery, due to its training being confined to natural images and the narrow features and textures of these objects blending into their surroundings. To address these challenges, we propose Geographical SAM (GeoSAM), a SAM-based framework that fine-tunes SAM using automatically generated multi-modal prompts. Specifically, GeoSAM integrates point prompts from a pre-trained task-specific model as primary visual guidance, and text prompts generated by a large language model as secondary semantic guidance, enabling the model to better capture both spatial structure and contextual meaning. GeoSAM outperforms existing approaches for mobility infrastructure segmentation in both familiar and completely unseen regions by at least 5% in mIoU, representing a significant leap in leveraging foundation models to segment mobility infrastructure, including both road and pedestrian infrastructure in geographical images. The source code is publicly available.

Membership Inference Attacks (MIAs) have recently been employed to determine whether a specific text was part of the pre-training data of Large Language Models (LLMs). However, existing methods often misinfer non-members as members, leading to a high false positive rate, or depend on additional reference models for probability calibration, which limits their practicality. To overcome these challenges, we introduce a novel framework called Automatic Calibration Membership Inference Attack (ACMIA), which utilizes a tunable temperature to calibrate output probabilities effectively. This approach is inspired by our theoretical insights into maximum likelihood estimation during the pre-training of LLMs. We introduce ACMIA in three configurations designed to accommodate different levels of model access and increase the probability gap between members and non-members, improving the reliability and robustness of membership inference. Extensive experiments on various open-source LLMs demonstrate that our proposed attack is highly effective, robust, and generalizable, surpassing state-of-the-art baselines across three widely used benchmarks. The source code is publicly available.

Vision Transformers (ViTs) have become prominent models for solving various vision tasks. However, the interpretability of ViTs has not kept pace with their promising performance. While there has been a surge of interest in developing post hoc solutions to explain ViTs’ outputs, these methods do not generalize to different downstream tasks and various transformer architectures. Furthermore, if ViTs are not properly trained with the given data and do not prioritize the region of interest, the post hoc methods become less effective. To overcome this limitation, we introduce a novel training procedure that inherently enhances ViT’s interpretability. Our interpretability-aware ViT (IA-ViT) draws inspiration from a fresh insight: both the class patch and image patches consistently generate predicted distributions and attention maps. IA-ViT is composed of a feature extractor, a predictor, and an interpreter, which are trained jointly with an interpretability-aware training objective. Consequently, the interpreter simulates the behavior of the predictor and provides a faithful explanation through its single-head self-attention mechanism. Our comprehensive experimental results demonstrate the effectiveness of IA-ViT in several image classification tasks, with both qualitative and quantitative evaluations of model performance and interpretability. Our code is available at: https://github.com/qiangyao1988/IA-ViT.

Segment Anything Model (SAM) is one of the pioneering prompt-based foundation models for image segmentation and has been rapidly adopted for various medical imaging applications. However, in clinical settings, cre-ating effective prompts is notably challenging and time-consuming, requiring the expertise of domain specialists such as physicians. This requirement significantly dimin-ishes SAM's primary advantage—its interactive capability with end users—in medical applications. Moreover, recent studies have indicated that SAM, originally designed for 2D natural images, performs suboptimally on 3D medical image segmentation tasks. This subpar performance is attributed to the domain gaps between natural and medical images and the disparities in spatial arrangements between 2D and 3D images, particularly in multi-organ segmentation applications. To overcome these challenges, we present a novel technique termed AutoProSAM. This method au-tomates 3D multi-organ CT-based segmentation by lever-aging SAM's foundational model capabilities without relying on domain experts for prompts. The approach utilizes parameter-efficient adaptation techniques to adapt SAMfor 3D medical imagery and incorporates an effective automatic prompt learning paradigm specific to this domain. By eliminating the need for manual prompts, it enhances SAM's capabilities for 3D medical image segmentation and achieves state-of-the-art (SOTA) performance in CT-based multi-organ segmentation tasks. The code is in this link.

