Autoregressive large language models (LLMs) exhibit impressive performance across various tasks but struggle with simple arithmetic, such as addition of two or more operands. We show that this struggle arises from LLMs' use of a simple one-digit lookahead heuristic, which works fairly well (but not perfect) for two-operand addition but fails in multi-operand cases, where the carry-over logic is more complex. Our probing experiments and digit-wise accuracy evaluation show that LLMs fail precisely where a one-digit lookahead is insufficient to account for cascading carries. We analyze the impact of tokenization strategies on arithmetic performance and show that all investigated models, regardless of tokenization, are inherently limited in the addition of multiple operands due to their reliance on a one-digit lookahead heuristic. Our findings reveal fundamental limitations that prevent LLMs from generalizing to more complex numerical reasoning.

Recent studies highlight the promise of LLM-based prompt optimization, especially with TextGrad, which automates differentiation'' via texts and backpropagates textual feedback. This approach facilitates training in various real-world applications that do not support numerical gradient propagation or loss calculation. In this paper, we systematically explore the potential and challenges of incorporating textual gradient into Federated Learning (FL). Our contributions are fourfold. Firstly, we introduce a novel FL paradigm, Federated Textual Gradient (FedTextGrad), that allows clients to upload locally optimized prompts derived from textual gradients, while the server aggregates the received prompts. Unlike traditional FL frameworks, which are designed for numerical aggregation, FedTextGrad is specifically tailored for handling textual data, expanding the applicability of FL to a broader range of problems that lack well-defined numerical loss functions. Secondly, building on this design, we conduct extensive experiments to explore the feasibility of FedTextGrad. Our findings highlight the importance of properly tuning key factors (e.g., local steps) in FL training. Thirdly, we highlight a major challenge in FedTextGrad aggregation: retaining essential information from distributed prompt updates. Last but not least, in response to this issue, we improve the vanilla variant of FedTextGrad by providing actionable guidance to the LLM when summarizing client prompts by leveraging the Uniform Information Density principle. Through this principled study, we enable the adoption of textual gradients in FL for optimizing LLMs, identify important issues, and pinpoint future directions, thereby opening up a new research area that warrants further investigation.

Large Language Models (LLMs) have transformed text generation through inherently probabilistic context-aware mechanisms, mimicking human natural language. In this paper, we systematically investigate the performance of various LLMs when generating random numbers, considering diverse configurations such as different model architectures, numerical ranges, temperature, and prompt languages. Our results reveal that, despite their stochastic transformers-based architecture, these models often exhibit deterministic responses when prompted for random numerical outputs. In particular, we find significant differences when changing the model, as well as the prompt language, attributing this phenomenon to biases deeply embedded within the training data. Models such as DeepSeek-R1 can shed some light on the internal reasoning process of LLMs, despite arriving to similar results. These biases induce predictable patterns that undermine genuine randomness, as LLMs are nothing but reproducing our own human cognitive biases.

Stance detection on social media aims to identify attitudes expressed in tweets towards specific targets. Current studies prioritize Large Language Models (LLMs) over Small Language Models (SLMs) due to the overwhelming performance improving provided by LLMs. However, heavily relying on LLMs for stance detection, regardless of the cost, is impractical for real-world social media monitoring systems that require vast data analysis. To this end, we propose \textbf{\underline{Co}}llaborative Stance Detection via Small-Large Language Model Consistency \textbf{\underline{Ver}}ification (\textbf{CoVer}) framework, which enhances LLM utilization via context-shared batch reasoning and logical verification between LLM and SLM. Specifically, instead of processing each text individually, CoVer processes texts batch-by-batch, obtaining stance predictions and corresponding explanations via LLM reasoning in a shared context. Then, to exclude the bias caused by context noises, CoVer introduces the SLM for logical consistency verification. Finally, texts that repeatedly exhibit low logical consistency are classified using consistency-weighted aggregation of prior LLM stance predictions. Our experiments show that CoVer outperforms state-of-the-art methods across multiple benchmarks in the zero-shot setting, achieving 0.54 LLM queries per tweet while significantly enhancing performance. Our CoVer offers a more practical solution for LLM deploying for social media stance detection.

Regular updates are essential for maintaining up-to-date knowledge in large language models (LLMs). Consequently, various model editing methods have been developed to update specific knowledge within LLMs. However, training-based approaches often struggle to effectively incorporate new knowledge while preserving unrelated general knowledge. To address this challenge, we propose a novel framework called Geometric Knowledge Editing (GeoEdit). GeoEdit utilizes the geometric relationships of parameter updates from fine-tuning to differentiate between neurons associated with new knowledge updates and those related to general knowledge perturbations. By employing a direction-aware knowledge identification method, we avoid updating neurons with directions approximately orthogonal to existing knowledge, thus preserving the model's generalization ability. For the remaining neurons, we integrate both old and new knowledge for aligned directions and apply a "forget-then-learn" editing strategy for opposite directions. Additionally, we introduce an importance-guided task vector fusion technique that filters out redundant information and provides adaptive neuron-level weighting, further enhancing model editing performance. Extensive experiments on two publicly available datasets demonstrate the superiority of GeoEdit over existing state-of-the-art methods.

