DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models

Mathematical reasoning poses a significant challenge for language models due to its complex and structured nature. In this paper, we introduce DeepSeekMath 7B, which continues pre-training DeepSeek-Coder-Base-v1.5 7B with 120B math-related tokens sourced from Common Crawl, together with natural language and code data. DeepSeekMath 7B has achieved an impressive score of 51.7% on the competition-level MATH benchmark without relying on external toolkits and voting techniques, approaching the performance level of Gemini-Ultra and GPT-4. Self-consistency over 64 samples from DeepSeekMath 7B achieves 60.9% on MATH. The mathematical reasoning capability of DeepSeekMath is attributed to two key factors: First, we harness the significant potential of publicly available web data through a meticulously engineered data selection pipeline. Second, we introduce Group Relative Policy Optimization (GRPO), a variant of Proximal Policy Optimization (PPO), that enhances mathematical reasoning abilities while concurrently optimizing the memory usage of PPO.

DeepSeek LLM: Scaling Open-Source Language Models with Longtermism

The rapid development of open-source large language models (LLMs) has been truly remarkable. However, the scaling law described in previous literature presents varying conclusions, which casts a dark cloud over scaling LLMs. We delve into the study of scaling laws and present our distinctive findings that facilitate scaling of large scale models in two commonly used open-source configurations, 7B and 67B. Guided by the scaling laws, we introduce DeepSeek LLM, a project dedicated to advancing open-source language models with a long-term perspective. To support the pre-training phase, we have developed a dataset that currently consists of 2 trillion tokens and is continuously expanding. We further conduct supervised fine-tuning (SFT) and Direct Preference Optimization (DPO) on DeepSeek LLM Base models, resulting in the creation of DeepSeek Chat models. Our evaluation results demonstrate that DeepSeek LLM 67B surpasses LLaMA-2 70B on various benchmarks, particularly in the domains of code, mathematics, and reasoning. Furthermore, open-ended evaluations reveal that DeepSeek LLM 67B Chat exhibits superior performance compared to GPT-3.5.

Federated Remote Physiological Measurement with Imperfect Data

The growing need for technology that supports remote healthcare is being acutely highlighted by an aging population and the COVID-19 pandemic. In health-related machine learning applications the ability to learn predictive models without data leaving a private device is attractive, especially when these data might contain features (e.g., photographs or videos of the body) that make identifying a subject trivial and/or the training data volume is large (e.g., uncompressed video). Camera-based remote physiological sensing facilitates scalable and low-cost measurement, but is a prime example of a task that involves analysing high bit-rate videos containing identifiable images and sensitive health information. Federated learning enables privacy-preserving decentralized training which has several properties beneficial for camera-based sensing. We develop the first mobile federated learning camera-based sensing system and show that it can perform competitively with traditional state-of-the-art supervised approaches. However, in the presence of corrupted data (e.g., video or label noise) from a few devices the performance of weight averaging quickly degrades. To address this, we leverage knowledge about the expected noise profile within the video to intelligently adjust how the model weights are averaged on the server. Our results show that this significantly improves upon the robustness of models even when the signal-to-noise ratio is low