In the diverse field of medical imaging, automatic segmentation has numerous applications and must handle a wide variety of input domains, such as different types of Computed Tomography (CT) scans and Magnetic Resonance (MR) images. This heterogeneity challenges automatic segmentation algorithms to maintain consistent performance across different modalities due to the requirement for spatially aligned and paired images. Typically, segmentation models are trained using a single modality, which limits their ability to generalize to other types of input data without employing transfer learning techniques. Additionally, leveraging complementary information from different modalities to enhance segmentation precision often necessitates substantial modifications to popular encoder-decoder designs, such as introducing multiple branched encoding or decoding paths for each modality. In this work, we propose a simple Multi-Modal Segmentation (MulModSeg) strategy to enhance medical image segmentation across multiple modalities, specifically CT and MR. It incorporates two key designs: a modality-conditioned text embedding framework via a frozen text encoder that adds modality awareness to existing segmentation frameworks without significant structural modifications or computational overhead, and an alternating training procedure that facilitates the integration of essential features from unpaired CT and MR inputs. Through extensive experiments with both Fully Convolutional Network and Transformer-based backbones, MulModSeg consistently outperforms previous methods in segmenting abdominal multi-organ and cardiac substructures for both CT and MR modalities. The code is available in this link.

Federated learning (FL) enables multiple clients to collaboratively train machine learning models without revealing their private training data. In conventional FL, the system follows the server-assisted architecture (server-assisted FL), where the training process is coordinated by a central server. However, the server-assisted FL framework suffers from poor scalability due to a communication bottleneck at the server, and trust dependency issues. To address challenges, decentralized federated learning (DFL) architecture has been proposed to allow clients to train models collaboratively in a serverless and peer-to-peer manner. However, due to its fully decentralized nature, DFL is highly vulnerable to poisoning attacks, where malicious clients could manipulate the system by sending carefully-crafted local models to their neighboring clients. To date, only a limited number of Byzantine-robust DFL methods have been proposed, most of which are either communication-inefficient or remain vulnerable to advanced poisoning attacks. In this paper, we propose a new algorithm called BALANCE (Byzantine-robust averaging through local similarity in decentralization) to defend against poisoning attacks in DFL. In BALANCE, each client leverages its own local model as a similarity reference to determine if the received model is malicious or benign. We establish the theoretical convergence guarantee for BALANCE under poisoning attacks in both strongly convex and non-convex settings. Furthermore, the convergence rate of BALANCE under poisoning attacks matches those of the state-of-the-art counterparts in Byzantine-free settings. Extensive experiments also demonstrate that BALANCE outperforms existing DFL methods and effectively defends against poisoning attacks.

Existing works in federated learning (FL) often assume either full client or uniformly distributed client participation. However, in reality, some clients may never participate in FL training (aka incomplete client participation) due to various system heterogeneity factors. A popular solution is the server-assisted federated learning (SA-FL) framework, where the server uses an auxiliary dataset. Despite empirical evidence of SA-FL’s effectiveness in addressing incomplete client participation, theoretical understanding of SA-FL is lacking. Furthermore, the effects of incomplete client participation in conventional FL are poorly understood. This motivates us to rigorously investigate SA-FL. Toward this end, we first show that conventional FL is not PAC-learnable under incomplete client participation in the worst case. Then, we show that the PAC-learnability of FL with incomplete client participation can indeed be revived by SA-FL, which theoretically justifies the use of SA-FL for the first time. Lastly, to provide practical guidance for SA-FL training under incomplete client participation, we propose the SAFARI (server-assisted federated averaging) algorithm that enjoys the same linear convergence speedup guarantees as classic FL with ideal client participation assumptions, offering the first SA-FL algorithm with convergence guarantee. Extensive experiments on different datasets show SAFARI significantly improves the performance under incomplete client participation.

In this work, we propose algorithms for solving a class of Bilevel Optimization (BLO) problems, with applications in areas such as signal processing, networking and machine learning. Specifically, we develop a novel barrier-based gradient approximation algorithm that transforms the constrained BLO problem to a problem with only linear equality constraints in the LL task. For the reformulated problem, we compute the implicit gradient and develop a gradient-based scheme, involving only a single gradient descent step and the (approximate) solution of the linearly constrained strongly convex LL task at each iteration. We establish, under certain assumptions, the non-asymptotic convergence guarantees of the proposed method to stationary points. Finally, we perform a number of experiments that show the potential of the proposed algorithm.

