Causal Reasoning: Charting a Revolutionary Course for Next-Generation AI-Native Wireless Networks

C. Thomas, and W. Saad are with the Wireless@VT, Bradley Department of Electrical and Computer Engineering, Virginia Tech, Arlington, VA, USA, Emails<EMAIL_ADDRESS><EMAIL_ADDRESS>C. Chaccour is with Ericsson, Inc., Plano, Texas, USA, Email<EMAIL_ADDRESS>M. Debbah is with Khalifa University of Science and Technology in Abu Dhabi and also with CentraleSupelec, University Paris-Saclay, 91192 Gif-sur-Yvette, France, Email<EMAIL_ADDRESS>C. S. Hong is with the Department of Computer Science and Engineering, School
of Computing, Kyung Hee University, Yongin-si
17104, Republic of Korea, Email<EMAIL_ADDRESS>
Despite the basic premise that next-generation wireless networks (e.g., 6G) will be artificial intelligence (AI)-native, to date, most existing efforts remain either qualitative or incremental extensions to existing “AI for wireless” paradigms. Indeed, creating AI-native wireless networks faces significant technical challenges due to the limitations of data-driven, training-intensive AI. These limitations include the black-box nature of the AI models, their curve-fitting nature, which can limit their ability to reason and adapt, their reliance on large amounts of training data, and the energy inefficiency of large neural networks. In response to these limitations, this article presents a comprehensive, forward-looking vision that addresses these shortcomings by introducing a novel framework for building AI-native wireless networks; grounded in the emerging field of causal reasoning. Causal reasoning, founded on causal discovery, causal representation learning, and causal inference, can help build explainable, reasoning-aware, and sustainable wireless networks. Embracing such a human-like AI foundation can revolutionize the design of AI-native wireless networks, laying the foundations for creating self-sustaining networks that ensure uninterrupted connectivity.

Towards fulfilling this vision, we first highlight several wireless networking challenges that can be addressed by causal discovery and representation, including ultra-reliable beamforming for terahertz (THz) systems, near-accurate physical twin modeling for digital twins, training data augmentation, and semantic communication. We showcase how incorporating causal discovery can assist in achieving dynamic adaptability, resilience, and cognition in addressing these challenges. Furthermore, we outline potential frameworks that leverage causal inference to achieve the overarching objectives of future-generation networks, including intent management, dynamic adaptability, human-level cognition, reasoning, and the critical element of time sensitivity.
We conclude by offering recommendations shaping the roadmap toward causality-driven AI-native next-generation wireless networking. Our ultimate goal is to create scientific foundations for AI-native networks that inspire  further unconventional and forward-thinking research in causal reasoning within 6G and beyond thereby charting a course towards next-generation AI-native wireless systems.

§ INTRODUCTION

Causal AI vision for next-generation wireless networks.

As we peer into the future of next-generation wireless networks (e.g., 6G and beyond), the incorporation of AI across the protocol stack of wireless systems is no longer just a theoretical concept—it is becoming a tangible reality <cit.>. AI-native wireless systems must leverage ML and AI algorithms to design, optimize, and operate various aspects of the wireless system, including transceiver design, resource allocation, interference management, spectrum sharing, and more. However, developing AI native 6G wireless systems necessitates the design of novel AI frameworks that are tailored to several unique challenges of wireless systems: 1) dynamic adaptability to ensure rapid adjustments to changing network conditions, user demands, and other environmental factors; 2) time criticality, whereby 6G systems must deliver ultra-low latency and unwavering reliability, particularly for applications demanding split-second responsiveness; 3) intent management, enabling networks to autonomously translate high-level business intents into network configurations in a closed-loop fashion, ensuring intent assurance across the network while maintaining overall network reliability;
4) resilience, enabling 6G networks to withstand disruptions and maintain connectivity even in challenging scenarios; 5) non-linear signal dynamics, that must be properly modeled to accurately capture the time-varying nature of multi-modal wireless signals, e.g., audio, video, haptics and olfactory signals; and 6) human-level cognition and reasoning that must be integrated into the wireless system for intelligent decision-making, self-optimization, and efficient resource management, ultimately enabling both sample efficiency and communication efficiency, thereby achieving more with less data and resources.

Despite significant progress in AI-native wireless networks, existing solutions (e.g., <cit.>) remain predominantly data-driven and based on statistical learning.
These traits pose certain challenges in overcoming the aforementioned challenges.
Firstly, statistical AI models require extensive data volumes, to ensure reliable performance. However, obtaining extensive datasets is not always feasible in wireless networks. Secondly, current AI model parameters are closely linked to their training data, requiring frequent and recurrent retraining to maintain effectiveness as the wireless and RAN environments undergo rapid changes.
This consumes substantial communication and computational resources. The resulting training overhead could disrupt the communication phase, consequently impacting the stringent requirements of emerging wireless services, in terms of uninterrupted availability and near-zero end-to-end latency. Furthermore, existing AI tools frequently encounter challenges when it comes to reasoning, particularly when tasked with producing novel insights or combining already-seen experiences to generate fresh combinations or make logical deductions.
Finally, the reliance of statistical AI on complex NN and often opaque architectures makes it challenging to identify the root causes of any performance deviations or network operation issues at the granular level across the network stack, interfaces, and the profusion of devices and sensors.

To overcome these limitations, as envisioned in Fig. <ref>, it is imperative to design new AI frameworks that: 1) enable reasoning and generalization by exhibiting consistent performance across diverse wireless data distributions (inductive reasoning), as well as an ability to combine already seen experiences to generate novel logical conclusions (deductive reasoning), 2) possess the properties of explainability and transparency which means they can operate reliably while providing insights into how and why they make specific decisions, thereby developing a deeper understanding of their actions across the wireless network protocol stack, and 3) promote the advancement of sustainable and green networks by improving sample efficiency and creating more lightweight ML models. Several methodologies can facilitate the development of generalizable AI, such as transfer learning, meta-learning, domain adaptation, and continual learning <cit.>. However, these approaches still require extensive and diverse datasets for efficacy and typically rely on NN that lack transparency and interpretability. An alternative approach could involve collecting a substantial amount of wireless data through extensive sensing, similar to the data acquisition methods used for LLM like ChatGPT. This approach, called data-driven networking with foundation models <cit.>, can bolster AI models' adaptability in wireless contexts. While such generative AI models are useful as writing assistants, their models are known to generate spurious data points that impair the wireless network resilience and could yield faulty predictions. In fact, as shown in <cit.>, ChatGPT today is seeing more errors than when initially introduced due to challenges like model collapse and catastrophic forgetting. Hence, deploying ChatGPT-like AI models for wireless networks, especially in mission-critical and time-critical settings, may be risky and brittle (e.g. autonomous vehicles or digital twins of industrial plants). Additionally, gigantic NN architectures are compute-hungry and require significant processing, thus leading to energy-inefficient networking which contradicts the ongoing pursuit of energy-conscious sustainability objectives.

Essentially, if we are to efficiently design AI-native wireless networks, we must create AI framework that excel in performance and in emulating human-like reasoning capabilities. “Human-like reasoning capabilities" refer to the ability of AI systems to think, make decisions, and understand information analogously  to how humans do, encompassing common sense, reasoning, contextual understanding, adaptability, as well as ethical and explanatory capabilities.
Such models could alleviate the challenges associated with conventional ML approaches by providing a deeper understanding of their decision-making processes and achieving superior generalization across an array of tasks and scenarios as required by next-generation AI-native wireless networks. Here, a promising avenue lies in the realm of causal reasoning <cit.> and <cit.>.

Causal reasoning involves recognizing cause-and-effect relations within the wireless data, helping the AI models understand how changes in one component of the system can impact or predict outcomes in other components, and, facilitating informed decision-making and effective problem-solving.
Causality is realized through the processes of causal discovery, representation, and inference.

Causal discovery enables the creation of explainable AI-native wireless models, allowing us to describe the network decisions that result in specific outcomes unlike the opacity of transfer or meta or continual learning schemes. Meanwhile, causal inference and representation facilitate human-like reasoning by leveraging concepts like interventions and counterfactuals, which can be performed either online or offline on the learned causal model. In causal ML, “interventions" involve actively manipulating one or more network variables to observe the effects on other variables. “Counterfactuals" refer to hypothetical scenarios where we assess what would have happened if certain interventions or changes had or had not occurred, providing insights into the causal impact of those interventions.
Causal inference empowers wireless systems to extend the applicability of their predictions and decision-making capabilities across various data distributions (generalizability), assuming a consistent data generation process (causal understanding). This results in more resilient and efficient knowledge transfer across domains compared to transfer learning, enhanced sample efficiency (leading to sustainability) compared to meta-learning, and dynamic adaptability to varying task or data distributions without the risk of catastrophic forgetting associated with continual learning.
As shown in Fig. <ref>, advances in designing causal reasoning frameworks will allow the development of AI-native wireless networks characterized by the previously discussed attributes that include reasoning awareness, intent management, resilience, dynamic adaptability, and real-time synchronization which align with the objectives of next-generation wireless networks, namely 6G and beyond.

