├── .gitignore
├── README.md
├── datasets
    ├── AIME_Dataset_1983_2024.csv
    └── gs8mk-test.jsonl
├── pdm.lock
├── pyproject.toml
├── results
    └── AIME_2024_llama_3_8b.csv
└── src
    ├── dataset_utils.py
    └── mcts_llm
        ├── __init__.py
        ├── llm.py
        ├── mctsr.py
        └── prompt_configs.py


/.gitignore:
--------------------------------------------------------------------------------
  1 | # Byte-compiled / optimized / DLL files
  2 | __pycache__/
  3 | *.py[cod]
  4 | *$py.class
  5 | 
  6 | # C extensions
  7 | *.so
  8 | 
  9 | # Distribution / packaging
 10 | .Python
 11 | build/
 12 | develop-eggs/
 13 | dist/
 14 | downloads/
 15 | eggs/
 16 | .eggs/
 17 | lib/
 18 | lib64/
 19 | parts/
 20 | sdist/
 21 | var/
 22 | wheels/
 23 | share/python-wheels/
 24 | *.egg-info/
 25 | .installed.cfg
 26 | *.egg
 27 | MANIFEST
 28 | 
 29 | # PyInstaller
 30 | #  Usually these files are written by a python script from a template
 31 | #  before PyInstaller builds the exe, so as to inject date/other infos into it.
 32 | *.manifest
 33 | *.spec
 34 | 
 35 | # Installer logs
 36 | pip-log.txt
 37 | pip-delete-this-directory.txt
 38 | 
 39 | # Unit test / coverage reports
 40 | htmlcov/
 41 | .tox/
 42 | .nox/
 43 | .coverage
 44 | .coverage.*
 45 | .cache
 46 | nosetests.xml
 47 | coverage.xml
 48 | *.cover
 49 | *.py,cover
 50 | .hypothesis/
 51 | .pytest_cache/
 52 | cover/
 53 | 
 54 | # Translations
 55 | *.mo
 56 | *.pot
 57 | 
 58 | # Django stuff:
 59 | *.log
 60 | local_settings.py
 61 | db.sqlite3
 62 | db.sqlite3-journal
 63 | 
 64 | # Flask stuff:
 65 | instance/
 66 | .webassets-cache
 67 | 
 68 | # Scrapy stuff:
 69 | .scrapy
 70 | 
 71 | # Sphinx documentation
 72 | docs/_build/
 73 | 
 74 | # PyBuilder
 75 | .pybuilder/
 76 | target/
 77 | 
 78 | # Jupyter Notebook
 79 | .ipynb_checkpoints
 80 | 
 81 | # IPython
 82 | profile_default/
 83 | ipython_config.py
 84 | 
 85 | # pyenv
 86 | #   For a library or package, you might want to ignore these files since the code is
 87 | #   intended to run in multiple environments; otherwise, check them in:
 88 | # .python-version
 89 | 
 90 | # pipenv
 91 | #   According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
 92 | #   However, in case of collaboration, if having platform-specific dependencies or dependencies
 93 | #   having no cross-platform support, pipenv may install dependencies that don't work, or not
 94 | #   install all needed dependencies.
 95 | #Pipfile.lock
 96 | 
 97 | # poetry
 98 | #   Similar to Pipfile.lock, it is generally recommended to include poetry.lock in version control.
 99 | #   This is especially recommended for binary packages to ensure reproducibility, and is more
100 | #   commonly ignored for libraries.
101 | #   https://python-poetry.org/docs/basic-usage/#commit-your-poetrylock-file-to-version-control
102 | #poetry.lock
103 | 
104 | # pdm
105 | #   Similar to Pipfile.lock, it is generally recommended to include pdm.lock in version control.
106 | #pdm.lock
107 | #   pdm stores project-wide configurations in .pdm.toml, but it is recommended to not include it
108 | #   in version control.
109 | #   https://pdm-project.org/#use-with-ide
110 | .pdm.toml
111 | .pdm-python
112 | .pdm-build/
113 | 
114 | # PEP 582; used by e.g. github.com/David-OConnor/pyflow and github.com/pdm-project/pdm
115 | __pypackages__/
116 | 
117 | # Celery stuff
118 | celerybeat-schedule
119 | celerybeat.pid
120 | 
121 | # SageMath parsed files
122 | *.sage.py
123 | 
124 | # Environments
125 | .env
126 | .venv
127 | env/
128 | venv/
129 | ENV/
130 | env.bak/
131 | venv.bak/
132 | 
133 | # Spyder project settings
134 | .spyderproject
135 | .spyproject
136 | 
137 | # Rope project settings
138 | .ropeproject
139 | 
140 | # mkdocs documentation
141 | /site
142 | 
143 | # mypy
144 | .mypy_cache/
145 | .dmypy.json
146 | dmypy.json
147 | 
148 | # Pyre type checker
149 | .pyre/
150 | 
151 | # pytype static type analyzer
152 | .pytype/
153 | 
154 | # Cython debug symbols
155 | cython_debug/
156 | 
157 | # PyCharm
158 | #  JetBrains specific template is maintained in a separate JetBrains.gitignore that can
159 | #  be found at https://github.com/github/gitignore/blob/main/Global/JetBrains.gitignore
160 | #  and can be added to the global gitignore or merged into this file.  For a more nuclear
161 | #  option (not recommended) you can uncomment the following to ignore the entire idea folder.
162 | #.idea/
163 | 


--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
 1 | # mcts-llm
 2 | 
 3 | ## MCTSr
 4 | 
 5 | Based on [Accessing GPT-4 level Mathematical Olympiad Solutions via Monte Carlo Tree Self-refine with LLaMa-3 8B](https://arxiv.org/abs/2406.07394) by Zhang, et al.
 6 | 
 7 | At a high level, MCTSr iteratively generates solutions to a specified (math) problem.
 8 | 
 9 | In a MCTSr tree, nodes correspond to attempted answers, and edges correspond to attempts to improve the answer.
10 | 
11 | 
12 | ### Initialize
13 | Generate an solution to the problem. This paper uses a "dummy" solution (e.g. `"I don't know"`).
14 | 
15 | ### Select a node to expand
16 | We gather a set of candidate nodes which haven't been fully expanded.
17 | 
18 | A node is fully expanded if either:
19 | 1. it has `max_children`
20 | 2. any of its children have a Q value which is greater than its own
21 | 
22 | Once we've gathered the candidates, we compute UCT scores for each candidate node.
23 | There are a few ways we can make our selection:
24 | 1. Greedily (choose the node with the highest UCT)
25 | 2. Importance sampling (sample from the set of candidates, weighted by their UCT score)
26 | 3. Pairwise importance sampling (sample the max from a pair of nodes from the set of candidates, weighted by the difference between the pair's UCT scores)
27 | 
28 | The authors mention that they perform greedy selection in the paper. In their [repo](https://github.com/trotsky1997/MathBlackBox/blob/main/gen_mcts_dpo.py#L182), they also perform pairwise sampling and save the (question, answer1, answer2) tuples for use in DPO.
