Least-to-Most Prompting Enables Complex Reasoning in Large Language Models

Motivation

• Humans typically learn from few demonstrations, explain their reasoning, and solve harder problems, whereas machine learning commonly requires more labeled data, lacks transparency, and matches training and test difficulty.These differences motivate methods that improve data efficiency, interpretability, and generalization beyond demonstrated problem difficulty.Source: §1 · p. 1

Motivation and contribution

• Least-to-most prompting targets chain-of-thought prompting’s poor performance on problems harder than its demonstrations by enabling easy-to-hard generalization.The method decomposes a complex problem into easier subproblems, then solves them sequentially using answers from earlier subproblems.Source: §1 · pp. 1–2

Method

• The strategy uses two few-shot prompting stages—subproblem decomposition followed by sequential solution—without model training or finetuning.Each subproblem is solved with access to previously solved subproblems; Figure 1 illustrates this process for a math word problem.Source: §1 · p. 2, Figure 1 · p. 2

Empirical scope

• Empirical results on symbolic manipulation, compositional generalization, and math reasoning show that least-to-most prompting generalizes to problems harder than those demonstrated.The approach is presented as applying a progressive sequence of prompts, a technique borrowed from educational psychology.Source: §1 · p. 2

• Least-to-most prompting solves complex problems by decomposing them into a series of simpler subproblems and addressing them sequentially.Source: §2 · pp. 2–3
• The decomposition stage uses constant examples to demonstrate how to break down the specific question.Source: §2 · p. 2
• The subproblem-solving stage combines constant solution examples, previously answered subquestions and generated solutions, and the next question.Source: §2 · p. 2
• In the illustrated procedure, the model identifies an intermediate subproblem, solves it, appends its answer, and then solves the original problem as the final subproblem.The example first asks, “How long does each trip take?”, obtains that each trip takes 5 minutes, and uses this answer in the next prompt.Source: §2 · pp. 2–3
• Least-to-most prompting can be combined with chain-of-thought or self-consistency, and its two stages can merge into a single-pass prompt for some tasks.Source: §2 · p. 3

3.1 SYMBOLIC MANIPULATION; 3.2 COMPOSITIONAL GENERALIZATION; 3.3 MATH REASONING

• Least-to-most prompting decomposes inputs into sequential subproblems and solves each using prior subproblem responses, with SCAN mapping prompts designed to cover command semantics.For GSM8K, decomposition and sequential subproblem solving are combined in one prompt; for SCAN, separate decomposition and mapping prompts are used.Source: §3.1 · pp. 3–4, §3.2 · p. 5, §3.3 · p. 7

3.1 SYMBOLIC MANIPULATION

• 74.0% accuracy: least-to-most prompting outperforms chain-of-thought prompting’s 38.4% with eight independent exemplars on length-12 last-letter lists.Standard prompting achieves 0%, while chain-of-thought performance declines faster as list length increases.Source: §3.1 · pp. 4–5, Table 4 · p. 4

3.1 SYMBOLIC MANIPULATION; 3.2 COMPOSITIONAL GENERALIZATION

• Most remaining errors are composition failures: symbolic outputs drop or duplicate letters, while SCAN errors misinterpret “twice,” “thrice,” or “after.”Least-to-most prompting is therefore substantially stronger than chain-of-thought prompting but does not reach perfect accuracy on difficult cases.Source: §3.1 · p. 5, §3.2 · p. 6

3.2 COMPOSITIONAL GENERALIZATION

• 99.7% accuracy: code-davinci-002 with least-to-most prompting solves SCAN under the length split and maintains the same solving rate across other splits and the full dataset.The comparison evaluates least-to-most against chain-of-thought and standard few-shot prompting across language models.Source: Table 8 · p. 6, §3.2 · p. 6

