From Theory to Practice: Implementing Meta-Learning in 6G Wireless Infrastructure

Abstract

The vision of the sixth generation of communication systems, commonly known as 6G, entails a connected world that provides ubiquitous connectivity and fosters the digital transformation of society. As the number of devices, services, and users continues to grow, intelligent solutions are expected to facilitate this transformation. This paper considers meta-learning as a pivotal paradigm for 6G systems, detailing its principles, algorithms, and theoretical underpinnings. The methodology involves integrating meta-learning with three potential 6G technologies: RF-based communication systems, optical communication systems, and molecular communication systems. The findings reveal the distinct characteristics of these technologies and demonstrate the potential benefits and challenges of incorporating meta-learning algorithms. Practical implications highlight how meta-learning can enhance the efficiency and adaptability of 6G systems, addressing the growing demand for intelligent and seamless communication networks.

1. Introduction

The technological advancement in communication systems has fostered a fully connected society. Over the past three decades, we have witnessed a rapid rise in the usage and deployment of various communication technologies, from the introduction of cellular concepts to the deployment of high-speed data transmission using massive multiple-input multiple-output (MIMO) systems. Researchers have created an interrelated and interconnected world through the fifth generation (5G) of communication networks. The recent developments in 5G promise paradigm-defining technologies such as augmented reality (AR) and virtual reality (VR), supporting applications like e-learning and e-health, and connected medicine. These applications have significantly increased data traffic, with global mobile data traffic expected to grow to 607 exabytes (EB) per month by 2025 and 5016 EB by 2030, according to the International Telecommunication Union (ITU) [1].

To cater to this exponential traffic demand, researchers globally are exploring the terahertz (THz) frequency band for spectral efficiency and frequency reuse. Additionally, as users rapidly adopt smart technologies, 6G systems aim to overcome the existing challenges of AI and ML models in wireless communication systems, transforming connected people and things into connected intelligence. 6G communication systems are envisioned to surpass conventional wireless communication systems by supporting higher data rates, accommodating huge traffic demands, and providing broader coverage areas. Moreover, 6G aims to reduce energy consumption, expand the frequency band, enhance security and trustworthiness, and minimize delays and latency, thus establishing intelligent communication systems. 6G will follow the trend of a smart and connected society, contributing significantly to smart cities and sustainable transport while aligning with green transition goals.

However, the integration of AI and ML into 6G communication systems presents both opportunities and challenges. These advanced computational models are expected to be the cornerstone of 6G infrastructure, driving innovations and efficiencies previously unattainable. AI and ML enable more intelligent, automated, and user-centric approaches to network management and optimization in 6G systems. The adaptability and learning capabilities of these models allow for dynamic network adjustments to meet varying demands, leading to improved resource management and network efficiency. AI-driven technologies in 6G will pave the way for advanced applications such as smart cities, autonomous systems, and IoT ecosystems, where seamless, real-time communication is crucial. The integration of AI and ML in 6G is set to transform data processing, from how data are gathered and analyzed to their utilization for decision-making. This transformation is vital for supporting the massive data volumes expected in 6G networks, enabling real-time data analysis and intelligent decision-making processes at the network edge [2,3,4]. Figure 1 illustrates the fundamental utilization scenarios of AI-enabled wireless communication systems.

In this article, we provide an introduction to meta-learning by covering principles, algorithms, and theory and integrate meta-learning with three potential technologies for 6G systems: RF-based communication systems, optical communication systems, and molecular communication systems. We investigate their respective characteristics and explore their seamless integration with meta-learning-based algorithms, aiming to shed light on the potential benefits and challenges associated with their incorporation.

1.1. Contributions

This survey paper aims to offer targeted insights into meta-learning-enabled wireless communication systems to support the next generation of communication systems. This article represents a pioneering effort in the field, presenting a comprehensive study of meta-learning algorithms integrated with different wireless communication systems. Some of the major contributions of the article are listed as follows:

• We introduce the novel meta-learning algorithm and discuss its potential to address the limitations of traditional machine learning methods in communication systems. The inherent advantages of meta-learning models surpass those of the current machine learning (ML) algorithms and can address significant existing challenges, thereby extending the capabilities of intelligent networks. We presented a comprehensive overview of novel meta-learning algorithms and models, highlighting state-of-the-art solutions in the context of wireless communication systems.
• We designed and simulated a meta-learning-enabled decoder to support three distinct wireless communication systems: radio frequency-based communication systems, optical wireless communication systems (OWCs), and molecular communication systems (MCSs). These three technologies were selected to demonstrate the versatility and effectiveness of meta-learning algorithms in various scenarios. Each wireless communication domain presents unique challenges due to differences in their channel models.

OWCs transmit data through optical channels, which are prone to interference from various light sources and perform optimally with line-of-sight alignment. MCS channels, being diffusive in nature, pose their own set of challenges. Radio frequency-based wireless communication channels, on the other hand, are subject to multipath fading, signal attenuation, and interference from other electromagnetic sources. These channels require sophisticated techniques to manage frequency reuse and to mitigate issues like path loss and shadowing. Despite these differences, our results show that meta-learning can be effectively incorporated into each of these scenarios, outperforming conventional methods. We present a selection of original results to provide readers with a comprehensive understanding of the advantages and capabilities of meta-learning-enabled communication systems.

These contributions significantly advance the field by demonstrating the applicability and benefits of meta-learning in diverse and challenging wireless communication environments. By addressing the unique characteristics and challenges of different communication systems, this work paves the way for more adaptable and efficient future communication networks.

Driven by the fast-paced advancement in the fields of wireless communication systems, research in this domain is burgeoning. This section provides an overview of relevant research in the area of wireless communication systems and artificial intelligence.

The author of [2] provides an introduction to key concepts in machine learning algorithms and their applicability to different domains of wireless communication. In [3], the authors consider a heterogeneous environment comprising different wireless access technologies and discuss different AI techniques that could facilitate such infrastructures by allowing self-reconfiguration, self-healing, and self-optimization. The potential of employing machine learning algorithms in different wireless communication scenarios has been studied in [5,6,7,8,9].

