Gradients are Not All You Need
This addresses a fundamental limitation in differentiable programming for practitioners in machine learning and numerical simulation, though it is incremental as it builds on known issues.
The paper identifies a chaos-based failure mode in differentiable programming that affects various applications like recurrent neural networks and learned optimizers, linking it to the Jacobian spectrum and providing criteria for when it disrupts optimization.
Differentiable programming techniques are widely used in the community and are responsible for the machine learning renaissance of the past several decades. While these methods are powerful, they have limits. In this short report, we discuss a common chaos based failure mode which appears in a variety of differentiable circumstances, ranging from recurrent neural networks and numerical physics simulation to training learned optimizers. We trace this failure to the spectrum of the Jacobian of the system under study, and provide criteria for when a practitioner might expect this failure to spoil their differentiation based optimization algorithms.