Qwen2.5-Math-1.5B-HigherMath

A GGUF (Q4_K_M) fine-tune of Qwen2.5-Math-1.5B-Instruct that makes the model follow one output convention: step-by-step reasoning, LaTeX for math, final answer inside \boxed{} — on university-style problems in calculus, linear algebra, ODEs, series and probability.

TL;DR

  • What it does: produces consistently formatted, step-by-step LaTeX solutions instead of free-form prose. Runs on CPU in ~0.9 GB.
  • What the evidence shows: the reported accuracies (98.50% → 99.50%, n = 200, University Math-200) come from a single-run, non-paired evaluation. The 95% confidence intervals overlap, so the difference is not statistically established and is not claimed as a result.
  • What it does not do: no tools, no Python, no calculator. Not a general assistant or a coding model, and not a benchmark-topping math model.

Quick start

# 1. Download the GGUF from this repo, then:
ollama create qwen-math-higher-math -f Modelfile
ollama run qwen-math-higher-math

Modelfile — the context and output limits matter more than they look:

FROM ./qwen-math-q4_k_m.gguf
PARAMETER temperature 0
PARAMETER num_ctx 8192       # 4096 truncates long chain-of-thought solutions
PARAMETER num_predict 4096   # higher-math solutions routinely exceed 2048 tokens
PARAMETER stop "<|im_end|>"
PARAMETER stop "<|endoftext|>"

Always send the system prompt — without it the format discipline degrades:

Please reason step by step.
Use LaTeX for mathematical expressions.
Do not use Python, a calculator, or any external tools.
Put your final answer inside \boxed{}.

Problem:
{problem}

Python:

from ollama import chat

SYSTEM = (
    "Please reason step by step. Use LaTeX for mathematical expressions. "
    "Do not use Python, a calculator, or any external tools. "
    "Put your final answer inside \\boxed{}."
)

resp = chat(
    model="qwen-math-higher-math",
    messages=[{"role": "system", "content": SYSTEM},
              {"role": "user", "content": "Find the derivative of f(x) = x^3 ln(x)."}],
    options={"temperature": 0, "num_predict": 4096, "num_ctx": 8192, "seed": 0},
)
print(resp["message"]["content"])

Parsing the answer: take the last \boxed{...} with balanced-brace matching, then compare with math-verify — string comparison alone marks correct answers wrong (1/2 vs \frac{1}{2}).


Intended use

Suitable for:

  • university-level problem solving where a written derivation matters as much as the answer;
  • limits, derivatives, single and multiple integrals, series and convergence tests;
  • first- and second-order ODEs;
  • matrices, determinants, eigenvalues;
  • probability, Bayes' theorem, combinatorics;
  • producing LaTeX derivations for notes, tutoring material, dataset generation.

Not suitable for: PDEs, measure theory, topology, complex analysis beyond the basics — the fine-tuning data does not cover them; general chat, coding, tool use; any setting where an unverified answer is acted upon without checking.


Model details

Training configuration (fine-tuning method, learning rate, schedule, epochs, hardware and wall time) was not recorded for this release. Only the final GGUF is published. Reproducing the exact fine-tune from this card is therefore not possible; it is listed as a known gap.

Property Value
Base model Qwen/Qwen2.5-Math-1.5B-Instruct (Apache-2.0)
Parameters 1.5B
Architecture Qwen2, chat template included
Fine-tuning data 1,500 filtered examples from AI-MO/NuminaMath-CoT (Apache-2.0)
Quantization shipped GGUF Q4_K_M, 986 MB
Inference mode chain-of-thought only; no tool use, Python or calculator
License Apache-2.0 (inherited from base model and dataset)

Evaluation

Decoding was greedy (temperature = 0), one generation per problem, pass@1; answers are extracted from the last \boxed{} and compared with math-verify. The two models were scored in separate, non-paired runs, and the exact run settings of each (in particular the quantization used for the baseline) are not documented in this release. The intervals below are Wilson intervals for each accuracy separately; no p-value for a difference can be computed, and none is reported.

Results

Single-run evaluation (separate runs, not paired — no p-value can be computed):

Benchmark n Base correct Fine-tune correct Δ
University Math-200 200 197/200 (98.50%, 95% CI 95.68%–99.49%) 199/200 (99.50%, 95% CI 97.22%–99.91%) +1.00 p.p.
MATH-500 500 373/500 (74.60%, 95% CI 70.61%–78.22%) 368/500 (73.60%, 95% CI 69.57%–77.27%) -1.00 p.p.
GSM8K-100 100 86/100 (86.00%, 95% CI 77.86%–91.47%) 82/100 (82.00%, 95% CI 73.33%–88.30%) -4.00 p.p.