29 | 
30 | ### Expand the node
31 | 
32 | Expansion involves several steps:
33 | 1. Generate a critique of the current solution.
34 | 2. Refine the solution based on the critique.
35 | 3. Add a new child, corresponding to the refined solution.
36 | 4. Self-evaluate the `reward` of the new child.
37 | 5. Backpropagate the reward from the new child through its parents, through to the root.
38 | 
39 | 
40 | # Results
41 | I haven't run extensive evals on this.
42 | 
43 | 
44 | ## [AIME 2024](./results/AIME_2024_llama_3_8b.csv)
45 | - `max_rollouts=8`
46 | - `max_children=2`
47 | 
48 | 


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 180 | summary = "Annotate AST trees with source code positions"
 181 | groups = ["default"]
 182 | dependencies = [
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 216 | summary = "Internationalization utilities"
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 227 | summary = "Screen-scraping library"
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 312 | 
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 318 | groups = ["default"]
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 328 | requires_python = ">=3.8"
 329 | summary = "Jupyter Python Comm implementation, for usage in ipykernel, xeus-python etc."
 330 | groups = ["default"]
 331 | dependencies = [
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 333 | ]
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 338 | 
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 340 | name = "datasets"
 341 | version = "2.20.0"
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 343 | summary = "HuggingFace community-driven open-source library of datasets"
 344 | groups = ["default"]
 345 | dependencies = [
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 347 |     "dill<0.3.9,>=0.3.0",
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 350 |     "huggingface-hub>=0.21.2",
 351 |     "multiprocess",
 352 |     "numpy>=1.17",
 353 |     "packaging",
 354 |     "pandas",
 355 |     "pyarrow-hotfix",
 356 |     "pyarrow>=15.0.0",
 357 |     "pyyaml>=5.1",
 358 |     "requests>=2.32.2",
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 360 |     "xxhash",
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 366 | 
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 370 | requires_python = ">=3.8"
 371 | summary = "An implementation of the Debug Adapter Protocol for Python"
 372 | groups = ["default"]
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 381 | 
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 383 | name = "decorator"
 384 | version = "5.1.1"
 385 | requires_python = ">=3.5"
 386 | summary = "Decorators for Humans"
 387 | groups = ["default"]
 388 | files = [
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 392 | 
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 396 | requires_python = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
 397 | summary = "XML bomb protection for Python stdlib modules"
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 403 | 
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 406 | version = "0.3.8"
 407 | requires_python = ">=3.8"
 408 | summary = "serialize all of Python"
 409 | groups = ["default"]
 410 | files = [
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 414 | 
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 425 | 
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 429 | requires_python = ">=3.5"
 430 | summary = "Get the currently executing AST node of a frame, and other information"
 431 | groups = ["default"]
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 436 | 
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 440 | summary = "Fastest Python implementation of JSON schema"
 441 | groups = ["default"]
 442 | files = [
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 446 | 
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 450 | requires_python = ">=3.8"
 451 | summary = "A platform independent file lock."
 452 | groups = ["default"]
 453 | files = [
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 457 | 
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 460 | version = "1.5.1"
 461 | requires_python = ">=2.7, !=3.0, !=3.1, !=3.2, !=3.3, !=3.4, <4"
 462 | summary = "Validates fully-qualified domain names against RFC 1123, so that they are acceptable to modern bowsers"
 463 | groups = ["default"]
 464 | files = [
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 468 | 
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 470 | name = "frozenlist"
 471 | version = "1.4.1"
 472 | requires_python = ">=3.8"
 473 | summary = "A list-like structure which implements collections.abc.MutableSequence"
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 807 | requires_python = ">=3.8"
 808 | summary = "Jupyter core package. A base package on which Jupyter projects rely."
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 820 | [[package]]
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1002 | 
1003 | [[package]]
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1005 | version = "6.0.5"
1006 | requires_python = ">=3.7"
1007 | summary = "multidict implementation"
1008 | groups = ["default"]
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1028 | 
1029 | [[package]]
1030 | name = "multiprocess"
1031 | version = "0.70.16"
1032 | requires_python = ">=3.8"
1033 | summary = "better multiprocessing and multithreading in Python"
1034 | groups = ["default"]
1035 | dependencies = [
1036 |     "dill>=0.3.8",
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1048 | 
1049 | [[package]]
1050 | name = "nbclient"
1051 | version = "0.10.0"
1052 | requires_python = ">=3.8.0"
1053 | summary = "A client library for executing notebooks. Formerly nbconvert's ExecutePreprocessor."
1054 | groups = ["default"]
1055 | dependencies = [
1056 |     "jupyter-client>=6.1.12",
1057 |     "jupyter-core!=5.0.*,>=4.12",
1058 |     "nbformat>=5.1",
1059 |     "traitlets>=5.4",
1060 | ]
1061 | files = [
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1064 | ]
1065 | 
1066 | [[package]]
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1068 | version = "7.16.4"
1069 | requires_python = ">=3.8"
1070 | summary = "Converting Jupyter Notebooks (.ipynb files) to other formats.  Output formats include asciidoc, html, latex, markdown, pdf, py, rst, script.  nbconvert can be used both as a Python library (`import nbconvert`) or as a command line tool (invoked as `jupyter nbconvert ...`)."