This work develops analysis and algorithms for solving a class of bilevel optimization problems where the lower-level (LL) problems have linear constraints. Most of the existing approaches for constrained bilevel problems rely on value function-based approximate reformulations, which suffer from issues such as non-convex and non-differentiable constraints. In contrast, in this work, we develop an implicit gradient-based approach, which is easy to implement, and is suitable for machine learning applications. We first provide an in-depth understanding of the problem, by showing that the implicit objective for such problems is in general non-differentiable. However, if we add some small (linear) perturbation to the LL objective, the resulting implicit objective becomes differentiable almost surely. This key observation opens the door for developing (deterministic and stochastic) gradient-based algorithms similar to the state-of-the-art ones for unconstrained bi-level problems. We show that when the implicit function is assumed to be strongly-convex, convex, and weakly-convex, the resulting algorithms converge with guaranteed rate. Finally, we experimentally corroborate the theoretical findings and evaluate the performance of the proposed framework on numerical and adversarial learning problems.

In recent years, decentralized bilevel optimization has gained significant attention thanks to its versatility in modeling a wide range of multi-agent learning problems, such as multi-agent reinforcement learning and multi-agent meta-learning. However, one unexplored and fundamental problem in this area is how to solve decentralized stochastic bilevel optimization problems with domain constraints while achieving low sample and communication complexities. This problem often arises from multi-agent learning problems with safety constraints. As shown in this paper, constrained decentralized bilevel optimization is far more challenging than its unconstrained counterpart due to the complex coupling structure, which necessitates new algorithm design and analysis techniques. Toward this end, we investigate a class of constrained decentralized bilevel optimization problems, where multiple agents collectively solve a nonconvex-strongly-convex bilevel problem with constraints in the upper-level variables. We propose an algorithm called Prometheus (proximal tracked stochastic recursive estimator) that achieves the first $\mathcal{O}(\epsilon^{-1})$ results in both sample and communication complexities for constrained decentralized bilevel optimization, where $\epsilon>0$ is a desired stationarity error. Collectively, the results in this work contribute to a theoretical foundation for low sample- and communication-complexity constrained decentralized bilevel learning.

Federated Learning (FL) is a distributed learning paradigm that allows multiple clients to learn a joint model by utilizing privately held data at each client. Significant research efforts have been devoted to develop advanced algorithms that deal with the situation where the data at individual clients have heterogeneous distributions. In this work, we show that data heterogeneity can be dealt from a different perspective. That is, by utilizing a certain overparameterized multi-layer neural network at each client, even the vanilla FedAvg (a.k.a. the Local SGD) algorithm can accurately optimize the training problem: When each client has a neural network with one wide layer of size $N$ (where $N$ is the number of total training samples), followed by layers of smaller widths, FedAvg converges linearly to a solution that achieves (almost) zero training loss, without requiring any assumptions on the clients’ data distributions. To our knowledge, this is the first work that demonstrates such resilience to data heterogeneity for FedAvg when trained on multi-layer neural networks. Our experiments also confirm that, neural networks of large size can achieve better and more stable performance for FL problems.

Decentralized bilevel optimization has received increasing attention recently due to its foundational role in many emerging multi-agent learning paradigms (e.g., multi-agent meta-learning and multi-agent reinforcement learning) over peer-to-peer edge networks. However, to work with the limited computation and communication capabilities of edge networks, a major challenge in developing decentralized bilevel optimization techniques is to lower sample and communication complexities. This motivates us to develop a new decentralized bilevel optimization called DIAMOND (decentralized single-timescale stochastic approximation with momentum and gradient-tracking). The contributions of this paper are as follows: i) our DIAMOND algorithm adopts a single-loop structure rather than following the natural double-loop structure of bilevel optimization, which offers low computation and implementation complexity; ii) compared to existing approaches, the DIAMOND algorithm does not require any full gradient evaluations, which further reduces both sample and computational complexities; iii) through a careful integration of momentum information and gradient tracking techniques, we show that the DIAMOND algorithm enjoys $\mathcal{O}\left( {{ \in ^{ - 3/2}}} \right)$ in sample and communication complexities for achieving an ϵ-stationary solution, both of which are independent of the dataset sizes and significantly outperform existing works. Extensive experiments also verify our theoretical findings.

