Wireless Federated Langevin Monte Carlo: Repurposing Channel Noise for Bayesian Sampling and Privacy

Most works on federated learning (FL) focus on the most common frequentist formulation of learning whereby the goal is minimizing the global empirical loss. Frequentist learning, however, is known to be problematic in the regime of limited data as it fails to quantify epistemic uncertainty in prediction. Bayesian learning provides a principled solution to this problem by shifting the optimization domain to the space of distribution in the model parameters. This paper studies for the first time Bayesian FL in wireless systems by proposing and analyzing a gradient-based Markov Chain Monte Carlo (MCMC) method -- Wireless Federated Langevin Monte Carlo (WFLMC). The key idea of this work is to repurpose channel noise for the double role of seed randomness for MCMC sampling and of privacy-preserving mechanism. To this end, based on the analysis of the Wasserstein distance between sample distribution and global posterior distribution under privacy and power constraints, we introduce a power allocation strategy as the solution of a convex program. The analysis identifies distinct operating regimes in which the performance of the system is power-limited, privacy-limited, or limited by the requirement of MCMC sampling. Both analytical and simulation results demonstrate that, if the channel noise is properly accounted for under suitable conditions, it can be fully repurposed for both MCMC sampling and privacy preservation, obtaining the same performance as in an ideal communication setting that is not subject to privacy constraints.

Multiscale Wavelet Transfer Entropy with Application to Corticomuscular Coupling Analysis

Objective: Functional coupling between the motor cortex and muscle activity is commonly detected and quantified by cortico-muscular coherence (CMC) or Granger causality (GC) analysis, which are applicable only to linear couplings and are not sufficiently sensitive: some healthy subjects show no significant CMC and GC, and yet have good motor skills. The objective of this work is to develop measures of functional cortico-muscular coupling that have improved sensitivity and are capable of detecting both linear and non-linear interactions. Methods: A multiscale wavelet transfer entropy (TE) methodology is proposed. The methodology relies on a dyadic stationary wavelet transform to decompose electroencephalogram (EEG) and electromyogram (EMG) signals into functional bands of neural oscillations. Then, it applies TE analysis based on a range of embedding delay vectors to detect and quantify intra- and cross-frequency band cortico-muscular coupling at different time scales. Results: Our experiments with neurophysiological signals substantiate the potential of the developed methodologies for detecting and quantifying information flow between EEG and EMG signals for subjects with and without significant CMC or GC, including non-linear cross-frequency interactions, and interactions across different temporal scales. The obtained results are in agreement with the underlying sensorimotor neurophysiology. Conclusion: These findings suggest that the concept of multiscale wavelet TE provides a comprehensive framework for analysing cortex-muscle interactions. Significance: The proposed methodologies will enable developing novel insights into movement control and neurophysiological processes more generally.

Black-Box and Modular Meta-Learning for Power Control via Random Edge Graph Neural Networks

In this paper, we consider the problem of power control for a wireless network with an arbitrarily time-varying topology, including the possible addition or removal of nodes. A data-driven design methodology that leverages graph neural networks (GNNs) is adopted in order to efficiently parametrize the power control policy mapping the channel state information (CSI) to transmit powers. The specific GNN architecture, known as random edge GNN (REGNN), defines a non-linear graph convolutional filter whose spatial weights are tied to the channel coefficients. While prior work assumed a joint training approach whereby the REGNN-based policy is shared across all topologies, this paper targets adaptation of the power control policy based on limited CSI data regarding the current topology. To this end, we propose both black-box and modular meta-learning techniques. Black-box meta-learning optimizes a general-purpose adaptation procedure via (stochastic) gradient descent, while modular meta-learning finds a set of reusable modules that can form components of a solution for any new network topology. Numerical results validate the benefits of meta-learning for power control problems over joint training schemes, and demonstrate the advantages of modular meta-learning when data availability is extremely limited.

Learning to Learn to Demodulate with Uncertainty Quantification via Bayesian Meta-Learning

Meta-learning, or learning to learn, offers a principled framework for few-shot learning. It leverages data from multiple related learning tasks to infer an inductive bias that enables fast adaptation on a new task. The application of meta-learning was recently proposed for learning how to demodulate from few pilots. The idea is to use pilots received and stored for offline use from multiple devices in order to meta-learn an adaptation procedure with the aim of speeding up online training on new devices. Standard frequentist learning, which can yield relatively accurate hard classification decisions, is known to be poorly calibrated, particularly in the small-data regime. Poor calibration implies that the soft scores output by the demodulator are inaccurate estimates of the true probability of correct demodulation. In this work, we introduce the use of Bayesian meta-learning via variational inference for the purpose of obtaining well-calibrated few-pilot demodulators. In a Bayesian framework, each neural network weight is represented by a distribution, capturing epistemic uncertainty. Bayesian meta-learning optimizes over the prior distribution of the weights. The resulting Bayesian ensembles offer better calibrated soft decisions, at the computational cost of running multiple instances of the neural network for demodulation. Numerical results for single-input single-output Rayleigh fading channels with transmitters non-linearities are provided that compare symbol error rate and expected calibration error for both frequentist and Bayesian meta-learning, illustrating how the latter is both more accurate and better-calibrated.