A recent paper on explainable AI (XAI) for 6G use cases highlighted the importance of transparency and interpretability in AI-driven communication systems [10]. The authors discussed various XAI techniques and their applications in 6G, emphasizing the need for explainable models to ensure trust and reliability in AI systems.

Edge computing is an emerging paradigm that pushes the AI frontiers to the network edge, as opposed to centralized cloud computing. The aim of edge computing is to bring computing and storage capacities closer to the users, which will have a significant impact on decreasing network latency. The authors of [11,12] have conducted studies discussing recent trends in intelligent edge computing for AI training and AI model interfacing, with the latter focusing on future 6G wireless networks. The authors of [13] explored the key components of edge ML and theoretical concepts behind designing neural network architectures and their training, while attempting to answer research questions regarding latency, security, and reliability under hardware and privacy restrictions. The authors of [14] provided insights into integrating multi-access edge computing with open radio access networks for beyond 5G (or 6G) networks.

Deep learning (DL), a sub-field of machine learning, has recently been gaining attention as it brings improvements over the conventional ML techniques by reducing the need for hand-crafted feature sets used for training [15] while improving accuracy. Many attempts have been made to facilitate the applications of wireless communication by employing deep learning models. Recently, Ozpoyraz et al. presented a comprehensive study that investigates DL applications from the perspective of four major concepts for 6G wireless communication systems specific to the physical layer (PHY), including massive MIMO systems, advanced multicarrier waveforms, RIS-empowered systems, and PHY security. Yeh et al. [16] presented a deep learning-based solution for intelligent and automated network slicing in 5G Open RAN (ORAN) deployment. They introduced a framework for dynamic RAN slicing using AI to meet multi-service SLAs. The proposed framework included modules for traffic load prediction and radio resource planning, demonstrating significant improvements in network resource management and service quality. Huang et al. investigated deep learning-based wireless communication techniques specific to applications in PHY layers such as multiple access, channel estimation, and performance optimization [17]. In [18], a review of deep learning applications in wireless communication systems is presented, where the authors present the applications in PHY, MAC, and routing layers while also discussing future research trends. Ref. [19] presented a survey of different works that tailor deep learning models to mobile networking tasks. The authors in [20] discussed the roles of deep learning in intelligent edge applications to provide higher throughput and resource allocation. The utilization of deep learning models specific to certain wireless communication scenarios has also been presented by the authors of [21,22]. In [21], the authors present a review of deep neural network models and investigate how they can benefit different IoT sectors, and, in [22], the authors present an overview of the deep learning architectures and algorithms relevant to the network traffic control systems. In [23], an analysis of the literature on deep learning for wireless communication networks is provided; the authors considered several case studies and showed that deep learning proves extremely useful for network design. The authors of [14] presented a review of existing DL-based radio access networks (RANs) as well as their (DL) integration with open-RANs (O-RANs). In their work, they also present two case studies on DL deployment in O-RAN while discussing open research problems in O-RAN architectures and how DL techniques can be used to tackle those problems. The authors of [24] present a literature review on applications of deep reinforcement learning, an emerging technique in AI, to address issues related to network access, security, wireless caching, data offloading, etc., specific to modern communication networks.

Building on the previous discussion, integrating machine learning and AI into wireless communication systems (WCSs) indeed offers significant potential, but it also presents various challenges. The dynamic nature of wireless networks, characterized by fluctuating signal strengths and complex interference patterns, poses a significant hurdle for consistent model training and accurate predictions. The issue of data scarcity or non-uniform distribution in these networks can further complicate model training, leading to biased or underfitting models. As WCSs evolve towards 6G, addressing these challenges will be crucial for harnessing the full potential of AI and machine learning in enhancing wireless communication technologies.

Meta-learning is a promising research topic within artificial intelligence with great potential for advancements. It has introduced a pioneering notion known as “learning to learn”, which is currently garnering significant attention [25,26,27]. It diverges from traditional AI approaches that solve tasks from scratch with a fixed learning algorithm. Instead, meta-learning aspires to refine the learning algorithm itself, capitalizing on experiences from multiple learning episodes. This innovative approach offers solutions to several challenges inherent in deep learning, such as data and computation bottlenecks, and enhances generalization capabilities. Lee et al. [28] proposed a representation of the channel through metamodeling that caters to black-box and data-driven channel models. The works on meta-learning in WCSs have been summarized in

Table 1. A summary of works that used meta-learning in different wireless communication applications.

Related Work	Key Contributions
[28]	Proposed a channel metamodeling approach to understand the underlying channel characteristics
[29]	Presented a new meta-learning benchmark based on channel coding
[30]	Developed an algorithm to improve the convergence rate of federated meta-learning and a proposed resource allocation strategy.
[31]	Proposed a framework for adaptive beam-forming design based on the idea of embedding in metric-based meta-learning.
[32]	Proposed a MAML-based NN decoder that allows fast adaption to varying channels.
[33]	Proposed a meta-learning-based channel estimation approach called RoemNet.
[34]	Provided a brief introduction to meta-learning with respect to communication systems.
[35]	Used a meta-learning-based approach to find a common initialization vector to allow faster convergence.
[36]	Trained a decoder, in an IoT scenario, using meta-training data to allow quick adaptations to varying channel conditions.
[37]	Compared meta-learning with GNNs trained for a single task using the beamforming problem.
[38]	Proposed a meta-learning-based channel acquisition and passive beamforming technique using fewer pilot symbols in RIS systems.
[39]	Employed federated meta-learning to propose a framework for 6G-enabled consumer electronics device intrusion detection within a Meta-Verse environment
[40]	Proposed a one-dimensional Multi-Scale Dilated Convolution Neural Network (MSDCNN) and a meta-transfer metric learning using scale function (MLS) to improve time series classification in 6G-supported Intelligent Transportation Systems (ITSs).

.

1.2. Meta-Learning in Wireless Communication Systems

The promising results of meta-learning have gained traction in the design of data-driven methods for wireless communication systems. It facilitates the rapid learning of the characteristics of a wireless channel and enables the prediction of its behavior, thereby aiding in the optimization of wireless system transmission parameters. The aforementioned body of works focused mainly on RF-based systems, and it has not yet been investigated in MCSs or OWCSs. Ref. [29] catered to the classical channel coding problem through meta-learning by proposing a channel code learner benchmark trained on channel distribution and rapidly adapting to new channels.

