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Stanford CME295 Transformers & LLMs | Autumn 2025 | Lecture 6 - LLM Reasoning
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Stanford CME295 Transformers & LLMs | Autumn 2025 | Lecture 6 - LLM Reasoning

November 7, 2025

Nov 14, 20251h 47mWatch on YouTube

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At a glance

WHAT IT’S REALLY ABOUT

How LLMs learn reasoning via verifiable RL and GRPO training

  1. The lecture defines LLM reasoning as multi-step problem solving and frames “reasoning models” as models that output a reasoning chain before giving a final answer.
  2. It reviews how reasoning is benchmarked in coding and math, emphasizing verifiable correctness checks and sampling-based metrics such as Pass@k, along with the role of temperature in diversity vs. quality.
  3. It argues that RL is a natural fit for reasoning training because writing high-quality reasoning chains for SFT is difficult and because many reasoning tasks provide direct, verifiable reward signals.
  4. It introduces GRPO as a reasoning-focused alternative to PPO that computes advantages from groups of sampled completions rather than training a value function, and discusses recent modifications aimed at mitigating output length growth.
  5. It uses DeepSeek’s R1-Zero and R1 pipelines to show how verifiable-reward RL, small cold-start SFT, rejection-sampled SFT data, and mixed RL objectives can be combined, and it closes with distillation via teacher-generated reasoning traces to train smaller student models.

IDEAS WORTH REMEMBERING

5 ideas

Reasoning training is positioned as an extension of the same RL machinery used for preference alignment.

The lecture frames pre-training as producing an autocomplete model, fine-tuning as making it useful for tasks like answering questions, and preference tuning (e.g., RLHF) as aligning to human preferences; the RL stage mechanics (advantages plus constraints against drifting too far) become the foundation for reasoning training.

In this lecture, a “reasoning model” is a model that generates intermediate reasoning text plus an answer.

Reasoning is defined (with a caveat that there’s no agreed definition) as the ability to solve problems—especially math and coding—via multi-step decomposition, operationalized by having the model output a reasoning chain before the final answer.

Verifiable rewards make RL an attractive way to train reasoning without large human-written chain-of-thought datasets.

The speaker argues that supervised fine-tuning is a poor starting point if you don’t already have high-quality reasoning chains, and also notes that human-written reasoning may not match the model’s most effective internal reasoning style; meanwhile many reasoning tasks have verifiable correctness signals.

Reasoning evaluation often relies on sampling multiple solutions and measuring success-at-k rather than single-shot accuracy.

For coding, correctness can be checked via test cases; for math, answers can be parsed and matched to ground truth; metrics include Pass@k (probability at least one of k sampled attempts succeeds), with temperature affecting the tradeoff between diversity and per-sample quality.

GRPO’s key practical appeal is dropping the value function by using group-relative advantages.

GRPO is introduced as a go-to RL algorithm for reasoning because it avoids training a separate value function: it estimates advantage by comparing each completion’s reward to the group’s reward statistics for the same prompt, rather than using a learned value model as in PPO.

WORDS WORTH SAVING

5 quotes

So the output of reasoning models are not only the answer, but also the reasoning itself.

— Afshin

we want to use RL to incentivize our model to think more if we start from scratch, meaning we don't have reasoning chains.

— Afshin

This is a bad incentive because what you're telling your model is, if you have a short bad sentence, it is worse than w- if you have a long bad sentence.

— Afshin

First, into showing how powerful can the RL stage be if you apply the verifiable rewards that Afshin, uh, mentioned.

— Shervin

So instead of fitting a probability distribution over the next token, you just fit the entire sequence.

— Shervin

Read the available transcript
Reasoning definition and chain-of-thought framingLimits of vanilla LLMs for reasoningCoding and math reasoning benchmarksPass@k and temperature effectsRL with verifiable rewards for reasoningGRPO vs PPO and advantage estimationLength growth and GRPO objective tweaks (DAPO, Dr. GRPO)

High quality AI-generated summary created from speaker-labeled transcript.

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