Modern ML methods for derivatives sit at a delicate interface between market prices, implied-volatility (IV) surfaces, and the simulated environments produced by market generators. To date, these models have largely operated in one of two coordinate systems: price space, where markets quote and no-arbitrage constraints are most naturally enforced, and IV space, where surfaces are smoothed, regularized, and evaluated. This talk presents a technique that unifies learning across both coordinates — using gradients from each via a differentiable Jäckel operator and a low-vega gating mechanism — enabling end-to-end batch training without the error-prone, expensive, hand-engineered filtering usually needed to discard incompatible IV values. I will present PIVOT (Price-Implied Volatility Operator Transform), a differentiable Jäckel IV operator that preserves the accuracy of the standard "Let's Be Rational" (LBR) solver in the forward pass while supplying implicit gradients through the Black–Scholes/Black-76 price map. This gives neural volatility-surface models a principled bridge between price-space and IV-space objectives, with explicit handling of the low-vega singular regime. Second, I will  present Fast-Vollib ( https://pypi.org/project/fast-vollib/), a CUDA-accelerated option-pricing library with NumPy, PyTorch, and JAX interfaces, built for high-throughput pricing-label generation in AI/ML batch training.