Quark

Quark is a 9B reasoning model for physics, science and maths, built by FirstPrinciples. The base model is Qwen3.5-9B with additional post-training: supervised fine-tuning on our curated physics, maths and coding mix.

It outperforms the base model on a range of benchmarks, and reaches graduate-level science scores comparable to much larger open models. An 8-bit (Q8_0) version, FirstPrinciples/quark-q8, is about half the size and matches bf16 on every benchmark below.

Quark is the first in a series of small, powerful scientific reasoning models. You can run it locally (see Usage) or on Theo Platform, a research platform for complex problems, where you can use it alongside other frontier models, check its results with Python, Mathematica and Sage, and keep each session as a research graph you can revise one step at a time.

Results

Accuracy (%), measured with EvalScope: thinking mode, up to 131,072 output tokens, and following the Qwen3.5 model card’s sampling settings. AIME 2025 is averaged over 16 samples per problem and GPQA Diamond over 8. HLE (text-only, 2,158 questions) is graded by Qwen3.5-27B as judge.

All were measured by us with the same setup.

Compared with other open models (scores as reported by each developer):

— = not reported. Sources: each model’s official model card; Quark (bf16) and its Q8_0 version measured by us (see above)

¹ Not reported by Qwen; measured by Artificial Analysis (reasoning mode, 2,158 text-only HLE questions).

Training data

Quark was fine-tuned on our curated mix of about 200,000 physics, science, maths and coding problems, each with a worked solution written by Qwen3.8-Flash-Next. Solutions were filtered by rejection sampling, keeping only correct ones. Duplicate questions were removed, and so was any question that shares at least half of a benchmark question’s word 13-grams (after lower-casing and keeping only letters and digits). We checked against the full GPQA Diamond, AIME 2025, MATH-500, MMLU-Pro, SuperGPQA and HLE (text-only) sets.

Usage

ollama run FirstPrinciples/quark

The recommended sampling settings and a 131,072-token context are built in. We recommend keeping the full 131,072 tokens: hard problems need long answers, and shorter limits cut them off.

The bf16 model does not fit on a 16 GB Mac. Use quark-q8 there, and lower the context inside the chat with /set parameter num_ctx 32768 (longer answers are then cut off); at 131,072 tokens it needs about 15 GB of GPU memory.

Thinking is on by default. Turn it off with /set nothink in the chat, or "think": false in the API. Ollama also serves an OpenAI-compatible API at http://localhost:11434/v1.

Recommended sampling (from the Qwen3.5 model card; the thinking settings are the defaults):

Example

A hard problem from AIME 2025 (II, problem 15), in thinking mode with the recommended sampling settings:

Let f(x) = (x − 18)(x − 72)(x − 98)(x − k) / x. There exist exactly three positive real values of k such that f has a minimum at exactly two real values of x. Find the sum of these three values of k.

How Quark solves it (summarised from its answer):

1. If the minimum value m is reached at two points u and v, the numerator minus mx must be a perfect square: (x − 18)(x − 72)(x − 98)(x − k) − mx = (x − u)²(x − v)²
2. Matching coefficients and eliminating u and v leaves one equation in k: (k² − 376k − 5120)² = 8128512·k
3. It factors as (k − 8)(k − 32)(k − 200)(k − 512) = 0, and checking the sign before squaring rules out k = 512.
4. So k = 8, 32, 200, and the answer is 240.

Both models’ full written answers are on the Hugging Face model card.

Limitations

• Needs a long output budget. At a 32K-token limit about 20% of GPQA answers are cut off and GPQA drops to 74.9, below the base model.
• Non-thinking mode is slightly weaker than the base model (AIME 56.7 vs 59.8, GPQA 76.8 vs 79.6).
• Specialised: trained only on single-turn science, maths and code questions; not trained for conversation, tool use, images or safety beyond what Qwen3.5-9B already has.

License

Apache 2.0