Can you provide examples of efficient batch processing in JAX

1. Mini-Batch Processing**

Mini-batch processing involves dividing the training data into smaller subsets for more efficient training. Here's a basic implementation using JAX:

python
import jax
import jax.numpy as jnp
from jax import random, grad, jit

def create_batches(data, batch_size):
    num_samples = len(data)
    indices = jnp.arange(num_samples)
    key = random.PRNGKey(0)
    shuffled_indices = random.permutation(key, indices)
    return jnp.array_split(data[shuffled_indices], num_samples // batch_size)

def batch_forward_pass(params, batch):
    W, b = params
    return jnp.dot(batch, W) + b

batch_size = 32
learning_rate = 0.01

@jit
def update_params(params, batch, targets):
    loss_fn = lambda p: jnp.mean((batch_forward_pass(p, batch) - targets)  2)
    grads = grad(loss_fn)(params)
    return [(w - learning_rate * dw) for w, dw in zip(params, grads)]

2. Dynamic Batch Sizing**

Dynamic batch sizing adapts the batch size during training to optimize performance and memory usage:

python
def dynamic_batch_size(data_size, memory_limit, compute_memory_usage):
    initial_batch_size = 32
    while initial_batch_size > 1:
        memory_required = compute_memory_usage(initial_batch_size)
        if memory_required = num_accumulation_steps:
            break
        batch_grads = compute_batch_gradient(params, batch)
        accumulated_grads = [acc + bg for acc, bg in zip(accumulated_grads, batch_grads)]
    return [(acc / num_accumulation_steps) for acc in accumulated_grads]

These examples demonstrate how JAX optimizes batch processing for efficient machine learning computations.