The applications of meta-learning in wireless communication systems extend beyond channel estimation, as demonstrated by the recent literature. Meta-learning can aid in the rapid determination of optimal resource allocation leading to the efficient use of resources and improved network performance. The authors of [30] proposed a non-uniform device selection technique while employing federated meta-learning techniques in a multi-access wireless system, which resulted in a faster convergence rate, and also provided a resource allocation algorithm that utilizes federated meta-learning in a multi-access wireless system, resulting in a faster convergence rate. They also provided a resource allocation algorithm to optimize different parameters crucial in multi-access wireless systems, including convergence rate, energy consumption, and wall-clock time.

Ref. [31] has proposed an adaptive beamforming design where the proposed algorithm first extracts key features in the pre-training step in conjunction with a fast regression algorithm for faster adaption to newer samples. The use cases presented in the next section are among the early works that applied meta-learning in molecular communication and visible light communication. Jiang et al. [32] utilized first-order MAML (FOMAML) to train an NN-based decoder that effectively adapts to channel variations, thus enhancing the performance of decoders on non-AWGN channels. In [33], the authors devised an algorithm, RoemNet, designed to work with the existing baseband OFDM system. In the proposed design, they incorporated multiple channels as multiple tasks to train a meta-learner that effectively learned the general parameters of these tasks and enabled an adequate initialization. RoemNet allowed them to obtain an effective channel estimation, given a small number of pilots.

The authors of [34] briefly introduce meta-learning specific to communication systems. Recent literature showcases the application of meta-learning in improving wireless communication systems’ performance by addressing channel variation issues. Meanwhile, Park et al. [36] proposed using meta-learning to identify a common initialization vector that would enable faster training on any channel, resulting in faster convergence, as demonstrated through various numerical results. Here, authors considered an IoT scenario where pilots from previous transmissions of other IoT devices were used as meta-training data. This allowed the demodulator to adapt to various channel conditions while sending only a few pilots. The results of this study were compared with various state-of-the-art meta-learning algorithms in a unified framework.

Zhao et al. [37] reviewed meta-learning applications for radio transmission. They demonstrated that meta-learning could significantly reduce the sample and time complexity for adapting to new scenarios. Their research compared meta-learning with graph neural networks (GNNs) trained for single tasks, particularly in solving beamforming problems. Their findings indicated that, while GNNs are more sample-efficient, meta-learning offers reduced time complexity for adaptation.

The authors of [38] investigated the problem of practical reconfigurable intelligent surface (RIS) systems such as channel acquisition and phase shift matrix design and proposed using meta-learning to automate the initialization of model parameters. This technique allowed quick adaptation to new tasks with limited samples. At the base station (BS), an inductive bias is trained using previously received pilot signals to closely approximate optimally trained models. This enables the rapid adaptation to new RIS channels with few training steps and pilots. The authors of [37] compare meta-learning and GNNs for wireless communication, showing that meta-learning can reduce this complexity by learning inductive biases from related tasks, while structural DNNs like graph neural networks (GNNs) can use permutation equivariance (PE) properties to improve efficiency.

The authors of [39] propose a novel anomaly detection framework called FML-DT, which is rooted in federated meta-learning and tailored for intrusion detection in Digital Twin (DT) 6G-enabled consumer electronics devices (CEDs) within metaverse environments. The proposed technique offers a novel solution that enhances the performance and effectiveness of IDS systems in real-world scenarios.

The authors of [40] proposed a pre-training strategy for few-shot time series classification called meta-transfer metric learning using scale function (MLS). MLS reduces computational costs and accelerates convergence by applying a scale function in meta-transfer learning, enabling models to handle varying class numbers without new hyperparameters. They also introduced a Multi-Scale Dilated Convolution Neural Network (MSDCNN) that uses dilated and multi-scale convolutions to reduce parameters and extract comprehensive time series features.

2. Conventional Learning

In traditional learning, the primary objective is to maximize the effectiveness of model parameters $\theta$, such as weights in neural networks, through the application of a designated training algorithm. Therefore, the process commences with the careful selection of a model and an appropriate training algorithm. This selection holds significant importance as it determines the inductive bias $\omega$ employed by the learning procedure to extrapolate from the training data to unseen test data.

If we are given a training dataset $D_{tr}$, then the predictive model $\widehat{y}=f_{\theta }\left(x\right)$ can be trained by solving an objective function $L(D;\theta ,\omega$):

$${\theta }^{*}=\underset{\theta }{argmin}L(D_{tr};\theta ,\omega )$$

(1)

where ${\theta }^{*}$ represents the optimized parameters that minimize the loss over the dataset $D_{tr}$. This parameter vector encapsulates the learned knowledge from the training data and serves as the foundation for making predictions on unseen data.

($\omega$) in (1) is the inductive bias that plays a key role in learning. It includes the model class, (e.g., neural networks with specific architectures), the learning procedure (e.g., optimization algorithms like Stochastic Gradient Descent), and hyperparameters (e.g., learning rate, initialization).

In conventional algorithms, the inductive bias is predetermined; however, in meta-learning, the goal is to optimize the learning algorithm itself so that it can quickly adapt to new tasks. This involves not only learning the model parameters $\theta$ but also learning the inductive bias $\omega$ that can best generalize across different tasks. By doing so, a meta-learner becomes capable of learning new tasks with minimal additional data, essentially learning how to learn. This is a key difference from conventional learning, where the inductive bias is static and must be carefully crafted by the practitioner. Meta-learning seeks to automate this aspect, making the learning process more adaptive and efficient.

In wireless communication systems, conventional learning has been applied to various aspects, such as channel estimation and decoding. For instance, a machine learning-based decoder in a wireless system would typically be trained on extensive data representing different channel conditions. It would then use this learned knowledge to decode signals under similar conditions effectively. While conventional learning has been instrumental in advancing wireless communication technologies, it faces several limitations:

• Data Dependency: It requires a considerable amount of task-specific data for training. This can be a challenge in scenarios with limited or evolving data.
• Adaptability: Conventional learning models are generally trained for specific scenarios and lack the flexibility to adapt to new or unseen conditions without extensive retraining.
• Computational Complexity: The process can be computationally intensive, particularly for complex models like deep neural networks.