3.3 MATH REASONING

• 62.39% versus 60.97%: least-to-most prompting only slightly improves overall GSM8K accuracy, but raises performance on problems requiring at least five steps from 39.07% to 45.23%.It also outperforms chain-of-thought prompting by a large margin on numerical DROP problems.Source: Table 11 · p. 7, §3.3 · p. 7, Table 12 · p. 8

Compositional generalization

• Prior SCAN methods use neural-symbolic architectures, grammar induction, data augmentation, or neural architectures to improve compositional generalization.Neural-symbolic and grammar-based approaches can achieve 100% accuracy, whereas augmentation methods and end-to-end neural networks do not generalize to longer test inputs.Source: §4 · p. 8

Easy-to-hard generalization

• Least-to-most prompting achieves easy-to-hard generalization by decomposing complex problems into a series of easier problems solved sequentially.Related approaches generalize through Neural Logic Machines or additional recurrent computation during inference on larger block worlds, mazes, and chess puzzles.Source: §4 · p. 8

Task decomposition

• Unlike trained question-decomposition and iterative-prompting methods, least-to-most prompting generates dependent subquestions, solves them in order, and chains decomposition with subproblem solving.Earlier methods include independent multi-hop subquestions with answer aggregation, continuous virtual tokens, rule-based SQL decomposition, and user-constructed language-model chains.Source: §4 · pp. 8–9

5 LIMITATIONS

• Decomposition prompts typically fail to generalize across domains, so math-based demonstrations do not effectively teach decomposition for common-sense reasoning without a new prompt.For example, a prompt demonstrating math word-problem decomposition is ineffective for questions such as “Did Aristotle use a laptop?”Source: §5 · p. 9
• Even within mathematics, decomposition can be difficult to generalize, although nearly all GSM8K problems are solvable when their correct decompositions are provided.Exceptional results on last-letter concatenation and SCAN arise because decomposition in those tasks is relatively straightforward.Source: §5 · p. 9

• Least-to-most prompting uses top-down decomposition and bottom-up resolution generation to solve harder problems, significantly surpassing standard and chain-of-thought prompting across three reasoning domains.The empirical findings cover symbolic manipulation, compositional generalization, and mathematical reasoning.Source: §6 · p. 9
• Prompting may be suboptimal for teaching reasoning because it instructs models without considering feedback, motivating fully bidirectional conversations with immediate feedback.Least-to-most prompting is presented as a step toward more efficient and effective bidirectional interaction.Source: §6 · p. 9

7.1 PROMPT CONTEXT FOR DECOMPOSING A WORD LIST INTO SUBPROBLEMS

• 100% accuracy is achieved for word-list decomposition with text-davinci-002, including lists up to size 12 from only one exemplar each for sizes 2 and 3.The decomposition prompt constructs sequential sublists, such as prefixes of a word list, as the subproblems.Source: §7.1 · p. 14

7.2 PROMPT CONTEXTS WITH MORE AND DIFFERENT EXAMPLES

• The passages show direct and intermediate-output solutions: “think, machine” yields “ke”, while “think, machine, learning” yields “keg” by appending “g” to “ke”.A direct solution concatenates the last letters of all words, whereas an intermediate solution reuses “think, machine” outputs “ke” before adding “g”.Source: §7.2.1 · p. 14, §7.2.2 · p. 14, §7.2.4 · p. 15

7.3 DATA GENERATION AND ADDITIONAL RESULTS

• The dataset contains 500 random examples for each list size 2, 4, 6, 8, 10, and 12, generated from 9,694 common English words after profanity filtering.Each example maps a random word sequence to the corresponding sequence of final letters.Source: §7.3 · p. 16
• 74.0% for least-to-most versus 38.4% for chain-of-thought at L = 12, even though the former uses a 2-shot 123-token prompt and the latter an 8-shot 573-token prompt.Across prompt sizes, least-to-most consistently outperforms chain-of-thought, while standard prompting remains at 0% accuracy; the comparison is summarized in Table 13.Source: §7.3 · p. 16, Table 13 · p. 17