§.§ Contributions

The main contribution of this article is a novel and holistic vision that articulates fundamental principles necessary
to build next-generation causality-driven, AI-native wireless networks. Our key contributions include:

* We first present the fundamental building blocks of causal reasoning, and we motivate the need for incorporating them in future wireless networks through a simple example.

* We identify the inherent challenges in current AI-native wireless systems, like lack of explainability, limited reasoning capability, and energy inefficiency. We then discuss the potential of causal reasoning for addressing these challenges.

* We demonstrate how causal discovery and representation can expedite the advancement of interpretable and cognition-enhanced wireless systems by deciphering the causal relationships within wireless data as a graph and subsequently dissecting cause-and-effect dynamics. The cause-and-effect dynamics are analyzed by CGM to facilitate dynamic channel tracking in THz systems, precise DT modeling, training data augmentation, and the development of resilient wireless networks. We also showcase how causal discovery and causal representation provide a more rigorous interpretation of the semantic information intrinsic to wireless data when compared to state-of-the-art methods.

* We introduce a robust analytical framework based on causal inference for addressing wireless control problems. This framework leverages the learned CGM and incorporates causal RL, causal MAB, and causal multi-objective optimization. We further outline how causality can address challenges related to partial observability, scalability, and real-time communication protocol design in ISAC systems.
Leveraging interventional and counterfactual reasoning within causal ML, these frameworks aim to achieve the wireless goals of dynamic adaptability, intent management, and time criticality.

In a nutshell, this paper will serve as an authoritative guide and a meticulously crafted roadmap for understanding the indispensable AI principles required to construct and manage next-generation AI-native networks, equipping them with human-like reasoning capabilities.

§ CAUSALITY PRIMER

Our first key step is to fundamentally explain why and how wireless models can benefit from causal structure learning. Towards this aim, this section provides a primer on causality, exploring its fundamental concepts and its relevance to wireless systems.

Mapping a propagation environment to a causal diagram. For simplicity, the diagram shows the causal dependencies for a single path, while the discussions in the paper is revolved around a more general case, that encompassed multiple scattering elements and multiple channel paths.

§.§ Why do Statistical ML Models Fall Short in Reasoning over Wireless Networks?

Causality provides insights into the actual cause-and-effect dynamics within a system, akin to the “physics" of the system, and hence goes beyond mere correlation or statistical dependency. Consider a simple wireless beam training example for a THz system where pure statistical deep learning methods may fail. In
this example, the system is provided with a dataset containing channel or network parameters $(X)$ and their corresponding labels $(Y)$ that represent a beam index. The model's objective is to learn a mapping function, $Y = f(X)$, that accurately predicts the labels based on the observed channel data. In this purely statistical approach, the model's learning process relies on identifying and capturing statistical dependencies (in short, the joint distribution $P(X,Y)$ between input $(X)$ and output $(Y)$ variables. To illustrate why a pure statistical approach is insufficient, we expand the simple beam tracking example as illustrated in Fig. <ref>.
The physics behind the generation of the channel geometry encompassing location parameters and scatter parameters ($S$) are represented by variables $\bmu_e,\bmu_s,$ and $\bmu_p$, that are exogenous to the channel model. The dependency of these exogenous variables on the channel geometry parameters via $f_e, f_s,$ and $f_p$, cannot be accurately determined. As shown in Fig. <ref>, the propagation geometry parameters determine the angle of arrival (AoA) $\theta_{i,l}$, delay $\tau_{i,l}$, and path amplitudes $\alpha_{i,l}$, and their relationships are governed by either deterministic or random functions <cit.>. The channel vector at any subcarrier $s$ and time $t$ can be analytically represented as:

_s,t    = ∑_i=0^I∑_l=0^L-1 f_α_i,l(x_p,f_c)_R(θ_i,l)e^-j2πsΔfτ_t^(i,l)

= (,x_b,x_u,_p,f_c,),

where subscript $(i,l)$ corresponds to the $i^{th}$ scatterer and $l^{th}$ path, with $\theta_{i,l} = f^{\theta}_{i,l}(x_b,x_u,S,x_p)$, and $\tau_{i,l} = f^{\tau}_{i,l}(x_b,x_u,S,x_p)$. $\btheta, \bmx_p$, and $\balpha$ represent the vectors of AoA, position, and amplitude corresponding to distinct scatterers.  $x_b$, and $x_u$ are the locations of BS, and UE, respectively. $\bmb_R$ represents the array response vector.
$i=l=0$ captures the LoS path. Conventional ML solutions approximate the non-linear function $\bmg(\btheta,x_b,x_u,\bmx_p,f_c,\balpha)$, given the extracted channel parameters from the training data. The BS employs received pilot observations and UE feedback during the UL as their ML training data.
In THz bands, increased penetration losses and reduced reflection coefficients (captured by $S$) heighten vulnerability to signal blockages, endangering transmission reliability <cit.>. A sudden obstruction, such as a moving object or a person, disrupts the LoS path between the UE and BS, leads to channel $\bmg_I(\btheta,x_b,x_u,\bmx_p,f_c,\balpha)$. This channel exhibits substantial power fluctuations, far more pronounced than those encountered in mmWave or sub-6 GHz bands. Classical ML models could handle smaller variations in non-linear channel models, however, they cannot capture the immense dynamic variations typical of THz frequencies.  This limitation arises from their inherent curve-fitting nature, where the NN parameters are closely linked to the specific dataset used for their training.
Furthermore, such black-box models cannot explain the rationale behind the selection of a specific beam index for a given set of channel parameters. One potential remedy to this issue involves training the ML algorithm using an extensive dataset, with the assumption that, on average, system performance remains consistent. Nonetheless, this approach has its drawbacks. Firstly, it demands substantial training data, which may not always be readily available. Secondly, it leads to ML models with a large number of parameters, resulting in higher energy consumption as well as bulkier hardware. Hence, a fundamental question arises: how can we transition to a AI model that can adapt its performance to various channel distributions, be resilient to unforeseen scenarios, and provide interpretable results, unlike black-box models? One answer is through the use of causal reasoning <cit.>. In causal ML, the system can obtain an understanding of the causal relationships that lead to the generation of the channel as well as the relations among network variables that determine the user QoE. These causal relationships can be captured using directed edges in a graph (see Fig. <ref>). For instance, $\bmh$ is an effect of parameters $\btheta,\btau,\balpha,$ and $W$ as well as RAN parameters (these cause variables are called parents of node $\bmh$), and can be represented using a deterministic or random function. Understanding these dependencies enables AI inference engines to manipulate them in real-time, thereby 1) enhancing the network's predictive capabilities; and 2) ensuring better network decisions aligned with long-term goals, promoting seamless network connectivity. Next, we look at how grasping these causal relationships confers advantages over traditional deep learning-based wireless systems.

§.§ How Can We Embed Causality Awareness into AI-Native Wireless Models?

In our example, the wireless environment is represented by $X = \{x_b,x_u,x_p, S\}$ that encompasses factors like the physical object layout, which influences channel conditions, and users' locations. Components of $X$ are represented by the possibly non-linear functions $f_e,f_s,$ and $f_p$.
Here, to assess the influence of $X$ on $Y$, in addition to utilizing offline data such as UL channel measurements, a causality-based framework integrates online data generated from various experiments using the causal structure. These experiments, also called interventions, can be defined as picking the functions $f_i, \forall i \in \{e,s,p,\theta,\tau,\alpha\}$ from a set $\mF_i$ of different environment as well as RAN characteristics. Using interventions, system designers can understand how different factors within the wireless environment, represented by $X$, influence the QoE experienced by end users, represented by $Y$. Classical AI-native systems cannot achieve this, as they lack an understanding of inherent causal relationships. The best they can do is generate extensive set of random data distributions to train the AI model, resulting in sample inefficiency. This example illustrates the potential implications of causality in wireless systems.

Activity     Typical
Question     Wireless Network Example     AI Model
$\mL_1:$ Associational $p(y\mid x)$     Seeing
(e.g., UL channel measurements,
multi-modal sensors for DT)     What is?
How would seeing
change my belief
in $Y$?     What does channel quality
tells us about QoE at the user?      Supervised and
variational auto-encoders,
transformers, large lanugage models.
$\mL_2:$ Interventional $p(y\mid {do}(x))$    Doing
(e.g., dynamic network slicing decisions,
dynamic mobile-edge computing
offloading decisions)     What if?

