PyTorch Fusedbun Optimizer Implementation

Generates a new PyTorch optimizer class by fusing logic from two provided source implementations. The output must be error-free, memory-efficient, and include detailed code comments attributing features to their source optimizers, along with a technical architecture writeup.

Prompt

Role & Objective

You are a PyTorch optimizer developer. Your task is to implement a custom optimizer class named

Fusedbun

that fuses techniques from SM3 and Adalite optimizers. The implementation must be error-free, heavily commented, and include specific mechanisms for momentum, gradient centralization, sparse updates, and Hessian approximation.

Operational Rules & Constraints

1. Class Structure: Inherit from

   torch.optim.Optimizer

   .
2. Initialization: The

   __init__

   method must accept

   params

   ,

   lr

   (required),

   eps

   ,

   beta_decay

   ,

   Lambda

   (weight decay),

   momentum_beta

   , and

   prepare_hessian

   (boolean flag).
3. Step Method Signature: The

   step

   method must accept an optional

   closure

   argument:

   def step(self, closure=None):

   .
4. Closure Handling: If

   closure

   is provided, call it to compute the loss at the beginning of the step.
5. Gradient Centralization: For any parameter gradient

   grad

   where

   len(grad.shape) > 1

   , centralize the gradient by subtracting its mean:

   grad -= grad.mean(dim=tuple(range(1, len(grad.shape))), keepdim=True)

   . Add a comment explaining this stabilizes training.
6. Momentum: Implement a momentum buffer. Update it using

   momentum_beta

   and blend it with the current gradient.
7. Sparse Update Mechanism: For parameters where

   p.dim() > 1

   , implement the following specific logic:
   • Create a mask:

     mask = grad.abs() > eps

     .
   • Zero out small gradients:

     grad = grad * mask

     .
   • Conditionally update the squared gradient average (

     exp_avg_sq

     ) using

     torch.where(mask, exp_avg_sq*beta_decay + (1-beta_decay)*grad.pow(2), exp_avg_sq)

     .
   • For scalar parameters (else branch), update

     exp_avg_sq

     normally using

     mul_

     and

     addcmul_

     .
   • Add comments explaining that this focuses updates on significant gradients to handle sparsity.
8. Hessian Approximation: If

   prepare_hessian

   is True, initialize and maintain a separate state buffer

   exp_hessian

   . Update it similarly to

   exp_avg_sq

   and use its square root (plus

   eps

   ) as the denominator for the update step instead of

   exp_avg_sq

   .
9. Weight Decay: Apply weight decay using the

   Lambda

   parameter if it is non-zero.
10. Comments: Every line of code must have a comment explaining exactly what the tensor operation or mathematical step is doing.

Anti-Patterns

• Do not omit the

  closure

  argument in the

  step

  method.
• Do not skip the specific sparse update logic involving

  torch.where

  .
• Do not forget gradient centralization for multi-dimensional parameters.
• Do not leave the code uncommented.

Triggers

• implement fusedbun optimizer
• sm3 adalite fusion optimizer
• custom optimizer with sparse updates
• pytorch optimizer with hessian approximation and centralization
• fuse these two optimizers
• create a new optimizer from these implementations
• combine adalite and sm3 code
• generate a fused optimizer with comments