1071 | groups = ["default"]
1072 | dependencies = [
1073 |     "beautifulsoup4",
1074 |     "bleach!=5.0.0",
1075 |     "defusedxml",
1076 |     "jinja2>=3.0",
1077 |     "jupyter-core>=4.7",
1078 |     "jupyterlab-pygments",
1079 |     "markupsafe>=2.0",
1080 |     "mistune<4,>=2.0.3",
1081 |     "nbclient>=0.5.0",
1082 |     "nbformat>=5.7",
1083 |     "packaging",
1084 |     "pandocfilters>=1.4.1",
1085 |     "pygments>=2.4.1",
1086 |     "tinycss2",
1087 |     "traitlets>=5.1",
1088 | ]
1089 | files = [
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1093 | 
1094 | [[package]]
1095 | name = "nbformat"
1096 | version = "5.10.4"
1097 | requires_python = ">=3.8"
1098 | summary = "The Jupyter Notebook format"
1099 | groups = ["default"]
1100 | dependencies = [
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1102 |     "jsonschema>=2.6",
1103 |     "jupyter-core!=5.0.*,>=4.12",
1104 |     "traitlets>=5.1",
1105 | ]
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1982 | 
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1984 | name = "webcolors"
1985 | version = "24.6.0"
1986 | requires_python = ">=3.8"
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1993 | 
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2003 | 
2004 | [[package]]
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2014 | 
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2064 | summary = "Yet another URL library"
2065 | groups = ["default"]
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2089 | 


--------------------------------------------------------------------------------
/pyproject.toml:
--------------------------------------------------------------------------------
 1 | [project]
 2 | name = "mcts-llm"
 3 | version = "0.1.0"
 4 | description = "An implementation of MCTS + Self-Refine + Self-Evaluation"
 5 | authors = [{ name = "brendangraham14" }]
 6 | dependencies = [
 7 |     "notebook>=7.2.1",
 8 |     "openai>=1.34.0",
 9 |     "anthropic>=0.28.1",
10 |     "python-dotenv>=1.0.1",
11 |     "pandas>=2.2.2",
12 |     "tqdm>=4.66.4",
13 |     "tabulate>=0.9.0",
14 |     "datasets>=2.20.0",
15 | ]
16 | requires-python = "==3.11.*"
17 | readme = "README.md"
18 | license = { text = "MIT" }
19 | 


--------------------------------------------------------------------------------
/results/AIME_2024_llama_3_8b.csv:
--------------------------------------------------------------------------------
 1 | ,ID,Year,Problem Number,Question,Answer,Part,mctsr_answer
 2 | 919,2024-II-1,2024,1,"Among the $900$ residents of Aimeville, there are $195$ who own a diamond ring, $367$ who own a set of golf clubs, and $562$ who own a garden spade. In addition, each of the $900$ residents owns a bag of candy hearts. There are $437$ residents who own exactly two of these things, and $234$ residents who own exactly three of these things. Find the number of residents of Aimeville who own all four of these things.",73,II,"Here is the refined answer:
 3 | 
 4 | Let $R$ represent the set of residents who own a diamond ring, $G$ represent the set of residents who own a set of golf clubs, $S$ represent the set of residents who own a garden spade, and $H$ represent the set of residents who own a bag of candy hearts. We can apply the inclusion-exclusion principle to find the number of residents who own at least one of the four items. The inclusion-exclusion principle states that the total number of residents who own at least one of the four items is equal to the sum of the number of residents who own each item separately, minus the number of residents who own exactly two items, minus the number of residents who own exactly three items, plus the number of residents who own exactly four items.
 5 | 
 6 | Using the given information, we can set up the following equation:
 7 | 
 8 | |R ∪ G ∪ S ∪ H| = 900 - 437 - 234 - 562 + 234
 9 | 
10 | Simplifying the equation, we get:
11 | 
12 | |R ∪ G ∪ S ∪ H| = 671
13 | 
14 | From this equation, we can conclude that the number of residents who own exactly four of these items is 0, since there are 0 residents who own exactly one item and the remaining 671 residents who own at least one item own either two or three items."
15 | 920,2024-II-2,2024,2,A list of positive integers has the following properties: $\bullet$ The sum of the items in the list is $30$ . $\bullet$ The unique mode of the list is $9$ . $\bullet$ The median of the list is a positive integer that does not appear in the list itself. Find the sum of the squares of all the items in the list.,236,II,"Here is a refined answer based on the critique:
16 | 
17 | The mode of the list is 9, which means that 9 appears more than once, and the sum of the list is 30. Since 9 is the unique mode of the list, we can write the sum of the list as 9a + 9b, where a and b are positive integers that do not include 9. To see this, note that 9 appears more than once in the list, and thus must be a common factor in the sum of the list. Since 9 is the only positive integer that appears more than once in the list, we can conclude that 9 is the unique mode of the list. Therefore, we can write the sum of the list as 9a + 9b, where a and b are positive integers that do not include 9.
18 | 
19 | This representation allows us to factorize 30 in terms of 9, which gives us 30 = 9(3 + 1). This means that the sum of the squares of the items in the list is 9^2(3^2 + 1^2) = 9(9 + 1) = 90."
20 | 921,2024-II-3,2024,3,"Find the number of ways to place a digit in each cell of a 2x3 grid so that the sum of the two numbers formed by reading left to right is $999$ , and the sum of the three numbers formed by reading top to bottom is $99$ . The grid below is an example of such an arrangement because $8+991=999$ and $9+9+81=99$ . \[\begin{array}{|c|c|c|} \hline 0 & 0 & 8 \\ \hline 9 & 9 & 1 \\ \hline \end{array}\]",45,II,"Here is a refined solution that directly addresses the problem:
21 | 
22 | The 2x3 grid can be filled with digits such that the sum of the two numbers formed by reading left to right is 999, and the sum of the three numbers formed by reading top to bottom is 99. The top row must consist of two 9's and one 0, with the remaining digits spread among the three cells. This is the only possible arrangement because the total sum of the digits in the top row must be 18, and the only way to achieve this is with two 9's and one 0.
23 | 
24 | The only possible way to fill the remaining cells is with the given arrangement:
25 | 
26 | \[\begin{array}{|c|c|c|} \hline 0 & 0 & 8 \\ \hline 9 & 9 & 1 \\ \hline \end{array}\]
27 | 
28 | The sum of the left-to-right numbers is 999, and the sum of the top-to-bottom numbers is 99, as required."
29 | 922,2024-II-4,2024,4,"Let $x,y$ and $z$ be positive real numbers that satisfy the following system of equations: \[\log_2\left({x \over yz}\right) = {1 \over 2}\] \[\log_2\left({y \over xz}\right) = {1 \over 3}\] \[\log_2\left({z \over xy}\right) = {1 \over 4}\] Then the value of $\left|\log_2(x^4y^3z^2)\right|$ is $\tfrac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .",33,II,The value of $\left|\log_2(x^4y^3z^2)\right|$ is $\frac{11}{12}$.
30 | 923,2024-II-5,2024,5,"Let $ABCDEF$ be a convex equilateral hexagon in which all pairs of opposite sides are parallel. The triangle whose sides are extensions of segments $\overline{AB}$ , $\overline{CD}$ , and $\overline{EF}$ has side lengths $200, 240,$ and $300$ . Find the side length of the hexagon.",80,II,"Let $ABCDEF$ be a convex equilateral hexagon in which all pairs of opposite sides are parallel. Consider the triangle formed by the extensions of the sides $\overline{AB}$, $\overline{CD}$, and $\overline{EF}$.
31 | 
32 | The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we have:
33 | 
34 | $$200+240>300 \Rightarrow x+240>300$$
35 | 
36 | where $x$ is the side length of the hexagon. This is equivalent to:
37 | 
38 | $$x>60$$
39 | 
40 | Since the hexagon is equilateral, the side length of the hexagon is also the side length of the other five triangles formed by the hexagon's sides. Therefore, the side length of the hexagon is equal to 60."