What if I do $X$?
What if I increase
the number of antennas,
would my BF quality be adjusted
for better user QoE?     Causal RL,
causal multi-armed bandit.
$\mL_3:$ Counterfactual $p(y_x\mid x^{\prime},y^{\prime})$    Imagining
(e.g., altering network infrastructure,
transmission schemes for
recuperating from malicious firmware
attack that corrupt the AI algorithms)     Why?
What if I
had acted
differently?     Was it the frequency band,
rather than the number of antennas,
that had a detrimental effect on user QoE?     Theory of mind based reasoning <cit.>,
counterfactual explanation policies
using RL<cit.>.

Different levels of reasoning using causal logic, with wireless examples.

Next, we investigate how we can achieve the goals of explainability, generalizability, and energy efficiency using the fundamental building blocks of causality: Causal discovery, causal inference, and causal representation learning (CRL).

Causal discovery provides an algorithmic method to learn the inherent causal structure within observed wireless data, encompassing channel information, network topology, or any multi-modal source data.
In contrast to statistical AI models, where the correlation between entities (features) within the data is inferred, a causal model accurately portrays the relationships among them that have an explanation (via directionality). Therefore, causal discovery offers an approach to design explainable AI-native wireless networks.

One popular approach to represent a causal model through a graph is to use the language of SCM <cit.> to describe the underlying mechanisms that drive a specific phenomenon of interest. SCM, formally defined next, remain the most tractable way to perform causal logic, thus, hereinafter, we will be giving our examples via SCM.

An SCM is a collection of elements $<\mU, \mV, \mF, P(\bmU)>$, where $\mV$ represents endogenous variables (cause and effect variables), and $\mU$ represents exogenous variables (random, unknown noise). The structural functions $f_i \in \mF$ are designed so that $f_i(\textrm{PA}_i, \bmu_i)$ determines $\bmv_i$, where $\textrm{PA}_i \subset \mV$ and $\bmu_i \subset \mU$ specify the sets of parents (in the graph) and exogeneous inputs, respectively. The exogenous distribution $P(\bmu_i)$ determines the values of $\bmu_i$, and thus the distribution of endogenous variables $\mV.$

Causal discovery assumed variables $\bmv_i$ to be random variables connected by a causal graph. However, real-world wireless observations are usually not structured into those variables. For example, high-dimensional channel information or raw source data that is either video or images or holograms. Herein, it is essential to exploit the concept of CRL.

CRL involves mapping large dimensional observations $\bmD\!=\!\left[d_1,\cdots,d_D\right]^T\!$ into a lower dimensional representation involving causal variables $\bmv_1,\cdots,\bmv_n$, captured as:
_i = f_i(PA_i,_i), ∀i.

We now turn our attention to leveraging the causal model for making informed decisions and drawing meaningful inferences through the concept of causal inference.

Causal inference seeks to leverage the knowledge of the causal structure obtained from the causal discovery phase and the learned representations from CRL to make predictions and answer questions about the effects of interventions or counterfactuals over variables of interest. The utilization of causal inference thus empowers wireless systems with both inductive and deductive reasoning capabilities.

Causal inference can be effectively implemented using two key concepts:

* do-calculus: The do-operator is a mathematical tool used to represent a physical intervention or manipulation of a variable in a causal model <cit.>. In the context of a causal model represented as $Z \rightarrow X \rightarrow Y$, applying the do-operator to $X$ involves removing all incoming edges (that represent the generation of a particular variable from its descendants) to $X$ and setting to a specific value, $x_0$. This can be represented as ${do}(X) = x_0$.  For example, in Fig. <ref>, using a do-operator, the system designer can analyze the impact of different environments by considering ${do}(X)$ as implementing different propagation environments, e.g., Rayleigh, Rician, or purely LoS. Alternatively, the $\textrm{do}-$operator in this scenario can mimic the dynamics of user/scatterer locations as:
x_t = f^(i)(x_t-1) + n_t, i ∈
where $f^{(i)}(x_{t-1})$ can be a non-linear function and $n_t$ an additive noise component. $\mathcal{I}$ constitutes the set of interventions, encompassing a diverse range of functions that portray different forms of user or scatterer movements. These variations could span scenarios such as high-speed train travel or particle displacements within environments experiencing strong winds. Alternatively, $f^{(i)}$ could refer to random functions that produce novel combinations of scatterers.
This simulation of intervention can be performed online, without any human intervention. Interventions allow us to study the causal effects of directly manipulating $X$ on the subsequent variables in the causal model, such as its effect on the outcome variable $Y$, while ignoring the causal relationships from $Z$ to $X$.

* Counterfactuals: Counterfactual problems entail the process of reasoning about the causes behind events, envisioning the outcomes of different actions in hindsight, and determining which actions could have led to the desired results.
In the previous example of the channel's impact on QoS, a potential counterfactual question could be: “In a THz system, would the network's QoS have been more resilient to blockage if a RIS were placed near the UE/BS, to alter the propagation environment?" Analytically, this example counterfactual query can be formulated as optimizing the RIS phase shifters:

[^∗]    = max_ [Y|_o,y_o],

[Y|_o,y_o] - Y_g^2 ≤ϵ,

where $\bmx_o$ is the set of observed channel parameters, $\bmy_o$ is the observed QoS (e.g., throughput or delay or reliability), and $\bphi$ is the vector of RIS phase shifts. $Y_g$ is the target QoS value and $\epsilon$ is an arbitrary small quantity.
Hence, using counterfactuals, AI models can go beyond just observing the impact of an intervened environment. They can generalize their model behavior to hypothetical scenarios where fundamental changes to the network setup, such as introducing new technologies or altering configurations, could improve performance under various conditions.
In traditional wireless problems, the objective is to find the optimal solution for a predefined objective function under specific constraints. In contrast, counterfactuals empower the AI system to adjust these objectives and constraints based on higher-level requirements, offering a more flexible and adaptive approach to problem-solving. Hence, the counterfactual formulation in (<ref>) outperforms conventional optimization approaches in wireless problems.

In Table. <ref>, we provide several wireless examples that can capture interventional and counterfactual queries. In comparison to traditional deep learning or model-based optimization, a causal approach with counterfactuals and interventions has major advantages. First, during training, causality allows training the AI model on a diverse set of interventional and counterfactual queries as captured by (<ref>) and (<ref>), in addition to statistical observations. This approach fosters distribution invariance, ensuring robustness of the causal ML algorithm to all interventional and counterfactual distributions. The second advantage involves the practical implications of understanding causal relationships within wireless networks for short-term and long-term planning. Certain network decisions, such as power allocation (for instance, transitioning from equal power allocation to an interference-aware water-filling algorithm), computational resource optimization (assigning downlink RAN computations to either renewable or non-renewable energy nodes for sustainable wireless), or scheduling algorithm changes, can potentially be executed in real-time with minimal impact on QoE performance. This is achievable because causal AI algorithms can compute minimal resource allocation or signal strategy changes by optimizing long-term average rewards (e.g., QoE, given the network's current state). The resulting causal inference process also incorporates previous experiences and can be formulated as a counterfactual query, as demonstrated in (<ref>). Conversely, long-term planning may involve addressing issues like blocked wireless links to specific UE, which may require the introduction of RIS on buildings as a potential solution. These longer-term initiatives may necessitate human intervention.

Next, we delve into the limitations and challenges faced by current AI-native wireless networks.

§ CLASSICAL VS. CAUSAL REASONING-BASED AI-NATIVE WIRELESS NETWORKS

This section outlines the prominent hurdles prevalent in contemporary AI-powered wireless systems, and the potential of causality to overcome them.

§.§ Lack of Explainability and Trustworthiness

§.§.§ Why are existing AI models not interpretable?

In model-based Bayesian systems, the mapping from the data $X$ to $Y = f(X)$ is achieved by assuming a specific model, ${Y} = A(\btheta)X + N$, where $\btheta$ represents the set of estimated parameters. This is a common model for several wireless communication problems including channel estimation, data detection, and resource allocation <cit.>. In Bayesian systems, explainability is evident since the model provides clear insights into which set of parameters contributes to a particular outcome.
For instance, in a single-user downlink scenario, it is apparent from the receiver SNR expression ($Y$) why maximizing it is achieved through maximum ratio transmission ($X$).  However, when dealing with non-linear underlying signal models that are difficult to accurately capture, deep learning systems often outperform Bayesian model-based systems. Despite their superior performance, deep learning models face key challenges such as sample bias and overfitting.
By using black-box models, AI algorithms cannot comprehend the root causes behind deviations from particular performance objectives.
As a result, these algorithms cannot discern the minimal configuration changes needed in terms of resource allocation or control signaling approaches to tackle performance issues effectively. This limitation impacts their capacity to autonomously restore the system to the designated target QoE. This demands periodic retraining to sustain uninterrupted connectivity and ensure the expected QoE. This can be exemplified using the THz blockage example discussed in Section. <ref>.

