Reasoning from scratch 第5讲：对数概率打分与自我改进
Raschka 又更新了，这期手把手教你用 PyTorch 算 token 概率给模型答案打分，还搭了一个 self-refinement 循环，最后跑 MATH-500 看效果。
Sebastian Raschka 发布 Reasoning from scratch 系列第 5 期视频，讲解推理时扩展中的两个基础概念。前半部分用 PyTorch 从零计算 token 概率和序列的对数似然，并解释数值稳定性处理，用它构建基于规则和平均对数概率的答案打分器。后半部分演示自我改进（self-refinement）流程：让 LLM 生成批评意见再修改答案，并用 MATH-500 基准评估效果。
Reasoning from scratch, round number 5! This time, talking about log-probability scoring (also a great fundamental concept for loss functions like cross-entropy in pre-training and distillation) and self-refinement.
00:00 Introduction and inference-time scaling recap 05:02 Loading the pretrained LLM 08:00 Comparing and scoring model answers 10:18 Building a rule-based scorer 17:53 Token probabilities and sequence likelihood 26:47 Computing token probabilities in PyTorch 30:12 Token indexing and shifted targets 37:27 Log probabilities and numerical stability 45:57 Scoring answers with average log probabilities 56:24 How self-refinement works 59:07 Generating critiques and revised answers 1:01:00 Implementing the self-refinement loop 1:05:57 MATH-500 evaluation results 1:07:35 Takeaways and next steps