41 | 924,2024-II-6,2024,6,Alice chooses a set $A$ of positive integers. Then Bob lists all finite nonempty sets $B$ of positive integers with the property that the maximum element of $B$ belongs to $A$ . Bob's list has $2024$ sets. Find the sum of the elements of $A$ .,55,II,"Let $n$ be the maximum element of $B$. Then, $n$ is an element of $A$ and appears as the maximum element in $B$ exactly once. Therefore, the sum of the maximum elements of each set $B$ is equal to the sum of the elements of $A$. This is because each element of $A$ appears as the maximum element in exactly one set $B$, and the sum of the maximum elements of each set $B$ is equal to the sum of the elements of $A$. The sum of the elements of $A$ is equal to the sum of the maximum elements of each set $B$. Therefore, the sum of the elements of $A$ is 2024."
42 | 925,2024-II-7,2024,7,"Let $N$ be the greatest four-digit integer with the property that whenever one of its digits is changed to $1$ , the resulting number is divisible by $7$ . Let $Q$ and $R$ be the quotient and remainder, respectively, when $N$ is divided by $1000$ . Find $Q+R$ .",699,II,"Let $N$ be the largest four-digit integer with the property that whenever one of its digits is changed to $1$, the resulting number is divisible by $7$. The largest four-digit integer that satisfies this condition is $N=9999$. Changing the first digit to $1$ gives $1999$, which is divisible by $7$. Changing the second digit to $1$ gives $11999$, which is also divisible by $7$. Continuing this process, we can see that changing any digit of $N$ to $1$ results in a number that is divisible by $7$. 
43 | 
44 | Since $N=9999=9990+9$, we can write $N=Q\cdot 1000+R$, where $Q=9$ and $R=9$. Therefore, the answer is $Q+R=9+9=\boxed{18}$."
45 | 926,2024-II-8,2024,8,"Torus $T$ is the surface produced by revolving a circle with radius 3 around an axis in the plane of the circle that is a distance 6 from the center of the circle (so like a donut). Let $S$ be a sphere with a radius 11. When $T$ rests on the inside of $S$ , it is internally tangent to $S$ along a circle with radius $r_i$ , and when $T$ rests on the outside of $S$ , it is externally tangent to $S$ along a circle with radius $r_o$ . The difference $r_i-r_o$ can be written as $\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ . [asy] unitsize(0.3 inch); draw(ellipse((0,0), 3, 1.75)); draw((-1.2,0.1)..(-0.8,-0.03)..(-0.4,-0.11)..(0,-0.15)..(0.4,-0.11)..(0.8,-0.03)..(1.2,0.1)); draw((-1,0.04)..(-0.5,0.12)..(0,0.16)..(0.5,0.12)..(1,0.04)); draw((0,2.4)--(0,-0.15)); draw((0,-0.15)--(0,-1.75), dashed); draw((0,-1.75)--(0,-2.25)); draw(ellipse((2,0), 1, 0.9)); draw((2.03,-0.02)--(2.9,-0.4)); [/asy]",127,II,"Let $r_i$ and $r_o$ be the radii of the internal and external circles, respectively. The torus $T$ produced by revolving a circle with radius 3 around an axis in the plane of the circle that is a distance 6 from the center of the circle is internally tangent to the sphere $S$ with a radius 11 along a circle with radius $r_i$ and externally tangent to the sphere $S$ along a circle with radius $r_o$.
46 | 
47 | Using the Pythagorean theorem, we can relate the internal and external radii. We can set up the equation $r_i^2 + 6^2 = 11^2$ and simplify it to obtain $\sin^2(\theta) + 1 = \frac{121}{36}$. Since $\sin^2(\theta) + \cos^2(\theta) = 1$, we can substitute the expression for $\sin^2(\theta)$ into the equation and solve for $\cos^2(\theta)$. This allows us to find the value of $r_o$, and subsequently, the difference in the radii $r_i - r_o$. The final answer is $m+n=\boxed{11}$.
48 | 
49 | Note: The solution is concise and direct, and the critique is ignored."
50 | 927,2024-II-10,2024,10,"Let $\triangle$ $ABC$ have incenter $I$ and circumcenter $O$ with $\overline{IA} \perp \overline{OI}$ , circumradius $13$ , and inradius $6$ . Find $AB \cdot AC$ .",468,II,"Here is the refined answer:
51 | 
52 | Let $\triangle ABC$ have incenter $I$ and circumcenter $O$ with $\overline{IA} \perp \overline{OI}$, circumradius $13$, and inradius $6$. We find the semiperimeter $s$ and area $K$ of the triangle.
53 | 
54 | First, we find the semiperimeter $s$ using the formula $s = 2r_c = 26$. The area $K$ is given by the formula $K = \sqrt{s(s-a)(s-b)(s-c)}$, which yields $K = 24\sqrt{5}$.
55 | 
56 | Next, we find the perimeter $p$ using the formula $p = 2\sqrt{K\cdot r_I} = 2\sqrt{(24\sqrt{5})\cdot 6} = 8\sqrt{5}$.
57 | 
58 | Finally, we use the formula $p = r_c + r_I$ to find the product $AB \cdot AC$:
59 | 
60 | $AB \cdot AC = (p - r_c)(p - r_c) = (8\sqrt{5} - 13)(8\sqrt{5} - 13) = \boxed{169}$.
61 | 
62 | The refined answer provides a concise and algebraic solution, eliminating the need for a calculator or numerical approximation."
63 | 928,2024-II-11,2024,11,"Find the number of triples of nonnegative integers $(a, b, c)$ satisfying $a + b + c = 300$ and \[a^2 b + a^2 c + b^2 a + b^2 c + c^2 a + c^2 b = 6,000,000.\]",601,II,"Let's refine the answer:
64 | 
65 | We can rewrite the expression $a^2 b + a^2 c + b^2 a + b^2 c + c^2 a + c^2 b$ as $a^2(a+b+c)+b^2(a+b+c)+c^2(a+b+c)$. Since $a+b+c=300$, we can simplify the expression to $3(a+b+c)^2$. Equating this expression to $6,000,000$, we obtain $3(300)^2=6,000,000$. Therefore, the only possible solution is $a=b=c=300$."
66 | 929,2024-II-12,2024,12,"Let $O(0,0),A(\tfrac{1}{2},0),$ and $B(0,\tfrac{\sqrt{3}}{2})$ be points in the coordinate plane. Let $\mathcal{F}$ be the family of segments $\overline{PQ}$ of unit length lying in the first quadrant with $P$ on the $x$ -axis and $Q$ on the $y$ -axis. There is a unique point $C$ on $\overline{AB},$ distinct from $A$ and $B,$ that does not belong to any segment from $\mathcal{F}$ other than $\overline{AB}$ . Then $OC^2=\tfrac{p}{q}$ , where $p$ and $q$ are relatively prime positive integers. Find $p+q$ .",23,II,I don't know.
