UniGeM: Unifying Data Mixing and Selection via Geometric Exploration and Mining

The scaling of Large Language Models (LLMs) is increasingly limited by data quality. Most methods handle data mixing and sample selection separately, which can break the structure in code corpora. We introduce \textbf{UniGeM}, a framework that unifies mixing and selection by treating data curation as a \textit{manifold approximation} problem without training proxy models or relying on external reference datasets. UniGeM operates hierarchically: \textbf{Macro-Exploration} learns mixing weights with stability-based clustering; \textbf{Micro-Mining} filters high-quality instances by their geometric distribution to ensure logical consistency. Validated by training 8B and 16B MoE models on 100B tokens, UniGeM achieves \textbf{2.0$\times$ data efficiency} over a random baseline and further improves overall performance compared to SOTA methods in reasoning-heavy evaluations and multilingual generalization.

Beyond the Black Box: Theory and Mechanism of Large Language Models

The rapid emergence of Large Language Models (LLMs) has precipitated a profound paradigm shift in Artificial Intelligence, delivering monumental engineering successes that increasingly impact modern society. However, a critical paradox persists within the current field: despite the empirical efficacy, our theoretical understanding of LLMs remains disproportionately nascent, forcing these systems to be treated largely as ``black boxes''. To address this theoretical fragmentation, this survey proposes a unified lifecycle-based taxonomy that organizes the research landscape into six distinct stages: Data Preparation, Model Preparation, Training, Alignment, Inference, and Evaluation. Within this framework, we provide a systematic review of the foundational theories and internal mechanisms driving LLM performance. Specifically, we analyze core theoretical issues such as the mathematical justification for data mixtures, the representational limits of various architectures, and the optimization dynamics of alignment algorithms. Moving beyond current best practices, we identify critical frontier challenges, including the theoretical limits of synthetic data self-improvement, the mathematical bounds of safety guarantees, and the mechanistic origins of emergent intelligence. By connecting empirical observations with rigorous scientific inquiry, this work provides a structured roadmap for transitioning LLM development from engineering heuristics toward a principled scientific discipline.

Unveiling the Mechanisms of Explicit CoT Training: How Chain-of-Thought Enhances Reasoning Generalization

Training large language models (LLMs) with high-quality Chain-of-Thought (CoT) annotations has become a widely adopted strategy due to its significant enhancement of reasoning capabilities. To fully comprehend this approach, two questions naturally arise: (Q1) What advantages does training with CoT offer compared to training without CoT? (Q2) If there are advantages, what are the underlying mechanisms of explicit CoT training? Analyzing the advantages and mechanisms of CoT training is challenging due to the many factors involved. To address this, we conduct a detailed analysis using clear and controllable data distributions and, for the first time, reveal that CoT training offers the following advantages: (1) Training with CoT markedly improves reasoning generalization, extending it from in-distribution (ID) to both ID and out-of-distribution (OOD) scenarios, while also speeding up convergence; (2) Even when training with CoT includes a certain range of erroneous reasoning steps, it still enables the model to learn reasoning patterns, leading to systematic generalization. We further explore the underlying mechanisms from a circuit perspective: (1) The data distribution (e.g., ratio $\lambda$ and pattern) plays a crucial role in influencing the model's systematic generalization; (2) CoT training (with two-hop facts) internalizes reasoning into a two-stage generalizing circuit, where the number of stages corresponds to the explicit reasoning steps during training. Our findings elucidate the mechanisms underlying explicit CoT training and offer critical insights into tuning strategies for LLMs to achieve robust generalization.

Theoretical Insights into Fine-Tuning Attention Mechanism: Generalization and Optimization

Large Language Models (LLMs), built on Transformer architectures, exhibit remarkable generalization across a wide range of tasks. However, fine-tuning these models for specific tasks remains resource-intensive due to their extensive parameterization. In this paper, we investigate two remarkable phenomena observed during the fine-tuning of LLMs, particularly focusing on the attention mechanism: (1) Different Impact, optimizing the $\mathbf{W}_v$ matrix significantly improves performance over optimizing the $\mathbf{W}_k$ matrix. Fine-tuning only the $\mathbf{W}_q$ and $\mathbf{W}_v$ matrices is computationally efficient, delivering results that are comparable to, or even better than, fine-tuning all three matrices $\mathbf{W}_q$, $\mathbf{W}_k$, and $\mathbf{W}_v$. (2) Efficient Convergence, employing distinct learning rates for these matrices is crucial for optimal performance, with a higher learning rate for the $\mathbf{W}_v$ matrix expediting convergence. However, theoretical analyses of these phenomena are still relatively limited. We present a theoretical analysis of these phenomena from two perspectives: (i) Generalization, where we demonstrate that fine-tuning only $\mathbf{W}_q$ and $\mathbf{W}_v$ improves generalization bounds, enhances memory efficiency, and (ii) Optimization, where we emphasize that the feature learning of the attention mechanism is efficient, particularly when using distinct learning rates for the matrices, which leads to more effective fine-tuning. Building on these insights, we propose a new strategy that improves fine-tuning efficiency in terms of both storage and time. Experimental results on benchmark datasets validate the effectiveness of this approach, supporting our theoretical findings. Our analysis lays the theoretical groundwork for configuring and improving lightweight algorithms in LLMs fine-tuning.

Enhancing In-Context Learning Performance with just SVD-Based Weight Pruning: A Theoretical Perspective

Pre-trained large language models (LLMs) based on Transformer have demonstrated striking in-context learning (ICL) abilities. With a few demonstration input-label pairs, they can predict the label for an unseen input without any parameter updates. In this paper, we show an exciting phenomenon that SVD-based weight pruning can enhance ICL performance, and more surprising, pruning weights in deep layers often results in more stable performance improvements in shallow layers. However, the underlying mechanism of those findings still remains an open question. To reveal those findings, we conduct an in-depth theoretical analysis by presenting the implicit gradient descent (GD) trajectories of ICL and giving the mutual information based generalization bounds of ICL via full implicit GD trajectories. This helps us reasonably explain the surprising experimental findings. Besides, based on all our experimental and theoretical insights, we intuitively propose a simple, model-compression and derivative-free algorithm for downstream tasks in enhancing ICL inference. Experiments on benchmark datasets and open source LLMs display the method effectiveness\footnote{The code is available at \url{https://github.com/chen123CtrlS/EnhancingICL_SVDPruning}}.