On many problems, letting a model think longer beats making it fourteen times bigger.
L9 · Models That Think Longer
A model that is right 95 times in 100 on every step still fails a ten-step problem four times in ten. This chapter follows the ways around that: writing the steps down, asking several times and taking the vote, checking each step, and training with rewards a program can verify. You will see how o1 and DeepSeek-R1 came out of those ideas, where thinking longer wastes money or tells a story that is not what happened, and how to read a reasoning score without being fooled.
- One Guess Is Not Enough
- Steps on the Page
- Ask Again, Take the Vote
- Thinking Time or a Bigger Model
- A Checker Picks the Best
- Grade the Answer or the Working
- Rewards You Can Check
- What the Training Grew
- The Reasoning Models
- Searching a Tree of Thoughts
- Tools in the Middle of a Thought
- Teaching Small Models to Think
- When Thinking Goes Wrong
- Measuring Reasoning Honestly