Large Language Models (LLMs) increasingly rely on prolonged reasoning chains to solve complex tasks. However, this trial-and-error approach often leads to high computational overhead and error propagation, where early mistakes can derail subsequent steps. To address these issues, we introduce Meta-Reasoner, a framework that dynamically optimizes inference-time reasoning by enabling LLMs to "think about how to think." Drawing inspiration from human meta-cognition and dual-process theory, Meta-Reasoner operates as a strategic advisor, decoupling high-level guidance from step-by-step generation. It employs "contextual multi-armed bandits" to iteratively evaluate reasoning progress, and select optimal strategies (e.g., backtrack, clarify ambiguity, restart from scratch, or propose alternative approaches), and reallocates computational resources toward the most promising paths. Our evaluations on mathematical reasoning and puzzles highlight the potential of dynamic reasoning chains to overcome inherent challenges in the LLM reasoning process and also show promise in broader applications, offering a scalable and adaptable solution for reasoning-intensive tasks.

To improve Multimodal Large Language Models' (MLLMs) ability to process images and complex instructions, researchers predominantly curate large-scale visual instruction tuning datasets, which are either sourced from existing vision tasks or synthetically generated using LLMs and image descriptions. However, they often suffer from critical flaws, including misaligned instruction-image pairs and low-quality images. Such issues hinder training efficiency and limit performance improvements, as models waste resources on noisy or irrelevant data with minimal benefit to overall capability. To address this issue, we propose a \textbf{Vi}sual-Centric \textbf{S}election approach via \textbf{A}gents Collaboration (ViSA), which centers on image quality assessment and image-instruction relevance evaluation. Specifically, our approach consists of 1) an image information quantification method via visual agents collaboration to select images with rich visual information, and 2) a visual-centric instruction quality assessment method to select high-quality instruction data related to high-quality images. Finally, we reorganize 80K instruction data from large open-source datasets. Extensive experiments demonstrate that ViSA outperforms or is comparable to current state-of-the-art models on seven benchmarks, using only 2.5\% of the original data, highlighting the efficiency of our data selection approach. Moreover, we conduct ablation studies to validate the effectiveness of each component of our method. The code is available at https://github.com/HITsz-TMG/ViSA.

Knowledge Tracing (KT) is a fundamental technology in intelligent tutoring systems used to simulate changes in students' knowledge state during learning, track personalized knowledge mastery, and predict performance. However, current KT models face three major challenges: (1) When encountering new questions, models face cold-start problems due to sparse interaction records, making precise modeling difficult; (2) Traditional models only use historical interaction records for student personalization modeling, unable to accurately track individual mastery levels, resulting in unclear personalized modeling; (3) The decision-making process is opaque to educators, making it challenging for them to understand model judgments. To address these challenges, we propose a novel Dual-channel Difficulty-aware Knowledge Tracing (DDKT) framework that utilizes Large Language Models (LLMs) and Retrieval-Augmented Generation (RAG) for subjective difficulty assessment, while integrating difficulty bias-aware algorithms and student mastery algorithms for precise difficulty measurement. Our framework introduces three key innovations: (1) Difficulty Balance Perception Sequence (DBPS) - students' subjective perceptions combined with objective difficulty, measuring gaps between LLM-assessed difficulty, mathematical-statistical difficulty, and students' subjective perceived difficulty through attention mechanisms; (2) Difficulty Mastery Ratio (DMR) - precise modeling of student mastery levels through different difficulty zones; (3) Knowledge State Update Mechanism - implementing personalized knowledge acquisition through gated networks and updating student knowledge state. Experimental results on two real datasets show our method consistently outperforms nine baseline models, improving AUC metrics by 2% to 10% while effectively addressing cold-start problems and enhancing model interpretability.

Data and pipeline parallelism are ubiquitous for training of Large Language Models (LLM) on distributed nodes. Driven by the need for cost-effective training, recent work explores efficient communication arrangement for end to end training. Motivated by LLM's resistance to layer skipping and layer reordering, in this paper, we explore stage (several consecutive layers) skipping in pipeline training, and challenge the conventional practice of sequential pipeline execution. We derive convergence and throughput constraints (guidelines) for pipelining with skipping and swapping pipeline stages. Based on these constraints, we propose SkipPipe, the first partial pipeline framework to reduce the end-to-end training time for LLMs while preserving the convergence. The core of SkipPipe is a path scheduling algorithm that optimizes the paths for individual microbatches and reduces idle time (due to microbatch collisions) on the distributed nodes, complying with the given stage skipping ratio. We extensively evaluate SkipPipe on LLaMa models from 500M to 8B parameters on up to 20 nodes. Our results show that SkipPipe reduces training iteration time by up to $55\%$ compared to full pipeline. Our partial pipeline training also improves resistance to layer omission during inference, experiencing a drop in perplexity of only $7\%$ when running only half the model. Our code is available at https://github.com/gensyn-ai/skippipe.

Logical reasoning is essential for large language models (LLMs) to ensure accurate and coherent inference. However, LLMs struggle with reasoning order variations and fail to generalize across logically equivalent transformations. LLMs often rely on fixed sequential patterns rather than true logical understanding. To address this issue, we introduce an order-centric data augmentation framework based on commutativity in logical reasoning. We first randomly shuffle independent premises to introduce condition order augmentation. For reasoning steps, we construct a directed acyclic graph (DAG) to model dependencies between steps, which allows us to identify valid reorderings of steps while preserving logical correctness. By leveraging order-centric augmentations, models can develop a more flexible and generalized reasoning process. Finally, we conduct extensive experiments across multiple logical reasoning benchmarks, demonstrating that our method significantly enhances LLMs' reasoning performance and adaptability to diverse logical structures. We release our codes and augmented data in https://anonymous.4open.science/r/Order-Centric-Data-Augmentation-822C/.