Chapter 17. Numerical and Systems Concerns

Automatic differentiation computes derivatives by executing arithmetic. On a real machine, arithmetic uses finite precision. This means AD gives the derivative of the...

9 items

Section	Title
1	Chapter 17. Numerical and Systems Concerns
2	Stability of Reverse Mode
3	Overflow and Underflow
4	Memory Explosion
5	Gradient Vanishing and Explosion
6	Determinism and Reproducibility
7	Parallelism
8	GPU and TPU Execution
9	Distributed Gradient Computation

Writes › Book › Auto Diff › Chapter 17. Numerical and Systems Concerns ›

Chapter 17. Numerical and Systems Concerns

Automatic differentiation computes derivatives by executing arithmetic. On a real machine, arithmetic uses finite precision. This means AD gives the derivative of the...

Writes › Book › Auto Diff › Chapter 17. Numerical and Systems Concerns ›

Stability of Reverse Mode

Reverse mode automatic differentiation computes gradients by propagating adjoint values backward through a computational graph. In exact arithmetic, the reverse accumulation...

Writes › Book › Auto Diff › Chapter 17. Numerical and Systems Concerns ›

Overflow and Underflow

Floating point systems represent numbers within a finite range. When a computed value exceeds the largest representable magnitude, overflow occurs. When a value becomes too...

Writes › Book › Auto Diff › Chapter 17. Numerical and Systems Concerns ›

Memory Explosion

Reverse-mode automatic differentiation trades computation for memory. To compute gradients efficiently, the backward pass requires access to intermediate values produced...

Writes › Book › Auto Diff › Chapter 17. Numerical and Systems Concerns ›

Gradient Vanishing and Explosion

Gradient-based optimization relies on propagating derivative information through many layers, time steps, or computational transformations. In deep systems, these gradients...

Writes › Book › Auto Diff › Chapter 17. Numerical and Systems Concerns ›

Determinism and Reproducibility

Automatic differentiation systems are often assumed to be deterministic. Given identical inputs, identical parameters, and identical code, many users expect identical...

Writes › Book › Auto Diff › Chapter 17. Numerical and Systems Concerns ›

Parallelism

Automatic differentiation is usually described as a transformation of programs or computational graphs. In real systems, it is also a parallel execution problem. Large...

Writes › Book › Auto Diff › Chapter 17. Numerical and Systems Concerns ›

GPU and TPU Execution

Modern automatic differentiation systems are built around accelerator hardware. GPUs and TPUs provide enormous throughput for tensor operations, making large-scale...

Writes › Book › Auto Diff › Chapter 17. Numerical and Systems Concerns ›

Distributed Gradient Computation

Distributed gradient computation appears when a differentiable program no longer fits comfortably on one device or one machine. The reason may be model size, data volume,...