In this work, we develop an implicit gradient-type (IG-AL) algorithm for bilevel optimization with strongly convex linear inequality constrained lower-level problems. Many learning problems of interest, including problems in distributed optimization, machine learning, economics, and transport research are captured by the above formulation. The key characteristics of the proposed algorithm are: (i) the use of a primal-dual augmented Lagrangian method for solving the lower-level problem, and (ii) construction of an implicit gradient (derived using the KKT conditions of the lower-level problem) for solving the upper-level problem. Importantly, the proposed algorithm avoids the (expensive) projection step to a half-space inherent to gradient descent-based alternatives. The performance of the proposed algorithm is evaluated on a set of numerical experiments.

Present-day federated learning (FL) systems deployed over edge networks consists of a large number of workers with high degrees of heterogeneity in data and/or computing capabilities, which call for flexible worker participation in terms of timing, effort, data heterogeneity, etc. To satisfy the need for flexible worker participation, we consider a new FL paradigm called “Anarchic Federated Learning” (AFL) in this paper. In stark contrast to conventional FL models, each worker in AFL has the freedom to choose i) when to participate in FL, and ii) the number of local steps to perform in each round based on its current situation (e.g., battery level, communication channels, privacy concerns). However, such chaotic worker behaviors in AFL impose many new open questions in algorithm design. In particular, it remains unclear whether one could develop convergent AFL training algorithms, and if yes, under what conditions and how fast the achievable convergence speed is. Toward this end, we propose two Anarchic Federated Averaging (AFA) algorithms with two-sided learning rates for both cross-device and cross-silo settings, which are named AFA-CD and AFA-CS, respectively. Somewhat surprisingly, we show that, under mild anarchic assumptions, both AFL algorithms achieve the best known convergence rate as the state-of-the-art algorithms for conventional FL. Moreover, they retain the highly desirable linear speedup effect with respect of both the number of workers and local steps in the new AFL paradigm. We validate the proposed algorithms with extensive experiments on real-world datasets.

Adversarial training (AT) is a widely recognized defense mechanism to gain the robustness of deep neural networks against adversarial attacks. It is built on min-max optimization (MMO), where the minimizer (i.e., defender) seeks a robust model to minimize the worst-case training loss in the presence of adversarial examples crafted by the maximizer (i.e., attacker). However, the conventional MMO method makes AT hard to scale. Thus, Fast-AT and other recent algorithms attempt to simplify MMO by replacing its maximization step with the single gradient sign-based attack generation step. Although easy to implement, FAST-AT lacks theoretical guarantees, and its empirical performance is unsatisfactory due to the issue of robust catastrophic overfitting when training with strong adversaries. In this paper, we advance Fast-AT from the fresh perspective of bi-level optimization (BLO). We first show that the commonly-used Fast-AT is equivalent to using a stochastic gradient algorithm to solve a linearized BLO problem involving a sign operation. However, the discrete nature of the sign operation makes it difficult to understand the algorithm performance. Inspired by BLO, we design and analyze a new set of robust training algorithms termed Fast Bi-level AT (Fast-BAT), which effectively defends sign-based projected gradient descent (PGD) attacks without using any gradient sign method or explicit robust regularization. In practice, we show that our method yields substantial robustness improvements over multiple baselines across multiple models and datasets.