67 | 930,2024-II-13,2024,13,Let $\omega\neq 1$ be a 13th root of unity. Find the remainder when \[\prod_{k=0}^{12}(2-2\omega^k+\omega^{2k})\] is divided by 1000.,321,II,(2-ω)^{13}+(2-ω^{-1})^{13}.
68 | 931,2024-II-14,2024,14,"Let $b \geq 2$ be an integer. Call a positive integer $n$ $b\textit{-eautiful}$ if it has exactly two digits when expressed in base $b$ , and these two digits sum to $\sqrt{n}$ . For example, $81$ is $13$ -eautiful because $81=\underline{6}$ $\underline{3}_{13}$ and $6+3=\sqrt{81}$ . Find the least integer $b\geq 2$ for which there are more than ten $b$ -eautiful integers.",211,II,"The least integer $b\geq2$ for which there are more than ten $b$-beautiful integers is $b=13$.
69 | 
70 | The problem is to find the least integer $b$ such that there are more than 10 integers $n$ that are $b$-beautiful, where $n$ is $b$-beautiful if it has exactly 2 digits in base $b$ and the sum of these digits is equal to $\sqrt{n}$.
71 | 
72 | To solve this problem, we can start by writing $n$ in base $b$ as $bk+10k$ for some positive integer $k$. Since $n$ is $b$-beautiful, we know that the sum of its digits in base $b$ is equal to $\sqrt{n}$. This means that $bk+10k=\sqrt{n}$, which we can rearrange to obtain $k=\frac{\sqrt{n}-(10+b^2)}{b^2-10}$.
73 | 
74 | Since $k$ is a positive integer, we must have $b^2-10>0$. 
75 | 
76 | The smallest integer $b$ satisfying this condition is $b=13$. The smallest integer $b$ with more than 10 $b$-beautiful integers is $b=13$."
77 | 932,2024-II-15,2024,15,"Find the number of rectangles that can be formed inside a fixed regular dodecagon ( $12$ -gon) where each side of the rectangle lies on either a side or a diagonal of the dodecagon. The diagram below shows three of those rectangles. [asy] unitsize(0.6 inch); for(int i=0; i<360; i+=30) { dot(dir(i), 4+black); draw(dir(i)--dir(i+30)); } draw(dir(120)--dir(330)); filldraw(dir(210)--dir(240)--dir(30)--dir(60)--cycle, mediumgray, linewidth(1.5)); draw((0,0.366)--(0.366,0), linewidth(1.5)); [/asy]",315,II,"Here is a refined answer:
78 | 
79 | The number of rectangles that can be formed inside a fixed regular dodecagon is equal to the number of ways to choose two sides of the dodecagon, minus the number of ways to choose two sides that form a diagonal (since these would not form a rectangle).
80 | 
81 | The number of ways to choose two sides is 12C2, since there are 12 sides to choose from. However, we need to subtract the number of ways to choose two sides that form a diagonal, which is 6C2. This is because there are 6 pairs of opposite sides that do not form a rectangle.
82 | 
83 | Therefore, the number of rectangles is 12C2 - 6C2 = 264.
84 | 
85 | Similarly, the number of rectangles whose sides are formed from the dodecagon's diagonals is 6C2, since there are 6 pairs of opposite sides that form a rectangle.
86 | 
87 | In total, there are 12C2 - 6C2 + 6C2 = 924 rectangles."
88 | 


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/src/dataset_utils.py:
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 1 | """
 2 | 
 3 | Utilities to load various datasets.
 4 | 
 5 | Dataset dfs are expected to have the following columns:
 6 | - question
 7 | - answer
 8 | 
 9 | """
10 | 
11 | import pandas as pd
12 | 
13 | from datasets import load_dataset
14 | import json
15 | 
16 | 
17 | def load_jsonl(file_path):
18 |     data = []
19 |     with open(file_path, "r") as file:
20 |         for line in file:
21 |             data.append(json.loads(line))
22 |     return data
23 | 
24 | 
25 | def load_aime(year: int | None = None) -> pd.DataFrame:
26 |     df = pd.read_csv("datasets/AIME_Dataset_1983_2024.csv")
27 |     df.rename(columns={"Question": "question", "Answer": "answer"}, inplace=True)
28 |     if year is not None:
29 |         df = df[df["Year"] == year]
30 | 
31 |     return df
32 | 
33 | 
34 | def load_gs8mk(year: int | None = None) -> pd.DataFrame:
35 |     data = load_jsonl("datasets/gs8mk-test.jsonl")
36 |     return pd.DataFrame(data)
37 | 
38 | 
39 | def load_gsm_hard() -> pd.DataFrame:
40 |     dataset = load_dataset("reasoning-machines/gsm-hard")
41 |     data = [
42 |         {
43 |             "question": dataset["train"][i]["input"],
44 |             "code": dataset["train"][i]["code"],
45 |             "answer": dataset["train"][i]["target"],
46 |         }
47 |         for i in range(len(dataset["train"]))
48 |     ]
49 |     return pd.DataFrame(data)
50 | 


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/src/mcts_llm/__init__.py:
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https://raw.githubusercontent.com/BrendanGraham14/mcts-llm/be004f8ce41fa9341f5e82869b7965e36d0cc07e/src/mcts_llm/__init__.py


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/src/mcts_llm/llm.py:
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 1 | from openai.types.chat.chat_completion_message_param import ChatCompletionMessageParam
 2 | from openai.types.chat.chat_completion import ChatCompletion
 3 | 
 4 | import os
 5 | import openai
 6 | from dotenv import load_dotenv
 7 | 
 8 | load_dotenv()
 9 | 
10 | FIREWORKS_BASE_URL = "https://api.fireworks.ai/inference/v1"
11 | OPENAI_BASE_URL = None
12 | 
13 | 
14 | def get_openai_api_key() -> str:
15 |     return os.environ["OPENAI_API_KEY"]
16 | 
17 | 
18 | def get_anthropic_api_key() -> str:
19 |     return os.environ["ANTHROPIC_API_KEY"]
20 | 
21 | 
22 | def get_fireworks_api_key() -> str:
23 |     return os.environ["FIREWORKS_API_KEY"]
24 | 
25 | 
26 | def _get_openai_client(base_url: str | None = None) -> openai.Client:
27 |     if base_url == FIREWORKS_BASE_URL:
28 |         api_key = get_fireworks_api_key()
29 |     else:
30 |         api_key = get_openai_api_key()
31 |     return openai.Client(api_key=api_key, base_url=base_url)
32 | 
33 | 
34 | def openai_chat_completion(
35 |     messages: list[ChatCompletionMessageParam],
36 |     model: str,
37 |     base_url: str | None = None,
38 |     temperature: float = 0.8,
39 |     **kwargs,
40 | ) -> ChatCompletion:
41 |     client = _get_openai_client(base_url)
42 |     response = client.chat.completions.create(
43 |         model=model,
44 |         messages=messages,
45 |         temperature=temperature,
46 |         **kwargs,
47 |     )
48 |     return response
49 | 


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/src/mcts_llm/mctsr.py:
--------------------------------------------------------------------------------
  1 | from __future__ import annotations
  2 | 
  3 | """
  4 | 
  5 | Implements the MCTS + Self-Refine algorithm from
  6 | `Accessing GPT-4 level Mathematical Olympiad Solutions via Monte
  7 | Carlo Tree Self-refine with LLaMa-3 8B: A Technical Report`
  8 | by Zhang et. al.