As the field of wireless communication evolves, there is a growing need for models that can quickly adapt to changing conditions and learn from limited data. This has led to an increased interest in meta-learning approaches, which offer greater flexibility and efficiency in learning across a variety of tasks and conditions.

Table 2. Differences between key aspects of conventional learning and meta-learning.

Aspect	Conventional Learning	Meta-Learning
Approach	Focuses on learning from a specific dataset to optimize model parameters.	Involves learning how to learn, optimizing a learning strategy across tasks.
Data Requirements	Requires large amounts of task-specific data for training.	Can effectively learn from limited data; leverages previous learning experiences.
Adaptability	Trained for a specific task; limited adaptability to new tasks without retraining.	Rapidly adapts to new tasks with minimal additional data.
Training Methodology	Involves training a model on a single task using a fixed dataset.	Consists of two levels of learning: base-learning (task-specific) and meta-learning (across tasks).
Performance Metrics	Evaluated based on its accuracy and efficiency for a particular task.	Assessed by its ability to quickly adapt and perform across multiple tasks.
Optimization Focus	Optimized for best performance on a specific dataset.	Focuses on finding a generalizable model that can perform well on a range of tasks.
Application Scenarios	Suitable for scenarios with abundant data and well-defined tasks.	Ideal for environments with dynamic conditions and varying data availability.
Energy and Time Efficiency	May require extensive training time and computational resources for each new task.	More efficient in terms of training time and energy for new tasks due to prior learning.
Algorithmic Complexity	Relatively simpler algorithms focusing on a specific problem.	More complex algorithms that involve learning at multiple levels (task and meta-task).
Flexibility	Limited flexibility in dealing with changes in data distribution or task requirements.	High flexibility in adapting to new tasks and data distributions.

highlights fundamental differences between conventional learning and meta-learning, especially as they apply to wireless communication systems.

3. Methodological Framework for Meta-Learning

Unlike conventional machine learning, which enhances model predictions over multiple data instances, meta-learning focuses on improving a learning algorithm across numerous episodes. This process involves an inner (base-)learning algorithm sampled from a task family, and an outer (meta-)learning algorithm that optimizes the inner algorithm’s performance against an overarching objective like generalization performance or learning speed.

The inner loop is responsible for learning specific tasks. For each task, the model adjusts its parameters (often the weights in the case of neural networks) to perform well on this particular task. In practice, this usually involves training on a task-specific dataset. For instance, if the task is image classification, the model will train on a set of images and their labels. At the end of the inner loop, the model ideally becomes proficient at the specific task it has been trained on. However, this proficiency is often limited to tasks similar to those it has seen during training.

The outer loop aims to improve the model’s ability to learn new tasks. Rather than focusing on task-specific performance, the outer loop optimizes the learning process itself. The model’s learning algorithm or meta-parameters (like initial weights or learning rate) are adjusted based on the model’s performance across a range of tasks. This could mean changing how the model is initialized, how it updates its parameters, or even the model architecture itself. This loop takes into account how well the model adapts to new tasks after being trained in the inner loop. The goal is to find a set of meta-parameters or a learning strategy that allows the model to quickly adapt to new, unseen tasks with minimal training data. The optimization here is meta in nature, meaning that it is about optimizing the optimizer or the learning strategy, as illustrated in Figure 2 and Figure 3.

This capability is widely regarded as a prerequisite for achieving artificial intelligence. Meta-learning is especially relevant when data availability is restricted or obtaining new data is prohibitively expensive. By acquiring the ability to learn how to learn, a meta-learning system can swiftly adapt to new tasks and make informed decisions based on limited data. Consequently, it constitutes a powerful tool for various potential applications, specifically in wireless communications.

The term “meta-learning” has been used in diverse manners in the existing literature, reflecting different conceptualizations and perspectives. In this section, we aim to establish precise definitions of meta-learning and establish relevant terminologies that will subsequently serve as fundamental concepts throughout the remainder of this article. We have also used the commonly accepted nomenclature of meta-learning as articulated by Finn et al. [41].

3.1. Theoretical Models of Meta-Learning

Building on top of the conventional model given in (1), meta-learning seeks to optimize meta-parameters across a distribution of tasks k sampled from a task distribution $P_k$ where $(k=1,2,\dots KϵP_k)$. s are typically a function of the model parameters $\theta$ and inductive bias $\omega$. Each task k has its own dataset $D_k$ that consists of the training set ($D_k^{tr}$) and testing set ($D_k^{te}$). The training set is sampled with k data points from each of the classes present in the dataset and is also called a support set. Similarly, the testing set is sampled with different k data points from each of the classes and is also referred to as query sets.

For each task k, the model with parameters $\theta$ is trained on $D_k^{tr}$. The training updates the parameters to ${\theta }_k^{*}$.

$${\theta }_k^{*}=\underset{\theta }{argmin}\underset{k\sim P_k}{\mathbb{E}}L(D_k^{tr},\theta )$$

(2)

Here, ${\theta }_k^{*}$ represents the optimal parameters for the task k. The meta-parameters $\omega$ are optimized based on the model’s performance across multiple tasks. This performance is evaluated on the query sets of each task, using the task-specific parameters ${\theta }_k^{*}$. The meta-training can then be mathematically defined as

$${\omega }^{*}=\underset{\omega }{argmin}\underset{k\sim P_k}{\mathbb{E}}L(D_k^{test},{\theta }_k^{*}\left(\omega \right))$$

(3)

The expectation $\mathbb{E}$ is over the task distribution, and $L(D_k^{test},{\theta }_k^{*}\left(\omega \right))$ measures the loss on the query set of task k after learning with parameters ${\theta }_k^{*}$ that were adapted in (2).

