Precoder Learning by Leveraging Unitary Equivariance Property

Incorporating mathematical properties of a wireless policy to be learned into the design of deep neural networks (DNNs) is effective for enhancing learning efficiency. Multi-user precoding policy in multi-antenna system, which is the mapping from channel matrix to precoding matrix, possesses a permutation equivariance property, which has been harnessed to design the parameter sharing structure of the weight matrix of DNNs. In this paper, we study a stronger property than permutation equivariance, namely unitary equivariance, for precoder learning. We first show that a DNN with unitary equivariance designed by further introducing parameter sharing into a permutation equivariant DNN is unable to learn the optimal precoder. We proceed to develop a novel non-linear weighting process satisfying unitary equivariance and then construct a joint unitary and permutation equivariant DNN. Simulation results demonstrate that the proposed DNN not only outperforms existing learning methods in learning performance and generalizability but also reduces training complexity.

Quantization Design for Deep Learning-Based CSI Feedback

Deep learning-based autoencoders have been employed to compress and reconstruct channel state information (CSI) in frequency-division duplex systems. Practical implementations require judicious quantization of encoder outputs for digital transmission. In this paper, we propose a novel quantization module with bit allocation among encoder outputs and develop a method for joint training the module and the autoencoder. To enhance learning performance, we design a loss function that adaptively weights the quantization loss and the logarithm of reconstruction loss. Simulation results show the performance gain of the proposed method over existing baselines.

Distributed Resource Block Allocation for Wideband Cell-free System

This paper studies distributed resource block (RB) allocation in wideband orthogonal frequency-division multiplexing (OFDM) cell-free systems. We propose a novel distributed sequential algorithm and its two variants, which optimize RB allocation based on the information obtained through over-the-air (OTA) transmissions between access points (APs) and user equipments, enabling local decision updates at each AP. To reduce the overhead of OTA transmission, we further develop a distributed deep learning (DL)-based method to learn the RB allocation policy. Simulation results demonstrate that the proposed distributed algorithms perform close to the centralized algorithm, while the DL-based method outperforms existing baseline methods.

Learning of Uplink Resource Allocation with Multiuser QoS Constraints

In the paper the joint optimization of uplink multiuser power and resource block (RB) allocation are studied, where each user has quality of service (QoS) constraints on both long- and short-blocklength transmissions. The objective is to minimize the consumption of RBs for meeting the QoS requirements, leading to a mixed-integer nonlinear programming (MINLP) problem. We resort to deep learning to solve the problem with low inference complexity. To provide a performance benchmark for learning based methods, we propose a hierarchical algorithm to find the global optimal solution in the single-user scenario, which is then extended to the multiuser scenario. The design of the learning method, however, is challenging due to the discrete policy to be learned, which results in either vanishing or exploding gradient during neural network training. We introduce two types of smoothing functions to approximate the involved discretizing processes and propose a smoothing parameter adaption method. Another critical challenge lies in guaranteeing the QoS constraints. To address it, we design a nonlinear function to intensify the penalties for minor constraint violations. Simulation results demonstrate the advantages of the proposed method in reducing the number of occupied RBs and satisfying QoS constraints reliably.

Gradient-Driven Graph Neural Networks for Learning Digital and Hybrid Precoder

The optimization of multi-user multi-input multi-output (MU-MIMO) precoders is a widely recognized challenging problem. Existing work has demonstrated the potential of graph neural networks (GNNs) in learning precoding policies. However, existing GNNs often exhibit poor generalizability for the numbers of users or antennas. In this paper, we develop a gradient-driven GNN design method for the learning of fully digital and hybrid precoding policies. The proposed GNNs leverage two kinds of knowledge, namely the gradient of signal-to-interference-plus-noise ratio (SINR) to the precoders and the permutation equivariant property of the precoding policy. To demonstrate the flexibility of the proposed method for accommodating different optimization objectives and different precoding policies, we first apply the proposed method to learn the fully digital precoding policies. We study two precoder optimization problems for spectral efficiency (SE) maximization and log-SE maximization to achieve proportional fairness. We then apply the proposed method to learn the hybrid precoding policy, where the gradients to analog and digital precoders are exploited for the design of the GNN. Simulation results show the effectiveness of the proposed methods for learning different precoding policies and better generalization performance to the numbers of both users and antennas compared to baseline GNNs.

Learning Wideband User Scheduling and Hybrid Precoding with Graph Neural Networks

Spatial-frequency scheduling and hybrid precoding in wideband multi-user multi-antenna systems have never been learned jointly due to the challenges arising from the massive user combinations on resource blocks (RBs) and the shared analog precoder among RBs. In this paper, we strive to jointly learn the scheduling and precoding policies with graph neural networks (GNNs), which have emerged as a powerful tool for optimizing resource allocation thanks to their potential in generalizing across problem scales. By reformulating the joint optimization problem into an equivalent functional optimization problem for the scheduling and precoding policies, we propose a GNN-based architecture consisting of two cascaded modules to learn the two policies. We discover a same-parameter same-decision (SPSD) property for wireless policies defined on sets, revealing that a GNN cannot well learn the optimal scheduling policy when users have similar channels. This motivates us to develop a sequence of GNNs to enhance the scheduling module. Furthermore, by analyzing the SPSD property, we find when linear aggregators in GNNs impede size generalization. Based on the observation, we devise a novel attention mechanism for information aggregation in the precoder module. Simulation results demonstrate that the proposed architecture achieves satisfactory spectral efficiency with short inference time and low training complexity, and is generalizable to the numbers of users, RBs, and antennas at the base station and users.