7.2 PROMPT CONTEXTS WITH MORE AND DIFFERENT EXAMPLES

• Least-to-most retains its accuracy advantage over chain-of-thought when both methods use the same examples, despite chain-of-thought achieving higher accuracy with two independent rather than dependent examples.The appendix compares prompt contexts with 2, 4, and 8 demonstrations to test whether example length or example selection explains the gain.Source: §7.2 · p. 14, §7.3 · p. 16

7.3 DATA GENERATION AND ADDITIONAL RESULTS

• Code-davinci-002 outperforms text-davinci-002 and code-davinci-001 on longer or all list sizes, indicating stronger handling of iteration and recursion.For L = 4, least-to-most reaches 96% with code-davinci-002 versus 19.6% with code-davinci-001; text-davinci-002 declines faster as lists grow.Source: §7.3 · p. 17, Table 13 · p. 17

7.4 ERROR ANALYSIS: LEAST-TO-MOST PROMPTING

• Adding two examples eliminates wrong-template errors in least-to-most prompting, while concatenation errors increase from list length 4 to 12 under the 2-example prompt.The analysis attributes this pattern to more concatenations in longer lists but a constant number of base-template applications.Source: §7.4 · pp. 17–18

7.5 EXAMPLE OUTPUTS FROM CODE-DAVINCI-002

• Standard prompting fails on representative lists, whereas chain-of-thought succeeds by explicitly extracting each word’s last letter and concatenating the results.The appendix provides examples across multiple list lengths using four demonstration examples.Source: §7.5 · p. 18, §7.5.1 · p. 19, §7.5.2 · pp. 19–20

7.5.2 CHAIN-OF-THOUGHT PROMPTING: SUCCESS

• Chain-of-thought prompting correctly extracts each word’s final letter and concatenates them in the listed successful examples.The examples produce “latlrlnedr” and “syedysspnytt”.Source: §7.5.2 · pp. 20–21

7.5.3 CHAIN-OF-THOUGHT PROMPTING: FAILURE

• Chain-of-thought prompting produces concatenation errors in the listed failure examples, including “ness”, “teyssy”, “gsdcsyde”, “eyhtsynslgh”, and “gsgyeyowdst”.These outputs differ from the required final-letter concatenations shown by the intermediate reasoning.Source: §7.5.3 · pp. 21–22

7.5.4 LEAST-TO-MOST PROMPTING: SUCCESS

• Least-to-most prompting solves the listed successful examples by extending the prior partial output one word at a time.For example, “worm, jackson, widow, car” progresses from “mn” to “mnw” to “mnwr”, while another instance ends at “eygnetncoetd”.Source: §7.5.4 · pp. 22, 24, 25

7.5.5 LEAST-TO-MOST PROMPTING: FAILURE

• Least-to-most prompting also fails on listed examples, producing outputs such as “rnnn” and “edederk” for the four- and six-word inputs.The intermediate steps are shown, but the final concatenated outputs do not match the listed words’ final-letter sequences.Source: §7.5.5 · pp. 25–26
• A ten-word example yields “yettarely” by extending the seven-word output “yettarel” with the final letter “y” from “integrity”.This demonstrates the same sequential concatenation behavior on a separate input.Source: §7.5.5 · p. 26
• Least-to-most prompting incrementally appends each word’s final letter, as shown by outputs evolving from “nl” to “nlenroees” and finally “nlenroeast”.The sequence proceeds through “nle”, “nlen”, “nlenr”, “nlenro”, “nlenroe”, and “nlenroee” before adding the final letters of “zeus” and “joint”.Source: §7.5.5 · p. 27
• A twelve-word sequence similarly grows from “da” to “darleyddsty” as each successive word contributes its final letter.Intermediate outputs include “dar”, “darl”, “darln”, “darle”, “darley”, “darleyd”, “darleydd”, “darleydds”, and “darleyddst”.Source: §7.5.5 · pp. 27–28