After the completion of meta-training, the performance of the meta-parameters is assessed by drawing a new meta-test task ($k^Q$), which is drawn from the same distribution as that of the tasks used in the meta-training phase. The inductive bias is applied to the corresponding dataset ($D_{k^Q}^{tr}$) and tested on ($D_{k^Q}^{te}$). During the meta-test step, the new inductive bias ${\omega }^{*}$ is used to train the base model (inner loop) on each previously unseen task $(q\sim Q)$:

$${\theta }^{*}=\underset{\theta }{argmax}logp\left(\theta \right|{\omega }^{*},D_{k^Q}^{tr})$$

(4)

The previous discussion sums up the flow of meta-learning in multiple-task scenarios. Meta-learning algorithms are differentiated based on how inductive bias is estimated, e.g., Ref. [42] proposed a Bayesian fast-adaption method for meta-learning and Ref. [43] formulated the problem as a fully Bayesian inference problem. Primarily, the goal is to simplify the implementation of meta-learning which has been a major research topic over the past few years; see, e.g., [41,44,45,46]. Based on these works, meta-learning can be categorized into three distinct types: model-based, metric-based, and optimization-based meta-learning, each with its unique strategies for inducing rapid learning adaptation.

3.1.1. Model-Based Meta-Learning

Model-based meta-learning is one of the primary approaches in meta-learning. In this approach, the learning model itself incorporates mechanisms to remember or internalize information from tasks it has previously encountered. This approach often employs memory-augmented neural networks or models with dynamic components that can alter their behavior based on the data they see.

The model-based meta-learning is equipped with an internal memory or state that stores information about the tasks it has learned. This memory aids in the quick adaptation to new tasks. The model’s internal structure can change dynamically in response to new data, allowing it to apply previously learned knowledge to new situations.

Model-based meta-learning excels in scenarios where tasks share underlying structures or patterns. The internal memory or state of the model allows for leveraging past experiences, making it particularly effective in few-shot learning and tasks with limited data. However, one of the main challenges in model-based ML is the design of the memory mechanism. It needs to be capable of storing relevant information without becoming overwhelmed by less useful data. Additionally, ensuring that the model generalizes well to truly novel tasks, not just variations of previously seen ones, can be complex.

To allow a better understanding of the algorithm, the pseudo-code of model-based meta-learning is given in Algorithm 1:

Algorithm 1 Model-based meta-learning

1: Initialize the model M with parameters $\theta$ and initial state s   2: for each meta-training iteration do   3:     Sample a batch of tasks k from the task distribution $P_k$   4:     for each task k in K do   5:         Split K into support set $D_k^{tr}$ and query set $D_k^{test}$   6:         Update the model’s state $s_k$ based on $D_k^{tr}$:   7:              $s_k^{\prime }=\mathrm{UpdateState}(M,D_k^{tr},\theta ,s)$   8:         Evaluate the model on $D_k^{test}$ using the updated state $s_k^{\prime }$:   9:              $los{s}_k=\mathrm{ComputeLoss}(M,D_k^{test},\theta ,s_k^{\prime })$ 10:     end for 11:     Update the model parameters $\theta$ based on the aggregated loss across tasks: 12:          $\theta =\mathrm{UpdateParameters}(\theta ,\left\{los{s}_k\right\})$ 13: end for 14: The model M with updated parameters $\theta$ is now ready for rapid adaptation to new tasks     Function UpdateState(Model M, SupportSet D_tr, Parameters $\theta$, State s): Process $D_{tr}$ through M with parameters $\theta$ and state s Update and return the new state $s^{\prime }$     Function ComputeLoss(Model M, QuerySet D_test, Parameters $\theta$, State $s^{\prime }$): Make predictions on $D_{test}$ using M with $\theta$ and updated state $s^{\prime }$ Calculate and return the loss based on the predictions and true labels     Function UpdateParameters(Parameters $\theta$, Losses$\left\{los{s}_k\right\}$): Perform an optimization step (e.g., gradient descent) to minimize the aggregated losses Return the updated parameters $\theta$

3.1.2. Metric-Based Meta-Learning

Metric-based meta-learning is an approach within meta-learning that focuses on learning a measure of similarity (or a metric) between data points. It is particularly effective in few-shot learning scenarios, where the goal is to classify new data points based on a small number of examples. In metric-based meta-learning, the learning model is trained to embed input data points into a feature space where similar points are close together, and dissimilar points are far apart. The key idea is to learn a metric or distance function that can be used to compare new data points with a small set of labeled examples (support set) to make predictions.

At the heart of metric-based meta-learning is an embedding function that maps input data into a feature space. This function is represented by a neural network with parameters $\theta$ that transforms raw data into embeddings where similar instances are closer together, and dissimilar ones are further apart. The approach relies on a well-defined metric that quantifies the similarity or distance between these embeddings. Common choices include Euclidean distance, cosine similarity, and Mahalanobis distance.

Metric-based meta-learning excels in few-shot learning tasks where the model must make accurate predictions after seeing only a few examples. By learning a robust similarity measure, the model can effectively compare new, unseen data points with a small number of labeled examples (support set) to make predictions. The pseudocode of metric-based meta-learning is given in Algorithm 2.

Metric-based meta-learning is a powerful technique for quickly adapting to new tasks by learning a space in which data points can be effectively compared. Its strength lies in its ability to make the most out of limited data, making it an invaluable approach among various meta-learning techniques. The success of metric-based meta-learning heavily relies on the quality of the learned embeddings. The embedding function must be capable of capturing the nuances and variances across tasks.

Algorithm 2 Metric-based meta-learning

1: Initialize the model M with parameters $\theta$   2: for each meta-training iteration do   3:       Sample a batch of tasks k from the task distribution $P_K$   4:       for each task k in K do   5:             Split k into support set $D_k^{tr}$ and query set $D_k^{test}$   6:             Embed all points in $D_k^{tr}$ and $D_k^{test}$ using M:   7:                  $Embedded\_D_k^{tr}=\mathrm{Embed}(M,D_k^{tr},\theta )$   8:                  $Embedded\_D_k^{test}=\mathrm{Embed}(M,D_k^{test},\theta )$   9:             Compute pairwise distances between points in $Embedded\_D_k^{test}$ and $Embedded\_D_k^{tr}$ 10:             Assign labels to query points based on nearest neighbors in the support set 11:             Calculate the loss based on the accuracy of these assignments 12:         end for 13:         Update the model parameters $\theta$ based on the loss 14: end for 15: The model M with updated parameters $\theta$ is now ready for new tasks Function Embed(Model M, DataSet D, Parameters $\theta$): Return the set of embedded points for each data point in D using M with parameters $\theta$

3.1.3. Optimization-Based Meta-Learning

Optimization-based meta-learning is a prominent approach within meta-learning, focusing on optimizing the learning process itself. This approach aims to determine optimal initial parameters or learning strategies that enable rapid adaptation to new tasks. The central idea of optimization-based meta-learning is to learn optimal initial conditions (like model parameters or learning rates) that can be quickly fine-tuned for various tasks. This approach is grounded in the hypothesis that there exists a set of initial conditions from which a model can rapidly adapt to a new task with minimal additional training.

