A Survey of Scaling in Large Language Model Reasoning

The rapid advancements in large Language models (LLMs) have significantly enhanced their reasoning capabilities, driven by various strategies such as multi-agent collaboration. However, unlike the well-established performance improvements achieved through scaling data and model size, the scaling of reasoning in LLMs is more complex and can even negatively impact reasoning performance, introducing new challenges in model alignment and robustness. In this survey, we provide a comprehensive examination of scaling in LLM reasoning, categorizing it into multiple dimensions and analyzing how and to what extent different scaling strategies contribute to improving reasoning capabilities. We begin by exploring scaling in input size, which enables LLMs to process and utilize more extensive context for improved reasoning. Next, we analyze scaling in reasoning steps that improves multi-step inference and logical consistency. We then examine scaling in reasoning rounds, where iterative interactions refine reasoning outcomes. Furthermore, we discuss scaling in training-enabled reasoning, focusing on optimization through iterative model improvement. Finally, we review applications of scaling across domains and outline future directions for further advancing LLM reasoning. By synthesizing these diverse perspectives, this survey aims to provide insights into how scaling strategies fundamentally enhance the reasoning capabilities of LLMs and further guide the development of next-generation AI systems.

A Shared Low-Rank Adaptation Approach to Personalized RLHF

Reinforcement Learning from Human Feedback (RLHF) has emerged as a pivotal technique for aligning artificial intelligence systems with human values, achieving remarkable success in fine-tuning large language models. However, existing RLHF frameworks often assume that human preferences are relatively homogeneous and can be captured by a single, unified reward model. This assumption overlooks the inherent diversity and heterogeneity across individuals, limiting the adaptability of RLHF to personalized scenarios and risking misalignments that can diminish user satisfaction and trust in AI systems. In this paper, we address these challenges by introducing Low-Rank Adaptation (LoRA) into the personalized RLHF framework. We apply LoRA in the the aggregated parameter space of all personalized reward functions, thereby enabling efficient learning of personalized reward models from potentially limited local datasets. Our approach exploits potential shared structures among the local ground-truth reward models while allowing for individual adaptation, without relying on restrictive assumptions about shared representations as in prior works. We further establish sample complexity guarantees for our method. Theoretical analysis demonstrates the effectiveness of the proposed approach in capturing both shared and individual-specific structures within heterogeneous human preferences, addressing the dual challenge of personalization requirements and practical data constraints. Experimental results on real-world datasets corroborate the efficiency of our algorithm in the personalized RLHF setting.

Transformer-based Wireless Symbol Detection Over Fading Channels

Pre-trained Transformers, through in-context learning (ICL), have demonstrated exceptional capabilities to adapt to new tasks using example prompts without model update. Transformer-based wireless receivers, where prompts consist of the pilot data in the form of transmitted and received signal pairs, have shown high detection accuracy when pilot data are abundant. However, pilot information is often costly and limited in practice. In this work, we propose the DEcision Feedback INcontExt Detection (DEFINED) solution as a new wireless receiver design, which bypasses channel estimation and directly performs symbol detection using the (sometimes extremely) limited pilot data. The key innovation in DEFINED is the proposed decision feedback mechanism in ICL, where we sequentially incorporate the detected symbols into the prompts as pseudo-labels to improve the detection for subsequent symbols. Furthermore, we proposed another detection method where we combine ICL with Semi-Supervised Learning (SSL) to extract information from both labeled and unlabeled data during inference, thus avoiding the errors propagated during the decision feedback process of the original DEFINED. Extensive experiments across a broad range of wireless communication settings demonstrate that a small Transformer trained with DEFINED or IC-SSL achieves significant performance improvements over conventional methods, in some cases only needing a single pilot pair to achieve similar performance of the latter with more than 4 pilot pairs.

Cost-Aware Optimal Pairwise Pure Exploration

Pure exploration is one of the fundamental problems in multi-armed bandits (MAB). However, existing works mostly focus on specific pure exploration tasks, without a holistic view of the general pure exploration problem. This work fills this gap by introducing a versatile framework to study pure exploration, with a focus on identifying the pairwise relationships between targeted arm pairs. Moreover, unlike existing works that only optimize the stopping time (i.e., sample complexity), this work considers that arms are associated with potentially different costs and targets at optimizing the cumulative cost that occurred during learning. Under the general framework of pairwise pure exploration with arm-specific costs, a performance lower bound is derived. Then, a novel algorithm, termed CAET (Cost-Aware Pairwise Exploration Task), is proposed. CAET builds on the track-and-stop principle with a novel design to handle the arm-specific costs, which can potentially be zero and thus represent a very challenging case. Theoretical analyses prove that the performance of CAET approaches the lower bound asymptotically. Special cases are further discussed, including an extension to regret minimization, which is another major focus of MAB. The effectiveness and efficiency of CAET are also verified through experimental results under various settings.

Federated Learning for Diffusion Models

Diffusion models are powerful generative models that can produce highly realistic samples for various tasks. Typically, these models are constructed using centralized, independently and identically distributed (IID) training data. However, in practical scenarios, data is often distributed across multiple clients and frequently manifests non-IID characteristics. Federated Learning (FL) can leverage this distributed data to train diffusion models, but the performance of existing FL methods is unsatisfactory in non-IID scenarios. To address this, we propose FedDDPM-Federated Learning with Denoising Diffusion Probabilistic Models, which leverages the data generative capability of diffusion models to facilitate model training. In particular, the server uses well-trained local diffusion models uploaded by each client before FL training to generate auxiliary data that can approximately represent the global data distribution. Following each round of model aggregation, the server further optimizes the global model using the auxiliary dataset to alleviate the impact of heterogeneous data on model performance. We provide a rigorous convergence analysis of FedDDPM and propose an enhanced algorithm, FedDDPM+, to reduce training overheads. FedDDPM+ detects instances of slow model learning and performs a one-shot correction using the auxiliary dataset. Experimental results validate that our proposed algorithms outperform the state-of-the-art FL algorithms on the MNIST, CIFAR10 and CIFAR100 datasets.

