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.

How to Train the Teacher Model for Effective Knowledge Distillation

Recently, it was shown that the role of the teacher in knowledge distillation (KD) is to provide the student with an estimate of the true Bayes conditional probability density (BCPD). Notably, the new findings propose that the student's error rate can be upper-bounded by the mean squared error (MSE) between the teacher's output and BCPD. Consequently, to enhance KD efficacy, the teacher should be trained such that its output is close to BCPD in MSE sense. This paper elucidates that training the teacher model with MSE loss equates to minimizing the MSE between its output and BCPD, aligning with its core responsibility of providing the student with a BCPD estimate closely resembling it in MSE terms. In this respect, through a comprehensive set of experiments, we demonstrate that substituting the conventional teacher trained with cross-entropy loss with one trained using MSE loss in state-of-the-art KD methods consistently boosts the student's accuracy, resulting in improvements of up to 2.6\%.

Adversarial Training via Adaptive Knowledge Amalgamation of an Ensemble of Teachers

Adversarial training (AT) is a popular method for training robust deep neural networks (DNNs) against adversarial attacks. Yet, AT suffers from two shortcomings: (i) the robustness of DNNs trained by AT is highly intertwined with the size of the DNNs, posing challenges in achieving robustness in smaller models; and (ii) the adversarial samples employed during the AT process exhibit poor generalization, leaving DNNs vulnerable to unforeseen attack types. To address these dual challenges, this paper introduces adversarial training via adaptive knowledge amalgamation of an ensemble of teachers (AT-AKA). In particular, we generate a diverse set of adversarial samples as the inputs to an ensemble of teachers; and then, we adaptively amalgamate the logtis of these teachers to train a generalized-robust student. Through comprehensive experiments, we illustrate the superior efficacy of AT-AKA over existing AT methods and adversarial robustness distillation techniques against cutting-edge attacks, including AutoAttack.

Robustness Against Adversarial Attacks via Learning Confined Adversarial Polytopes

Deep neural networks (DNNs) could be deceived by generating human-imperceptible perturbations of clean samples. Therefore, enhancing the robustness of DNNs against adversarial attacks is a crucial task. In this paper, we aim to train robust DNNs by limiting the set of outputs reachable via a norm-bounded perturbation added to a clean sample. We refer to this set as adversarial polytope, and each clean sample has a respective adversarial polytope. Indeed, if the respective polytopes for all the samples are compact such that they do not intersect the decision boundaries of the DNN, then the DNN is robust against adversarial samples. Hence, the inner-working of our algorithm is based on learning \textbf{c}onfined \textbf{a}dversarial \textbf{p}olytopes (CAP). By conducting a thorough set of experiments, we demonstrate the effectiveness of CAP over existing adversarial robustness methods in improving the robustness of models against state-of-the-art attacks including AutoAttack.

Bayes Conditional Distribution Estimation for Knowledge Distillation Based on Conditional Mutual Information

It is believed that in knowledge distillation (KD), the role of the teacher is to provide an estimate for the unknown Bayes conditional probability distribution (BCPD) to be used in the student training process. Conventionally, this estimate is obtained by training the teacher using maximum log-likelihood (MLL) method. To improve this estimate for KD, in this paper we introduce the concept of conditional mutual information (CMI) into the estimation of BCPD and propose a novel estimator called the maximum CMI (MCMI) method. Specifically, in MCMI estimation, both the log-likelihood and CMI of the teacher are simultaneously maximized when the teacher is trained. Through Eigen-CAM, it is further shown that maximizing the teacher's CMI value allows the teacher to capture more contextual information in an image cluster. Via conducting a thorough set of experiments, we show that by employing a teacher trained via MCMI estimation rather than one trained via MLL estimation in various state-of-the-art KD frameworks, the student's classification accuracy consistently increases, with the gain of up to 3.32\%. This suggests that the teacher's BCPD estimate provided by MCMI method is more accurate than that provided by MLL method. In addition, we show that such improvements in the student's accuracy are more drastic in zero-shot and few-shot settings. Notably, the student's accuracy increases with the gain of up to 5.72\% when 5\% of the training samples are available to the student (few-shot), and increases from 0\% to as high as 84\% for an omitted class (zero-shot). The code is available at \url{https://github.com/iclr2024mcmi/ICLRMCMI}.

AdaFed: Fair Federated Learning via Adaptive Common Descent Direction

Federated learning (FL) is a promising technology via which some edge devices/clients collaboratively train a machine learning model orchestrated by a server. Learning an unfair model is known as a critical problem in federated learning, where the trained model may unfairly advantage or disadvantage some of the devices. To tackle this problem, in this work, we propose AdaFed. The goal of AdaFed is to find an updating direction for the server along which (i) all the clients' loss functions are decreasing; and (ii) more importantly, the loss functions for the clients with larger values decrease with a higher rate. AdaFed adaptively tunes this common direction based on the values of local gradients and loss functions. We validate the effectiveness of AdaFed on a suite of federated datasets, and demonstrate that AdaFed outperforms state-of-the-art fair FL methods.

Conditional Mutual Information Constrained Deep Learning for Classification

The concepts of conditional mutual information (CMI) and normalized conditional mutual information (NCMI) are introduced to measure the concentration and separation performance of a classification deep neural network (DNN) in the output probability distribution space of the DNN, where CMI and the ratio between CMI and NCMI represent the intra-class concentration and inter-class separation of the DNN, respectively. By using NCMI to evaluate popular DNNs pretrained over ImageNet in the literature, it is shown that their validation accuracies over ImageNet validation data set are more or less inversely proportional to their NCMI values. Based on this observation, the standard deep learning (DL) framework is further modified to minimize the standard cross entropy function subject to an NCMI constraint, yielding CMI constrained deep learning (CMIC-DL). A novel alternating learning algorithm is proposed to solve such a constrained optimization problem. Extensive experiment results show that DNNs trained within CMIC-DL outperform the state-of-the-art models trained within the standard DL and other loss functions in the literature in terms of both accuracy and robustness against adversarial attacks. In addition, visualizing the evolution of learning process through the lens of CMI and NCMI is also advocated.

A Secure Key Sharing Algorithm Exploiting Phase Reciprocity in Wireless Channels

This article presents a secure key exchange algorithm that exploits reciprocity in wireless channels to share a secret key between two nodes $A$ and $B$. Reciprocity implies that the channel phases in the links $A\rightarrow B$ and $B\rightarrow A$ are the same. A number of such reciprocal phase values are measured at nodes $A$ and $B$, called shared phase values hereafter. Each shared phase value is used to mask points of a Phase Shift Keying (PSK) constellation. Masking is achieved by rotating each PSK constellation with a shared phase value. Rotation of constellation is equivalent to adding phases modulo-$2\pi$, and as the channel phase is uniformly distributed in $[0,2\pi)$, the result of summation conveys zero information about summands. To enlarge the key size over a static or slow fading channel, the Radio Frequency (RF) propagation path is perturbed to create several independent realizations of multi-path fading, each used to share a new phase value. To eavesdrop a phase value shared in this manner, the Eavesdropper (Eve) will always face an under-determined system of linear equations which will not reveal any useful information about its actual solution value. This property is used to establish a secure key between two legitimate users.