In recent years, decentralized bilevel optimization problems have received increasing attention in the networking and machine learning communities. However, for decentralized bilevel optimization over networks with limited computation and communication capabilities, how to achieve low sample and communication complexities are two fundamental challenges. In this paper, we make the first attempt to investigate the class of decentralized bilevel optimization problems with nonconvex and strongly-convex structure corresponding to the outer and inner subproblems, respectively. Our main contributions in this paper are two-fold: i) We first propose a deterministic algorithm called interact (inner-gradient-descent-outer-tracked-gradient) that requires the sample complexity of O(nϵ-1) and communication complexity of O(ϵ-1) to solve the bilevel optimization problem, where n and ϵ > 0 are the number of samples at each agent and the desired stationarity gap, respectively. ii) To relax the need for full gradient evaluations in each iteration, we propose a stochastic variance-reduced version of interact (svr-interact), which improves the sample complexity to [EQUATION] while achieving the same communication complexity as the deterministic algorithm. Our numerical experiments also corroborate our theoretical findings.

Federated Learning (FL) refers to the paradigm where multiple worker nodes (WNs) build a joint model by using local data. Despite extensive research, for a generic non-convex FL problem, it is not clear, how to choose the WNs' and the server's update directions, the minibatch sizes, and the local update frequency, so that the WNs use the minimum number of samples and communication rounds to achieve the desired solution. This work addresses the above question and considers a class of stochastic algorithms where the WNs perform a few local updates before communication. We show that when both the WN's and the server's directions are chosen based on certain stochastic momentum estimator, the algorithm requires $\tilde{\mathcal{O}}(\epsilon^{-3/2})$ samples and $\tilde{\mathcal{O}}(\epsilon^{-1})$ communication rounds to compute an $\epsilon$-stationary solution. To the best of our knowledge, this is the first FL algorithm that achieves such {\it near-optimal} sample and communication complexities simultaneously. Further, we show that there is a trade-off curve between local update frequencies and local minibatch sizes, on which the above sample and communication complexities can be maintained. {Finally, we show that for the classical FedAvg (a.k.a. Local SGD, which is a momentum-less special case of the STEM), a similar trade-off curve exists, albeit with worse sample and communication complexities. Our insights on this trade-off provides guidelines for choosing the four important design elements for FL algorithms, the update frequency, directions, and minibatch sizes to achieve the best performance.}

This paper proposes a new algorithm -- the \underline{S}ingle-timescale Do\underline{u}ble-momentum \underline{St}ochastic \underline{A}pprox\underline{i}matio\underline{n} (SUSTAIN) -- for tackling stochastic unconstrained bilevel optimization problems. We focus on bilevel problems where the lower level subproblem is strongly-convex and the upper level objective function is smooth. Unlike prior works which rely on \emph{two-timescale} or \emph{double loop} techniques, we design a stochastic momentum-assisted gradient estimator for both the upper and lower level updates. The latter allows us to control the error in the stochastic gradient updates due to inaccurate solution to both subproblems. If the upper objective function is smooth but possibly non-convex, we show that {SUSTAIN}~requires $O(\epsilon^{-3/2})$ iterations (each using $O(1)$ samples) to find an $\epsilon$-stationary solution. The $\epsilon$-stationary solution is defined as the point whose squared norm of the gradient of the outer function is less than or equal to $\epsilon$. The total number of stochastic gradient samples required for the upper and lower level objective functions matches the best-known complexity for single-level stochastic gradient algorithms. We also analyze the case when the upper level objective function is strongly-convex.

In this work, we propose a joint collaboration-compression framework for the random signal detection problem in a resource constrained wireless sensor network (WSN). Specifically, we propose a framework where the local sensors first collaborate (via a linear collaboration matrix) with each other. Then a subset of sensors linearly compress their aggregated information before communicating with the fusion center (FC). We propose a novel metric called generalized deflection coefficient (GDC) for evaluating the detection performance which is shown to be tightly upper bounded by the Kullback-Leibler divergence for Gaussian observations. We jointly design the linear collaboration and compression strategies under power constraints via alternating maximization of the proposed GDC metric. Finally, numerical results are provided to demonstrate the effectiveness of the proposed framework.