§.§.§ Causal modeling for explainable wireless networks

To address the aforementioned challenge, we offer insights into the interpretability of causal models.

For example, as shown in Fig. <ref>, in dynamic network slicing problems, variable $Y$ plays the role of a QoE metric, which provides insights into user satisfaction and network performance based on resource allocation. Variables $\bmc_i$ represent control parameters like power or resource block allocation, signaling waveforms or computational resources for individual network slices. Each slice may have have its own varying bandwidth, latency, and reliability requirements that must be met by the resource management framework. The intermediate variables could encompass network metrics such as SNR, channel quality metrics, or average queue length at the transmitter. Some of these metrics may directly impact the final QoE metric, while others, like variables $\bmX_0$, may represent miscellaneous control information irrelevant to the QoE. The objective is to compute the set of intervention variables $\mC_s \in \mC$ (defining all causal variables in the graph) and their corresponding intervention levels $\bmc_s$ to optimize the expected target outcome $\bmY$. Unlike traditional ML-driven wireless solutions, leveraging a causal graph empowers the AI algorithm to calculate optimal interventions, such as resource allocation variables, within a broader set $\mC$. This set may contain alterations to the generation of network variables compared to just utilizing observational data. Consequently, the outcome will be resource allocation algorithms that maintain invariance to these interventions as long as the causal relationships remain intact. Formally, the goal is to find:

[_s^*, _s^*] = __s∈, _s∈_s 𝔼_P(|do(_s=_s))[].

A pivotal question emerges at this juncture: What renders the framework above interpretable? This can be answered using the framework in <cit.>. Herein, the explanation of any occurrence, referred to as the explanandum $\bmY$ (formally representing “why did $\bmY$ occur?"), is accomplished through a sequence of causal relationships operating at various levels, along with the intervened values of the causal variables, called the explanans. The level of detail in the explanation depends on the intended audience, which can vary from an end-user subscribing to the network service to a modem system engineer with in-depth knowledge of BS infrastructure and signal processing. Explanations can then be tailored to either a micro-level, encompassing the entire sequence of detailed relations and processes, or a macro-level, which provides a high-level, natural language description of the process. Moreover, these explanations can be communicated offline or used autonomously online to provide various resource allocation and signaling scheme proposals to meet the expected business goals in intent-based wireless networks. An example of an online approach to leverage these explanations is to implement (causal) RL with human feedback, akin to <cit.>, but with explanations acting as the feedback component. Problem (<ref>) that involves the intervention set and their values can be effectively solved using causal Bayesian optimization (CBO) <cit.>. CBO offers computational feasibility compared to traditional approaches like MCMC. It operates akin to Bayesian inference but explicitly considers the optimization problem's causal structure. While this example primarily focuses on the causal relationships between resource allocation variables and QoE, we stress that the CBO framework can be used for explainability in a broad range of wireless scenarios.

Structural causal model representing inherent causal relations among network variables.

§.§ Inability to Reason and Generalize

Although explainability can be facilitated by the description of causal sequences underlying specific network behaviors, achieving a level of generalizability across multiple data distributions and domains (inductive reasoning) necessitates a distinct examination. We next discuss why traditional AI falls short here, and how causality can be leveraged for generalizability.

§.§.§ Limited reasoning capacity of ANN

Generalization involves extending knowledge and capabilities across various domains, such as wireless environments (channels), network intents (energy consumption and end-to-end reliability), and control tasks (resource allocation and link adaptation). Current developments in AI-native 5G air interfaces as per 3GPP release 17 <cit.>, primarily involves converting model-based signal processing approaches for beam management, channel estimation, and positioning into individual AI components. Most of these existing ML solutions for wireless networking <cit.> rely on ANNs, like transformers, CNN, or RNN. However, ANN lack distribution invariance. Hence, an ANN approach consumes significant communication and computational resources due to the training overhead which would impede real-time immersive experiences, a crucial aspect of 6G.

§.§.§ Generalizability via causal reasoning

Causal reasoning can allow overcoming the above challenges of learning in wireless networks.

Incorporating reasoning into AI-based wireless systems necessitates a level of generalizability, as defined next: Consider a fixed model class $M \in \mM$. Physically, $\mM$ may represent various wireless propagation environments or wireless control tasks. The model class $M$ encompasses various functions $f_i \in \mF$ (see the SCM definition in Section. <ref>) that collectively form a specific observational distribution across various network variables $\mP_M$. Let $\mI$ be a set of interventions on the SCM, which is representative of external manipulations that bring about changes in environment or RAN intent distributions. For the set of model classes $\mM$, we define distribution generalization as follows.

Pair $(\mP_M, \mM)$ is considered to admit distribution generalization to $\mI$ if, for any given $\epsilon > 0$, there exists a function $f^{\ast}_{\epsilon} \in \mF$ such that, for all models $ \widetilde{M}\in \mM$ where $\mP_{\widetilde{M}}=\mP_M$, the following condition holds:

sup_i∈ [(Y - f_ϵ^∗(X))^2] - inf_f_♢∈ sup_i∈ [(Y - f_♢(X))^2]≤ϵ.

Distribution generalization in (<ref>) does not require the existence of a minimax solution in $\mF$. Rather, one must only find an approximate solution $f_{\epsilon}^{\ast}(X)$ that is close to the minimax solution for all interventions on the wireless environment. Apart from distribution generalization, domain generalization can also be achieved through training across various interventional and counterfactual distributions, depending on how domains are defined. In some wireless contexts, domains can be characterized by differing contextual variables (with causal relations invariant), treatable as exogenous variables and can be manipulated through interventions. In contrast, the fundamental data domain varies in other cases (medical application vs. live sports event), making it challenging to address solely through interventions or counterfactuals. In contrast to conventional ML approaches that require extensive training data from various random data distributions, causal ML leverages a single causal graph encompassing multiple data distributions generated using intervened SCM, and accomplishes this efficiently with fewer samples.  Hence, this approach ensures the ultra-low latency, time criticality, and high accuracy synchronization needs of cyber-physical systems in 6G, while fostering seamless interactions between digital and physical realms. The training efficiency of causal ML leads to energy-efficient algorithms, in contrast to other approaches to generalization such as transfer learning, meta-learning, and continual learning, as detailed next.

§.§ Energy Efficiency

§.§.§ Energy inefficient AI-native wireless networks

Traditional AI approaches, as mentioned previously, can create generalizable solutions through extensive training. However, the resultant AI models (foundation models being an example) for wireless networks yield NN with a large number of parameters. For e.g., LLM are being hailed as a game-changer for wireless networks. Particularly, they are being touted as solutions to the development of self-governing networks with intelligent decision-making at the edge <cit.>.

In intent-based networks, LLM can be utilized as proposal and evaluator agents since they can perform self-criticism and self-reflection over past network actions, learn from mistakes and better align the actions with the system's intent.
However, despite their promising potential, LLMs include billions of parameters which makes them energy-inefficient (during both training and inference) and unsustainable.

§.§.§ Causality as a tool for energy efficiency and sustainability

Conventional methods aimed at enhancing energy efficiency, such as NN pruning, can result in a reduction in performance. This is particularly undesirable for wireless networks given their stringent performance requirements highlighted in Section <ref>. Here, a more promising avenue is to leverage the capabilities of causal ML, to build lightweight foundation models. Next, we delve into the factors that could foster sustainability in wireless networking through causal ML.

* Lighter models: Causal models excel at simplifying complex relationships by focusing on essential causal factors. This simplification results in models that require less parameters, computations, and memory. By being lighter, these models consume less energy during both training and inference.

* Reduced training rounds and recurrent retraining: Causal models efficiently capture causal relationships among the wireless data that remain stable across different contexts. This results in less training rounds while also avoiding recurrent training. The reduced training significantly decreases the computational burden associated with large-scale models, contributing to overall computational efficiency.

* Reduced transmission: By communicating just the causal states present in the data, one can reduce the amount of information transmitted, e.g., through causality-based SC <cit.>, thereby decreasing communication energy consumption.

Next, we turn our attention to practically realizing the above benefits using the distinct stages of causality outlined in Section <ref>.

Simple example of a structural causal model.