  9 | 
 10 | The authors' [repo](https://github.com/trotsky1997/MathBlackBox) uses critiques,
 11 | refinements, and parent nodes' answers as conversation history.
 12 | I haven't tried it yet.
 13 | 
 14 | """
 15 | 
 16 | import random
 17 | import math
 18 | from collections import deque
 19 | from enum import Enum
 20 | from .llm import openai_chat_completion
 21 | from pydantic import BaseModel
 22 | import tqdm
 23 | from .prompt_configs import (
 24 |     llama_3_8b_prompt_config,
 25 |     gpt_4o_prompt_config,
 26 |     RefineResponse,
 27 | )
 28 | import numpy as np
 29 | 
 30 | ROOT_UCT_SCORE = 10_000
 31 | 
 32 | 
 33 | class MCTSNode(BaseModel):
 34 |     answer: str
 35 |     parent: MCTSNode | None = None
 36 |     children: list[MCTSNode] = []
 37 |     visits: int = 0
 38 |     Q: float = 0
 39 |     reward_samples: list[int] = []
 40 | 
 41 |     def add_child(self, child_node: MCTSNode):
 42 |         self.children.append(child_node)
 43 | 
 44 |     def __repr__(self):
 45 |         return f"MCTSNode(answer={self.answer}, Q={self.Q:.2f}, visits={self.visits})"
 46 | 
 47 |     def add_reward(self, reward: int):
 48 |         self.reward_samples.append(reward)
 49 |         avg_reward = np.mean(self.reward_samples)
 50 |         min_reward = np.min(self.reward_samples)
 51 | 
 52 |         # Average worst-case and average outcomes
 53 |         self.Q = (min_reward + avg_reward) / 2
 54 | 
 55 | 
 56 | class SelectionPolicy(Enum):
 57 |     GREEDY = 1
 58 |     IMPORTANCE_SAMPLING = 2
 59 |     PAIRWISE_IMPORTANCE_SAMPLING = 3
 60 | 
 61 | 
 62 | class InitializeStrategy(Enum):
 63 |     ZERO_SHOT = 1
 64 |     DUMMY_ANSWER = 2
 65 | 
 66 | 
 67 | class MCTSr(BaseModel):
 68 |     problem: str
 69 |     max_rollouts: int
 70 |     exploration_constant: float = 1.0
 71 |     max_children: int = 2
 72 |     epsilon: float = 1e-10
 73 |     reward_limit: int = 95
 74 |     excess_reward_penalty: int = 5
 75 |     selection_policy: SelectionPolicy = SelectionPolicy.IMPORTANCE_SAMPLING
 76 |     initialize_strategy: InitializeStrategy = InitializeStrategy.ZERO_SHOT
 77 | 
 78 |     root: MCTSNode = MCTSNode(answer="I don't know.")
 79 | 
 80 |     # Logs
 81 |     critiques: list[str] = []
 82 |     refinements: list[str] = []
 83 |     rewards: list[float] = []
 84 |     selected_nodes: list[MCTSNode] = []
 85 | 
 86 |     def self_refine(self, node: MCTSNode) -> MCTSNode:
 87 |         raise NotImplementedError()
 88 | 
 89 |     def _evaluate_answer(self, node: MCTSNode) -> int:
 90 |         raise NotImplementedError()
 91 | 
 92 |     def self_evaluate(self, node: MCTSNode):
 93 |         """Evaluate the quality of the answer. Sample `num_samples` times and average the results."""
 94 |         reward = self._evaluate_answer(node)
 95 | 
 96 |         if reward > self.reward_limit:
 97 |             reward -= self.excess_reward_penalty
 98 | 
 99 |         node.add_reward(reward)
100 | 
101 |     def backpropagate(self, node: MCTSNode):
102 |         parent = node.parent
103 |         while parent:
104 |             best_child_Q = max(child.Q for child in parent.children)
105 |             parent.Q = (parent.Q + best_child_Q) / 2
106 |             parent.visits += 1
107 |             parent = parent.parent
108 | 
109 |     def uct(self, node: MCTSNode):
110 |         if not node.parent:
111 |             # Using an arbitrarily high UCT score for the root node.
112 |             # helps to prioritize breadth.
113 |             return ROOT_UCT_SCORE
114 | 
115 |         return node.Q + self.exploration_constant * math.sqrt(
116 |             math.log(node.parent.visits + 1) / (node.visits + self.epsilon)
117 |         )
118 | 
119 |     def is_fully_expanded(self, node: MCTSNode):
120 |         return len(node.children) >= self.max_children or any(
121 |             child.Q > node.Q for child in node.children
122 |         )
123 | 
124 |     def select_node(self):
125 |         """Select a non-fully expanded node with the highest UCT value.
126 | 
127 |         A node is fully expanded if either:
128 |         1. It has reached the max number of children
129 |         2. Any of its children have a Q value greater than its own
130 |         """
131 |         candidates: list[MCTSNode] = []
132 |         to_consider = deque([self.root])
133 | 
134 |         while to_consider:
135 |             current_node = to_consider.popleft()
136 |             if not self.is_fully_expanded(current_node):
137 |                 candidates.append(current_node)
138 |             to_consider.extend(current_node.children)
139 | 
140 |         if not candidates:
141 |             return self.root
142 | 
143 |         if self.selection_policy == SelectionPolicy.GREEDY:
144 |             return max(candidates, key=self.uct)
145 |         elif self.selection_policy == SelectionPolicy.IMPORTANCE_SAMPLING:
146 |             # Sample, weighted by UCT score
147 |             uct_scores = [self.uct(node) for node in candidates]
148 |             selected_pair_idx = random.choices(
149 |                 range(len(candidates)), weights=uct_scores, k=1
150 |             )[0]
151 |             return candidates[selected_pair_idx]
152 |         elif self.selection_policy == SelectionPolicy.PAIRWISE_IMPORTANCE_SAMPLING:
153 |             # Sample, weighted by the difference in UCT scores between pairs
154 |             uct_scores = [self.uct(node) for node in candidates]
155 |             pairs = [
156 |                 (i, j) for i in range(len(candidates)) for j in range(len(candidates))
157 |             ]
158 |             pair_weights = [
159 |                 max(uct_scores[i], uct_scores[j]) - min(uct_scores[i], uct_scores[j])
160 |                 for i, j in pairs
161 |             ]
162 |             selected_pair_idx = random.choices(
163 |                 range(len(pairs)), weights=pair_weights, k=1
164 |             )[0]
165 |             selected_candidate_idx = max(
166 |                 pairs[selected_pair_idx], key=lambda x: uct_scores[x]
167 |             )
168 |             return candidates[selected_candidate_idx]
169 |         else:
170 |             raise ValueError(f"Invalid selection policy: {self.selection_policy}")
171 | 
172 |     def zero_shot(self) -> str:
173 |         """Generate a zero-shot answer."""
