Daily Papers

We study numerically the 6D (2,0) superconformal bootstrap using the soft-Actor-Critic (SAC) algorithm as a stochastic optimizer. We focus on the four-point functions of scalar superconformal primaries in the energy-momentum multiplet. Starting from the supergravity limit, we perform searches for adiabatically varied central charges and derive two curves for a collection of 80 CFT data (70 of these data correspond to unprotected long multiplets and 10 to protected short multiplets). We conjecture that the two curves capture the A- and D-series (2,0) theories. Our results are competitive when compared to the existing bounds coming from standard numerical bootstrap methods, and data obtained using the OPE inversion formula. With this paper we are also releasing our Python implementation of the SAC algorithm, BootSTOP. The paper discusses the main functionality features of this package.

We introduce the use of reinforcement-learning (RL) techniques to the conformal-bootstrap programme. We demonstrate that suitable soft Actor-Critic RL algorithms can perform efficient, relatively cheap high-dimensional searches in the space of scaling dimensions and OPE-squared coefficients that produce sensible results for tens of CFT data from a single crossing equation. In this paper we test this approach in well-known 2D CFTs, with particular focus on the Ising and tri-critical Ising models and the free compactified boson CFT. We present results of as high as 36-dimensional searches, whose sole input is the expected number of operators per spin in a truncation of the conformal-block decomposition of the crossing equations. Our study of 2D CFTs uses only the global so(2,2) part of the conformal algebra, and our methods are equally applicable to higher-dimensional CFTs. When combined with other, already available, numerical and analytical methods, we expect our approach to yield an exciting new window into the non-perturbative structure of arbitrary (unitary or non-unitary) CFTs.

Supervised Fine-Tuning (SFT) is commonly used to train language models to imitate annotated responses for given instructions. In this paper, we challenge this paradigm and propose Critique Fine-Tuning (CFT), a strategy where models learn to critique noisy responses rather than simply imitate correct ones. Inspired by human learning processes that emphasize critical thinking, CFT encourages deeper analysis and nuanced understanding-traits often overlooked by standard SFT. To validate the effectiveness of CFT, we construct a 50K-sample dataset from WebInstruct, using GPT-4o as the teacher to generate critiques in the form of (input=[query; noisy response], output=critique). CFT on this dataset yields a consistent 4-10% improvement over SFT on six math benchmarks with different base models like Qwen2.5, Qwen2.5-Math and DeepSeek-Math. We further expand to MetaMath and NuminaMath datasets and observe similar gains over SFT. Notably, our Qwen2.5-Math-CFT model-trained on just 50K samples-matches or outperforms competitive models such as AceMath and Qwen2.5-Math-Instruct on most benchmarks, both of which use over 2M samples. Ablation studies show that CFT is robust to the source of noisy response and teacher critique model. Through these findings, we argue that critique-based training offers a more effective alternative to advance the reasoning of language models.

Although retrieval-augmented generation(RAG) significantly improves generation quality by retrieving external knowledge bases and integrating generated content, it faces computational efficiency bottlenecks, particularly in knowledge retrieval tasks involving hierarchical structures for Tree-RAG. This paper proposes a Tree-RAG acceleration method based on the improved Cuckoo Filter, which optimizes entity localization during the retrieval process to achieve significant performance improvements. Tree-RAG effectively organizes entities through the introduction of a hierarchical tree structure, while the Cuckoo Filter serves as an efficient data structure that supports rapid membership queries and dynamic updates. The experiment results demonstrate that our method is much faster than naive Tree-RAG while maintaining high levels of generative quality. When the number of trees is large, our method is hundreds of times faster than naive Tree-RAG. Our work is available at https://github.com/TUPYP7180/CFT-RAG-2025.