Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification

Recent progress in large language models (LLMs) like GPT-4 and PaLM-2 has brought significant advancements in addressing math reasoning problems. In particular, OpenAI's latest version of GPT-4, known as GPT-4 Code Interpreter, shows remarkable performance on challenging math datasets. In this paper, we explore the effect of code on enhancing LLMs' reasoning capability by introducing different constraints on the \textit{Code Usage Frequency} of GPT-4 Code Interpreter. We found that its success can be largely attributed to its powerful skills in generating and executing code, evaluating the output of code execution, and rectifying its solution when receiving unreasonable outputs. Based on this insight, we propose a novel and effective prompting method, explicit \uline{c}ode-based \uline{s}elf-\uline{v}erification~(CSV), to further boost the mathematical reasoning potential of GPT-4 Code Interpreter. This method employs a zero-shot prompt on GPT-4 Code Interpreter to encourage it to use code to self-verify its answers. In instances where the verification state registers as ``False'', the model shall automatically amend its solution, analogous to our approach of rectifying errors during a mathematics examination. Furthermore, we recognize that the states of the verification result indicate the confidence of a solution, which can improve the effectiveness of majority voting. With GPT-4 Code Interpreter and CSV, we achieve an impressive zero-shot accuracy on MATH dataset \textbf{(53.9\% $\to$ 84.3\%)}.Comment: Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verificatio

PerFedRec++: Enhancing Personalized Federated Recommendation with Self-Supervised Pre-Training

Federated recommendation systems employ federated learning techniques to safeguard user privacy by transmitting model parameters instead of raw user data between user devices and the central server. Nevertheless, the current federated recommender system faces challenges such as heterogeneity and personalization, model performance degradation, and communication bottleneck. Previous studies have attempted to address these issues, but none have been able to solve them simultaneously. In this paper, we propose a novel framework, named PerFedRec++, to enhance the personalized federated recommendation with self-supervised pre-training. Specifically, we utilize the privacy-preserving mechanism of federated recommender systems to generate two augmented graph views, which are used as contrastive tasks in self-supervised graph learning to pre-train the model. Pre-training enhances the performance of federated models by improving the uniformity of representation learning. Also, by providing a better initial state for federated training, pre-training makes the overall training converge faster, thus alleviating the heavy communication burden. We then construct a collaborative graph to learn the client representation through a federated graph neural network. Based on these learned representations, we cluster users into different user groups and learn personalized models for each cluster. Each user learns a personalized model by combining the global federated model, the cluster-level federated model, and its own fine-tuned local model. Experiments on three real-world datasets show that our proposed method achieves superior performance over existing methods

CEPC Conceptual Design Report: Volume 2 - Physics & Detector

The Circular Electron Positron Collider (CEPC) is a large international scientific facility proposed by the Chinese particle physics community to explore the Higgs boson and provide critical tests of the underlying fundamental physics principles of the Standard Model that might reveal new physics. The CEPC, to be hosted in China in a circular underground tunnel of approximately 100 km in circumference, is designed to operate as a Higgs factory producing electron-positron collisions with a center-of-mass energy of 240 GeV. The collider will also operate at around 91.2 GeV, as a Z factory, and at the WW production threshold (around 160 GeV). The CEPC will produce close to one trillion Z bosons, 100 million W bosons and over one million Higgs bosons. The vast amount of bottom quarks, charm quarks and tau-leptons produced in the decays of the Z bosons also makes the CEPC an effective B-factory and tau-charm factory. The CEPC will have two interaction points where two large detectors will be located. This document is the second volume of the CEPC Conceptual Design Report (CDR). It presents the physics case for the CEPC, describes conceptual designs of possible detectors and their technological options, highlights the expected detector and physics performance, and discusses future plans for detector R&D and physics investigations. The final CEPC detectors will be proposed and built by international collaborations but they are likely to be composed of the detector technologies included in the conceptual designs described in this document. A separate volume, Volume I, recently released, describes the design of the CEPC accelerator complex, its associated civil engineering, and strategic alternative scenarios

