AI and Deep Learning for THz Ultra-Massive MIMO: From Model-Driven Approaches to Foundation Models

In this paper, we explore the potential of artificial intelligence (AI) to address the challenges posed by terahertz ultra-massive multiple-input multiple-output (THz UM-MIMO) systems. We begin by outlining the characteristics of THz UM-MIMO systems, and identify three primary challenges for the transceiver design: 'hard to compute', 'hard to model', and 'hard to measure'. We argue that AI can provide a promising solution to these challenges. We then propose two systematic research roadmaps for developing AI algorithms tailored for THz UM-MIMO systems. The first roadmap, called model-driven deep learning (DL), emphasizes the importance to leverage available domain knowledge and advocates for adopting AI only to enhance the bottleneck modules within an established signal processing or optimization framework. We discuss four essential steps to make it work, including algorithmic frameworks, basis algorithms, loss function design, and neural architecture design. Afterwards, we present a forward-looking vision through the second roadmap, i.e., physical layer foundation models. This approach seeks to unify the design of different transceiver modules by focusing on their common foundation, i.e., the wireless channel. We propose to train a single, compact foundation model to estimate the score function of wireless channels, which can serve as a versatile prior for designing a wide variety of transceiver modules. We will also guide the readers through four essential steps, including general frameworks, conditioning, site-specific adaptation, and the joint design of foundation models and model-driven DL.

Dependence Induced Representations

We study the problem of learning feature representations from a pair of random variables, where we focus on the representations that are induced by their dependence. We provide sufficient and necessary conditions for such dependence induced representations, and illustrate their connections to Hirschfeld--Gebelein--R\'{e}nyi (HGR) maximal correlation functions and minimal sufficient statistics. We characterize a large family of loss functions that can learn dependence induced representations, including cross entropy, hinge loss, and their regularized variants. In particular, we show that the features learned from this family can be expressed as the composition of a loss-dependent function and the maximal correlation function, which reveals a key connection between representations learned from different losses. Our development also gives a statistical interpretation of the neural collapse phenomenon observed in deep classifiers. Finally, we present the learning design based on the feature separation, which allows hyperparameter tuning during inference.

Towards xAI: Configuring RNN Weights using Domain Knowledge for MIMO Receive Processing

Deep learning is making a profound impact in the physical layer of wireless communications. Despite exhibiting outstanding empirical performance in tasks such as MIMO receive processing, the reasons behind the demonstrated superior performance improvement remain largely unclear. In this work, we advance the field of Explainable AI (xAI) in the physical layer of wireless communications utilizing signal processing principles. Specifically, we focus on the task of MIMO-OFDM receive processing (e.g., symbol detection) using reservoir computing (RC), a framework within recurrent neural networks (RNNs), which outperforms both conventional and other learning-based MIMO detectors. Our analysis provides a signal processing-based, first-principles understanding of the corresponding operation of the RC. Building on this fundamental understanding, we are able to systematically incorporate the domain knowledge of wireless systems (e.g., channel statistics) into the design of the underlying RNN by directly configuring the untrained RNN weights for MIMO-OFDM symbol detection. The introduced RNN weight configuration has been validated through extensive simulations demonstrating significant performance improvements. This establishes a foundation for explainable RC-based architectures in MIMO-OFDM receive processing and provides a roadmap for incorporating domain knowledge into the design of neural networks for NextG systems.

Learning at the Speed of Wireless: Online Real-Time Learning for AI-Enabled MIMO in NextG

Integration of artificial intelligence (AI) and machine learning (ML) into the air interface has been envisioned as a key technology for next-generation (NextG) cellular networks. At the air interface, multiple-input multiple-output (MIMO) and its variants such as multi-user MIMO (MU-MIMO) and massive/full-dimension MIMO have been key enablers across successive generations of cellular networks with evolving complexity and design challenges. Initiating active investigation into leveraging AI/ML tools to address these challenges for MIMO becomes a critical step towards an AI-enabled NextG air interface. At the NextG air interface, the underlying wireless environment will be extremely dynamic with operation adaptations performed on a sub-millisecond basis by MIMO operations such as MU-MIMO scheduling and rank/link adaptation. Given the enormously large number of operation adaptation possibilities, we contend that online real-time AI/ML-based approaches constitute a promising paradigm. To this end, we outline the inherent challenges and offer insights into the design of such online real-time AI/ML-based solutions for MIMO operations. An online real-time AI/ML-based method for MIMO-OFDM channel estimation is then presented, serving as a potential roadmap for developing similar techniques across various MIMO operations in NextG.

Operator SVD with Neural Networks via Nested Low-Rank Approximation

Computing eigenvalue decomposition (EVD) of a given linear operator, or finding its leading eigenvalues and eigenfunctions, is a fundamental task in many machine learning and scientific computing problems. For high-dimensional eigenvalue problems, training neural networks to parameterize the eigenfunctions is considered as a promising alternative to the classical numerical linear algebra techniques. This paper proposes a new optimization framework based on the low-rank approximation characterization of a truncated singular value decomposition, accompanied by new techniques called nesting for learning the top-$L$ singular values and singular functions in the correct order. The proposed method promotes the desired orthogonality in the learned functions implicitly and efficiently via an unconstrained optimization formulation, which is easy to solve with off-the-shelf gradient-based optimization algorithms. We demonstrate the effectiveness of the proposed optimization framework for use cases in computational physics and machine learning.

