We introduce TeleQnA, the first benchmark dataset designed to evaluate the knowledge of Large Language Models (LLMs) in telecommunications. Comprising 10,000 questions and answers, this dataset draws from diverse sources, including standards and research articles. This paper outlines the automated question generation framework responsible for creating this dataset, along with how human input was integrated at various stages to ensure the quality of the questions. Afterwards, using the provided dataset, an evaluation is conducted to assess the capabilities of LLMs, including GPT-3.5 and GPT-4. The results highlight that these models struggle with complex standards related questions but exhibit proficiency in addressing general telecom-related inquiries. Additionally, our results showcase how incorporating telecom knowledge context significantly enhances their performance, thus shedding light on the need for a specialized telecom foundation model. Finally, the dataset is shared with active telecom professionals, whose performance is subsequently benchmarked against that of the LLMs. The findings illustrate that LLMs can rival the performance of active professionals in telecom knowledge, thanks to their capacity to process vast amounts of information, underscoring the potential of LLMs within this domain. The dataset has been made publicly accessible on GitHub.

We study the problem of learning to play a repeated multi-player game with an unknown reward function and bandit feedback. The central challenge arises from the need to balance exploration and exploitation under bandit feedback while strategically responding to other players. To address this, we propose Thompson Sampling-based algorithms that leverage available information about opponents’ actions and reward structures, resulting in a significant reduction in regret bound. Building on these insights, we introduce the Optimism-then-NoRegret framework, which encompasses various game algorithms as special cases. Simulation evaluations on three distinct types of games show that our proposed algorithms consistently and substantially outperform standard baselines.

Large Language Models (LLMs) can self-improve through reinforcement learning, where they generate trajectories to explore and discover better solutions. However, this exploration process is computationally expensive, often forcing current methods to assign limited exploration budgets to each task. This uniform allocation creates problematic edge cases: easy tasks consistently succeed while difficult tasks consistently fail, both producing zero gradients during training updates for the widely used Group Relative Policy Optimization (GRPO). We address this problem from the lens of exploration budget allocation. Viewing each task's exploration as an "item" with a distinct "value" and "cost", we establish a connection to the classical knapsack problem. This formulation allows us to derive an optimal assignment rule that adaptively distributes resources based on the model's current learning status. When applied to GRPO, our method increases the effective ratio of non-zero policy gradients by 20-40

Gridization, the process of partitioning space into grids where users share similar channel characteristics, serves as a fundamental prerequisite for efficient large-scale network optimization. However, existing methods like Geographical or Beam Space Gridization (GSG or BSG) are limited by reliance on unavailable location data or the flawed assumption that similar signal strengths imply similar channel properties. We propose Channel Space Gridization (CSG), a pioneering framework that unifies channel estimation and gridization for the first time. Formulated as a joint optimization problem, CSG uses only beam-level reference signal received power (RSRP) to estimate Channel Angle Power Spectra (CAPS) and partition samples into grids with homogeneous channel characteristics. To perform CSG, we develop the CSG Autoencoder (CSG-AE), featuring a trainable RSRP-to-CAPS encoder, a learnable sparse codebook quantizer, and a physics-informed decoder based on the Localized Statistical Channel Model. On recognizing the limitations of naive training scheme, we propose a novel Pretraining-Initialization-Detached-Asynchronous (PIDA) training scheme for CSG-AE, ensuring stable and effective training by systematically addressing the common pitfalls of the naive training paradigm. Evaluations reveal that CSG-AE excels in CAPS estimation accuracy and clustering quality on synthetic data. On real-world datasets, it reduces Active Mean Absolute Error (MAE) by 30% and Overall MAE by 65% on RSRP prediction accuracy compared to salient baselines using the same data, while improving channel consistency, cluster sizes balance, and active ratio, advancing the development of gridization for large-scale network optimization.

The globally optimal robust adaptive beamforming (RAB) solution is studied for worst-case signal-to-interference-plus-noise ratio (SINR) maximization (the maximin SINR problem) under convex and closed uncertainty sets for the desired signal covariance and interference-plus-noise covariance (INC) matrices, considering a general-rank signal model. First, the corresponding minimax SINR problem is reformulated as a convex optimization problem. In particular, this problem becomes a semidefinite programming (SDP) problem when the uncertainty sets can be represented by finitely many linear matrix inequality constraints. It is then shown that, for a general-rank signal model, the maximin and minimax SINR problems are equivalent when the uncertainty sets are convex and closed, in the sense that they share the same optimal value and the same set of optimal solutions. The requirement of closedness is weaker than the compactness assumption previously used to establish the equivalence between minimax and maximin SINR problems for the rank-one signal model, a state-of-the-art result reported approximately two decades ago. Consequently, an optimal solution to the minimax SINR problem is also globally optimal for the maximin SINR problem, and this solution can be obtained by solving the equivalent SDP of the minimax problem in a single step. In contrast, existing iterative approximation algorithms for the maximin SINR problem yield only locally optimal solutions. Simulation results demonstrate that these approximation algorithms return suboptimal values that can be strictly smaller than the optimal value of the minimax problem, and that the beamformer output SINR obtained via the minimax formulation is higher than that achieved by beamformers derived from the maximin problem using approximation algorithms.

