In-depth Analysis of Graph-based RAG in a Unified Framework

Graph-based Retrieval-Augmented Generation (RAG) has proven effective in integrating external knowledge into large language models (LLMs), improving their factual accuracy, adaptability, interpretability, and trustworthiness. A number of graph-based RAG methods have been proposed in the literature. However, these methods have not been systematically and comprehensively compared under the same experimental settings. In this paper, we first summarize a unified framework to incorporate all graph-based RAG methods from a high-level perspective. We then extensively compare representative graph-based RAG methods over a range of questing-answering (QA) datasets -- from specific questions to abstract questions -- and examine the effectiveness of all methods, providing a thorough analysis of graph-based RAG approaches. As a byproduct of our experimental analysis, we are also able to identify new variants of the graph-based RAG methods over specific QA and abstract QA tasks respectively, by combining existing techniques, which outperform the state-of-the-art methods. Finally, based on these findings, we offer promising research opportunities. We believe that a deeper understanding of the behavior of existing methods can provide new valuable insights for future research.

Jailbreaking LLMs' Safeguard with Universal Magic Words for Text Embedding Models

The security issue of large language models (LLMs) has gained significant attention recently, with various defense mechanisms developed to prevent harmful outputs, among which safeguards based on text embedding models serve as a fundamental defense. Through testing, we discover that the distribution of text embedding model outputs is significantly biased with a large mean. Inspired by this observation, we propose novel efficient methods to search for universal magic words that can attack text embedding models. The universal magic words as suffixes can move the embedding of any text towards the bias direction, therefore manipulate the similarity of any text pair and mislead safeguards. By appending magic words to user prompts and requiring LLMs to end answers with magic words, attackers can jailbreak the safeguard. To eradicate this security risk, we also propose defense mechanisms against such attacks, which can correct the biased distribution of text embeddings in a train-free manner.

Phase Transitions in Large Language Models and the $O(N)$ Model

Large language models (LLMs) exhibit unprecedentedly rich scaling behaviors. In physics, scaling behavior is closely related to phase transitions, critical phenomena, and field theory. To investigate the phase transition phenomena in LLMs, we reformulated the Transformer architecture as an $O(N)$ model. Our study reveals two distinct phase transitions corresponding to the temperature used in text generation and the model's parameter size, respectively. The first phase transition enables us to estimate the internal dimension of the model, while the second phase transition is of \textit{higher-depth} and signals the emergence of new capabilities. As an application, the energy of the $O(N)$ model can be used to evaluate whether an LLM's parameters are sufficient to learn the training data.

rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking

We present rStar-Math to demonstrate that small language models (SLMs) can rival or even surpass the math reasoning capability of OpenAI o1, without distillation from superior models. rStar-Math achieves this by exercising "deep thinking" through Monte Carlo Tree Search (MCTS), where a math policy SLM performs test-time search guided by an SLM-based process reward model. rStar-Math introduces three innovations to tackle the challenges in training the two SLMs: (1) a novel code-augmented CoT data sythesis method, which performs extensive MCTS rollouts to generate step-by-step verified reasoning trajectories used to train the policy SLM; (2) a novel process reward model training method that avoids na\"ive step-level score annotation, yielding a more effective process preference model (PPM); (3) a self-evolution recipe in which the policy SLM and PPM are built from scratch and iteratively evolved to improve reasoning capabilities. Through 4 rounds of self-evolution with millions of synthesized solutions for 747k math problems, rStar-Math boosts SLMs' math reasoning to state-of-the-art levels. On the MATH benchmark, it improves Qwen2.5-Math-7B from 58.8% to 90.0% and Phi3-mini-3.8B from 41.4% to 86.4%, surpassing o1-preview by +4.5% and +0.9%. On the USA Math Olympiad (AIME), rStar-Math solves an average of 53.3% (8/15) of problems, ranking among the top 20% the brightest high school math students. Code and data will be available at https://github.com/microsoft/rStar.

Understand the Effectiveness of Shortcuts through the Lens of DCA

Difference-of-Convex Algorithm (DCA) is a well-known nonconvex optimization algorithm for minimizing a nonconvex function that can be expressed as the difference of two convex ones. Many famous existing optimization algorithms, such as SGD and proximal point methods, can be viewed as special DCAs with specific DC decompositions, making it a powerful framework for optimization. On the other hand, shortcuts are a key architectural feature in modern deep neural networks, facilitating both training and optimization. We showed that the shortcut neural network gradient can be obtained by applying DCA to vanilla neural networks, networks without shortcut connections. Therefore, from the perspective of DCA, we can better understand the effectiveness of networks with shortcuts. Moreover, we proposed a new architecture called NegNet that does not fit the previous interpretation but performs on par with ResNet and can be included in the DCA framework.