Average Reward Reinforcement Learning for Wireless Radio Resource Management

In this paper, we address a crucial but often overlooked issue in applying reinforcement learning (RL) to radio resource management (RRM) in wireless communications: the mismatch between the discounted reward RL formulation and the undiscounted goal of wireless network optimization. To the best of our knowledge, we are the first to systematically investigate this discrepancy, starting with a discussion of the problem formulation followed by simulations that quantify the extent of the gap. To bridge this gap, we introduce the use of average reward RL, a method that aligns more closely with the long-term objectives of RRM. We propose a new method called the Average Reward Off policy Soft Actor Critic (ARO SAC) is an adaptation of the well known Soft Actor Critic algorithm in the average reward framework. This new method achieves significant performance improvement our simulation results demonstrate a 15% gain in the system performance over the traditional discounted reward RL approach, underscoring the potential of average reward RL in enhancing the efficiency and effectiveness of wireless network optimization.

Decision Feedback In-Context Symbol Detection over Block-Fading Channels

Pre-trained Transformers, through in-context learning (ICL), have demonstrated exceptional capabilities to adapt to new tasks using example prompts \textit{without model update}. Transformer-based wireless receivers, where prompts consist of the pilot data in the form of transmitted and received signal pairs, have shown high estimation accuracy when pilot data are abundant. However, pilot information is often costly and limited in practice. In this work, we propose the \underline{DE}cision \underline{F}eedback \underline{IN}-Cont\underline{E}xt \underline{D}etection (DEFINED) solution as a new wireless receiver design, which bypasses channel estimation and directly performs symbol detection using the (sometimes extremely) limited pilot data. The key innovation in DEFINED is the proposed decision feedback mechanism in ICL, where we sequentially incorporate the detected symbols into the prompts to improve the detections for subsequent symbols. Extensive experiments across a broad range of wireless communication settings demonstrate that DEFINED achieves significant performance improvements, in some cases only needing a single pilot pair.

Higher-order Cross-structural Embedding Model for Time Series Analysis

Time series analysis has gained significant attention due to its critical applications in diverse fields such as healthcare, finance, and sensor networks. The complexity and non-stationarity of time series make it challenging to capture the interaction patterns across different timestamps. Current approaches struggle to model higher-order interactions within time series, and focus on learning temporal or spatial dependencies separately, which limits performance in downstream tasks. To address these gaps, we propose Higher-order Cross-structural Embedding Model for Time Series (High-TS), a novel framework that jointly models both temporal and spatial perspectives by combining multiscale Transformer with Topological Deep Learning (TDL). Meanwhile, High-TS utilizes contrastive learning to integrate these two structures for generating robust and discriminative representations. Extensive experiments show that High-TS outperforms state-of-the-art methods in various time series tasks and demonstrate the importance of higher-order cross-structural information in improving model performance.

On the Learn-to-Optimize Capabilities of Transformers in In-Context Sparse Recovery

An intriguing property of the Transformer is its ability to perform in-context learning (ICL), where the Transformer can solve different inference tasks without parameter updating based on the contextual information provided by the corresponding input-output demonstration pairs. It has been theoretically proved that ICL is enabled by the capability of Transformers to perform gradient-descent algorithms (Von Oswald et al., 2023a; Bai et al., 2024). This work takes a step further and shows that Transformers can perform learning-to-optimize (L2O) algorithms. Specifically, for the ICL sparse recovery (formulated as LASSO) tasks, we show that a K-layer Transformer can perform an L2O algorithm with a provable convergence rate linear in K. This provides a new perspective explaining the superior ICL capability of Transformers, even with only a few layers, which cannot be achieved by the standard gradient-descent algorithms. Moreover, unlike the conventional L2O algorithms that require the measurement matrix involved in training to match that in testing, the trained Transformer is able to solve sparse recovery problems generated with different measurement matrices. Besides, Transformers as an L2O algorithm can leverage structural information embedded in the training tasks to accelerate its convergence during ICL, and generalize across different lengths of demonstration pairs, where conventional L2O algorithms typically struggle or fail. Such theoretical findings are supported by our experimental results.

Channel-Wise Mixed-Precision Quantization for Large Language Models

Large Language Models (LLMs) have demonstrated remarkable success across a wide range of language tasks, but their deployment on edge devices remains challenging due to the substantial memory requirements imposed by their large parameter sizes. Weight-only quantization presents a promising solution to reduce the memory footprint of LLMs. However, existing approaches primarily focus on integer-bit quantization, limiting their adaptability to fractional-bit quantization tasks and preventing the full utilization of available storage space on devices. In this paper, we introduce Channel-Wise Mixed-Precision Quantization (CMPQ), a novel mixed-precision quantization method that allocates quantization precision in a channel-wise pattern based on activation distributions. By assigning different precision levels to different weight channels, CMPQ can adapt to any bit-width constraint. CMPQ employs a non-uniform quantization strategy and incorporates two outlier extraction techniques that collaboratively preserve the critical information, thereby minimizing the quantization loss. Experiments on different sizes of LLMs demonstrate that CMPQ not only enhances performance in integer-bit quantization tasks but also achieves significant performance gains with a modest increase in memory usage. CMPQ thus represents an adaptive and effective approach to LLM quantization, offering substantial benefits across diverse device capabilities.