The dynamic competition against intelligent jammer systems presents a significant challenge to modern radar. Traditional active anti-jamming strategy learning methods often suffer from low sample efficiency and fail to fully exploit the structures of the adversary jammer. To reveal the inherent structure, this paper adopts an Online Convex Optimization (OCO) framework to capture the competition between a frequency agile radar and a digital radio frequency memory (DRFM)-based intelligent jammer. Recognizing that conventional OCO algorithms also suffer from suboptimal sample efficiency, two refined algorithms are developed that incorporate unbiased gradient estimators specifically tailored to the unique characteristics of DRFM-based jammers. Our theoretical analysis of the regret bound indicates significant improvements in long-term performance compared to standard OCO. The simulation results consistently show that our algorithms outperform traditional OCO and reinforcement learning baselines, achieving faster convergence and better anti-jamming performance.

Deploying metasurfaces (MTSs) to eliminate wireless blind spots requires jointly determining the physical placement of MTSs and the meta-atom phase shifts. Existing methods typically rely on explicit channel estimation, which incurs prohibitive overhead and is often intractable in real-world networks. To sidestep this bottleneck, we propose RFZero, a channel-state-information (CSI)-free deployment paradigm. Instead of estimating channels, RFZero extracts macro-environmental features from visual photos to guide MTS placement, and leverages reference signal received power (RSRP) feedback for dynamic phase-shift optimization. Most importantly, RFZero operates independently of base stations, thereby enabling seamless plug-and-play implementation. Real-world field tests confirm that RFZero completely eliminates all blind spots in a 100 m2 indoor area using just a pair of 1.5 m(2 )0.9 m MTSs.

Imitation learning learns a policy from expert trajectories. While the expert data is believed to be crucial for imitation quality, it was found that a kind of imitation learning approach, adversarial imitation learning (AIL), can have exceptional performance. With as little as only one expert trajectory, AIL can match the expert performance even in a long horizon, on tasks such as locomotion control. There are two mysterious points in this phenomenon. First, why can AIL perform well with only a few expert trajectories? Second, why does AIL maintain good performance despite the length of the planning horizon? In this paper, we theoretically explore these two questions. For a total-variation-distance-based AIL (called TV-AIL), our analysis shows a horizon-free imitation gap $\mathcal O(\{\min\{1, \sqrt{|\mathcal S|/N} \})$ on a class of instances abstracted from locomotion control tasks. Here $|\mathcal S|$ is the state space size for a tabular Markov decision process, and $N$ is the number of expert trajectories. We emphasize two important features of our bound. First, this bound is meaningful in both small and large sample regimes. Second, this bound suggests that the imitation gap of TV-AIL is at most 1 regardless of the planning horizon. Therefore, this bound can explain the empirical observation. Technically, we leverage the structure of multi-stage policy optimization in TV-AIL and present a new stage-coupled analysis via dynamic programming

Physical Cell Identity (PCI) assignment is essential for interference management in dense 5G networks. As cellular networks scale, PCI reuse becomes unavoidable, which may cause collisions, confusions, and multiple forms of modular interference. Jointly mitigating these effects gives rise to a large-scale, multi-objective combinatorial optimization problem that is difficult to solve efficiently at practical network scales. In this work, we propose a congruence decomposition framework with neural block solvers for large-scale PCI assignment. The proposed decomposition exploits the arithmetic structure of PCI values to decouple multiple modular interference objectives into a collection of blockwise Min-k-Partition subproblems, followed by a graph coloring procedure to resolve PCI conflicts. For the resulting NP-hard Min-k-Partition subproblems, we develop neural block solvers by parameterizing their relaxed quadratic formulations with graph neural networks, enabling efficient optimization at large scales. Discrete assignments are recovered through conditional expectation rounding with theoretical guarantees. Experiments on synthetic cellular graphs and real-world 5G networks show that the proposed method consistently outperforms existing modular-interference-aware baselines in modular interference reduction, conflict elimination, and computational efficiency.

