Neighborhoods Banding Together Reasoning Globally about Programs Lisa LippincottThe code here is written in a fantasy C++, with extensions supporting local reasoning.void foo() implementation { … …

text classification, language or code translation, code generation, and code documentation or reasoning. Please feel free to refer to Google’s prompting guides2,3 with simple and effective prompting the specific task. This ‘step back’ allows the LLM to activate relevant background knowledge and reasoning processes before attempting to solve the specific problem. By considering the broader and underlying Chain of Thought (CoT) 9 prompting is a technique for improving the reasoning capabilities of LLMs by generating intermediate reasoning steps. This helps the LLM generate more accurate answers. You can

. . . . . . . . . . . . . . . . . . . . . . . . 23 2.3 Reasoning about Connectives and Quantifiers . . . . . . . . . . . . . . 26 2.4 Reasoning about Equality . . . . . . . . . . . . . . . . . . . . 37 3.3 Forward Reasoning about Connectives and Quantifiers . . . . . . . . 39 3.4 Calculational Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.5 Forward Reasoning with Tactics . Proofs (CPP) and Interactive Theorem Proving (ITP) or in journals such as the Journal of Automated Reasoning (JAR). Equipped with a good knowledge of Lean, you will find it easy to move to an- other proof

collect 1.5M conversational sessions, which encompass various domains such as math, code, writing, reasoning, safety, and more, to perform Supervised Fine-Tuning (SFT) for DeepSeek-V2 Chat (SFT). Finally, 2020), C-Eval (Huang et al., 2023), and CMMLU (Li et al., 2023). Language understanding and reasoning datasets include HellaSwag (Zellers et al., 2019), PIQA (Bisk et al., 2020), ARC (Clark et al., ?}) . (34) Training Strategy. In our preliminary experiments, we find that the RL training on reasoning data, such as code and math prompts, exhibits unique characteristics that are distinct from the

which surpasses the performance of other leading models (GPT- 4o, Claude 3.5) on some reasoning tests 3/23: OpenAI releases GPT-4, a multimodal* model capable of processing both text line with Western competitors 1/25: DeepSeek releases its R1 & R1- Zero open- source reasoning models 2/25: OpenAI releases GPT-4.5, Anthropic releases Claude 3.7 Sonnet, & xAI releases professional subjects, such as math, law, medicine, and history. It measures both factual recall and reasoning ability, making it a standard for assessing general knowledge and problem-solving in large language

viewed as a proof as well, and these systems, too, help establish mathematical claims. Automated reasoning systems strive for power and efficiency, often at the expense of guaranteed soundness. Such systems construction of fully specified axiomatic proofs. The goal is to support both mathematical reasoning and reasoning about complex systems, and to verify claims in both domains. Lean’s underlying logic has the point, it can be viewed as a system for writing programs with a precise semantics, as well as reasoning about the functions that the programs compute. Lean also has mechanisms to serve as its own metaprogramming

makes it look somewhat like any informal mathematical proof. There is also a tiny bit of automated reasoning thrown in: the command by simp calls on Lean’s built-in simplifier to prove the assertion after points to another aspect of Lean, namely, that it can serve as a gateway to the use of automated reasoning. Terms in dependent type theory can be very verbose, and formal proofs can be especially long. One that serves as a gateway to the use of automation. Lean provides means of implementing automated reasoning procedures in such a way that they produce formal proofs that their results are correct. This imposes

进行训练，为后续的推理优化奠定基础。 3.1.1 核心创新 1：含 R1-Zero 的中间推理模型 如图7所示，推理导向的强化学习（Reasoning-Oriented Reinforcement Learn- ing）得到中间推理模型（Iterim reasoning model）, 图8会详细解释中间模 型的训练过程。 DeepSeek-R1 核心贡献：首次验证了通过纯强化学习也能大幅提升大模 中间模型占据主要训练精力的阶段，实际上完全通过推理导向的强化学习 直接训练而成，完全跳过了监督微调（SFT），如下图8所示，只在强化学习 的冷启动阶段使用了 SFT。 图 8: Interim reasoning model 训练方法 大规模推理导向的强化学习训练，必不可少的就是推理数据，手动标注就 太繁琐了，成本昂贵，所以 DeepSeek 团队为了解决这个问题，训了一个 R1-Zero 模型，这是核心创新。 AI，欢迎关注获取更多原创教程。资 料用心打磨且开源，是为了帮助更多人了解获取 AI 知识，严禁拿此资料引流、出书、等形式的商业活动 3.4 总结 DeepSeek-R1 中间推理模型生成：通过推理导向的强化学习（Reasoning-Oriented RL）， 直接生成高质量的推理数据（CoT 示例），减少人工标注依赖。通用强化学 习优化：基于帮助性和安全性奖励模型，优化推理与非推理任务表现，构建 通用性强的模型。最终，DeepSeek-R1

Types in Agda [http://oxij.org/note/BrutalDepTypes/] Thorsten Altenkirch. Computer Aided Formal Reasoning [http://www.cs.nott.ac.uk/~txa/g53cfr/] - online lecture notes Daniel Licata. Dependently Typed [https://people.inf.elte.hu/divip/AgdaTutorial/Index.html] Courses using Agda Computer Aided Reasoning [http://www.cs.nott.ac.uk/~txa/g53cfr/] Material for a 3rd / 4th year course (g53cfr, g54 cfr) at Viewing equalities as functions out of the interval makes it possible to do a lot of equality reasoning in a very direct way: sym : ∀ {ℓ} {A : Set ℓ} {x y : A} → x ≡ y → y ≡ x sym p = λ i → p (~ i)

Types in Agda [http://oxij.org/note/BrutalDepTypes/] Thorsten Altenkirch. Computer Aided Formal Reasoning [http://www.cs.nott.ac.uk/~txa/g53cfr/] - online lecture notes Daniel Licata. Dependently Typed [https://people.inf.elte.hu/divip/AgdaTutorial/Index.html] Courses using Agda Computer Aided Reasoning [http://www.cs.nott.ac.uk/~txa/g53cfr/] Material for a 3rd / 4th year course (g53cfr, g54 cfr) at Viewing equalities as functions out of the interval makes it possible to do a lot of equality reasoning in a very direct way: sym : ∀ {ℓ} {A : Set ℓ} {x y : A} → x ≡ y → y ≡ x sym p = λ i → p (~ i)