CEPC Conceptual Design Report: Volume 2 - Physics & Detector

The Circular Electron Positron Collider (CEPC) is a large international scientific facility proposed by the Chinese particle physics community to explore the Higgs boson and provide critical tests of the underlying fundamental physics principles of the Standard Model that might reveal new physics. The CEPC, to be hosted in China in a circular underground tunnel of approximately 100 km in circumference, is designed to operate as a Higgs factory producing electron-positron collisions with a center-of-mass energy of 240 GeV. The collider will also operate at around 91.2 GeV, as a Z factory, and at the WW production threshold (around 160 GeV). The CEPC will produce close to one trillion Z bosons, 100 million W bosons and over one million Higgs bosons. The vast amount of bottom quarks, charm quarks and tau-leptons produced in the decays of the Z bosons also makes the CEPC an effective B-factory and tau-charm factory. The CEPC will have two interaction points where two large detectors will be located. This document is the second volume of the CEPC Conceptual Design Report (CDR). It presents the physics case for the CEPC, describes conceptual designs of possible detectors and their technological options, highlights the expected detector and physics performance, and discusses future plans for detector R&D and physics investigations. The final CEPC detectors will be proposed and built by international collaborations but they are likely to be composed of the detector technologies included in the conceptual designs described in this document. A separate volume, Volume I, recently released, describes the design of the CEPC accelerator complex, its associated civil engineering, and strategic alternative scenarios

CEPC Conceptual Design Report: Volume 2 - Physics & Detector

The Circular Electron Positron Collider (CEPC) is a large international scientific facility proposed by the Chinese particle physics community to explore the Higgs boson and provide critical tests of the underlying fundamental physics principles of the Standard Model that might reveal new physics. The CEPC, to be hosted in China in a circular underground tunnel of approximately 100 km in circumference, is designed to operate as a Higgs factory producing electron-positron collisions with a center-of-mass energy of 240 GeV. The collider will also operate at around 91.2 GeV, as a Z factory, and at the WW production threshold (around 160 GeV). The CEPC will produce close to one trillion Z bosons, 100 million W bosons and over one million Higgs bosons. The vast amount of bottom quarks, charm quarks and tau-leptons produced in the decays of the Z bosons also makes the CEPC an effective B-factory and tau-charm factory. The CEPC will have two interaction points where two large detectors will be located. This document is the second volume of the CEPC Conceptual Design Report (CDR). It presents the physics case for the CEPC, describes conceptual designs of possible detectors and their technological options, highlights the expected detector and physics performance, and discusses future plans for detector R&D and physics investigations. The final CEPC detectors will be proposed and built by international collaborations but they are likely to be composed of the detector technologies included in the conceptual designs described in this document. A separate volume, Volume I, recently released, describes the design of the CEPC accelerator complex, its associated civil engineering, and strategic alternative scenarios

CEPC Technical Design Report -- Accelerator

The Circular Electron Positron Collider (CEPC) is a large scientific project initiated and hosted by China, fostered through extensive collaboration with international partners. The complex comprises four accelerators: a 30 GeV Linac, a 1.1 GeV Damping Ring, a Booster capable of achieving energies up to 180 GeV, and a Collider operating at varying energy modes (Z, W, H, and ttbar). The Linac and Damping Ring are situated on the surface, while the Booster and Collider are housed in a 100 km circumference underground tunnel, strategically accommodating future expansion with provisions for a Super Proton Proton Collider (SPPC). The CEPC primarily serves as a Higgs factory. In its baseline design with synchrotron radiation (SR) power of 30 MW per beam, it can achieve a luminosity of 5e34 /cm^2/s^1, resulting in an integrated luminosity of 13 /ab for two interaction points over a decade, producing 2.6 million Higgs bosons. Increasing the SR power to 50 MW per beam expands the CEPC's capability to generate 4.3 million Higgs bosons, facilitating precise measurements of Higgs coupling at sub-percent levels, exceeding the precision expected from the HL-LHC by an order of magnitude. This Technical Design Report (TDR) follows the Preliminary Conceptual Design Report (Pre-CDR, 2015) and the Conceptual Design Report (CDR, 2018), comprehensively detailing the machine's layout and performance, physical design and analysis, technical systems design, R&D and prototyping efforts, and associated civil engineering aspects. Additionally, it includes a cost estimate and a preliminary construction timeline, establishing a framework for forthcoming engineering design phase and site selection procedures. Construction is anticipated to begin around 2027-2028, pending government approval, with an estimated duration of 8 years. The commencement of experiments could potentially initiate in the mid-2030s