In current 5G massive multiple-input multiple-output (MIMO) cellular networks, the performance of beamforming hinges critically on the accuracy of downlink channel state information (CSI), particularly in frequency division duplexing (FDD) systems. The absence of channel reciprocity in FDD systems introduces notable challenges, resulting in substantial communication overhead when transmitting downlink CSI directly. To tackle this obstacle, a limited feedback strategy is adopted to compress the downlink CSI into a manageable number of bits. Nevertheless, this compression complicates the accurate retrieval of downlink CSI, reducing the beamforming performance. This paper thoroughly examines the limited feedback mechanism, scrutinizing its structural design and the values it generates. Drawing upon these insights, we introduce an online algorithm that alternates between exploration and estimation to enhance beamforming for single-stream and multi-stream configurations. Our proposed method significantly elevates beamforming vector quality by adeptly decoding downlink CSI from the limited feedback. Additionally, it leverages existing information to refine the feedback process, leading to the generation of more precise CSI. As numerical results demonstrate, the complementary nature of estimation and exploration leads to outstanding performance in optimal beamforming acquisition.

We present Exact Causal Attention (ECA), a Strassen-style algorithm that computes exact Causal Attention using 10% fewer operations. ECA improves a special class of matrix multiplications where either one operand or the output matrix is upper- or lower-triangular. This includes all matrix multiplication operations in the forward and backward pass of Causal Attention, such as masked product Mask(QK^T). ECA is built upon algebraic identities discovered via machine learning and combinatorial search. We note that ECA cannot accelerate fused kernels such as FlashAttention on GPU. This is because ECA requires materialization of large intermediate expressions in the memory, while FlashAttention does not. However, it provides an alternative approach for compute-bound applications and can potentially be useful in scenarios with FLOPs considerations.

We present RXTX, a new algorithm for computing the product of matrix by its transpose $XX^{t}$ for $X\in \mathbb{R}^{n\times m}$. RXTX uses $5\%$ fewer multiplications and $5\%$ fewer operations (additions and multiplications) than State-of-the-Art algorithms. Note that the accelerations not only holds asymptotically for large matrices with $n \rightarrow \infty$, but also for small matrices including $n = 4$. The algorithm was discovered by combining Machine Learning-based search methods with Combinatorial Optimization.

In this paper, we consider the network slicing (NS) problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and manage network resources to meet diverse quality of service (QoS) requirements. We propose a mixed-integer nonlinear programming (MINLP) formulation for the considered NS problem that can flexibly route the traffic flow of the services on multiple paths and provide end-to-end delay and reliability guarantees for all services. To overcome the computational difficulty due to the intrinsic nonlinearity in the MINLP formulation, we transform the MINLP formulation into an equivalent mixed-integer linear programming (MILP) formulation and further show that their continuous relaxations are equivalent. In sharp contrast to the continuous relaxation of the MINLP formulation which is a nonconvex nonlinear programming problem, the continuous relaxation of the MILP formulation is a polynomial-time solvable linear programming problem, which significantly facilitates the algorithmic design. Based on the newly proposed MILP formulation, we develop a customized column generation (cCG) algorithm for solving the NS problem. The proposed cCG algorithm is a decomposition-based algorithm and is particularly suitable for solving large-scale NS problems. Numerical results demonstrate the efficacy of the proposed formulations and the proposed cCG algorithm.

This paper considers a typical application case of the integrated sensing and communications (ISAC) in which the receiver wishes to not only enhance its channel capacity but also localize the transmitter in aid of metasurfaces (MTSs). In view of practical situations, we assume that the MTSs consist of lowresolution (e.g., 1-bit) phase shifters and that the channel state information (CSI) is completely unknown. The key step in the proposed method is to retrieve the phase difference information from the received signal strength (RSS) through a novel technique called blind beamforming. We then utilize the phase difference information to align the reflected channels and thereby enhance signal-to-noise ratio (SNR), and also recover the position of the target with the MTSs treated as anchors. According to our field tests carried out at 2.6 GHz frequency band, the proposed method gives much more precise localization than the benchmarks, aside from increasing the SNR by up to around 10 dB.

Factorizing a low-rank matrix into two matrix factors with low dimensions from its noisy observations is a classical but challenging problem arising from real-world applications. This paper develops decentralized matrix factorization algorithms, i.e., factorizing a matrix whose columns are stored distributively over a network without a central agent. The performance of existing algorithms relies heavily on the accuracy of the matrix rank estimate. However, acquiring an accurate estimate is difficult in the distributed setting. In this paper and its Part II, we address this problem by introducing a novel regularization into the objective function to induce the solution with correct rank. Based on this, we propose a rank-adaptive decentralized MF algorithm. In Part I, we delineate the algorithm development from the centralized with known rank, decentralized with known rank, to the rank-adaptive decentralized settings. For the centralized algorithm, we present the first globally linear convergence analysis for the alternating gradient descent method. In the Part II, we analyze conditions for which the proposed rank-adaptive decentralized MF algorithm converges to the global solution with the correct rank. Numerical experiments based on both synthetic and real-world datasets are presented in this paper to demonstrate the effectiveness of the proposed algorithms and corroborate the theoretical claims.

