The Prompt Report Part 2: Plan and Solve, Tree of Thought, and Decomposition Prompting

Greg Schoeninger

Oct 31, 2024

In the last blog, we went over prompting techniques 1-3 of The Prompt Report. This arXiv Dive, we were lucky to have the authors of the paper join us to go through some of the more advanced techniques. To watch the whole conversation and see the authors answers to our questions, dive into the video below.

First off, The Prompt Report is an excellent survey of the prompting landscape and I have been going down rabbit hole after rabbit hole. To be honest, I come from a traditional machine-learning background, so had been dismissing prompting a bit. This paper changed my mind. It is fascinating and definitely deserves to be a field of study on its own.

Second off, I just want to shout out to the Oxen.ai team. All the work I am about to show today couldn’t have been done without them. We are rolling out the ability to run arbitrary models on datasets for evaluation, synthetic data and labeling use cases.

The tool that you’ll see today really helps with this part of the paper. You’ll see how easy it is to use as we go through some examples and it’s free to try, we give $10 of free compute credits, so hammer it, let us know what you think, and let us know what creative prompt and problems you solve with it in our discord.

Last week we covered the first half of the taxonomy that is laid out in the paper.

Each one of these nodes is a paper in itself, so they will be like mini arXiv Dive snacks that we can work through. This paper is great in the way it builds up from simple prompting techniques to more complex ones. The ones we are going to go over today are a gold mine for synthetic data and testing the ability of LLMs to reason.

Within the 58 categories, there are 6 top-level categories.

✅ Zero-Shot
✅ Few-Shot
✅ Thought Generation
Decomposition
Ensembling
Self-Criticism

As I said, the methods today will be a synthetic data generation gold mine ⚱️👑. If we can prompt these models to reason, judge their own reasoning, and then filter down the responses to correct answers, then we can use this data for training the next iteration of models.

This is most likely what OpenAI is doing with O1, and they are “hiding” the reasoning tokens from us so that we cannot just use it as training data for our own models. One of the core tenets of arXiv Dives is “Anyone can build it”. Especially with open-source models like Llama coming out, you can use some of the larger models + these prompting techniques to get high quality synthetic data and train your own variants.

I went through and tried to find some concrete examples from each sub paper so that we can try and discuss.

Thought Generation

Last week we left off with some “Thought Generation” examples such as “Chain of Thought” reasoning. You’ll see this abbreviated as CoT in a lot of the following papers because they often reference this technique as a baseline to compare against.

Even if you look at the outputs for gpt-4o it is clear that the model has been trained to “think step by step.” One of the sub papers mentioned a dataset called “SCAN” that has a bunch of directional reasoning problems.

Given a set of instructions as follows:

walk opposite right thrice after run opposite right

So I prompted the LLM to take the instructions and predict which direction the person is facing.

The tokens it generated included “Chain of Thought” reasoning that the model was clearly trained to output.

Today, you’ll see how we can use models to generate data like this, and then let your imagination run wild for how you could use these types of prompts in real world applications or for synthetic data to train reasoning capabilities into smaller models.

Decomposition

A common way that humans solve complex problems is by decomposing them into simpler sub-problems.

Least-to-Most Prompting

This technique first has the model generate sub questions, based on the user input. Then answers the sub question one by one.

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

Chain-of-thought prompting has demonstrated remarkable performance on various natural language reasoning tasks. However, it tends to perform poorly on tasks which requires solving problems harder than the exemplars shown in the prompts. To overcome this challenge of easy-to-hard generalization, we propose a novel prompting strategy, least-to-most prompting. The key idea in this strategy is to break down a complex problem into a series of simpler subproblems and then solve them in sequence. Solving each subproblem is facilitated by the answers to previously solved subproblems. Our experimental results on tasks related to symbolic manipulation, compositional generalization, and math reasoning reveal that least-to-most prompting is capable of generalizing to more difficult problems than those seen in the prompts. A notable finding is that when the GPT-3 code-davinci-002 model is used with least-to-most prompting, it can solve the compositional generalization benchmark SCAN in any split (including length split) with an accuracy of at least 99% using just 14 exemplars, compared to only 16% accuracy with chain-of-thought prompting. This is particularly noteworthy because neural-symbolic models in the literature that specialize in solving SCAN are trained on the entire training set containing over 15,000 examples. We have included prompts for all the tasks in the Appendix.

arXiv.orgDenny Zhou

SCAN Dataset:
https://github.com/brendenlake/SCAN

There are some example prompts at the end of the paper.