In an optimization-based ML algorithm, the model learns a set of initial parameters that are not task-specific but provide a good starting point for a variety of tasks. The model can quickly adapt these parameters to new tasks using only a few training examples. It involves two nested learning processes: an inner loop that performs task-specific learning and an outer loop that optimizes the initial parameters across tasks.

The pseudocode for optimization-based ML is given in Algorithm 3.

Algorithm 3 Optimization-based meta-learning

1: Initialize model parameters $\theta$   2: for each meta-training iteration do   3:       Sample a batch of tasks k from the task distribution $P_K$   4:       for each task k in K do   5:           Adapt $\theta$ to task k to get ${\theta }_k^{\prime }$:   6:                ${\theta }_i^{\prime }=\theta -\alpha {\nabla }_{\theta }L(k;\theta )$   7:           Evaluate adapted model on k   8:       end for   9:       Update initial parameters $\theta$ based on performance across tasks: 10:            $\theta =\theta -\beta {\nabla }_{\theta }{\sum }_{k}L(k;{\theta }_k^{\prime })$ 11: end for 12: The model with updated initial parameters $\theta$ is now ready for rapid adaptation to new tasks

4. Use Cases

In this section, we attempt to highlight different and rather innovative wireless communication areas and how they can be facilitated by using meta-learning and compare it with specific classes of learning algorithms. We used the classic communication problem of designing optimal decoders and demodulators in RF-WCSs, OWCs, and MCSs. A typical communication link comprises transmitting and receiving nodes, where the receiver is equipped with demodulators and decoders that assist in estimating the channel. For this purpose, a known training sequence (pilot symbols) is transmitted to estimate the channel state information (CSI) by utilizing the shared knowledge between the transmitter and the receiver. Simple least mean square (LS) or linear minimum mean square error (LMMSE) methods are then used for channel estimation. This method has proven to be effective in many channel models; however, they fail to perform adequately in scenarios with limitations in the availability of channel models, e.g., in visible light communication or molecular communication. In MIMO systems, the pilot’s length is smaller compared to the number of antennas leading to poor performance of the aforementioned techniques. Additionally, the pilot symbols reduce the overall spectral efficiency of the communication link, as 8% of the information in IEEE 802.11 models comprises pilot symbols in a 20MHz channel [47].

In a traditional machine learning-based system, the received signal is fed as an input, and the transmitted symbols are retrieved at the output, where the demodulation and decoding are treated as a classification task. Neural network architectures are trained over extensive datasets comprising pilot symbols, allowing them to learn different distributions and correlations, which are then used for channel estimation. The training dataset directly affects the performance of the overall system, during testing, along with the adequacy of the parametric model.

Some of the recent works include [48], where the authors investigate the mean square error (MSE) difference between the machine learning-based channel estimation and the minimum mean square error (MMSE) estimation channel estimation and showed that there is an upper bound of the MSE difference even if the inputs are not from the training dataset. In [49], Massadi et al. proposed channel estimation based on training neural networks to learn MIMO channel statistics over a dataset, which is then used to jointly design pilots and estimate the channel, hence diminishing the need for covariance matrices. They showed that their proposed NN structure improved the normalized mean square error (NMSE) as compared to the techniques that used FFT pilots’ NN-based channel estimation.

The wide range of wireless communication standards and protocols operates in a diverse environment. Hence, the non-trivial components, such as encoders and decoders, should adapt according to the varying traffic statistics. The conventional machine learning protocols discussed previously train a model specific to a particular situation. Therefore, a more desired approach would be to train models that perform adequately in all configurations. More recently, meta-learning has drawn attention as it operates at a higher abstraction level and uses data from different configurations.

We consider a typical IoT scenario, with k = 1, 2… K devices and a base station (BS). The data bits are mapped to complex constellation symbols $s_k$, drawn from the set of all constellation symbols S. The signal received at the BS is then defined as

$$y_k=h_k{x}_k+n_k$$

(5)

where $h_k$ is the complex channel gain, $n_k$ is zero-mean additive white Gaussian noise (AWGN) with power spectral density $N_o/2$ and $x_k$ is the transmitted data after going through random transformations, which are given by the conditional distributions $P_k(.|s_k)$ that model the non-linearities of the IoT devices. The need to model the non-idealities only at the transmitting side and not at the receiving side arises because they are not too significant at the BS and can easily be mitigated through offline designs before the BS is deployed.

For the VLC system model, we have considered an indoor scenario with a room of dimensions 6 m × 6 m × 3 m, with plaster ceilings, walls, and a pinewood floor. There are $k=1,2$…K VLC-supported access points mounted to the ceilings. The end users are distributed uniformly throughout the area and can move in any direction with equal probability. The channel parameters used in the simulations are given in

Table 3. Channel parameters for VLC simulations.

Room Size	6 m × 6 m × 3 m
Materials	Walls: Plaster Ceiling: Plaster Floor: Pinewood
Object specifications	Cell phone: Black gloss paint Human body: Absorbing
Luminaire specifications	Number of luminaires: 9 Brand: Cree® CR6-800L Half viewing angle: 40° Power per each luminaire: 11 W
Receiver specifications	Receiver area: 1 cm2, FOV: 85°

.