§ CAUSAL DISCOVERY AND REPRESENTATION LEARNING FOR NEXT-GENERATION WIRELESS NETWORKS

As explained in Section <ref>, causal discovery involves learning the underlying causal graph representing the relations between different features present in the data (defined as causal variables) that can directly or indirectly affect the behavior of a wireless system. However, it is crucial to identify the relevant causal variables before learning the causal graph.
For example, consider the causal graph of Fig. <ref>. Here, the user's QoE is causally influenced by multiple factors such as the frequency band, channel, and the capabilities of the UE, including ML algorithms and processors. To isolate and analyze the specific impact of a causal variable, such as the frequency band, it is common to control or fix other causal dependencies (by do-calculus), like the channel environment and UE capabilities, at predetermined or set values. By doing so, one can observe and evaluate the direct causal effect of the frequency band on the user's QoE, without the confounding influence of other factors. This approach helps in understanding the implications of individual causal variables on the outcome of interest and allows for focused analysis and optimization of specific aspects in the system. Several pertinent problems in this domain warrant attention, and they are discussed next.

§.§ Causal Graphical Models (CGMs) for Near-accurate Dynamic Wireless Environment Modeling

We now discuss some open problems in wireless networks that can benefit from causal graphical modeling to achieve generalizable AI-native systems.

§.§.§ Ultra-reliable beamforming
for THz wireless

In THz wireless systems, ultra-massive MIMO enables LoS beamforming with multi-user interference cancellation under perfect CSI. However, dynamic channel conditions due to user mobility or environmental changes require real-time adaptive algorithms. These algorithms fall into two categories <cit.>: Bayesian statistics-based methods (e.g., KF) and data-intensive ML methods (e.g., MAB or RL). An accurate user mobility model is essential to effectively use model-based algorithms like the KF.

Additionally, with an increasing number of antennas, the channel estimation process becomes more intricate, increasing the processing time. Consequently, a temporal gap emerges between the pilot transmission phase, dedicated to channel estimation, and the practical application of the estimated channel for downlink beamforming. During this interim period, the channel's characteristics may undergo substantial changes, exerting a notable influence on the precision of downlink beamforming. ML models in this context encounter challenges, either from extensive retraining needs or due to longer inference times with larger, data-intensive models. To overcome those, a promising solution is to model the beam forming problem as a function of the causal dynamics (how the underlying CGM evolves over time) of the channel components. This involves modeling the joint distribution of beamforming vector $\bmv_t$, and the channel $\bmh_t$, i.e., $p(\bmv_t,\bmh_t\mid\bmz_{t-1}) = \int\limits_{\bmz_t}\underbrace{p(\bmh_t\mid\bmz_t)}_{\textrm{latent representation}}\underbrace{p(\bmz_t\mid\bmz_{t-1})}_{\textrm{causal dynamics}}p(\bmv_t\mid\bmz_t) d\bmz_t$ using variational causal networks <cit.>. As demonstrated in <cit.>, the proposed causality-aware beamforming solution allows dynamic adaptability and outperforms existing beam-tracking solutions that struggle to model time-varying channels accurately. Moreover, the resulting network spectral efficiency brings the system closer to a perfect CSI-based case. To model the causal dynamics, a promising approach is to use Granger causality <cit.>:

Non-linear Granger causality: Given $N$ stationary time-series $ \bmz = \left[z_1, \cdots, z_N \right]$
across time-steps $t = \{1, \cdots, T\}$ and a non-linear auto-regressive function $g_j$ , the time evolution of $z_j$ will be:

z_j^t+1 = g_j(^≤t,) + w_j^t+1.

In this setup, time-series $i$ Granger causes $j$, if $g_j$ depends on $z_i^{\leq t}$. This dependency is encoded in a causal DAG $\mG$. For a wireless channel, each $z_i$ here may represent the causal variables identified from the uplink channel measurements sufficient to describe the channel.

Granger causality provides two key advantages. First, it allows a generalization of the state space model to non-linear models, as represented by the NN model $g_j$. Second, training such causal reasoning enabled systems requires fewer samples for better generalization compared to conventional deep learning. This answers a key question: can causal ML tools be leveraged for sample-efficient channel estimation in time-varying systems?
Sample efficiency can be achieved since enforcing causal constraints on the channel dynamics results in a reduced dimensional state space over which channel estimation happens.

§.§.§ Causal discovery for accurate physical twin modeling in digital twins

The existing literature on physical twin modeling <cit.> predominantly relies on Bayesian inference methods. However, a limitation of this approach is its dependence on the specific data distribution used to construct the DT, which can restrict its applicability to diverse wireless environments. In contrast to this, causal discovery can be employed to model DT of the entire physical network environment ($p(\bms_{t+1}\mid\bms_t,\bma_t)$), including RAN architecture, edge servers, cloud services, and cell geography. The learned models of the environment dynamics, are sometimes
called as “network state" models <cit.>. Here, vector $\bms_t$ represents a latent representation generated from the observations received at the DT, which may include data from various sources e.g., cameras, LiDAR and satellite images. A network DT located at a cloud would replicate
various latent network features ($\bms_t$), including signals, coverage, interference, traffic behavior, and
user mobility, across different OSI layers. Vector $\bma_t$ is a versatile representation, encapsulating crucial network actions, including resource allocation decisions or autonomous tasks relevant to the physical system modeled by the DT. However, learning such models purely from observations will be biased due to the presence of confounding variables $\bmu_t$, which may be unknown to the BS or the cloud hosting the DT.

Contrary to the literature, CGM offers a better understanding of causal relationships among network variables, enhancing model precision (explainable models, as discussed in Section. <ref>) and network traffic prediction. This improves network optimization, resource allocation, and decision-making, boosting wireless network performance and efficiency. Real-time reconstruction and prediction via DT models are crucial for CI applications, offering sample efficiency and reduced training efforts for real-time network control and tasks across diverse applications.

§.§.§ CGM for wireless training data generation

A scarcity of training data can adversely impact the performance of AI-native network models that make real-time control decisions. These models must also be resilient against unexpected occurrences like hardware failures, cyber-attacks, or environmental shifts. Existing schemes include using score-based models and GAN to learn the posterior distribution of either the wireless channels or user locations <cit.>, and
using noisy uplink pilot signals as the observations.  However, these generative modeling schemes cannot fully exploit the underlying structure present in the data, particularly for high-frequency wireless systems, where the channel data exhibits high levels of structure (see (<ref>)). To overcome these challenges, CGM can be used to understand the intrinsic causal structure present in wireless channel data. Moreover, utilizing the learned causal graph $\mG$, makes it easier to create novel combinations of training data by interventions and counterfactuals as discussed in Section. <ref>.

The resulting generative AI algorithms are called causal generative models.
Exploiting training data augmentation through CGM extends beyond this example. The open problems in this context encompass 1) generating diverse network scenarios, including those arising from natural disasters, congested network traffic, software malfunctions, and hardware imperfections, 2) creating data that accurately reflects the complexity of large-scale wireless network deployments, considering interactions among numerous devices and users, particularly when employing DT models, and 3) developing methods for generating a diverse set of tasks suitable for applications of CI over wireless networks.

§.§ Resilient Wireless Networks

Resilience encapsulates a wireless system's ability to sustain functionality in the presence of errors, adapt to erroneous influences, and promptly recuperate its normal functionality. Broadly, the comprehensive notion of resilience encompasses various system attributes, namely detection, remediation, and recovery <cit.>.
Only few studies, e.g., <cit.>, and <cit.> attempted to define resilience for wireless networks.
These state-of-the-art methods rely on model-based non-convex optimization algorithms to build resilient communication systems. However, model-based algorithms are not effective when the dynamics of the wireless or RAN environment diverge from the assumptions inherent in the model, as explained in Section <ref>. In contrast, we propose a framework founded on causality principles aimed at revolutionizing the design of resilient wireless systems. Consider that as outlined in Fig.<ref>, BS powered by a DT is aware of the causal graph $\mG$ that represents the intricate causal relations among network variables. Using $\mG$, the BS can continuously monitor future QoE values while the wireless network is in a particular state $\bms_t$. While monitoring, the BS can detect prospective QoE violations in the near future. This can be formulated as computing the average QoE over a time duration $T$, given that the BS follows given resource allocation policy $\pi_t(\bma_t\mid\bms_t)$:

Y̅     = _p(Y|_t, do(_t→_t+T)) [Y],

_t ∈.

If $\bar{Y}$ is below a specific threshold, the network proceeds to the remediation phase, i.e., it solves the following counterfactual optimization:

_π(_t|_t)     _Y∼ [Y],

_t ∈,

where $\mA$ represents the space of feasible resource allocation variables capturing the system constraints. Here, $\mD = \mD_o \bigcup \mD_I$, where $\mD_o$ represents the observational dataset corresponding to the state transitions from time $t$ to $t+T$, given the current policy $\pi_t(\bma_t\mid\bms_t)$, and $\mD_I$ represents the interventional dataset. Here, various interventional distributions can be generated using causal generative modeling. Hence, the above detailed causal inference steps help to achieve the resilience goal in next-generation wireless networks.

