Optimize Prompts with pullback Feedback

Use pullback when feedback on an output should become feedback for the inputs that produced it. For prompt work, the input is often an instruction string.

Concept

Trace, IR, Execute · Transforms

import autoform as af


def answer_with_instruction(instruction: str, topic: str) -> str:
    prompt = af.format("{}\n\nTopic: {}", instruction, topic)
    msg = dict(role="user", content=prompt)
    # use any model configured for the active lm client
    return af.lm_call([msg], model="gpt-5.5")


# trace with placeholder values
ir = af.trace(answer_with_instruction)("Explain clearly.", "recursion")
pb_ir = af.pullback(ir)

instruction = "Explain the topic in one short paragraph."
topic = "recursion"
critique = "too abstract; include one concrete example"

for step in range(3):
    # pullback returns the output and feedback for each original input
    output, (instruction_hint, topic_hint) = pb_ir.call((instruction, topic), critique)
    print("step", step)
    print(output)
    print("instruction hint:", instruction_hint)
    print("topic hint:", topic_hint)
    instruction = instruction + "\nrevision guidance: " + instruction_hint

The original function still has one job: make an LM call from an instruction and a topic. pullback makes a second IR whose input is the original inputs plus feedback on the output.

This is not a special optimizer. It is a feedback channel. The update policy above is deliberately small: append the returned instruction hint to the next instruction. A production loop can score examples, keep the best instruction, or batch many (topic, critique) pairs with batch and pullback.

See Transforms for the call shapes and Primitives for how feedback moves through each recorded operation.