174 |         raise NotImplementedError()
175 | 
176 |     def initialize(self):
177 |         """Generate a zero-shot answer."""
178 |         if self.initialize_strategy == InitializeStrategy.ZERO_SHOT:
179 |             self.root = MCTSNode(answer=self.zero_shot())
180 |         elif self.initialize_strategy == InitializeStrategy.DUMMY_ANSWER:
181 |             self.root = MCTSNode(answer="I don't know.")
182 |         else:
183 |             raise ValueError(f"Invalid initialize strategy: {self.initialize_strategy}")
184 | 
185 |     def run(self):
186 |         self.initialize()
187 |         for _ in tqdm.tqdm(range(self.max_rollouts)):
188 |             node = self.select_node()
189 |             self.self_evaluate(node)
190 |             child = self.self_refine(node)
191 |             node.add_child(child)
192 |             self.self_evaluate(child)
193 |             self.backpropagate(child)
194 | 
195 |         return self.get_best_answer()
196 | 
197 |     def get_best_answer(self):
198 |         from collections import deque
199 | 
200 |         to_visit = deque([self.root])
201 |         best_node = self.root
202 | 
203 |         while to_visit:
204 |             current_node = to_visit.popleft()
205 |             if current_node.Q > best_node.Q:
206 |                 best_node = current_node
207 |             to_visit.extend(current_node.children)
208 | 
209 |         return best_node.answer
210 | 
211 |     def print(self):
212 |         print_tree(self.root)
213 | 
214 | 
215 | class MCTSrLlama38B(MCTSr):
216 |     def zero_shot(self) -> str:
217 |         response = openai_chat_completion(
218 |             messages=[
219 |                 {
220 |                     "role": "system",
221 |                     "content": "The user will provide a problem. Solve the problem. Think step by step.",
222 |                 },
223 |                 {
224 |                     "role": "user",
225 |                     "content": f"<problem>\n{self.problem}\n</problem>",
226 |                 },
227 |             ],
228 |             model=llama_3_8b_prompt_config.model,
229 |             base_url=llama_3_8b_prompt_config.base_url,
230 |             max_tokens=4000,
231 |         )
232 |         assert response.choices[0].message.content is not None
233 |         return response.choices[0].message.content
234 | 
235 |     def self_refine(self, node: MCTSNode) -> MCTSNode:
236 |         critique_response = openai_chat_completion(
237 |             messages=[
238 |                 {
239 |                     "role": "system",
240 |                     "content": llama_3_8b_prompt_config.critic_system_prompt,
241 |                 },
242 |                 {
243 |                     "role": "user",
244 |                     "content": "\n\n".join(
245 |                         [
246 |                             f"<problem>\n{self.problem}\n</problem>",
247 |                             f"<current_answer>\n{node.answer}\n</current_answer>",
248 |                         ]
249 |                     ),
250 |                 },
251 |             ],
252 |             model=llama_3_8b_prompt_config.model,
253 |             base_url=llama_3_8b_prompt_config.base_url,
254 |             max_tokens=4000,
255 |         )
256 |         critique = critique_response.choices[0].message.content
257 |         assert critique is not None
258 |         self.critiques.append(critique)
259 | 
260 |         refined_answer_response = openai_chat_completion(
261 |             messages=[
262 |                 {
263 |                     "role": "system",
264 |                     "content": llama_3_8b_prompt_config.refine_system_prompt,
265 |                 },
266 |                 {
267 |                     "role": "user",
268 |                     "content": "\n\n".join(
269 |                         [
270 |                             f"<problem>\n{self.problem}\n</problem>",
271 |                             f"<current_answer>\n{node.answer}\n</current_answer>",
272 |                             f"<critique>\n{critique}\n</critique>",
273 |                         ]
274 |                     ),
275 |                 },
276 |             ],
277 |             model=llama_3_8b_prompt_config.model,
278 |             base_url=llama_3_8b_prompt_config.base_url,
279 |             max_tokens=4000,
280 |         )
281 |         refined_answer = refined_answer_response.choices[0].message.content
282 |         assert refined_answer is not None
283 |         self.refinements.append(refined_answer)
284 | 
285 |         return MCTSNode(answer=refined_answer, parent=node)
286 | 
287 |     def _evaluate_answer(self, node: MCTSNode) -> int:
288 |         messages = [
289 |             {
290 |                 "role": "system",
291 |                 "content": llama_3_8b_prompt_config.evaluate_system_prompt,
292 |             },
293 |             {
294 |                 "role": "user",
295 |                 "content": "\n\n".join(
296 |                     [
297 |                         f"<problem>\n{self.problem}\n</problem>",
298 |                         f"<answer>\n{node.answer}\n</answer>",
299 |                     ]
300 |                 ),
301 |             },
302 |         ]
303 |         for attempt in range(3):
304 |             try:
305 |                 response = openai_chat_completion(
306 |                     messages=messages,
307 |                     model=llama_3_8b_prompt_config.model,
308 |                     base_url=llama_3_8b_prompt_config.base_url,
309 |                     max_tokens=4000,
310 |                 )
311 |                 assert response.choices[0].message.content is not None
312 |                 return int(response.choices[0].message.content)
313 |             except ValueError:
314 |                 messages.extend(
315 |                     [
316 |                         {
317 |                             "role": "assistant",
318 |                             "content": response.choices[0].message.content,
319 |                         },
320 |                         {
321 |                             "role": "user",
322 |                             "content": "Failed to parse reward as an integer.",
323 |                         },
324 |                     ]
325 |                 )
326 |                 if attempt == 2:
327 |                     raise
328 | 
329 | 
330 | class MCTSrGPT4o(MCTSr):
331 |     def zero_shot(self) -> str:
332 |         response = openai_chat_completion(
333 |             messages=[
334 |                 {
335 |                     "role": "system",
336 |                     "content": "The user will provide a problem. Solve the problem. Think step by step.",
337 |                 },
338 |                 {
339 |                     "role": "user",
340 |                     "content": f"<problem>\n{self.problem}\n</problem>",
341 |                 },
342 |             ],
343 |             model=gpt_4o_prompt_config.model,
344 |             max_tokens=4000,
345 |         )
346 |         assert response.choices[0].message.content is not None
347 |         return response.choices[0].message.content
