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tsrikant/vce-specialist-math-7b-gguf

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Model Card

VCE Specialist Mathematics 7B (GGUF — Q4KM)

Fine-tuned version of Qwen2.5-Math-7B-Instruct specialized for the Victorian Certificate of Education (VCE) Specialist Mathematics Study Design.

Trained using Unsloth QLoRA on an NVIDIA RTX 4090 over 500 curated, multi-part curriculum examination items spanning Tech-Free (Exam 1) and Tech-Active (Exam 2) standards.

Model Capabilities

  1. 1.✍️ [MODE: AUTHOR] — Authentic Exam Synthesis:
  2. 2.Authors multi-part Extended Response questions (Parts $a, b, c, d$) and Short Answer questions.
  3. 3.Generates authentic diagnostic multiple-choice distractors targeting common student misconceptions (e.g. sign errors, missing chain rule factors, incorrect integration limits).
  4. 4.Accurately balances mark allocations conforming to VCAA standards.
  1. 1.🧠 [MODE: SOLVER] — Step-by-Step VCAA Proofs:
  2. 2.Solves calculus, kinematics/mechanics, complex numbers, and vector problems step-by-step.
  3. 3.Explicitly annotates official VCAA marking criteria: Method marks (M1), Answer marks (A1), and Consequential marks.

Quickstart with Ollama

Option A: Direct Run

bash
ollama run hf.co/tsrikant/vce-specialist-math-7b-gguf:Q4_K_M
Note: For mathematical reasoning, keep temperature at 0.6 (do not use high temperatures like 1.0+ which induce algebraic hallucinations).

Option B: Custom Modelfile (Recommended for Local Studio)

Create a file named Modelfile:

dockerfile
FROM hf.co/tsrikant/vce-specialist-math-7b-gguf:Q4_K_M

SYSTEM """You are an expert VCE Specialist Mathematics educator and examination author adhering strictly to the Victorian Curriculum and Assessment Authority (VCAA) Study Design. Provide exact mathematical proofs, official method marks (M1, A1), and authentic diagnostic distractors."""

PARAMETER temperature 0.6
PARAMETER top_p 0.95
PARAMETER min_p 0.05
PARAMETER stop "<|im_end|>"
PARAMETER stop "<|endoftext|>"

Build and run:

bash
ollama create vce-specialist-math -f Modelfile
ollama run vce-specialist-math

Prompt Formats & Examples

The model is fine-tuned to recognize structured instruction headers:

1. Authoring Exam Questions ([MODE: AUTHOR])

text
[MODE: AUTHOR]
Topic: Differential Equations
Type: Extended Response
Difficulty: Exam 1 (Tech-Free)
Target Marks: 4 marks
Prompt: A 2 kg body moves along the x-axis subject to resistive force F = -4v.

Sample Output:

Question: A 2 kg particle moves along the $x$-axis subject to a resistive force $F = -4v$ N, where $v$ is its velocity in m/s. At $t = 0$, $x = 0$ and $v = 10$ m/s. a. Show that $v = 10e^{-2t}$. [2 marks] b. Find the distance traveled by the particle before coming to rest. [2 marks] Total: 4 marks

2. Solving with VCAA Method Marks ([MODE: SOLVER])

text
[MODE: SOLVER]
Evaluate the definite integral \int_0^1 \frac{x}{x^2 + 1} \, dx with VCAA method marks (M1, A1).

Sample Output:

To evaluate $\int0^1 \frac{x}{x^2 + 1} \, dx$: Notice that $\frac{d}{dx}(x^2 + 1) = 2x$. Rewrite the integrand: $$\int0^1 \frac{x}{x^2 + 1} \, dx = \frac{1}{2} \int0^1 \frac{2x}{x^2 + 1} \, dx \quad \textbf{(M1)}$$ Integrating gives: $$= \frac{1}{2} \left[ \ln(x^2 + 1) \right]0^1 \quad \textbf{(M1)}$$ Substitute upper and lower limits: $$= \frac{1}{2} (\ln 2 - \ln 1) = \frac{1}{2} \ln 2 \quad \textbf{(A1)}$$

Usage in LM Studio / llama.cpp

  1. 1.Download `qwen2.5-math-7b-instruct.Q4_K_M.gguf` (4.4 GB).
  2. 2.Load into LM Studio or run with llama-cli:
bash
llama-cli -m qwen2.5-math-7b-instruct.Q4_K_M.gguf \
  --temp 0.6 \
  -p "<|im_start|>system\nYou are an expert VCE Specialist Mathematics educator adhering to VCAA standards.<|im_end|>\n<|im_start|>user\n[MODE: SOLVER]\nFind the vector projection of a = 2i - j + 3k onto b = i + 2j - k.<|im_end|>\n<|im_start|>assistant\n"

Training Details

  • —Base Model: Qwen/Qwen2.5-Math-7B-Instruct
  • —Fine-Tuning Method: QLoRA (Rank 32, Alpha 64, Target: all linear layers)
  • —Dataset: 500 curated VCE Specialist Mathematics questions spanning:
  • —Functions, Relations & Graphs
  • —Complex Numbers
  • —Calculus (Differential & Integral)
  • —Differential Equations & Kinematics
  • —Vectors in 2D and 3D
  • —Mechanics (Forces, Equilibrium, Newton's Laws)
  • —Probability & Statistics
  • —Epochs: 3 (162 optimization steps)
  • —Training Loss: $1.0302 \rightarrow 0.4533$
  • —Validation Loss: $0.8630 \rightarrow 0.4751$ ($PPL \approx 1.608$)
  • —Quantization: GGUF Q4_K_M (4-bit Medium K-quant, 4.4 GB)
  • —Inference Speed: ~55–57 tokens/sec on Apple M-Series Silicon
  • —Associated LoRA Weights: tsrikant/vce-specialist-math-7b-lora