Thus far, we examined how various signal processing functions (joint computing, and control aspects) throughout the OSI layers can benefit from causal discovery. Next, we discuss how, causal discovery can contribute to transmission reduction (communication aspect).

§.§ Causal Discovery and Representation Learning for Semantic Communications

SC systems could significantly enhance network performance across multiple dimensions, including minimizing bits and improving latency, reliability, and resilience. However, existing SC approaches (see references in <cit.>) often lack a rigorous formulation of data semantics and rely on data-driven AI models for their semantic system design.

Here, the question to be addressed is: How can AI extract representations from a multi-model source datastream and control plane data, enabling contextual communication for minimal data transfer, generalizability across tasks and data, and high fidelity at the receiver? A promising candidate herein is to define the semantics at the transmit side as the inherent causal structure within the data extracted using causal discovery <cit.>, and <cit.>.

To learn the causal graph among source data features, one can use techniques like generative flow networks <cit.>. The causal graph can be learned as the posterior distribution of the entities under different interventions in the task distribution (in short, a multi-modal distribution compared to variational techniques <cit.>). After learning the causal graph, it is critical to understand how to embed the entities and relations in a multi-dimensional vector space that respects the causal structure and is minimalist. The answer to this lies in the CRL concept discussed next. The resulting semantic representation can be processed and communicated across the wireless channel.

§.§.§ CRL for SC systems

SCM facilitates the representation of causal relationships in a disentangled form, expressed as $P(\bms_1,\cdots,\bms_n) = \prod\limits_i P(\bms_i\mid PA(\bms_i))$.
We next define the concept of CRL analytically, which describes how to extract the representations from high-dimensional observations.

CRL is the $D-$dimensional embedding of the states, $\phi_i:\bms\rightarrow \mR^D$. $\phi_i$ is causal-invariant if $\forall \bms_c, \bms_e, \bms_1, \bms_2 \in \mS$, $\bma \in \mA$, $\phi_i(\bms_1)=\phi_i(\bms_2)$ if and only if the cause and effect set are same for both $\bms_1,\bms_2$
while satisfying $P(\bms_1\mid\bms_c,\bma)=P(\bms_2\mid\bms_c,\bma), P(\bms_e\mid\bms_1,\bma)=P(\bms_e\mid\bms_2,\bma)$.

From Definition <ref>, we conclude the following: if $\phi_i(\bms_1) \!=\! \phi_i(\bms_2)$, then the semantic information conveyed by $\bms_1$ and $\bms_2$ is the same. In other words, from an SC perspective, CRL enables a unique representation for states that share comparable cause-and-effect repertoires. This leads to a reduction in the amount of information conveyed compared to systems that do not employ CRL. Next, we briefly discuss how to define the semantic information present in the derived causal representation, a critical metric for formulating the SC problems.

§.§.§ Characterizing semantic information using IIT

In classical information theory, mutual information is symmetric, meaning that, for any two random variables $X$ and $Y$, $I(X;Y) = I(Y;X)$, and it measures the information conveyed by the association between two random variables. However, in the context of causality-based SC systems, the association between two variables is directed, emphasizing the causal relationships rather than mere information exchange. Hence, classical information theory cannot completely express the semantic information conveyed by a causal system. A promising alternative here is the IIT <cit.>.  In IIT, intrinsic information
present in $\bms^t$ is nonzero only if it has selective causes and selective effects within the system.

Inspired by this, integrated information for an SCM is intrinsic information that is generated by the whole mechanism (state + its cause and effect mechanisms) beyond the information generated by its parts. This means that the mechanism is irreducible with respect to information, thus clearly defining what represent or does not represent semantics (causal mechanisms with non-zero integrated information). Building on the aforementioned concepts of semantic representation and semantic information rooted in causality, there are at least two key open problems:

* Formulating robust transmission schemes for multi-user systems, where each user may utilize distinct semantic languages constructed from CRL and exhibit varying QoE requirements.

* Discovering causal relationships among the control information distributed across multiple network layers and designing scheduling algorithms that use the semantic representations obtained from source data and the control information.

These challenges can be effectively addressed through a fusion of causality and hypergame theory <cit.> or by incorporating theory of mind reasoning <cit.>.

§.§ Causal Discovery for Integrated Sensing and Communication (ISAC)

The ISAC paradigm synergistically combines sensing and communication functions, potentially sharing common spectral, signaling, and hardware resources. ISAC can have two possible advantages: integration gain, achieved by enhancing resource efficiency, and coordination gain, which involves co-design efforts to balance network performance (user QoE) or attain sensing benefits (higher sensing resolution). Some applications of ISAC include 1) multipath parameter estimation from nonlinear channel models (see Section. <ref>) for simultaneous localization and mapping (SLAM) of the environment, 2) integration of
sensing (using, e.g., LiDAR, radar, cameras) with communication to enable vehicular communication for safer and more efficient transportation, and 3) advanced immersive experiences within a metaverse by sensing the user's physical location, movements, and gestures and communicating this information to enhance interactions with the metaverse environment. ISAC applications require real-time monitoring, synchronization, and the processing of large amounts of distributed sensing data across multiple devices to leverage the benefits of integration and coordination gains. This leads to challenges that existing AI tools cannot handle, as explained next.

§.§.§ Why is data-driven AI insufficient for achieving the integration and cooordination gains of ISAC?

* Dynamic target tracking:
Accurately tracking objects in the wireless environment, especially for SLAM, becomes a challenging task due to the mobility of these objects. Additionally, dynamic beam alignment and tracking present further challenges, particularly when dealing with high mobility of scatterers or users. Due to the reasons discussed in Section <ref>, data-driven AI cannot accurately capture the time-varying dynamics of the underlying nonlinear signal models. Consequently, this limitation contributes to beam misalignment, thereby jeopardizing the QoE of the users.

* Resource efficiency in distributed sensing: Leveraging joint transmissions from multiple sensing nodes (multiple viewpoints) can enhance sensing capabilities. Likewise, jointly processing communication signals received by distributed receivers can improve sensing performance. However, designing joint sensing solutions for distributed systems is challenging, requiring consideration of factors such as synchronization, control overhead, as well as complex design issues related to joint sensing processing functions.
Moreover, resource efficiency, through the integration gain becomes challenging due to the substantial volume of sensing information that must be communicated, particularly for scenarios like the metaverse. Advanced distributed learning models and techniques, including transfer learning, federated learning, and graph neural networks, could potentially support the use of distributed sensing devices and facilitate the efficient integration of information collected from various locations. These models and techniques can also aid in compressing distributed sensing data and reducing coordination overhead. However, the recurrent retraining required by such data-driven AI models cannot help meet the real-time synchronization demands. Furthermore, the associated AI models lack scalability as the network size fluctuates dynamically. This is attributed to changes in the communication context as the number of sensing nodes varies, which can be viewed as shifts in the data domain.

§.§.§ How can causal discovery enhance transmission efficiency, and optimize real-time ISAC systems?

The challenges associated with dynamic target tracking and beam alignment can be efficiently addressed by applying the Granger causality concept, as explained in Section <ref>, to construct a nearly accurate model of the time-varying target object or UE device. In beam tracking, causal generative modeling can be employed to make precise predictions regarding the future positions of users or scatterers. Beam tracking can be further improved by using nonlinear minimum mean squared error (MMSE) methods that considers the predictions as prior information. We propose to consider nonlinear MMSE because of the nonlinear nature of the signal models (beamforming vector as a function of user and scatterer positions, which are the observations from sensors). The nonlinear MMSE method involves computing posterior distributions of beams by incorporating the causal dynamics described in Section <ref>.

Efficient communication-aided distributed sensing can be achieved through the utilization of causal reasoning games, <cit.>. Here, each sensing node can learn the causal graph, represented as an SCM, that captures the causal relations among different network decision variables (power, spectrum, beamforming vectors, ISAC waveforms). By employing counterfactual reasoning, each sensing node can estimate other users' communication strategies and data distributions, Additionally, each sensing node can optimize communication and sensing strategies by leveraging game-theoretic techniques and the estimated beliefs about other nodes. Hence, causal discovery using SCMs and game-theoretic tools allows sensing nodes to make informed decisions about what to communicate. This dynamic process enables also the optimization of spectrum and time resources (how to communicate). Consequently, causal discovery plays a pivotal role in improving resource efficiency within distributed sensing scenarios, enabling the fulfillment of the requirements for dynamic adaptability and real-time synchronization essential for next-generation wireless networks.

Next, we answer the following crucial question: how can we effectively leverage the learned causal graph to make informed control decisions and draw meaningful inferences for multiple tasks in real-time monitoring of autonomous wireless networks? The key to addressing this lies in causal inference.

