Mathematical reasoning tasks pose significant challenges for large language models (LLMs) because they require precise logical deduction and sequence analysis. In this work, we introduce the concept of critical tokens – elements within reasoning trajectories that significantly influence incorrect outcomes. We present a novel framework for identifying these tokens through rollout sampling and demonstrate their substantial divergence from traditional error tokens. Through extensive experiments on datasets such as GSM8K and MATH500, we show that identifying and replacing critical tokens significantly improves model accuracy. We propose an efficient methodology for pinpointing these tokens in large-scale datasets using contrastive estimation and extend this framework to enhance model training processes with direct preference optimization (DPO). Experimental results on GSM8K and MATH500 benchmarks with the widely used models Llama-3 (8B and 70B) and Deepseek-math (7B) demonstrate the effectiveness of the proposed approach, cDPO. Our results underscore the potential of leveraging critical tokens to reduce errors in reasoning tasks, advancing the development of AI systems capable of robust logical deduction.

Process Reward Models (PRMs) have shown promise in enhancing the mathematical reasoning capabilities of Large Language Models (LLMs) through Test-Time Scaling (TTS). However, their integration into multimodal reasoning remains largely unexplored. In this work, we take the first step toward unlocking the potential of PRMs in multimodal mathematical reasoning. We identify three key challenges: (i) the scarcity of high-quality reasoning data constrains the capabilities of foundation Multimodal Large Language Models (MLLMs), which imposes further limitations on the upper bounds of TTS and reinforcement learning (RL); (ii) a lack of automated methods for process labeling within multimodal contexts persists; (iii) the employment of process rewards in unimodal RL faces issues like reward hacking, which may extend to multimodal scenarios. To address these issues, we introduce URSA, a three-stage Unfolding multimodal pRocess-Supervision Aided training framework. We first construct MMathCoT-1M, a high-quality large-scale multimodal Chain-of-Thought (CoT) reasoning dataset, to build a stronger math reasoning foundation MLLM, URSA-8B. Subsequently, we go through an automatic process to synthesize process supervision data, which emphasizes both logical correctness and perceptual consistency. We introduce DualMath-1.1M to facilitate the training of URSA-8B-RM. Finally, we propose Process-Supervised Group-Relative-Policy-Optimization (PS-GRPO), pioneering a multimodal PRM-aided online RL method that outperforms vanilla GRPO. With PS-GRPO application, URSA-8B-PS-GRPO outperforms Gemma3-12B and GPT-4o by 8.4% and 2.7% on average across 6 benchmarks.

Holographic multiple-input multiple-output (HMIMO), is envisioned to be a key technology for enhancing the spectral efficiency for 6G. To achieve higher spectral efficiency, accurate channel state information (CSI) is required. However, due to the high-dimensional HMIMO channel induced by the large number of antenna elements, accurate CSI estimation typically demands a great number of pilots, which consumes plenty of communication resources. Diffusion models are capable of effectively capturing the distribution of channels. By leveraging the learned channel distribution as a prior, accurate channel estimation can be performed using only a limited number of pilot signals. In this paper, we propose a diffusion model-based channel estimation scheme for HMIMO systems. We first exploit the inherent redundancy of HMIMO channels in the wavenumber domain to perform the channel compression. Subsequently, a diffusion model is employed to capture the distribution of the compressed channel, and a cross-attention module is integrated to learn the relations between the received pilots and the compressed channel. Simulation results demonstrate that the proposed method can accurately recover the HMIMO channel with only a small amount of pilots.