2D-RC: Two-Dimensional Neural Network Approach for OTFS Symbol Detection

Orthogonal time frequency space (OTFS) is a promising modulation scheme for wireless communication in high-mobility scenarios. Recently, a reservoir computing (RC) based approach has been introduced for online subframe-based symbol detection in the OTFS system, where only a limited number of over-the-air (OTA) pilot symbols are utilized for training. However, this approach does not leverage the domain knowledge specific to the OTFS system. This paper introduces a novel two-dimensional RC (2D-RC) method that incorporates the structural knowledge of the OTFS system into the design for online symbol detection on a subframe basis. Specifically, as the channel response acts as a two-dimensional (2D) operation over the transmitted information symbols in the delay-Doppler (DD) domain, the 2D-RC is designed to have a 2D structure to equalize the channel. With the introduced architecture, the 2D-RC can benefit from the predictable channel representation in the DD domain. Moreover, unlike the previous work that requires multiple RCs to learn the channel feature, the 2D-RC only requires a single neural network for detection. Experimental results demonstrate the effectiveness of the 2D-RC approach across different OTFS system variants and modulation orders.

Towards Explainable Machine Learning: The Effectiveness of Reservoir Computing in Wireless Receive Processing

Deep learning has seen a rapid adoption in a variety of wireless communications applications, including at the physical layer. While it has delivered impressive performance in tasks such as channel equalization and receive processing/symbol detection, it leaves much to be desired when it comes to explaining this superior performance. In this work, we investigate the specific task of channel equalization by applying a popular learning-based technique known as Reservoir Computing (RC), which has shown superior performance compared to conventional methods and other learning-based approaches. Specifically, we apply the echo state network (ESN) as a channel equalizer and provide a first principles-based signal processing understanding of its operation. With this groundwork, we incorporate the available domain knowledge in the form of the statistics of the wireless channel directly into the weights of the ESN model. This paves the way for optimized initialization of the ESN model weights, which are traditionally untrained and randomly initialized. Finally, we show the improvement in receive processing/symbol detection performance with this optimized initialization through simulations. This is a first step towards explainable machine learning (XML) and assigning practical model interpretability that can be utilized together with the available domain knowledge to improve performance and enhance detection reliability.

A Geometric Framework for Neural Feature Learning

We present a novel framework for learning system design based on neural feature extractors by exploiting geometric structures in feature spaces. First, we introduce the feature geometry, which unifies statistical dependence and features in the same functional space with geometric structures. By applying the feature geometry, we formulate each learning problem as solving the optimal feature approximation of the dependence component specified by the learning setting. We propose a nesting technique for designing learning algorithms to learn the optimal features from data samples, which can be applied to off-the-shelf network architectures and optimizers. To demonstrate the application of the nesting technique, we further discuss multivariate learning problems, including conditioned inference and multimodal learning, where we present the optimal features and reveal their connections to classical approaches.

Universal Approximation of Linear Time-Invariant (LTI) Systems through RNNs: Power of Randomness in Reservoir Computing

Recurrent neural networks (RNNs) are known to be universal approximators of dynamic systems under fairly mild and general assumptions, making them good tools to process temporal information. However, RNNs usually suffer from the issues of vanishing and exploding gradients in the standard RNN training. Reservoir computing (RC), a special RNN where the recurrent weights are randomized and left untrained, has been introduced to overcome these issues and has demonstrated superior empirical performance in fields as diverse as natural language processing and wireless communications especially in scenarios where training samples are extremely limited. On the contrary, the theoretical grounding to support this observed performance has not been fully developed at the same pace. In this work, we show that RNNs can provide universal approximation of linear time-invariant (LTI) systems. Specifically, we show that RC can universally approximate a general LTI system. We present a clear signal processing interpretation of RC and utilize this understanding in the problem of simulating a generic LTI system through RC. Under this setup, we analytically characterize the optimal probability distribution function for generating the recurrent weights of the underlying RNN of the RC. We provide extensive numerical evaluations to validate the optimality of the derived optimum distribution of the recurrent weights of the RC for the LTI system simulation problem. Our work results in clear signal processing-based model interpretability of RC and provides theoretical explanation for the power of randomness in setting instead of training RC's recurrent weights. It further provides a complete optimum analytical characterization for the untrained recurrent weights, marking an important step towards explainable machine learning (XML) which is extremely important for applications where training samples are limited.

Learning to Estimate: A Real-Time Online Learning Framework for MIMO-OFDM Channel Estimation

In this paper we introduce StructNet-CE, a novel real-time online learning framework for MIMO-OFDM channel estimation, which only utilizes over-the-air (OTA) pilot symbols for online training and converges within one OFDM subframe. The design of StructNet-CE leverages the structure information in the MIMO-OFDM system, including the repetitive structure of modulation constellation and the invariant property of symbol classification to inter-stream interference. The embedded structure information enables StructNet-CE to conduct channel estimation with a binary classification task and accurately learn channel coefficients with as few as two pilot OFDM symbols. Experiments show that the channel estimation performance is significantly improved with the incorporation of structure knowledge. StructNet-CE is compatible and readily applicable to current and future wireless networks, demonstrating the effectiveness and importance of combining machine learning techniques with domain knowledge for wireless communication systems.