We consider the distributed stochastic optimization problem of minimizing a nonconvex function f in an adversarial setting. All the w worker nodes in the network are expected to send their stochastic gradient vectors to the fusion center (or server). However, some (at most α-fraction) of the nodes may be Byzantines, which may send arbitrary vectors instead. Vanilla implementation of distributed stochastic gradient descent (SGD) cannot handle such misbehavior from the nodes. We propose a robust variant of distributed SGD which is resilient to the presence of Byzantines. The fusion center employs a novel filtering rule that identifies and removes the Byzantine nodes. We show that T = Õ (1/wϵ2+ α2/ϵ2) iterations are needed to achieve an ϵ-approximate stationary point (x such that ∥∇f(x)∥2≤ ϵ) for the nonconvex learning problem. Unlike other existing approaches, the proposed algorithm is independent of the problem dimension.

In this paper, we present an efficient methodology to design precoders for distributed detection of unknown high dimensional signals. We consider a wireless sensor network, where several distributed sensors collaborate to perform binary hypothesis testing based on observations of an unknown high dimensional signal corrupted by noise. The sensors collect data over both temporal and spatial domains. Due to network resource constraints, each sensor performs a linear compression (through precoding) of the observed high dimensional signal at each time instant and forwards the compressed signal to the fusion center (FC). The FC then employs the generalized likelihood ratio test (GLRT) to make a decision on the presence or absence of the signal. We propose online linear precoding/compression strategies for such sensors that collect data over spatio-temporal domain, so that the detection performance at the FC is maximized under certain network resource constraints. Through the measure of non-centrality parameter and receiver operating characteristics (ROC), we show that our proposed precoder design achieves very good detection performance.

Random distortion testing (RDT) addresses the problem of testing whether or not a random signal, Ξ, deviates by more than a specified tolerance, τ, from a fixed value, ξ0[1]. The test is nonparametric in the sense that the distribution of the signal under each hypothesis is assumed to be unknown. The signal is observed in independent and identically distributed (i.i.d) additive noise. The need to control the probabilities of false alarm and missed detection while reducing the number of samples required to make a decision leads to the SeqRDT approach. We show that under mild assumptions on the signal, SeqRDT will follow the properties desired by a sequential test. Simulations show that the SeqRDT approach leads to faster decision making compared to its fixed sam-ple counterpart Block-RDT [2] and is robust to model mismatches compared to the Sequential Probability Ratio Test (SPRT) [3] when the actual signal is a distorted version of the assumed signal especially at low Signal-to-Noise Ratios (SNRs).

Present day distributed inference systems consist of sensors with different modalities working as a system to perform specific tasks. With multiple sensors sensing heterogeneous data over multiple time instants, diversity is an inherent aspect of such systems. In this work, we take the first step to characterize the diversity of a general heterogeneous sensing system performing inference tasks. We provide a unified definition for diversity which can be customized for the system in use. The use of the definition is illustrated by applying it to a specific detection system where the sensors collect data over heterogeneous sensing channels. We assume the data to be both temporally and spatially correlated and analyze the effect of dependence on the diversity of the detection system.

This paper considers the problem of high-dimensional signal detection in a large distributed network whose nodes can collaborate with their one-hop neighboring nodes (spatial collaboration). We assume that only a small subset of nodes communicate with the fusion center (FC). We design optimal collaboration strategies which are universal for a class of deterministic signals. By establishing the equivalence between the collaboration strategy design problem and sparse principal component analysis (PCA), we solve the problem efficiently and evaluate the impact of collaboration on detection performance.

In this paper, we analyze the effect of channel estimation errors on the performance of an uplink cellular network. We use a stochastic geometric approach, where the Mobile Users (MUs) and the Base Stations (BSs) are modeled as being randomly located on the 2-dimensional plane according to independent Poisson point processes. Each MU makes use of fractional distance-dependent power control, while transmitting both the training signal as well as the data signal in the uplink direction. We derive an analytical expression for the uplink coverage probability for a typical BS-MU pair, accounting for the effects of channel estimation errors and fractional power control. We numerically obtain the fractional power control that maximizes the coverage probability, and show that the optimal power control factor does not depend on the training duration. Further, we numerically compute the optimal training duration that maximizes the area spectral efficiency. The results provide critical insights into the design and optimization of uplink cellular networks in the presence of pilot contamination due to practical channel estimation.