Here is the full one I grabbed from the paper:

Here are some results we can look at:

Decomposed Prompting w/Tools

You may need external tools to solve certain problems. In order to get the LLM to use the tools you may want to give few-shot examples of when do use certain tools. Then use multiple LLM calls to call different functions and combine the responses.

The decomposition steps can even be tools that you want to call

Example Prompt:

Example Results:

Plan-and-Solve Prompting

This technique asks the LLM to “create a plan” before solving. This is a little more descriptive than your generic chain of thought prompting.

“Let’s first understand the problem and devise a plan to solve it. Then carry out the plan and solve the problem step by step.”

You can give the model additional instructions like “extract the relevant variables”

Last week we looked at GSM8k and realized that these models are pretty overfit to this dataset. Almost every prompt we tried we were getting 95+% accuracy. Right after we looked at some of the examples Apple came out with a spicy paper, that seemed to agree.

I saw that gretle.ai generated a dataset with some similar techniques, so I grabbed 100 rows to do some vibe checks.

Let’s try out the prompt above on some data:

The first prompt we tried got 75% accuracy on the 100 examples

The second was 76% accuracy on the same 100 examples 🤷‍♂️

It is starting to become pretty fun to run these experiments in Oxen.ai, I would highly recommend you test it out.

Tree-of-Thought

This was probably one of the more impactful prompting techniques of 2023. This paper argues that you can use LLMs to think more like System Two thinking in the Daniel Kahneman sense of system 1 vs system 2 thinking.

Tree-of-thought creates multiple possible steps then uses a tree-like search to evaluate progress at each step. It then decides which steps to continue with, and keeps creating more thoughts with the happy paths.

Tree of Thoughts: Deliberate Problem Solving with Large Language Models

Language models are increasingly being deployed for general problem solving across a wide range of tasks, but are still confined to token-level, left-to-right decision-making processes during inference. This means they can fall short in tasks that require exploration, strategic lookahead, or where initial decisions play a pivotal role. To surmount these challenges, we introduce a new framework for language model inference, Tree of Thoughts (ToT), which generalizes over the popular Chain of Thought approach to prompting language models, and enables exploration over coherent units of text (thoughts) that serve as intermediate steps toward problem solving. ToT allows LMs to perform deliberate decision making by considering multiple different reasoning paths and self-evaluating choices to decide the next course of action, as well as looking ahead or backtracking when necessary to make global choices. Our experiments show that ToT significantly enhances language models’ problem-solving abilities on three novel tasks requiring non-trivial planning or search: Game of 24, Creative Writing, and Mini Crosswords. For instance, in Game of 24, while GPT-4 with chain-of-thought prompting only solved 4% of tasks, our method achieved a success rate of 74%. Code repo with all prompts: https://github.com/princeton-nlp/tree-of-thought-llm.

arXiv.orgShunyu Yao

Still use ⛓️Chain-of-Thought (CoT) for all your prompting? May be underutilizing LLM capabilities🤠

Introducing 🌲Tree-of-Thought (ToT), a framework to unleash complex & general problem solving with LLMs, through a deliberate ‘System 2’ tree search.https://t.co/V6hjbUNjbt pic.twitter.com/IaZZdVeaTW
— Shunyu Yao (@ShunyuYao12) May 19, 2023

There are tasks that are hard to solve with straight chain of thought prompting.

Why? LLMs predict the next token one at a time, if you make a mistake, you can’t backtrack or fix it.

Tree of Thought can solve these problems 10x better than just a simple I/O prompt.

This one is going to be a little mind bending so stick with us.

Generate diverse “thoughts” of different ways to tackle the problem
For each thought, evaluate if you are on the right track
Use standard tree search like breadth first or depth first search to get to an output.

Thought Generation Prompt

Use numbers and basic arithmetic operations (+ - * /) to obtain 24.
Each step, you are only allowed to choose two of the remaining numbers
to obtain a new number.

