ankit-pn/gemma4-calculus-differentiation

Gemma 4 Calculus Differentiation (synthetic, symbolic)

A frozen synthetic dataset for single-variable differentiation in SymPy syntax, generated with sympy 1.14 using a fixed seed. It was built for a controlled supervised fine-tuning learning curve on Gemma 4 E2B — see GitHub and the resulting LoRA adapter.

Splits

Split	Rows	Description
train	4,096	Five families, unique expressions
validation	200	Same families, 40 per family
test	240	160 same families + 80 product × trig × chain composites absent from train/validation

Every split has a SHA-256 hash frozen in the generator manifest; all expressions are unique across the dataset.

Fields

{
  "family": "product",
  "expression": "(2*x - 4)*(9*x**4 - 8)",
  "question": "Differentiate f(x) = (2*x - 4)*(9*x**4 - 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.",
  "answer": "(2*x - 4)*(36*x**3) + 9*x**4*(2) - 8*(2)"
}

• family: polynomial, product, power_chain, trig_chain, rational, or product_trig_chain (test only)
• answer: symbolic derivative in SymPy syntax; graded by equivalence, not string match
• Terms are non-zero integers in [-9, 9]; powers up to 6

Generation

import sympy as sp
sp.sstr(sp.diff(sp.sympify(row["expression"]), sp.Symbol("x")))

The exact generator (generate.py) and grader (evaluate.py) are in the GitHub repository. The structural hold-out (product_trig_chain) tests whether the product and chain rules transfer to a composition the model never saw in training. In the reference experiment the fine-tuned adapter improved every trained family but regressed on this hold-out (14/80 base → 5/80 adapter), a clear negative-transfer signal — the split is doing its job.

Intended use

• Small-scale SFT experiments and evaluation of symbolic differentiation
• The test split should be evaluated once, after any model selection, to keep it meaningful

Limitations

• Synthetic and narrow: no exponentials, logarithms, inverse trig, multivariable, or higher-order derivatives
• Base models may have seen similar textbook derivatives during pretraining; this dataset measures task adaptation on a fresh distribution, not calculus acquisition
• English prompts only

License

Apache-2.0