Eval 02: Autodiff vs Calculus

Validates that PyTorch autodiff computes correct scores and Hessians by comparing against closed-form calculus formulas.

Configuration

Parameter	Value
Seed	42
Trials	20
Families	12

Results

Part 1: Oracle Comparison (7 families with closed-form)

Family	Score Error	Hessian Error	Status
linear	0.00e+00	0.00e+00	PASS
logit	1.67e-16	1.11e-16	PASS
poisson	1.74e-09	2.57e-09	PASS
gamma	2.22e-16	4.44e-16	PASS
gumbel	1.11e-16	2.22e-16	PASS
weibull	8.88e-16	7.11e-15	PASS
negbin	3.33e-16	5.55e-16	PASS

Result: 7/7 PASS

Part 2: Autodiff-Only (5 families without closed-form)

Family	Gradient Norm	Hessian Symmetry	Status
tobit	✓	✓	PASS
gaussian	✓	✓	PASS
probit	✓	✓	PASS
beta	✓	✓	PASS
zip	✓	✓	PASS

Result: 5/5 PASS

Part 3: Fitted θ̂ (7 families)

Tests autodiff on neural network outputs (not just oracle θ*).

Result: 7/7 PASS

Part 4: Package Integration (12 families)

Tests the full family.gradient() and family.hessian() methods.

Result: 12/12 PASS

Summary

Part	Tests	Result
Oracle Comparison	7	7/7 PASS
Autodiff-Only	5	5/5 PASS
Fitted θ̂	7	7/7 PASS
Package Integration	12	12/12 PASS
Total	31	31/31 PASS

Key Findings

• Autodiff matches calculus to machine precision (< 1e-14)

• Hessians are symmetric as expected

• Works on both oracle θ* and fitted θ̂

Run Command

python3 -m evals.eval_02_autodiff 2>&1 | tee evals/reports/eval_02_$(date +%Y%m%d_%H%M%S).txt