To satisfy the high data rate requirements, cellular systems will evolve towards the direction of higher carrier frequencies and larger antenna arrays. The conventional phased arrays are hard to fulfill such a vision due to its excessive power consumption induced by numerous phase shifters. To address this issue, Reconfigurable Refractive Surfaces (RRSs) provide a energy efficient solution without relying on phase shifters. With enlarged radiation aperture and increased working frequency, users are more likely to be located in the near field of the RRS. Moreover, the frequency selectivity of the RRS cannot be neglected given the wideband communications enabled by higher frequency bands. These two effects jointly aggravate the beam split problem where the signal strength of different frequency components cannot concentrate on the user, leading to a data rate degradation. In this paper, we study an RRS-based wideband near-field communication system with multiple users. Unlike most existing works, which only considered the beam split effect under near-field conditions, we jointly consider the influence of the frequency selectivity of RRS and near-field conditions on the beam split effect. To mitigate the beam split effect, the time-delay units are introduced in the RRS elements based on which a beamforming scheme is proposed to improve system data rate by jointly optimizing the digital beamformer, the phase shifts of RRS and the time-delay units. Simulation results demonstrate the effectiveness of our proposed scheme.

To meet rising data rate demands, cellular systems are expected to evolve towards higher carrier frequencies and larger antenna arrays, but conventional phased arrays face challenges in supporting such a prospection due to their excessive power consumption induced by numerous phase shifters required. Reconfigurable Refractive Surface (RRS) is an energy efficient solution to address this issue without relying on phase shifters. However, the increased radiation aperture size extends the range of the Fresnel region, leading the users to lie in the near-field zone. Moreover, given the wideband communications in higher frequency bands, we cannot ignore the frequency selectivity of the RRS. These two effects collectively exacerbate the beam split issue, where different frequency components fail to converge on the user simultaneously, and finally result in a degradation of the data rate. In this paper, we investigate a RRS-based wideband near-field multi-user communication system. Unlike most existing studies on wideband communications, which consider the beam split effect only with the near-field condition, we study the beam split effect under the influence of both the near-field condition and the frequency selectivity of the RRS. To mitigate the beam split effect, we propose a Delayed-RRS structure, based on which a beamforming scheme is proposed to optimize the user’s data rate. Through theoretical analysis and simulation results, we analyze the influence of the RRS’s frequency selectivity, demonstrate the effectiveness of the proposed beamforming scheme, and reveal the importance of jointly considering the near-field condition and the frequency selectivity of RRS.

Graph neural networks (GNNs), a class of deep learning models designed for performing information interaction on non-Euclidean graph data, have been successfully applied to node classification tasks in various applications such as citation networks, recommender systems, and natural language processing. Graph node classification is an important research field for node-level tasks in graph data mining. Recently, due to the limitations of shallow GNNs, many researchers have focused on designing deep graph learning models. Previous GNN architecture search works only solve shallow networks (e.g., less than four layers). It is challenging and nonefficient to manually design deep GNNs for challenges like over-smoothing and information squeezing, which greatly limits their capabilities on large-scale graph data. In this article, we propose a novel neural architecture search (NAS) method for designing deep GNNs automatically and further exploit the application potential on various node classification tasks. Our innovations lie in two aspects, where we first redesign the deep GNNs search space for architecture search with a decoupled mode based on propagation and transformation processes, and we then formulate and solve the problem as a multiobjective optimization to balance accuracy and computational efficiency. Experiments on benchmark graph datasets show that our method performs very well on various node classification tasks, and exploiting large-scale graph datasets further validates that our proposed method is scalable.

Large Language Models (LLMs) have emerged as powerful tools for Text-to-SQL tasks, exhibiting remarkable reasoning capabilities.Different from tasks such as math word problems and commonsense reasoning, SQL solutions have a relatively fixed pattern.This facilitates the investigation of whether LLMs can benefit from categorical thinking, mirroring how humans acquire knowledge through inductive reasoning based on comparable examples.In this study, we propose that employing query group partitioning allows LLMs to focus on learning the thought processes specific to a single problem type, consequently enhancing their reasoning abilities across diverse difficulty levels and problem categories.Our experiments reveal that multiple advanced LLMs, when equipped with PTD-SQL, can either surpass or match previous state-of-theart (SOTA) methods on the Spider and BIRD datasets.Intriguingly, models with varying initial performances have exhibited significant improvements, mainly at the boundary of their capabilities after targeted drilling, suggesting a parallel with human progress.Code is available at https://github.com/lrlbbzl/PTD-SQL.