Learning Precoding in Multi-user Multi-antenna Systems: Transformer or Graph Transformer?

Transformers have been designed for channel acquisition tasks such as channel prediction and other tasks such as precoding, while graph neural networks (GNNs) have been demonstrated to be efficient for learning a multitude of communication tasks. Nonetheless, whether or not Transformers are efficient for the tasks other than channel acquisition and how to reap the benefits of both architectures are less understood. In this paper, we take learning precoding policies in multi-user multi-antenna systems as an example to answer the questions. We notice that a Transformer tailored for precoding can reflect multiuser interference, which is essential for its generalizability to the number of users. Yet the tailored Transformer can only leverage partial permutation property of precoding policies and hence is not generalizable to the number of antennas, same as a GNN learning over a homogeneous graph. To provide useful insight, we establish the relation between Transformers and the GNNs that learn over heterogeneous graphs. Based on the relation, we propose Graph Transformers, namely 2D- and 3D-Gformers, for exploiting the permutation properties of baseband precoding and hybrid precoding policies. The learning performance, inference and training complexity, and size-generalizability of the Gformers are evaluated and compared with Transformers and GNNs via simulations.

Orbit: A Framework for Designing and Evaluating Multi-objective Rankers

Machine learning in production needs to balance multiple objectives: This is particularly evident in ranking or recommendation models, where conflicting objectives such as user engagement, satisfaction, diversity, and novelty must be considered at the same time. However, designing multi-objective rankers is inherently a dynamic wicked problem -- there is no single optimal solution, and the needs evolve over time. Effective design requires collaboration between cross-functional teams and careful analysis of a wide range of information. In this work, we introduce Orbit, a conceptual framework for Objective-centric Ranker Building and Iteration. The framework places objectives at the center of the design process, to serve as boundary objects for communication and guide practitioners for design and evaluation. We implement Orbit as an interactive system, which enables stakeholders to interact with objective spaces directly and supports real-time exploration and evaluation of design trade-offs. We evaluate Orbit through a user study involving twelve industry practitioners, showing that it supports efficient design space exploration, leads to more informed decision-making, and enhances awareness of the inherent trade-offs of multiple objectives. Orbit (1) opens up new opportunities of an objective-centric design process for any multi-objective ML models, as well as (2) sheds light on future designs that push practitioners to go beyond a narrow metric-centric or example-centric mindset.

What Is Wrong with My Model? Identifying Systematic Problems with Semantic Data Slicing

Machine learning models make mistakes, yet sometimes it is difficult to identify the systematic problems behind the mistakes. Practitioners engage in various activities, including error analysis, testing, auditing, and red-teaming, to form hypotheses of what can go (or has gone) wrong with their models. To validate these hypotheses, practitioners employ data slicing to identify relevant examples. However, traditional data slicing is limited by available features and programmatic slicing functions. In this work, we propose SemSlicer, a framework that supports semantic data slicing, which identifies a semantically coherent slice, without the need for existing features. SemSlicer uses Large Language Models to annotate datasets and generate slices from any user-defined slicing criteria. We show that SemSlicer generates accurate slices with low cost, allows flexible trade-offs between different design dimensions, reliably identifies under-performing data slices, and helps practitioners identify useful data slices that reflect systematic problems.

Recursive GNNs for Learning Precoding Policies with Size-Generalizability

Graph neural networks (GNNs) have been shown promising in optimizing power allocation and link scheduling with good size generalizability and low training complexity. These merits are important for learning wireless policies under dynamic environments, which partially come from the matched permutation equivariance (PE) properties of the GNNs to the policies to be learned. Nonetheless, it has been noticed in literature that only satisfying the PE property of a precoding policy in multi-antenna systems cannot ensure a GNN for learning precoding to be generalizable to the unseen number of users. Incorporating models with GNNs helps improve size generalizability, which however is only applicable to specific problems, settings, and algorithms. In this paper, we propose a framework of size generalizable GNNs for learning precoding policies that are purely data-driven and can learn wireless policies including but not limited to baseband and hybrid precoding in multi-user multi-antenna systems. To this end, we first find a special structure of each iteration of two numerical algorithms for optimizing precoding, from which we identify the key characteristics of a GNN that affect its size generalizability. Then, we design size-generalizable GNNs that are with these key characteristics and satisfy the PE properties of precoding policies in a recursive manner. Simulation results show that the proposed GNNs can be well-generalized to the number of users for learning baseband and hybrid precoding policies and require much fewer samples than existing counterparts to achieve the same performance.