§ CAUSAL INFERENCE FOR NEXT-GENERATION WIRELESS NETWORKS

Causal inference facilitates the execution of interventional and counterfactual reasoning across various wireless tasks. We identify specific wireless challenges where causal inference can contribute to achieving future wireless networking goals such as time criticality, intent management, and dynamic adaptability, as illustrated in Fig. <ref>.

§.§ Causal Inference for Wireless Control

The radio resource management problem is typically non-convex and becomes computationally complex, particularly for large networks. Moreover, in dynamic wireless networks, model-based signal processing algorithms may be unable to maintain consistent performance across various scenarios. In this context, RL has been a popular approach for wireless control problems. However, it is a passive approach that lacks reasoning capabilities and relies solely on observational data, typically presented as a set of state-action-reward tuples.

We next describe the key limitations of RL algorithms such as Q-learning, SARSA (state-action-reward-state-action), and deep Q-Networks (DQNs).

§.§.§ Why is RL using observational data alone insufficient for addressing wireless control problems?

Wireless resource allocation problems are often posed as partially-observable Markov decision processes (POMDPs) $\mM = \left(\mS,\mO,\mA,p_{i},p_{o},p_{t},r\right)$ with hidden states $\bms \in \mS$, observations $\bmo \in \mO$, actions $\bma \in \mA$, initial state distribution $p_{i}(\bms_0)$, state transition distribution $p_{t}(\bms_{t+1}\mid \bms_t, \bma_t)$, observation distribution
$p_{o}(\bmo_t\mid \bms_t)$, and reward
function $r : \mO \rightarrow \mR$.
The history of state-action pair at time $t$ is, $\bmh_t = (\bms_0, \bma_0, \cdots , \bms_t)$. Model-based RL relies on the estimation of the POMDP transition model $p_{s}(\bms_{t+1}\mid \bmh_t, \bma_t)$, decomposed into two sub-problems: 1) learning: given a dataset $\mD$, estimate a transition model $\widehat{q}(\bms_{t+1}\mid \bmh_t, \bma_t) \approx p_{s}(\bms_{t+1}\mid \bmh_t, \bma_t)$, 2) planning: given a history $\bmh_t$ and a transition model $\widehat{q}$, choose an optimal action $\bma_t$.
For a network, states may represent the local monitoring information available to slice $i$ associated with BS $b$. This may include the SNR measure, traffic arrival rate for slice $i$, and the available bandwidth.
We can define the actions for slice $i$ as the PRB allocation size (e.g., bandwidth).
To ensure optimal PRB allocation, it is crucial to achieve a balance between meeting transmission latency requirements and fulfilling traffic demands. This involves avoiding both under-provisioning, where insufficient resources are allocated, and over-provisioning, where excessive resources are allocated. By concurrently satisfying transmission latency and traffic requirements, the PRB allocation can effectively utilize resources while maintaining the desired QoE and avoiding unnecessary resource wastage or performance degradation.

Traditional RL methods for addressing the above problem are limited by their reliance on specific observation and state transition distributions, defined as $p_o$ and $p_t$, respectively. Furthermore, deep Q-learning-based NN lack interpretability, making it challenging to explain the rationale behind a specific action in response to a given state.
Thus, in this realm of RL for wireless networks, a fundamental question emerges: can offline data obtained from UL or DL observations be combined with online data from experimentation (via DT model simulations or causal generative models) to enhance the performance of a learning agent? Previous studies <cit.> addressed this problem using GANs, however, GAN primarily learns the posterior distribution of the data based on the provided dataset and hence they are not generalizable. We propose to overcome these major limitations by designing a causal RL framework which is an instance of causal inference, as discussed next.

§.§.§ Causal RL for real-time resource management

RL using causal inference involves two key elements: experimentation and observation. In decision problems like POMDPs, causal queries play a natural role where actions directly correspond to interventions. One such example is determining the causal effect of an action (intervention) on future rewards based on past information about the POMDP process. We can evaluate the causal query as $p_s(\bms_{t+1}\mid \bms_{0\rightarrow t},{do}(\bma_{0\rightarrow t}))$, where ${do}(\bma_{0\rightarrow t})$ can be generated by different possible distributions of $\bma_t$. By formulating decision problems as causal queries, we can explore how actions influence outcomes and make informed decisions based on their expected causal effects. Here, a particular set of causal queries may represent a specific task or a wireless environment.

For creating an NN model that can generalize across various wireless environments or tasks, the accumulated learning data obtained through causal queries can be distilled into an NN using “behavioral cloning"<cit.>. The learning history, which encompasses the causal state transitions, can be defined for a specific task or wireless environment $n$ as:
h_t^(n) = (_0,_0,_0,_1,⋯,_T,_T,_T,_T+1)_n.
Assume that the lifetimes of the agents, called learning histories, are generated by the source RL algorithm for a set of individual tasks or wireless environments $\{\mM_n\}_{n=1}^N$. This process creates a dataset $\mD = \{(h_t^{(n})\sim P_{\mM_n}\}$.

Next, by AD <cit.>, we distill the behavior of the source algorithm into a sequence model that maps long histories to probabilities over actions. AD includes training NN models $P_{\btheta}$ with parameters $\btheta$ using a negative log likelihood (NLL) loss. The NN parameters can be obtained by minimizing the following loss function:
() = ∑_n=1^N∑_t=1^T logP_(= _t^(n)|_t^(n-1),_t^(n)).

In scenarios involving multiple wireless tasks, this approach guarantees that the learned policy remains task-agnostic. When the source algorithm is trained across various wireless environments and subsequently distilled into a NN, it results in the development of a NN that is invariant to environment changes. In summary, training across a wide range of environments or tasks and then distilling this knowledge into a sequence model leads to the development of causal foundation models. Nevertheless, in hierarchical and distributed wireless networks, due to the intrinsic lack or uncertainty of available information (that may include channel state, computational, and communication resources available to interfering users) at each network node, we need to look beyond causal RL. Herein, a possible solution is the framework of MAB.

§.§.§ Causal bandit problem for real-time decision making in wireless networks

MAB represents a category of sequential optimization problems wherein, given a collection of arms (actions), a player selects an arm in each round to obtain a reward. Traditional MAB algorithms cannot satisfy the ultra-synchronization demands of 6G wireless systems systems because of their inability to maintain distribution invariance and their substantial need for extensive training data. In this context, possessing causal knowledge in the form of an SCM $\mathcal{M} = (\mV, \mE, \mF, P(\mE))$ enables wireless agents to acquire knowledge about the distribution of non-intervened variables, $p(\bmv^n\mid do(\zeta)=I)$, where $\zeta$ represents the action (arm) taken, $I$ captures the intervened values, and $\bmv^n \in \mV$. One of the variables in the set $\mV$  represents the target variable $Y$.
The objective is to minimize the cumulative regret $\mathcal{R} = \sum\limits_{n=1}^{T}(Y^n - \max_{\mathbf{\zeta}}\mathbb{E}[Y|\mathbf{I} = \mathbf{\zeta}])$. The expectation operator $\mbE$ is applied to the policy distribution (over arms) and the non-intervened variables, which distinguishes it from traditional MAB approaches where only the pairs $(\zeta,Y)$ are known. Consequently, additional knowledge in the form of an SCM ensures distribution invariance without requiring additional training data as is the case with conventional MAB.

MAB pose more significant challenges in multi-user scenarios, such as opportunistic spectrum access within a metaverse, where users need to collaborate to assess the KPI needs of other users. Another example is the optimization of RIS placement and phase shifts. Herein, it is essential to consider not only the causal relationships within the environment but also the inter dependencies among users' strategies. Likewise, when strategically evaluating the consequences of an action or contemplating the actions of other users in varying circumstances, one must naturally consider both interventions and counterfactual scenarios. A promising approach to solve such multi-user MAB problems is to consider a merger of causality and game theory <cit.>.

§.§ Causal Inference for Intent-based Wireless Networks

Intent-based wireless networks aim to translate human intentions (called business intent) into network configurations through automation and AI, improving network management, efficiency, and responsiveness. One example of business intent involves optimizing wireless network sustainability while ensuring a consistent QoE for end-users.
Despite industry interest <cit.>, the wireless literature lacks a comprehensive articulation of intent-based networks. Here, we explore how causal inference offers a promising approach to building intent-based networks.
Autonomous intent management is characterized by the following set of operations that form a closed loop.

* Intent assurance: Once the service KPI are defined, measurement agents consistently oversee the network variables, while assurance agents assess the network's compliance with its intended objectives.