Why the single-run numbers cannot be used as a result: the two models were scored in separate runs without a paired design, so the reported difference mixes model behaviour with run-to-run variation and has no confidence interval or p-value attached. With n of this size, differences of a few percentage points are well inside noise — note that the 95% intervals above overlap. No accuracy advantage is claimed for this fine-tune.

Format compliance

Format compliance is not measured in this release. The fine-tune targets this property, so it is the first thing a future evaluation should quantify: count the share of generations from which a \boxed{} answer can be extracted, separately from answer correctness.

About University Math-200

This is a custom set of problems, written for this project. It is not the official CollegeMath benchmark and it is not difficulty-calibrated against a public standard. The base model already solves 98.50% of it, which means the set is near-saturated: it works as a regression and format-discipline check, and it cannot demonstrate a specialization. A harder, externally sourced evaluation is the next step and is not in this release.

Topic composition: not documented in this release.

Contamination check

Not measured in this release. The fine-tuning data and the evaluation sets come from the same external corpus (NuminaMath-CoT and its sources), so overlap is plausible and the numbers above should be read with that caveat.

Qualitative difference: base vs fine-tune

Not quantified in this release. The fine-tune's stated target is the output convention — step-by-step derivation, LaTeX throughout, final answer inside \boxed{} — and that is the property a follow-up evaluation should measure directly, separately from answer correctness.

Known failure modes

  1. Drops the box on hard problems. When the derivation is long, the model sometimes finishes in prose ("…therefore the answer is 8") with no \boxed{}. Treat a missing box as a signal to re-ask, not as a wrong answer.
  2. Confidently wrong on unfamiliar topics. Outside the training distribution it produces fluent, structured derivations with an incorrect final answer.
  3. Arithmetic slips in long substitutions. Multi-step integration by parts and large matrix reductions occasionally lose a sign or a factor.
  4. Truncation. At num_predict 2048, an unreported share of solutions are cut mid-derivation — use num_predict 4096.

Performance

Not benchmarked in this release. Verified figure: size on disk, 986 MB (Q4_K_M). The model runs in Ollama on CPU.


Limitations

  • 1,500 training examples shape format and style, not mathematical capability. Gains in correctness at this data scale are not expected, and none have been demonstrated by the evaluation above.
  • Specialized: general conversation, coding and tool use degrade.
  • No tool use / code execution — arithmetic errors are possible and not self-corrected.
  • Long chain-of-thought needs num_ctx ≥ 8192; smaller contexts truncate solutions.
  • The fine-tune was evaluated in Q4_K_M; the baseline's quantization is not documented, and bf16 results are not reported. Quantization affects a 1.5B model more than a 7B+ one, so these figures may differ by a few points from a bf16 run.
  • The base model is designed for tool-integrated reasoning (TIR) with Python. Removing tool use lowers MATH-style scores by design, so these numbers are not comparable to published TIR results for Qwen2.5-Math-1.5B-Instruct.
  • Evaluation is pass@1 only; maj@k / self-consistency is not reported.
  • Not a substitute for checking the answer. The model produces plausible but wrong reasoning on unfamiliar problems.

Training data

1,500 problems selected from AI-MO/NuminaMath-CoT, filtered toward:

  • limits and continuity, differentiation rules;
  • definite, indefinite, improper and multiple integrals;
  • series and convergence tests;
  • first- and second-order ODEs;
  • matrices, determinants, eigenvalues;
  • probability, Bayes' theorem, combinatorics.

Chain-of-thought solutions only; no tool-integrated reasoning (no Python calls, no calculator traces) in the training data.


Reproduction

Property Value
Quantization GGUF Q4_K_M
Model size on disk 986 MB
Runtime Ollama on CPU
GGUF SHA256 not published
llama.cpp commit not recorded
Ollama version not recorded
Evaluation date not recorded

Citation

The underlying model and dataset:

@article{qwen2.5math,
  title   = {Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement},
  author  = {Qwen Team},
  journal = {arXiv preprint arXiv:2409.12122},
  year    = {2024}
}

@misc{numina,
  title        = {NuminaMath},
  author       = {AI-MO},
  howpublished = {\url{https://huggingface.co/datasets/AI-MO/NuminaMath-CoT}},
  year         = {2024}
}

This fine-tune:

@misc{U-Ug1kn_highermath_2026,
  title  = {Qwen2.5-Math-1.5B-HigherMath: a format-specialized GGUF fine-tune},
  author = {U-Ug1kn},
  year   = {2026},
  note   = {Fine-tune of Qwen2.5-Math-1.5B-Instruct on 1,500 NuminaMath-CoT examples},
  url    = {https://huggingface.co/U-Ug1kn/Qwen2.5-Math-1.5B-HigherMath}
}

Changelog

  • 2026-11-09 — card rewritten: evaluation now reported with confidence intervals and explicitly labelled as single-run (no paired test is claimed); contamination status and training provenance are stated as not recorded rather than omitted.
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