Universal Training of Neural Networks to Achieve Bayes Optimal Classification Accuracy

This work invokes the notion of $f$-divergence to introduce a novel upper bound on the Bayes error rate of a general classification task. We show that the proposed bound can be computed by sampling from the output of a parameterized model. Using this practical interpretation, we introduce the Bayes optimal learning threshold (BOLT) loss whose minimization enforces a classification model to achieve the Bayes error rate. We validate the proposed loss for image and text classification tasks, considering MNIST, Fashion-MNIST, CIFAR-10, and IMDb datasets. Numerical experiments demonstrate that models trained with BOLT achieve performance on par with or exceeding that of cross-entropy, particularly on challenging datasets. This highlights the potential of BOLT in improving generalization.

Regularized Top-$k$: A Bayesian Framework for Gradient Sparsification

Error accumulation is effective for gradient sparsification in distributed settings: initially-unselected gradient entries are eventually selected as their accumulated error exceeds a certain level. The accumulation essentially behaves as a scaling of the learning rate for the selected entries. Although this property prevents the slow-down of lateral movements in distributed gradient descent, it can deteriorate convergence in some settings. This work proposes a novel sparsification scheme that controls the learning rate scaling of error accumulation. The development of this scheme follows two major steps: first, gradient sparsification is formulated as an inverse probability (inference) problem, and the Bayesian optimal sparsification mask is derived as a maximum-a-posteriori estimator. Using the prior distribution inherited from Top-$k$, we derive a new sparsification algorithm which can be interpreted as a regularized form of Top-$k$. We call this algorithm regularized Top-$k$ (RegTop-$k$). It utilizes past aggregated gradients to evaluate posterior statistics of the next aggregation. It then prioritizes the local accumulated gradient entries based on these posterior statistics. We validate our derivation through numerical experiments. In distributed linear regression, it is observed that while Top-$k$ remains at a fixed distance from the global optimum, RegTop-$k$ converges to the global optimum at significantly higher compression ratios. We further demonstrate the generalization of this observation by employing RegTop-$k$ in distributed training of ResNet-18 on CIFAR-10, where it noticeably outperforms Top-$k$.

Over-the-Air Fair Federated Learning via Multi-Objective Optimization

In federated learning (FL), heterogeneity among the local dataset distributions of clients can result in unsatisfactory performance for some, leading to an unfair model. To address this challenge, we propose an over-the-air fair federated learning algorithm (OTA-FFL), which leverages over-the-air computation to train fair FL models. By formulating FL as a multi-objective minimization problem, we introduce a modified Chebyshev approach to compute adaptive weighting coefficients for gradient aggregation in each communication round. To enable efficient aggregation over the multiple access channel, we derive analytical solutions for the optimal transmit scalars at the clients and the de-noising scalar at the parameter server. Extensive experiments demonstrate the superiority of OTA-FFL in achieving fairness and robust performance compared to existing methods.

GP-FL: Model-Based Hessian Estimation for Second-Order Over-the-Air Federated Learning

Second-order methods are widely adopted to improve the convergence rate of learning algorithms. In federated learning (FL), these methods require the clients to share their local Hessian matrices with the parameter server (PS), which comes at a prohibitive communication cost. A classical solution to this issue is to approximate the global Hessian matrix from the first-order information. Unlike in idealized networks, this solution does not perform effectively in over-the-air FL settings, where the PS receives noisy versions of the local gradients. This paper introduces a novel second-order FL framework tailored for wireless channels. The pivotal innovation lies in the PS's capability to directly estimate the global Hessian matrix from the received noisy local gradients via a non-parametric method: the PS models the unknown Hessian matrix as a Gaussian process, and then uses the temporal relation between the gradients and Hessian along with the channel model to find a stochastic estimator for the global Hessian matrix. We refer to this method as Gaussian process-based Hessian modeling for wireless FL (GP-FL) and show that it exhibits a linear-quadratic convergence rate. Numerical experiments on various datasets demonstrate that GP-FL outperforms all classical baseline first and second order FL approaches.