8.1.1 STANDARD PROMPTING

• Standard prompting presents commands with corresponding action sequences, while chain-of-thought prompting reuses the least-to-most command-mapping context.The standard context includes examples for directional commands, composition, repetition, ordering, and nested transformations.Source: §8.1.1 · p. 29, §8.1.3 · p. 31

8.1.2 LEAST-TO-MOST PROMPTING

• Least-to-most prompting uses separate contexts for decomposing commands into simpler components and mapping commands to action sequences with explanations.The decomposition context provides ordered subcommands, while the mapping context recursively explains how intermediate outputs are combined.Source: §8.1.2 · pp. 29, 31
• Least-to-most command mapping recursively combines outputs for composition, repetition, ordering, and nested expressions such as “walk opposite left” and “walk around left”.For example, “walk opposite left” maps to “TURN LEFT” * 2 + “WALK”, while “walk around left” maps to (“TURN LEFT” + “WALK”) * 4.Source: §8.1.2 · pp. 30–31

8.2 ERROR ANALYSIS: LEAST-TO-MOST PROMPTING

• The error analysis identifies modifier-scope failures, connective-order failures, decomposition omissions, and copying mistakes as distinct least-to-most failure modes.Examples include applying “thrice” incorrectly to “around” expressions, treating “after” as “and”, skipping an intermediate decomposition, and omitting parentheses during copying.Source: §8.2 · pp. 31–33
• Text-davinci-002 made only two mistake types, whereas text-davinci-001 showed errors across all categories, including decomposition and copying errors eliminated by its successor.Text-davinci-002 errors involved applying “twice” or “thrice” after “around” and interpreting “after” as “and”.Source: §8.2 · p. 32, Table 15 · p. 32
• Text-davinci-002 also sometimes mistranslated “left” and “right” by dropping a command or inventing actions such as “LOOK LEFT”.These directional translation errors were not observed with the other analyzed models.Source: §8.2 · p. 32

8.3.1 CHAIN-OF-THOUGHT PROMPTING: SUCCESS

• The appendix includes successful chain-of-thought examples in which the model derives correct SCAN action sequences for nested “after”, conjunction, and repetition commands.The examples explicitly decompose commands and combine intermediate outputs into the final action sequence.Source: §8.3 · p. 33, §8.3.1 · pp. 33–34
• Chain-of-thought prompting produces the displayed golden outputs for compositions involving repeated run/walk commands and nested jump-after-turn commands.The solutions derive each complex command by concatenating constituent outputs and expanding repetition counts.Source: §8.3.1 · pp. 34–35

8.3.2 CHAIN-OF-THOUGHT PROMPTING: FAILURE

• Chain-of-thought prompting fails on compositions involving repeated look, run, walk, opposite, or after constructions, producing outputs that differ from the displayed golden sequences.The accompanying solutions nonetheless apply direct concatenation and repetition formulas to these commands.Source: §8.3.2 · pp. 35–36

8.3.3 LEAST-TO-MOST PROMPTING: SUCCESS

• Least-to-most prompting succeeds by decomposing complex commands into progressively simpler primitives and using their solved outputs to construct the displayed golden sequences.Examples include jump, turn, look, run, and walk compositions with around, thrice, twice, after, and opposite operators.Source: §8.3.3 · pp. 37–38

8.3.4 LEAST-TO-MOST PROMPTING: FAILURE

• Least-to-most prompting fails on “jump opposite right twice and jump around right thrice,” whose displayed output does not match the two-line golden sequence.Its decomposition separates the opposite-twice and around-thrice components before combining them.Source: §8.3.4 · pp. 40–41
• For “walk around left thrice after walk around right twice,” the generated solution places the left-around segment before the right-around segment, whereas the golden output places the right segment first.The decomposition and solution explicitly concatenate left then right, but the golden sequence begins with repeated “TURN RIGHT WALK” actions before the left actions.Source: §8.3.4 · pp. 41–42