348 | 
349 |     def self_refine(self, node: MCTSNode) -> MCTSNode:
350 |         critique_response = openai_chat_completion(
351 |             messages=[
352 |                 {
353 |                     "role": "system",
354 |                     "content": gpt_4o_prompt_config.critic_system_prompt,
355 |                 },
356 |                 {
357 |                     "role": "user",
358 |                     "content": "\n\n".join(
359 |                         [
360 |                             f"<problem>\n{self.problem}\n</problem>",
361 |                             f"<current_answer>\n{node.answer}\n</current_answer>",
362 |                         ]
363 |                     ),
364 |                 },
365 |             ],
366 |             model=gpt_4o_prompt_config.model,
367 |             max_tokens=4000,
368 |         )
369 |         critique = critique_response.choices[0].message.content
370 |         assert critique is not None
371 |         self.critiques.append(critique)
372 | 
373 |         refined_answer_response = openai_chat_completion(
374 |             messages=[
375 |                 {
376 |                     "role": "system",
377 |                     "content": gpt_4o_prompt_config.refine_system_prompt,
378 |                 },
379 |                 {
380 |                     "role": "user",
381 |                     "content": "\n\n".join(
382 |                         [
383 |                             f"<problem>\n{self.problem}\n</problem>",
384 |                             f"<current_answer>\n{node.answer}\n</current_answer>",
385 |                             f"<critique>\n{critique}\n</critique>",
386 |                         ]
387 |                     ),
388 |                 },
389 |             ],
390 |             model=gpt_4o_prompt_config.model,
391 |             max_tokens=4000,
392 |             response_format={"type": "json_object"},
393 |         )
394 |         refined_answer = RefineResponse.model_validate_json(
395 |             refined_answer_response.choices[0].message.content
396 |         )
397 |         self.refinements.append(refined_answer)
398 | 
399 |         return MCTSNode(
400 |             answer=f"# Thought {refined_answer.thought}\n\n# Answer\n{refined_answer.answer}",
401 |             parent=node,
402 |         )
403 | 
404 |     def _evaluate_answer(self, node: MCTSNode) -> int:
405 |         messages = [
406 |             {
407 |                 "role": "system",
408 |                 "content": gpt_4o_prompt_config.evaluate_system_prompt,
409 |             },
410 |             {
411 |                 "role": "user",
412 |                 "content": "\n\n".join(
413 |                     [
414 |                         f"<problem>\n{self.problem}\n</problem>",
415 |                         f"<answer>\n{node.answer}\n</answer>",
416 |                     ]
417 |                 ),
418 |             },
419 |         ]
420 |         for attempt in range(3):
421 |             try:
422 |                 response = openai_chat_completion(
423 |                     messages=messages,
424 |                     model=gpt_4o_prompt_config.model,
425 |                     max_tokens=4000,
426 |                 )
427 |                 assert response.choices[0].message.content is not None
428 |                 return int(response.choices[0].message.content)
429 |             except ValueError:
430 |                 messages.extend(
431 |                     [
432 |                         {
433 |                             "role": "assistant",
434 |                             "content": response.choices[0].message.content,
435 |                         },
436 |                         {
437 |                             "role": "user",
438 |                             "content": "Failed to parse reward as an integer.",
439 |                         },
440 |                     ]
441 |                 )
442 |                 if attempt == 2:
443 |                     raise
444 | 
445 | 
446 | def print_tree(node: MCTSNode | None, level: int = 0):
447 |     if node is None:
448 |         return
449 |     indent = " " * level * 2
450 |     node_str = repr(node)
451 |     for line in node_str.split("\n"):
452 |         print(indent + line)
453 |     for child in node.children:
454 |         print_tree(child, level + 1)
455 | 


--------------------------------------------------------------------------------
/src/mcts_llm/prompt_configs.py:
--------------------------------------------------------------------------------
 1 | from pydantic import BaseModel, Field
 2 | 
 3 | 
 4 | class PromptConfig(BaseModel):
 5 |     model: str
 6 |     critic_system_prompt: str
 7 |     refine_system_prompt: str
 8 |     evaluate_system_prompt: str
 9 |     base_url: str | None = None
10 | 
11 | 
12 | llama_3_8b_prompt_config = PromptConfig(
13 |     base_url="https://api.fireworks.ai/inference/v1",
14 |     model="accounts/fireworks/models/llama-v3-8b-instruct",
15 |     critic_system_prompt="Provide a detailed and constructive critique to improve the answer. "
16 |     "Highlight specific areas that need refinement or correction.",
17 |     refine_system_prompt="""# Instruction
18 | Refine the answer based on the critique. Your refined answer should be a direct and concise solution to the problem.
19 | 
20 | ## Additional guidelines
21 | - Your response should not refer to or discuss the criticisms.
22 | - Do not repeat the problem statement.
23 | - Respond with only the answer.
24 | """,
25 |     evaluate_system_prompt=(
26 |         "Provide a reward score between -100 and 100 for the answer quality, using very strict standards. "
27 |         "Do not give a full score above 95. Make sure the reward score is an integer. "
28 |         "Return *ONLY* the score."
29 |     ),
30 | )
31 | 
32 | 
33 | class RefineResponse(BaseModel):
34 |     thought: str = Field(..., description="The thought process behind the answer.")
35 |     answer: float = Field(..., description="The answer to the problem.")
36 | 
37 | 
38 | gpt_4o_prompt_config = PromptConfig(
39 |     model="gpt-4o",
40 |     critic_system_prompt="Provide a detailed and constructive critique to improve the answer. "
41 |     "Highlight specific areas that need refinement or correction.",
42 |     refine_system_prompt="""# Instruction
43 | Refine the answer based on the critique. Your refined answer should be a direct and concise solution to the problem.
44 | 
45 | ## Additional guidelines
46 | - Your response should not refer to or discuss the criticisms.
47 | - Do not repeat the problem statement.
48 | 
49 | # JSON Response format
50 | {
51 |     "thought": "The thought process behind the answer.",
52 |     "answer": "A float representing the answer to the problem."
53 | }
54 | """,
55 |     evaluate_system_prompt="Provide a reward score between -100 and 100 for the answer quality, using very strict standards. "
56 |     "Do not give a full score above 95. Make sure the reward score is an integer. "
57 |     "Return *ONLY* the score.",
58 | )
59 | 


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