Recursive amplification

Subquestions can have subquestions
Now we’d like to generalize the recipe above so that we can run it at different depths:
  • Depth 0: Just answer the question, no subquestions.
  • Depth 1: One layer of subquestions.
  • Depth 2: Use subquestions when answering subquestions.
  • Etc.
To do this, we add a depth parameter to answer_by_amplification and get_subs and only get subquestions if we’re at depth > 0. This simplifies the amplification recipe to:
from fvalues import F
from ice.recipe import recipe
from import ask_subquestions
from ice.utils import map_async
Question = str
Answer = str
Subs = list[tuple[Question, Answer]]
def render_background(subs: Subs) -> str:
if not subs:
return ""
subs_text = F("\n\n").join(F(f"Q: {q}\nA: {a}") for (q, a) in subs)
return F(f"Here is relevant background information:\n\n{subs_text}\n\n")
def make_qa_prompt(question: str, subs: Subs) -> str:
background_text = render_background(subs)
return F(
f"""{background_text}Answer the following question, using the background information above where helpful:
Question: "{question}"
Answer: "
async def get_subs(question: str, depth: int) -> Subs:
subquestions = await ask_subquestions(question=question)
subanswers = await map_async(
subquestions, lambda q: answer_by_amplification(question=q, depth=depth)
return list(zip(subquestions, subanswers))
async def answer_by_amplification(
question: str = "What is the effect of creatine on cognition?", depth: int = 1
subs = await get_subs(question, depth - 1) if depth > 0 else []
prompt = make_qa_prompt(question, subs=subs)
answer = await recipe.agent().complete(prompt=prompt, stop='"')
return answer
Now we have a parameterized recipe that we can run at different depths:

Depth 0

python --depth 0
Creatine has been shown to improve cognition in people with Alzheimer's disease and other forms of dementia.

Depth 1

python --depth 1
The effect of creatine on cognition is mixed. Some studies have found that creatine can help improve memory and reaction time, while other studies have found no significant effects. It is possible that the effects of creatine on cognition may vary depending on the individual.

Depth 2

python --depth 2
The effect of creatine on cognition is inconclusive. Some studies have found that creatine can improve cognitive function in healthy adults, while other studies have found no significant effects. More research is needed to determine the potential cognitive benefits of creatine.
The trace for depth 2, partially expanded:
Execution trace (view online)


  1. 1.
    Right now we’re answering subquestions without the context of the question they’re intended to help with. Provide the question (or questions) that are further up in the hierarchy as additional context to the model.
  2. 2.
    Running subquestions in parallel is nice because it’s fast, but has the disadvantage that the answers to later subquestions can’t inform what question to ask next. Modify the recipe to support sequential choice of questions based on earlier responses.
  3. 3.
    Now make the recipe from step 1 adaptive: Let the model decide whether to answer or whether to ask another subquestion. If you don’t limit the depth, what is the effective depth that the model ends up with for different questions?
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  1. 1.
    Christiano, Paul, Buck Shlegeris, and Dario Amodei. Supervising Strong Learners by Amplifying Weak Experts. October 19, 2018.
  2. 2.
    Leike, Jan, David Krueger, Tom Everitt, Miljan Martic, Vishal Maini, and Shane Legg. Scalable Agent Alignment via Reward Modeling: A Research Direction. arXiv cs.LG, November 19, 2018.
  3. 3.
    Wu, Jeff, Long Ouyang, Daniel M. Ziegler, Nisan Stiennon, Ryan Lowe, Jan Leike, and Paul Christiano. Recursively Summarizing Books with Human Feedback. arXiv, September 27, 2021.
  4. 4.
    Perez, Ethan, Patrick Lewis, Wen-tau Yih, Kyunghyun Cho, and Douwe Kiela. Unsupervised Question Decomposition for Question Answering. In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP), 8864–80. Online: Association for Computational Linguistics, 2020.