Transfer Bayesian Meta-learning via Weighted Free Energy Minimization

Meta-learning optimizes the hyperparameters of a training procedure, such as its initialization, kernel, or learning rate, based on data sampled from a number of auxiliary tasks. A key underlying assumption is that the auxiliary tasks, known as meta-training tasks, share the same generating distribution as the tasks to be encountered at deployment time, known as meta-test tasks. This may, however, not be the case when the test environment differ from the meta-training conditions. To address shifts in task generating distribution between meta-training and meta-testing phases, this paper introduces weighted free energy minimization (WFEM) for transfer meta-learning. We instantiate the proposed approach for non-parametric Bayesian regression and classification via Gaussian Processes (GPs). The method is validated on a toy sinusoidal regression problem, as well as on classification using miniImagenet and CUB data sets, through comparison with standard meta-learning of GP priors as implemented by PACOH.

Latency-Constrained Prediction of mmWave/THz Link Blockages through Meta-Learning

Wireless applications that use high-reliability low-latency links depend critically on the capability of the system to predict link quality. This dependence is especially acute at the high carrier frequencies used by mmWave and THz systems, where the links are susceptible to blockages. Predicting blockages with high reliability requires a large number of data samples to train effective machine learning modules. With the aim of mitigating data requirements, we introduce a framework based on meta-learning, whereby data from distinct deployments are leveraged to optimize a shared initialization that decreases the data set size necessary for any new deployment. Predictors of two different events are studied: (1) at least one blockage occurs in a time window, and (2) the link is blocked for the entire time window. The results show that an RNN-based predictor trained using meta-learning is able to predict blockages after observing fewer samples than predictors trained using standard methods.

Learning to Time-Decode in Spiking Neural Networks Through the Information Bottleneck

One of the key challenges in training Spiking Neural Networks (SNNs) is that target outputs typically come in the form of natural signals, such as labels for classification or images for generative models, and need to be encoded into spikes. This is done by handcrafting target spiking signals, which in turn implicitly fixes the mechanisms used to decode spikes into natural signals, e.g., rate decoding. The arbitrary choice of target signals and decoding rule generally impairs the capacity of the SNN to encode and process information in the timing of spikes. To address this problem, this work introduces a hybrid variational autoencoder architecture, consisting of an encoding SNN and a decoding Artificial Neural Network (ANN). The role of the decoding ANN is to learn how to best convert the spiking signals output by the SNN into the target natural signal. A novel end-to-end learning rule is introduced that optimizes a directed information bottleneck training criterion via surrogate gradients. We demonstrate the applicability of the technique in an experimental settings on various tasks, including real-life datasets.

A unified PAC-Bayesian framework for machine unlearning via information risk minimization

Machine unlearning refers to mechanisms that can remove the influence of a subset of training data upon request from a trained model without incurring the cost of re-training from scratch. This paper develops a unified PAC-Bayesian framework for machine unlearning that recovers the two recent design principles - variational unlearning (Nguyen et.al., 2020) and forgetting Lagrangian (Golatkar et.al., 2020) - as information risk minimization problems (Zhang,2006). Accordingly, both criteria can be interpreted as PAC-Bayesian upper bounds on the test loss of the unlearned model that take the form of free energy metrics.

Information-Theoretic Analysis of Epistemic Uncertainty in Bayesian Meta-learning

The overall predictive uncertainty of a trained predictor can be decomposed into separate contributions due to epistemic and aleatoric uncertainty. Under a Bayesian formulation, assuming a well-specified model, the two contributions can be exactly expressed (for the log-loss) or bounded (for more general losses) in terms of information-theoretic quantities (Xu and Raginsky, 2020). This paper addresses the study of epistemic uncertainty within an information-theoretic framework in the broader setting of Bayesian meta-learning. A general hierarchical Bayesian model is assumed in which hyperparameters determine the per-task priors of the model parameters. Exact characterizations (for the log-loss) and bounds (for more general losses) are derived for the epistemic uncertainty - quantified by the minimum excess meta-risk (MEMR)- of optimal meta-learning rules. This characterization is leveraged to bring insights into the dependence of the epistemic uncertainty on the number of tasks and on the amount of per-task training data. Experiments are presented that compare the proposed information-theoretic bounds, evaluated via neural mutual information estimators, with the performance of a novel approximate fully Bayesian meta-learning strategy termed Langevin-Stein Bayesian Meta-Learning (LS-BML).

Fast Power Control Adaptation via Meta-Learning for Random Edge Graph Neural Networks

Power control in decentralized wireless networks poses a complex stochastic optimization problem when formulated as the maximization of the average sum rate for arbitrary interference graphs. Recent work has introduced data-driven design methods that leverage graph neural network (GNN) to efficiently parametrize the power control policy mapping channel state information (CSI) to the power vector. The specific GNN architecture, known as random edge GNN (REGNN), defines a non-linear graph convolutional architecture whose spatial weights are tied to the channel coefficients, enabling a direct adaption to channel conditions. This paper studies the higher-level problem of enabling fast adaption of the power control policy to time-varying topologies. To this end, we apply first-order meta-learning on data from multiple topologies with the aim of optimizing for a few-shot adaptation to new network configurations.