8.4 EXPANDING PYTHON EXPRESSIONS USING PROMPTING

• 99.7% accuracy for both generating intermediate Python expressions and expanding them gives L2M more than 99% combined SCAN accuracy without a Python executor.The expansion accuracy was measured on a random sample of 1,000 Python expressions produced by the code-davinci-002 solution.Source: §8.4 · p. 45
• The prompt contains six examples illustrating the knowledge needed to expand additions, multiplications, nested expressions, and rewritten repetition counts.Examples include repeated JUMP, concatenated TURN RIGHT and WALK, nested grouped expressions, and multiplication of a multiplier by 4 and 2.Source: §8.4 · pp. 45–46
• Numbers and parentheses are added when unfolding multiplication so the model can track repetitions more easily.The demonstrations show this formatting for both simple and nested repeated expressions.Source: §8.4 · p. 46

9.1 RESULTS WITH TEXT-DAVIN C I-002 AND LM-540B

• The reported text-davinci-002 results use the numerical reasoning subset of DROP, while the accompanying table states that text-davinci-002 is consistently worse than code-davinci-002.The evaluation samples 500 randomly selected non-football and football examples; a separate result is reported for an LM with 540 billion parameters.Source: Table 16 · p. 46, §9.1 · p. 46

9.2.1 ZERO-SHOT PROMPTING

• Zero-shot prompting uses the format “Q: {question} A: The answer is,” adding “The answer is” at the beginning of the answer section.This format is specified for both reported prompting setups.Source: §9.2.1 · p. 46, §9.3.1 · p. 49

9.2.2 STANDARD PROMPTING WITH 3 EXAMPLES

• Standard prompting supplies three worked examples with direct answers, whereas chain-of-thought prompting supplies three examples with explanatory calculations.The examples cover time differences, percentage differences, sports statistics, touchdown combinations, halftime points, and scoreless quarters.Source: §9.2.2 · p. 47, §9.2.3 · pp. 47–48

9.2.4 LEAST-TO-MOST PROMPTING I: PROBLEM DECOMPOSITION (5 EXAMPLES)

• Least-to-most prompting first decomposes a complex question into simpler subquestions, then solves those subquestions and combines their answers.Examples include identifying component values before computing differences, sums, or totals.Source: §9.2.4 · p. 48, §9.2.5 · p. 48, §9.3.5 · p. 51

9.3.4 LEAST-TO-MOST PROMPTING I: PROBLEM DECOMPOSITION (6 EXAMPLES)

• The second DROP setup similarly demonstrates decomposition before solving, with six examples that ask for component scores, game records, field goals, pass totals, or scoreless quarters.Its follow-up problem-solving examples answer these intermediate questions and then compute the requested result.Source: §9.3.4 · pp. 50–51

9.3.5 LEAST-TO-MOST PROMPTING II: PROBLEM SOLVING (3 EXAMPLES)

• In the DROP examples, least-to-most solves intermediate factual questions before answering the combined question, such as deriving 21 yards from a 9-yard run and a 12-yard pass.The same sequential process derives 10 halftime points from a touchdown and a field goal and counts two scoreless quarters.Source: §9.3.5 · p. 51

9.4.1 CASE 1

• 787 Buick automobiles were built between 1904 and 1905 with least-to-most prompting, whereas chain-of-thought incorrectly computed 713.The correct calculation is 37 + 750 = 787; chain-of-thought instead used 750 - 37 = 713.Source: §9.4.1 · p. 52

9.4.2 CASE 2

• For the second case, chain-of-thought answered 3 months by comparing President Barrios’s death in November with the February expedition, while least-to-most first extracted the retreat month as April.The supplied least-to-most passage shows the decomposition step but not the final computed answer.Source: §9.4.2 · p. 53
• Least-to-most computes 7 months from April to November, while chain-of-thought uses an unrelated expedition fact and reaches the wrong final answer.The least-to-most chain first identifies Juan Díaz de Velasco’s retreat in April and President Barrios’s death in November.Source: §9.4.2 · p. 53