* Corrective actions: If the business goals have not been met, the node-level ML agents, known as proposal and policy evaluator agents, are consulted to offer predictions and recommendations. A conventional approach would involve using deep RL agents for both proposal (RL actions) and evaluation (reward computation) tasks. However, as discussed in Section. <ref>, the proposals generated using this approach may lack interpretability, necessitating retraining when the network environment or infrastructure undergoes changes. This poses a challenge to the autonomous intent management functionality.

These closed-loop operations pave the way for constructing a fully autonomous AI-native wireless network, provided that the underlying AI agents do not require recurrent training and the network decisions are interpretable, a requirement that classical AI solutions often cannot fulfill. In contrast, performing causal inference using a causal graph that describes the relations among network decision variables, which may span various OSI layers, offers the following benefits:

* Performing self-reflection or self-critique: As discussed in <cit.>, this approach is only feasible if the ML model is interpretable and explainable, which causality provides.

* Decomposing intents into subgoals and performing deductive reasoning: This can be accomplished by breaking down a larger SCM into smaller SCMs. Splitting SCM is beneficial because a decision made at a higher network layer may have ramifications across lower layers. This also helps perform interventions or counterfactuals in a distributed manner. The causal effects of interventions or counterfactuals performed in individual SCMs can be combined to achieve deductive reasoning, which provides novel insights about network decisions made at different OSI layers.

One promising approach to realize the above benefits is to compute parallel policies for each subgoal using either multi-objective RL (MO-RL) <cit.> or causal reasoning games <cit.>. After obtaining subgoal policies, the evaluator agent can use supervised learning to distill these
distributions into a new parameterized policy.
These recommendations are then used to execute autonomous actions through a closed-loop system that incorporates advanced analytics, automation, and AI. This autonomous execution ensures that the network operates efficiently, adapts to changing conditions, and achieves the desired service KPIs without the need for manual intervention.

§.§ Causal Inference for Integrated Sensing and Communication (ISAC)

In addition to the challenges related to resource efficiency and dynamic target tracking, as discussed in Section <ref>, ISAC applications also require effective management of non-linear signal models and joint waveform design for sensing and communication functionalities. Furthermore, they must enable dynamic resource sharing between sensing and communication functions to leverage the benefits of integration and coordination gains, as elaborated next.

§.§.§ Why is data-driven AI inadequate for achieving the integration and coordination gains of ISAC?

* Nonlinear signal processing: ISAC functions may require full-duplex transmitters and receivers to operate. For instance, the transmitter might be actively transmitting the ISAC waveform while, concurrently, the receiver captures the back-scattered or reflected signals for subsequent radar processing. Efficiently canceling self-interference (SI) at the antenna, analog, or digital domains requires a substantial understanding of circuit non-linear models, antenna coupling, and time-varying channel characteristics. However, approximating such time-varying SI using data-driven AI need not result in models that are accurate across time, or it could require recurrent retraining, which introduces significant overhead.

* ISAC waveform design: One key objective of ISAC systems is to use a single waveform for both radar and communication purposes. In such cases, the joint waveform must be rigorously designed to fulfill communication goals like data rates, latency, and QoE, all while preserving the desired sensing capabilities. This becomes particularly challenging when: 1) dealing with different requirements for communication and sensing systems, like peak-to-average power (PAPR) constraints for OFDM systems and signal quality for sensing, 2) accounting for hardware imperfections and non-linearities, and 3) managing highly-mobile scenarios where radar and communication channels change rapidly. Classical AI struggles to adapt to dynamic (non-stationary) channels and non-linear signal models that are specific to different devices or domains. Furthermore, addressing multi-objective optimizations presents substantial challenges in attaining Pareto-optimal solutions <cit.>. Pareto optimality, in the context of multi-objective optimization, refers to a state where no further improvement can be made in one objective without worsening at least one other objective. Because of the conflicting objectives and the large number of optimization variables related to communication and sensing, classical AI solutions may not achieve near-accurate Pareto-optimal solutions without extensive training.

* Resource sharing between sensing and communication in dynamic environments:  Allocating wireless resources like time, frequency, and power efficiently between sensing and communication is challenging due to tradeoffs between sensing quality and communication goals. ML can enhance resource allocation by using prior observations and context to optimize decisions. For instance, RNN can proactively predict user requests and RL can be used to explore resource optimization options. Nevertheless, RNN cannot handle large input sequences, such as extended user request histories or contexts. Additionally, RL is often constrained by the dataset it was trained on, limiting its adaptability to evolving, non-stationary conditions or novel scenarios.

§.§.§ How can causal inference address nonlinearity, joint waveform design, and optimize real-time resource sharing in ISAC systems?

To address the inherent nonlinearity of SI signals, a promising strategy involves leveraging causal discovery to gain insights into the underlying “physics" governing the data. The generation of these signals, influenced by hardware imperfections and the SI channel, is not random; it is guided by specific physical principles (electromagnetic as well as circuit theory-based). By constructing a causal graph that captures relationships among channel parameters, electronics hardware characteristics, and antenna coupling coefficients, the causal model can be extended to accommodate various distributions of channels, frequency bands, or antenna characteristics by applying interventional and counterfactual causal inference techniques mentioned in this section.

Causal MO-RL can efficiently handle multi-objective optimization in ISAC waveform design. For example, consider that sensing and communication signals occupy different subcarriers within an OFDM symbol under a multi-antenna transmitter. In this scenario, the optimization variables could include finding the optimal number of subcarriers, the complex coefficients for the sensing subcarriers, and the beampatterns for radar and communication signals. Radar signals may have a wider beamwidth requirement (since scatterers may be omnipresent) in contrast to communication users' narrower beam requirements. These variables are computed with the dual objective of minimizing the target detection error (e.g., delay and Doppler mean-squared error) at the sensing receiver and maximizing the user's QoE for the communication receiver. The multi-objective optimization has to be performed under several constraints that may include transmit power and PAPR. By integrating causal inference into MO-RL problems, it becomes possible to identify the minimal interventions needed to achieve specific objectives like maximizing QoE or sensing quality. The interventions here involve the number of subcarriers or the sensing signal characteristics, which depend on exogenous variables such as environment characteristics (e.g., scatterer parameters as discussed in Section. <ref>) that are time-varying and the allocated spatial or spectrum resources. Causal inference simplifies the solution space by estimating the minimal required interventions to be performed. Hence, it allows computation of near Pareto-optimal solutions, surpassing the capabilities of data-driven MO-RL that may be stuck in a local optima. Here, causal inference can significantly improve the overall performance of ISAC systems compared to generic waveforms that do not consider the causal dependency of user QoE or sensing quality on factors like environment geometry, user location, mobility patterns, and hardware imperfections. To create resource-sharing algorithms that are both generalizable and explainable, one can explore causal inference techniques such as causal RL and causal MAB, as earlier.

§ RECOMMENDATIONS

This article laid out a bold new vision for designing AI-native wireless systems (6G and beyond) founded on the principles of causal reasoning.
We conclude with three key recommendations:

* Causal Reasoning as a Bedrock for AI-Native Wireless Networks: Designing AI-native wireless networks is not going to be successful if it relies simply on reusing classical AI tools like autoencoders and ANNs to mimic existing wireless functions. Instead, there is a need to develop novel AI frameworks that incorporate the desirable properties of explainability, reasoning, generalizability, and sustainability. In this regard, we recommend embracing causal reasoning as the cornerstone of AI-native wireless systems as it enables several of these key characteristics. Causal reasoning can be integrated across the networking stack, including 1) source data sampling (selecting causal variables for extraction), 2) data encoding (using causal representations), 3) scheduling (incorporating causality awareness into user data and KPIs for resource management), and 4) communication (users seeking relevant interventions or counterfactuals to gain insights about network attributes).

* Refined Models with Causality to Mitigate Bias: We advocate transitioning away from excessive reliance on LLM and extensive data, characteristic of data-driven networking with foundation models in general. Instead, we emphasize the importance of refining models and features using causality to mitigate potential biases within AI frameworks. In other words, we recommend designing causality-based foundation models that can lead to interpretable and lighter ML models, which are crucial for achieving next-generation wireless network goals as shown in Fig. <ref>.

* Scalable AI-Native Wireless Networks using Layer-wise SCMs: Causal ML comes with its own set of challenges. The profusion of network variables spanning multiple wireless networking layers can result in intricate and expanding causal relationships, particularly as the network grows in scale. In this context, we recommend devising a path to scale causality-aware AI-native wireless networks without disrupting existing 3GPP architectures. A practical strategy to address this scalability challenge involves constructing layer-specific SCM and devising causality-aware algorithms tailored to specific OSI layers.
This distributed architecture can also align with the open RAN architecture of 5G and beyond, enabling causal reasoning across individual layers distributed across different network components or implemented as virtualized network functions.