Fixing JAX TypeError In Distributed Training With Slogdet
Dealing with complex JAX operations, especially within distributed training setups, can sometimes lead to rather cryptic errors. One such hurdle that developers might encounter is the TypeError: ShapedArray with Sharding ({V:data}) invalid in fori_loop backward pass (shard_map + slogdet). This error, while seemingly intimidating, points to a specific interaction between JAX's automatic differentiation (AD) system, distributed computing (jax.shard_map), and a particular linear algebra function (jnp.linalg.slogdet) when computing higher-order derivatives. Let's unpack this issue, explore its root causes, and discuss how to navigate it.
Understanding the Error: TypeError: ShapedArray with Sharding ({V:data}) invalid in fori_loop backward pass
At its core, this TypeError signifies that JAX's AD system encountered an unexpected data structure – a ShapedArray with specific sharding information – during the backward pass of a fori_loop. This often arises when you're trying to compute gradients of gradients (or even higher orders), a process essential for tasks like Laplacian or Hessian calculations, particularly when leveraging libraries like folx for efficiency. The error message itself provides crucial clues: invalid in fori_loop backward pass. This tells us the problem isn't in the forward computation but specifically during the gradient calculation within a loop structure.
When JAX computes gradients, it essentially reverses the operations of the forward pass. This involves a complex dance of JAX's internal transformations, including pjit (parallel jit) for distributed computations and ad (automatic differentiation) for gradient calculations. The shard_map function is a powerful tool for distributing computations across multiple devices, ensuring that your data and computations are efficiently spread. However, certain operations, especially those that are not straightforwardly invertible or have complex derivative rules, can cause friction within this distributed AD framework. The slogdet function, which computes the sign and logarithm of the determinant of a matrix, involves operations like matrix inversion and trace, which can be intricate to handle correctly in the reverse mode of differentiation, particularly in a sharded context.
The Role of jnp.linalg.slogdet
The jnp.linalg.slogdet function returns two values: the sign of the determinant and its logarithm. The logarithm is often preferred over the raw determinant to avoid numerical underflow or overflow issues with very large or very small determinants. Mathematically, the derivative of log|det(A)| with respect to A involves the inverse of A and its trace. When JAX needs to compute the gradient of a function that uses slogdet, it needs to compute the gradient of these inverse and trace operations. In a distributed setting, where A might be sharded across multiple devices, computing its inverse and then its trace in a way that is compatible with the automatic differentiation and sharding rules becomes a significant challenge. The TypeError suggests that JAX's AD machinery, specifically during the backward_pass3 and subsequent linear_transpose2 calls, fails to properly reconstruct or handle the ShapedArray with its associated sharding information when dealing with the results of slogdet's transpose rule.
Higher-Order Derivatives and folx
The problem is exacerbated when you're dealing with higher-order derivatives. Libraries like folx are designed to efficiently compute forward-mode Laplacian operators, which can be thought of as a