9.4.3 CASE 3

• Least-to-most correctly computes 17 years from Christian Widers’s 1580 marriage to her 1597 death, whereas chain-of-thought incorrectly uses James Peele’s 1585 death.The chain-of-thought answer is 12 because it subtracts 1585 from 1597, an unrelated date.Source: §9.4.3 · p. 53

9.4.4 CASE 4

• Least-to-most correctly identifies 93,000 Mormons and 12,000 Muslims, yielding 81,000 more Mormons; chain-of-thought reports 68,000 after misidentifying Muslims as 25,000.The failure analysis states that chain-of-thought got one intermediate fact wrong.Source: §9.4.4 · p. 54

9.4.5 CASE 5

• Least-to-most correctly computes 17 years from Catherine’s 1566 marriage to Killigrew to her 1583 death, while chain-of-thought incorrectly uses Jaél de Peigne’s 1590 marriage.Chain-of-thought therefore reports 7 instead of using Catherine’s marriage date.Source: §9.4.5 · p. 54

9.5 ERROR ANALYSIS: LEAST-TO-MOST PROMPTING

• Among 20 sampled least-to-most failures, 13 result from wrong problem solving, 4 from wrong problem decomposition, and 3 from incorrect ground truth.The three categories cover solving decomposed questions incorrectly, producing nonsensical or absent decompositions, and erroneous labels.Source: §9.5 · pp. 54–55

9.5.1 EXAMPLE OF WRONG PROBLEM DECOMPOSITION

• One decomposition failure simply rephrases the original question instead of producing a useful subproblem about the cities Polin laid waste to.The decomposed question repeats “How many cities did Polin laid waste to on his way to Constantinople?”Source: §9.5.1 · p. 55

9.5.2 EXAMPLE OF WRONG PROBLEM SOLVING

• One problem-solving failure incorrectly adds 3.64% and 2.18%, concluding that 5.82% of people were from two or more races in 2000.It then derives 94.18% for people not from two or more races.Source: §9.5.2 · p. 55

9.5.3 EXAMPLE OF WRONG GIVEN LABEL

• In one mislabeled example, the given label is 417 but the correct ground truth is 418, which least-to-most prompting obtains by summing 177, 22, and 219 births.The summed categories are Asians, Native Americans, and Hispanics.Source: §9.5.3 · pp. 55–56

10.1 EXPERIMENT RESULTS: ONE-SHOT PROMPTS

• Least-to-most prompting significantly outperforms chain-of-thought as the required reasoning steps exceed the two-step demonstration, despite only moderately higher overall accuracy.The one-shot comparison uses the same single two-step example for both methods and evaluates accuracy by expected solution length.Source: §10.1 · p. 56, Table 18 · p. 56

10.4.4 LEAST-TO-MOST (BEST) I - PROBLEM DECOMPOSITION: 7 EXAMPLES

• The best least-to-most method separates problem decomposition from problem solving, using 7 hand-crafted decomposition examples and 4 hand-crafted step-solution examples.The one-shot version instead merges decomposition and solution into one pass followed by a single request for the final answer.Source: §10.1 · p. 56, §10.2 · p. 57, §10.4.4 · p. 59

10.2 EXPERIMENT RESULTS: ENGINEERED PROMPTS

• 60.87% accuracy for Chain-of-Thought (1-shot) was close to 61.18% for the original 8-shot chain-of-thought prompt, supporting the 1-shot method as a reasonable baseline.The 1-shot chain-of-thought prompt is considerably simpler than the original 8-shot context.Source: §10.2 · p. 57
• Additional in-domain prompt engineering improves both chain-of-thought and least-to-most prompting, but least-to-most shows no overall accuracy improvement over chain-of-thought when most test questions fit the demonstrations.The engineered variants use multiple GSM8K training examples of arbitrary complexity; the reported accuracies are listed in Table 19.Source: §10.2 · pp. 56–57, Table 19 · p. 57