Rate-Constrained Quantization for Communication-Efficient Federated Learning

Quantization is a common approach to mitigate the communication cost of federated learning (FL). In practice, the quantized local parameters are further encoded via an entropy coding technique, such as Huffman coding, for efficient data compression. In this case, the exact communication overhead is determined by the bit rate of the encoded gradients. Recognizing this fact, this work deviates from the existing approaches in the literature and develops a novel quantized FL framework, called \textbf{r}ate-\textbf{c}onstrained \textbf{fed}erated learning (RC-FED), in which the gradients are quantized subject to both fidelity and data rate constraints. We formulate this scheme, as a joint optimization in which the quantization distortion is minimized while the rate of encoded gradients is kept below a target threshold. This enables for a tunable trade-off between quantization distortion and communication cost. We analyze the convergence behavior of RC-FED, and show its superior performance against baseline quantized FL schemes on several datasets.

Graph-based Algorithms for Linear Computation Coding

We revisit existing linear computation coding (LCC) algorithms, and introduce a new framework that measures the computational cost of computing multidimensional linear functions, not only in terms of the number of additions, but also with respect to their suitability for parallel processing. Utilizing directed acyclic graphs, which correspond to signal flow graphs in hardware, we propose a novel LCC algorithm that controls the trade-off between the total number of operations and their parallel executability. Numerical evaluations show that the proposed algorithm, constrained to a fully parallel structure, outperforms existing schemes.

Linear Computation Coding: Exponential Search and Reduced-State Algorithms

Linear computation coding is concerned with the compression of multidimensional linear functions, i.e. with reducing the computational effort of multiplying an arbitrary vector to an arbitrary, but known, constant matrix. This paper advances over the state-of-the art, that is based on a discrete matching pursuit (DMP) algorithm, by a step-wise optimal search. Offering significant performance gains over DMP, it is however computationally infeasible for large matrices and high accuracy. Therefore, a reduced-state algorithm is introduced that offers performance superior to DMP, while still being computationally feasible even for large matrices. Depending on the matrix size, the performance gain over DMP is on the order of at least 10%.

Statistical-CSI-Based Antenna Selection and Precoding in Uplink MIMO

Classical antenna selection schemes require instantaneous channel state information (CSI). This leads to high signaling overhead in the system. This work proposes a novel joint receive antenna selection and precoding scheme for multiuser multiple-input multiple-output uplink transmission that relies only on the long-term statistics of the CSI. The proposed scheme designs the switching network and the uplink precoders, such that the expected throughput of the system in the long term is maximized. Invoking results from the random matrix theory, we derive a closed-form expression for the expected throughput of the system. We then develop a tractable iterative algorithm to tackle the throughput maximization problem, capitalizing on the alternating optimization and majorization-maximization (MM) techniques. Numerical results substantiate the efficiency of the proposed approach and its superior performance as compared with the baseline.

Joint Receive Antenna Selection and Beamforming in RIS-Aided MIMO Systems

This work studies a low-complexity design for reconfigurable intelligent surface (RIS)-aided multiuser multiple-input multiple-output systems. The base station (BS) applies receive antenna selection to connect a subset of its antennas to the available radio frequency chains. For this setting, the BS switching network, uplink precoders, and RIS phase-shifts are jointly designed, such that the uplink sum-rate is maximized. The principle design problem reduces to an NP-hard mixed-integer optimization. We hence invoke the weighted minimum mean squared error technique and the penalty dual decomposition method to develop a tractable iterative algorithm that approximates the optimal design effectively. Our numerical investigations verify the efficiency of the proposed algorithm and its superior performance as compared with the benchmark.

A High-Level Comparison of Recent Technologies for Massive MIMO Architectures

Since the introduction of massive MIMO (mMIMO), the design of a transceiver with feasible complexity has been a challenging problem. Initially, it was believed that the main issue in this respect is the overall RF-cost. However, as mMIMO is becoming more and more a key technology for future wireless networks, it is realized, that the RF-cost is only one of many implementational challenges and design trade-offs. In this paper, we present, analyze and compare various novel mMIMO architectures, considering recent emerging technologies such as intelligent surface-assisted and Rotman lens based architectures. These are compared to the conventional fully digital (FD) and hybrid analog-digital beamforming (HADB) approaches. To enable a fair comparison, we account for various hardware imperfections and losses and utilize a novel, universal algorithm for signal precoding. Based on our thorough investigations, we draw a generic efficiency to quality trade-off for various mMIMO architectures. We find that in a typical cellular communication setting the reflect/transmit array based architectures sketch the best overall trade-off. Further, we show that in a qualitative ranking the power efficiency of the considered architectures is independent of the frequency range.