Input: 4 4 6 8
Steps:
4 + 8 = 12 (left: 4 6 12)
6 - 4 = 2 (left: 2 12)
2 * 12 = 24 (left: 24)
Answer: (6 - 4) * (4 + 8) = 24

Input: 2 9 10 12
Steps:
12 * 2 = 24 (left: 9 10 24)
10 - 9 = 1 (left: 1 24)
24 * 1 = 24 (left: 24)
Answer: (12 * 2) * (10 - 9) = 24

Input: 4 9 10 13
Steps:
13 - 10 = 3 (left: 3 4 9)
9 - 3 = 6 (left: 4 6)
4 * 6 = 24 (left: 24)
Answer: 4 * (9 - (13 - 10)) = 24

Input: 1 4 8 8
Steps:
8 / 4 = 2 (left: 1 2 8)
1 + 2 = 3 (left: 3 8)
3 * 8 = 24 (left: 24)
Answer: (1 + 8 / 4) * 8 = 24

Input: 5 5 5 9
Steps:
5 + 5 = 10 (left: 5 9 10)
10 + 5 = 15 (left: 9 15)
15 + 9 = 24 (left: 24)
Answer: ((5 + 5) + 5) + 9 = 24

Input: {input}
Steps:

Evaluator Prompt:

Evaluate if given numbers can reach 24 (sure/likely/impossible)
10 14
10 + 14 = 24
sure
11 12
11 + 12 = 23
12 - 11 = 1
11 * 12 = 132
11 / 12 = 0.91
impossible
4 4 10
4 + 4 + 10 = 8 + 10 = 18
4 * 10 - 4 = 40 - 4 = 36
(10 - 4) * 4 = 6 * 4 = 24
sure
4 9 11
9 + 11 + 4 = 20 + 4 = 24
sure
5 7 8
5 + 7 + 8 = 12 + 8 = 20
(8 - 5) * 7 = 3 * 7 = 21
I cannot obtain 24 now, but numbers are within a reasonable range
likely
5 6 6
5 + 6 + 6 = 17
(6 - 5) * 6 = 1 * 6 = 6
I cannot obtain 24 now, but numbers are within a reasonable range
likely
10 10 11
10 + 10 + 11 = 31
(11 - 10) * 10 = 10
10 10 10 are all too big
impossible
1 3 3
1 * 3 * 3 = 9
(1 + 3) * 3 = 12
1 3 3 are all too small
impossible
{input}

I tried this 5-Shot prompt last night, and that’s when I about decided it was time to go to bed…

Would I say this was the most effective use of ~$5?

Yes...I had fun 😅

Recursion of Thought

Recursion of Thought: A Divide-and-Conquer Approach to Multi-Context Reasoning with Language Models

Generating intermediate steps, or Chain of Thought (CoT), is an effective way to significantly improve language models’ (LM) multi-step reasoning capability. However, the CoT lengths can grow rapidly with the problem complexity, easily exceeding the maximum context size. Instead of increasing the context limit, which has already been heavily investigated, we explore an orthogonal direction: making LMs divide a problem into multiple contexts. We propose a new inference framework, called Recursion of Thought (RoT), which introduces several special tokens that the models can output to trigger context-related operations. Extensive experiments with multiple architectures including GPT-3 show that RoT dramatically improves LMs’ inference capability to solve problems, whose solution consists of hundreds of thousands of tokens.

arXiv.orgSoochan Lee

The idea here is similar to Chain of Thought, but every time you get to a “complicated problem” in the middle of the reasoning chain, it can send this problem to another prompt+LLM call.

Program of Thought (PoT)

Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks

Recently, there has been significant progress in teaching language models to perform step-by-step reasoning to solve complex numerical reasoning tasks. Chain-of-thoughts prompting (CoT) is by far the state-of-art method for these tasks. CoT uses language models to perform both reasoning and computation in the multi-step `thought’ process. To disentangle computation from reasoning, we propose `Program of Thoughts’ (PoT), which uses language models (mainly Codex) to express the reasoning process as a program. The computation is relegated to an external computer, which executes the generated programs to derive the answer. We evaluate PoT on five math word problem datasets (GSM, AQuA, SVAMP, TabMWP, MultiArith) and three financial-QA datasets (FinQA, ConvFinQA, TATQA) for both few-shot and zero-shot setups. Under both few-shot and zero-shot settings, PoT can show an average performance gain over CoT by around 12\% across all the evaluated datasets. By combining PoT with self-consistency decoding, we can achieve SoTA performance on all math problem datasets and near-SoTA performance on financial datasets. All of our data and code are released in Github https://github.com/wenhuchen/Program-of-Thoughts

arXiv.orgWenhu Chen

Use an LLM that specializes in coding (this paper used Codex) and have it output the reasoning steps as programming code like python. Then execute the code to get the correct answer.