We consider adaptive direct current biased optical orthogonal frequency division multiplexing (DCO-OFDM), which assigns data to all odd and even subcarriers as

$$\mathbf{X}=[0x_1\dots x_{N/2-1}0x_{N/2-1}^{*}\dots x_1^{*}]$$

(6)

where n = 0, 1, 2 … N − 1 is the number of subcarriers, an N-point inverse fast Fourier transformation (N-IFFT) is applied to X, which results in a real-valued waveform x at the output, whose nth element is given by

$$\mathit{x}\left[n\right]={\displaystyle \frac{1}{\sqrt{N}}}\sum _{k=0}^{N-1}X\left[k\right]e\frac{2jnk\pi }{N}$$

(7)

where n = 0, 1, 2 … N − 1 and X[k] is the modulation symbol that is drawn from 2-PSK and M-QAM with M = 4, 8, 16, 32, 64, 128, and 256. To avoid inter-symbol interference (ISI), a cyclic prefix, of length $N_{cp}$ is further added at the beginning of x[n]. To achieve the unipolar constraint of IM/DD, the waveform is biased with a DC offset ($A_{DC}$). The resulting time domain waveform is then given as

$$x\left(t\right)=\sum _{n=0}^{N+N_{cp}-1}x\left[n\right]\delta (t-n{T}_s)+A_{DC}$$

(8)

where $T_s$ is the sampling interval.

At the receiver’s end, the signal y(t) is defined as (9)

$$y\left(t\right)=R\sqrt{P_x}x\left(t\right)\otimes h\left(t\right)+n\left(t\right)$$

(9)

where R is the responsivity of the photodetector (A/W), $P_x$ is the total electrical power, h(t) is the channel impulse response, and n(t) is the additive white Gaussian noise (AWGN) with zero mean and variance of ${\sigma }_N^2$.

A series-to-parallel operation is performed on the received signal and the CP is removed. The fast Fourier transform (FFT) gives the complex-valued symbols in the frequency domain. The signal at the kth sub-carrier is now given as

$$Y\left[k\right]=R\sqrt{P_x}X\left[k\right]H\left[k\right]+N\left[k\right]$$

(10)

The receiver selects the photodetector, which gives the highest data rate while satisfying a target bit error rate (BER). The data rate (in bits per second) is given as

$$DataRate={\displaystyle \frac{1}{T_s}}{\displaystyle \frac{N/2-1}{L}}lo{g}_{2}M$$

(11)

where $L=N+N_{cp}$ is the total length of the OFDM symbol.

Similarly, for MCSs, a typical one-dimensional system with a transmitter and a receiver with a diffusive channel was considered. We constituted an MCvD-based nanonetwork, with $k=1,2,3$…K nodes, where the information is encoded over messenger molecule concentration waves. The MCvD system consists of the following process: the molecules are first encoded using channel-coding techniques and then emitted in the channel. During the particle emission process, the particle concentration ($N_{Tx}$) is modulated according to the input symbol ($S_k\left(t\right)$), the modulation type, and the signal waveform. The transmitter emits a pilot signal of molecules, which is followed by the encoded symbol. We focus on the MCS system with on–off key modulation (OOK). Let $b_{k_n}$ = $b_{k_0},b_{k_1},$…$b_{k_{\infty }}$ be the information sequence. The transmitter emits $N_{Tx}$ molecules in the form of an impulse to represent $b=1$ and no molecules are emitted for ($b=0$). The transmitted symbol is, therefore, represented as

$$s_{k_n}\left(t\right)=\sum _{n=0}^{\infty }{b}_{k_n}{N}_{tx}\delta (t-k{t}_s)$$

(12)

where $\delta \left(t\right)$ is the Dirac delta function.

After releasing the information carriers, they propagate in the channel modeled by Brownian motion. Upon interacting with the receiver, the molecules are received from the environment. It is assumed that the transmitter and receiver are synchronized and the time is divided into equal slots in which a single symbol $s_k$ is sent. The simulation parameters of MCSs are summarized in

Table 4. Simulation parameters for IoT and MCS.

Parameters	IoT	MCS
Modulation	16 QAM	OOK
Number of iterations	5000	10,000
Average SNR	30 dB	15 dB
Number of meta-training devices	10, 1000	10, 1000
$\eta$	0.1	0.1
$\kappa$	0.0001	0.0001

.

4.1. Problem Formulation

Our objective was to design a demodulator that could successfully recover the transmitted symbols s with the help of only a few pilots. Therefore, we assume that the BS can use the information from the previous transmissions of K devices and their meta-training dataset ($D_k^{tr}$), which consists of a P pair of pilots, $s_k$ and $y_k$, such that $D_k^{tr}=\{(s_k^{\left(p\right)},y_k^{\left(p\right)})$ for $p=1,\dots ,P\}$. Here, $(s_k^{\left(p\right)},y_k^{\left(p\right)})$ are the p pilot received signal pairs for the k meta-training device. N pilots are collected from the meta-test device in set $D_T=\{(s^{\left(p\right)},y^{\left(p\right)})$ for $p=1,\dots ,N\}$, where both datasets $D_T$ and $D_k^{tr}$ are used for training the demodulator. The demodulator ($\widehat{y}$) is then defined by a distribution that depends on the vector $\varphi$ i-e $\widehat{y}=p\left(s\right|y,\varphi )$.

To train the demodulator, ($\widehat{y}$), we assume that it is defined by a multilayered neural network, with L layers, expressed as

$$\widehat{y}={\displaystyle \frac{exp({\left[f_{{\varphi }^{L-1}}\left(f_{{\varphi }^{L-2}}(··f\left(f_{{\varphi }^1}\left(y\right)\right))\right)\right]}_s}{{\displaystyle \sum _{s^{\prime }ϵS}}\left(exp\right({\left[f_{{\varphi }^{L-1}}\left(f_{{\varphi }^{L-2}}(··f\left(f_{{\varphi }^1}\left(y\right)\right))\right)\right]}_s^{\prime }}}$$

(13)

Here, $f_{\varphi }^{\left(l\right)}\left(x\right)$ is the non-linear activation function, which is given by the weight matrix ($W^{\left(l\right)}$) and bias factor $b^{\left(l\right)}$ such that $f_{\varphi }^{\left(l\right)}\left(x\right)$ = $\sigma \left(W^{\left(l\right)x+b^{\left(l\right)}}\right)$. $\sigma (.)$ is a non-linear function, $\varphi$ is the vector of trainable parameters, and ${[.]}_s$ represents the elements belonging to the symbol s.

The problem can now be formulated as a typical meta-learning problem by assuming a demodulator with a context-variable $\phi$ and a shared parameter $\omega$ such that $\widehat{y}$ = $p\left(s\right|y,\phi ,\omega )$.

