Many programs do not compute their output by applying a fixed sequence of explicit operations. Instead, they define the output as the solution of another problem.
| Section | Title |
|---|---|
| 1 | Chapter 18. Advanced Topics |
| 2 | Differentiating Through Solvers |
| 3 | Differentiable Optimization Layers |
| 4 | Continuous-Time Adjoint Methods |
| 5 | Neural ODEs |
| 6 | Probabilistic Automatic Differentiation |
| 7 | Quantum Differentiation |
| 8 | Differentiable Programming Languages |
| 9 | Verified Differentiation |
| 10 | Unified Differentiable Infrastructure |
Chapter 18. Advanced TopicsMany programs do not compute their output by applying a fixed sequence of explicit operations. Instead, they define the output as the solution of another problem.
Differentiating Through SolversA solver is a program that computes a value by search, iteration, or factorization. Instead of evaluating a closed-form expression, it finds a value that satisfies a condition.
Differentiable Optimization LayersAn optimization layer is a program component whose output is the solution of an optimization problem. Instead of computing
Continuous-Time Adjoint MethodsMany systems evolve continuously over time rather than through discrete layers. A state variable changes according to a differential equation:
Neural ODEsClassical neural networks apply a finite sequence of transformations:
Probabilistic Automatic DifferentiationClassical automatic differentiation computes derivatives of deterministic programs.
Quantum DifferentiationQuantum computation introduces a computational model fundamentally different from classical programs.
Differentiable Programming LanguagesAutomatic differentiation began as a transformation applied to numerical programs. A differentiable programming language instead treats differentiation as a native semantic...
Verified DifferentiationAutomatic differentiation systems are usually trusted because they implement mathematically established rules such as the chain rule, product rule, and linearization of...
Unified Differentiable InfrastructureAutomatic differentiation began as a numerical technique for computing gradients of scalar functions.