Over pure chain of thought, program of thought generates much higher accuracies

TODO: Look up FinQA, ConvFin and TATQA datasets

Faithful Chain-of-Thought

https://arxiv.org/pdf/2301.13379

This is like a combination of PoT and CoT that uses python + natural language reasoning, but it uses different types of “symbolic languages” like python depending on the task.

Q: There are 15 trees in the grove. Grove workers will plant trees in the grove today. After they are done, there will be 21 trees. How many trees did the grove workers plant today?

To answer this question, write a Python program to answer the following subquestions:

How many trees are there in the end? (independent, support: ["there will be 21 trees"])
trees_end = 21
How many trees are there in the beginning? (independent, support: ["There are 15 trees"])
trees_begin = 15
How many trees did the grove workers plant today? (depends on 1 and 2, support: [])
trees_today = trees_end - trees_begin
Final Answer: How many trees did the grove workers plant today? (depends on 3, support: [])
answer = trees_today

... repeat this type of reasoning

Skeleton-of-Thought

Skeleton-of-Thought: Prompting LLMs for Efficient Parallel Generation

This work aims at decreasing the end-to-end generation latency of large language models (LLMs). One of the major causes of the high generation latency is the sequential decoding approach adopted by almost all state-of-the-art LLMs. In this work, motivated by the thinking and writing process of humans, we propose Skeleton-of-Thought (SoT), which first guides LLMs to generate the skeleton of the answer, and then conducts parallel API calls or batched decoding to complete the contents of each skeleton point in parallel. Not only does SoT provide considerable speed-ups across 12 LLMs, but it can also potentially improve the answer quality on several question categories. SoT is an initial attempt at data-centric optimization for inference efficiency, and showcases the potential of eliciting high-quality answers by explicitly planning the answer structure in language.

arXiv.orgXuefei Ning

This focuses on speed and parallel processing. Given a problem, create a template of sub-problems to be solved, then in parallel, go solve all the sub-problems, combined them, and get a final response.

Pretty much write a paper called X-of-Thought and you will get into this section.

Ensembling

This is another classic machine learning technique where you use multiple techniques, models, or prompts to solve a problem, then aggregate the responses into a final output. The easiest aggregation method is just voting and taking the majority.

Demonstration Ensembling (DENSE)

Exploring Demonstration Ensembling for In-context Learning

In-context learning (ICL) operates by showing language models (LMs) examples of input-output pairs for a given task, i.e., demonstrations. The standard approach for ICL is to prompt the LM with concatenated demonstrations followed by the test input. This approach suffers from some issues. First, concatenation offers almost no control over the contribution of each demo to the model prediction. This can be sub-optimal when some demonstrations are irrelevant to the test example. Second, due to the input length limit of some transformer models, it might be infeasible to fit many examples into the context, especially when dealing with long-input tasks. In this work, we explore Demonstration Ensembling (DENSE) as an alternative to simple concatenation. DENSE predicts outputs using subsets (i.e., buckets) of the demonstrations and then combines the output probabilities resulting from each subset to produce the final prediction. We study different ensembling methods using GPT-j and experiment on 12 language tasks. Our experiments show weighted max ensembling to outperform vanilla concatenation by as large as 2.4 average points. Code available at https://github.com/mukhal/icl-ensembling.

arXiv.orgMuhammad Khalifa

Conclusion

It was fascinating to read the Prompt Report and get to talk to Sander Schulhoff during the live dive. While originally, prompting only seemed like a solution for non-technical people, seeing these prompt techniques in practice have changed my approach to solving ML problems. I look forward to see the next developments in prompting and using it more in my workflow, tell us what you think!

Also make sure to claim your $10 free credit for Oxen's new model evaluation feature and let us know how your evaluations are going!

Arxiv Dives