During meta-training, we used two state-of-the-art meta-learning algorithms, namely model-agnostic meta-learning for fast adaptation of deep networks (MAML) [41] and Cavia [50].

4.2. Results

We compared the performance of meta-learning algorithms, i.e., MAML and CAVIA, with conventional learning, where the data from meta-training devices were not used and the weights of the demodulator were randomly initialized for the three communication settings. We assumed a binary fading channel for the IoT scenario where the bits were modulated with 16-ary quadrature amplitude modulation (16-QAM). Pilot symbols followed a fixed periodic sequence in the meta-training and meta-test sets. A total of K = 10 meta-training devices were considered and the meta-test device transmitted only one pilot symbol. The demodulator was a neural network with three layers (an input layer with two neurons, one hidden layer with 30 neurons, and a softmax output layer with four neurons). The hyperbolic tangent function was used as the activation function. The learning rate was fixed at $\eta =0.1$ and $\kappa =0.0001$ with a single local update and the ADAM optimizer was used to update the shared parameter. In the case of IoT, conventional learning failed to reach error rates less than 0.25. MAML and CAVIA both reached the optimum solutions with MAML outperforming CAVIA by 52%, averaged over the total number of iterations. The difference in performance was due to the underlying algorithm, as MAML adapts to a more significant number of parameters with respect to CAVIA, as shown in Figure 4a. Figure 4b shows the symbol error rate (SER) with respect to the number of iterations during meta-training in the case of VLC. The conventional learning fails to perform adequately for P = 1; it should be noted that the performance will increase as the number of pilots during training will increase. However, despite training over a single pilot, both MAML and CAVIA perform optimally. MAML outperforms CAVIA by 9%, averaged over the total number of iterations.

For molecular communication, we considered a diffusive channel with K = 10 MCS devices. Figure 4c shows SER vs. the total number of iterations. The conventional methods failed to reach error rates of less than 0.25; therefore, they are not shown in the figure.

We investigated the effect of an increasing number of pilots on the overall system’s performance. For this purpose, we simulated for up to 1600 pilots with 1000 meta-training devices, where the symbol error rate was obtained by taking the average of 100 different meta-test devices. In Figure 5a–c, it should be noted that CAVIA performs better with a smaller number of pilots as compared to MAML and the conventional methods. It is worth noting that the conventional ML algorithm performs just as well as meta-learning when the number of data points is increased.

5. Potential Limitations of Meta-Learning

Meta-learning, while offering promising advantages for 6G systems, also presents several challenges that could limit its effectiveness. One of the most significant limitations is the computational overhead involved. Unlike traditional machine learning, where a model is trained for a single task, meta-learning requires training across multiple tasks. This involves both inner and outer loops of learning, which increases the computational complexity. This complexity is especially problematic in resource-constrained environments typical of 6G, such as edge devices. The added computational demands could lead to higher energy consumption, potentially conflicting with one of the key goals of 6G systems—energy efficiency.

Another challenge lies in designing practical and representative meta-learning tasks. For meta-learning to be effective, the tasks used for training must accurately reflect the dynamic and unpredictable nature of 6G environments, where channel conditions, interference, and user demands can change rapidly. However, creating tasks that capture this full range of variability is complex. If the tasks are not representative of real-world conditions, the meta-learning model may not generalize well, reducing its ability to adapt to new scenarios. In this context, the success of meta-learning hinges on the quality and relevance of the tasks used during training.

Data availability and task diversity are also crucial for the success of meta-learning in 6G systems. Although meta-learning is designed to handle limited data, the effectiveness of this learning still depends on the diversity of the tasks used during the training process. In highly dynamic 6G networks, it can be difficult to collect and define a sufficient variety of relevant tasks for meta-training. Without a diverse range of tasks, the model’s ability to generalize to new and unseen scenarios may be compromised, reducing the adaptability that is essential in 6G environments.

Another concern is the adaptation time of meta-learning models. While meta-learning significantly improves the speed at which models can adapt to new tasks compared to traditional learning, it may still not be fast enough for certain real-time applications in 6G. Scenarios such as autonomous driving or remote surgeries demand ultra-low latency, and any delays in adaptation could have critical consequences. Therefore, finding the right balance between adaptation speed and meeting real-time performance requirements is a challenge that needs to be addressed for meta-learning to be fully applicable in such high-stakes applications.

In addition, the complexity of meta-learning models poses challenges for scalability. These models are inherently more sophisticated than traditional machine learning models, and deploying them across large, distributed 6G networks could prove difficult. This complexity is further exacerbated in heterogeneous network environments, where devices with varying computational capabilities must work together. Managing this complexity and ensuring that the models can scale effectively across different types of devices and network nodes is a significant hurdle.

6. Conclusions

In this paper, we investigated the application of meta-learning in 6G wireless communication systems and evaluated the performance of two prominent meta-learning algorithms, model-agnostic meta-learning (MAML) and Contextual Variable Meta-Learning (CAVIA), across three communication scenarios: IoT, optical wireless communication systems (OWCSs), and molecular communication systems (MCSs). Our findings indicate that meta-learning algorithms significantly outperform conventional learning methods, particularly in environments with limited training data.

In the IoT scenario with a binary fading channel and 16-QAM modulation, conventional learning methods failed to achieve error rates below 0.25, whereas both MAML and CAVIA reached optimal solutions, with MAML outperforming CAVIA by 52%. Similarly, in the OWCS setting, meta-learning algorithms demonstrated superior performance even with minimal pilot symbols, with MAML achieving a 9% performance improvement over CAVIA. For MCSs, conventional methods could not achieve error rates below 0.25, while meta-learning algorithms showed significant promise.

Our results also reveal that, while conventional machine learning can match the performance of meta-learning when ample training data are available, meta-learning excels in rapidly adapting to new tasks with minimal data, making it ideal for dynamic and data-constrained environments.

The significance of this research lies in demonstrating the potential of meta-learning to enhance the efficiency and robustness of 6G communication systems. By enabling quick adaptation and efficient learning in diverse and challenging communication environments, meta-learning algorithms pave the way for the development of more intelligent, adaptive, and resilient wireless networks. This work contributes to the ongoing efforts to meet the growing demands of future communication technologies and supports the advancement of smart, connected societies.