Large Language Models (LLMs) typically rely on Supervised Fine-Tuning (SFT) to specialize in downstream tasks, with the Cross Entropy (CE) loss being the de facto choice. However, CE maximizes the likelihood of observed data without accounting for alternative possibilities. As such, CE usually leads to reduced diversity in the model's outputs, which hinders further development that requires sampling to explore better responses. To address this limitation, this paper introduces a new game-theoretic formulation for SFT. In this framework, an auxiliary variable is introduced to regulate the learning process. We prove that the proposed game-theoretic approach connects to the problem of reverse KL minimization with entropy regularization. This regularization prevents over-memorization of training data and promotes output diversity. To implement this framework, we develop GEM, a new training algorithm that is computationally efficient as CE by leveraging some unique properties of LLMs. Empirical studies of pre-trained models from 3B to 70B parameters show that GEM achieves comparable downstream performance to CE while significantly enhancing output diversity. This increased diversity translates to performance gains in test-time compute scaling for chat and code generation tasks. Moreover, we observe that preserving output diversity has the added benefit of mitigating forgetting, as maintaining diverse outputs encourages models to retain pre-trained knowledge throughout the training process.

We present a new algorithm RXTX that computes product of matrix by its transpose XX^t. RXTX uses 5% less multiplications and additions than State-of-the-Art and achieves accelerations even for small sizes of matrix X. The algorithm was discovered by combining Machine Learning-based search methods with Combinatorial Optimization.

Deep neural networks (DNNs) are shown to be vulnerable to adversarial examples. A well-trained model can be easily attacked by adding small perturbations to the original data. One of the hypotheses of the existence of the adversarial examples is the off-manifold assumption: adversarial examples lie off the data manifold. However, recent research showed that on-manifold adversarial examples also exist. In this paper, we revisit the off-manifold assumption and want to study a question: at what level is the poor performance of neural networks against adversarial attacks due to on-manifold adversarial examples? Since the true data manifold is unknown in practice, we consider two approximated on-manifold adversarial examples on both real and synthesis datasets. On real datasets, we show that on-manifold adversarial examples have greater attack rates than off-manifold adversarial examples on both standard-trained and adversarially-trained models. On synthetic datasets, theoretically, We prove that on-manifold adversarial examples are powerful, yet adversarial training focuses on off-manifold directions and ignores the on-manifold adversarial examples. Furthermore, we provide analysis to show that the properties derived theoretically can also be observed in practice. Our analysis suggests that on-manifold adversarial examples are important, and we should pay more attention to on-manifold adversarial examples for training robust models.

Physical Cell Identity (PCI) is a critical parameter in 5G networks. Efficient and accurate PCI assignment is essential for mitigating mod-3 interference, mod-30 interference, collisions, and confusions among cells, which directly affect network reliability and user experience. In this paper, we propose a novel framework for PCI assignment by decomposing the problem into Min-3-Partition, Min-10-Partition, and a graph coloring problem, leveraging the Chinese Remainder Theorem (CRT). Furthermore, we develop a relaxation-free approach to the general Min-k-Partition problem by reformulating it as a quadratic program with a norm-equality constraint and solving it using a penalized mirror descent (PMD) algorithm. The proposed method demonstrates superior computational efficiency and scalability, significantly reducing interference while eliminating collisions and confusions in large-scale 5G networks. Numerical evaluations on real-world datasets show that our approach reduces computational time by up to 20 times compared to state-of-the-art methods, making it highly practical for real-time PCI optimization in large-scale networks. These results highlight the potential of our method to improve network performance and reduce deployment costs in modern 5G systems.

The matrix factorization (MF) model has a wide range of applications in signal processing and machine learning. Existing decentralized MF methods require to know the matrix rank a prior, which however is difficult to obtain especially when the data are distributively stored in a network. In the two-part paper, we study a rank-adaptive MF algorithm which proceeds in decentralized setting and meanwhile does not need to know the matrix rank precisely. In the Part-I paper, we have proposed to achieve the rank adaption through a novel l1-norm regularizer, and demonstrated its efficacy via numerical experiments. In this Part-II paper, our goal is to build the convergence conditions and the convergence rate of the proposed rank-adaptive algorithm. In particular, we first consider the decentralized MF algorithm with known rank and show that when the step size is set as O (t(-delta)) for delta is an element of (1/2,2/3], the algorithm converges to the global optima with rate O(t(-delta)) with high probability, whereas when the step-size is a constant, the algorithm converges with a linear rate, but only to the neighborhood of the global optima. Then we extend the analysis to the rank-adaptive algorithm.