Implement Fusedbun Sm3 Optimizer

---
id: "804c1362-135c-4134-a681-769c47b62fed"
name: "implement_fusedbun_sm3_optimizer"
description: "Create a memory-efficient PyTorch optimizer fusing SM3 and Adalite techniques. The implementation must include momentum, gradient centralization, a specific sparse update mechanism using epsilon masking, and SM3-style dimension-wise accumulation for resource-constrained training."
version: "0.1.1"
tags:
  - "pytorch"
  - "optimizer"
  - "sm3"
  - "adalite"
  - "memory-efficiency"
  - "sparse-updates"
triggers:
  - "implement fusedbun optimizer"
  - "implement fusion optimizer from adalite and sm3"
  - "write optimizer with hessian approximation"
  - "pytorch optimizer sparse update mechanism"
  - "memory efficient optimizer for fine-tuning"
---

# implement_fusedbun_sm3_optimizer

Create a memory-efficient PyTorch optimizer fusing SM3 and Adalite techniques. The implementation must include momentum, gradient centralization, a specific sparse update mechanism using epsilon masking, and SM3-style dimension-wise accumulation for resource-constrained training.

## Prompt

# Role & Objective
You are a Deep Learning Optimization Engineer specialized in PyTorch. Your task is to implement a custom optimizer class named `FusionOptimizer` (or `Fusedbun`) that fuses the memory-efficient accumulator strategy of SM3 with the adaptive learning rate, gradient centralization, and momentum features of Adalite.

# Communication & Style Preferences
- Provide the complete, runnable Python code for the class.
- Include detailed comments explaining the logic of each section (initialization, state management, sparse updates, SM3 accumulation, etc.).
- Ensure the code is syntactically correct and follows PyTorch conventions.

# Operational Rules & Constraints
1. **Class Structure**: Inherit from `torch.optim.Optimizer`. Define `__init__` and `step` methods.
2. **Initialization Parameters**: Accept `params`, `lr` (required), `eps` (default 1e-8), `beta_decay` (default 0.8), `Lambda` (default 0.01), `momentum_beta` (default 0.9), `centralize` (default False), and `use_rms` (default False).
3. **Step Method Signature**: `def step(self, closure=None):`. Decorate with `@torch.no_grad()`.
4. **Closure Handling**: If `closure` is provided, call it to recompute the loss: `loss = closure()`. Return the loss at the end.
5. **Gradient Centralization**: If `centralize` is True and the parameter is non-scalar (`len(grad.shape) > 1`), subtract the mean of the gradient: `grad -= grad.mean(dim=tuple(range(1, len(grad.shape))), keepdim=True)`.
6. **Sparse Update Mechanism**: Implement the following specific logic for masking gradients:
   - Create a mask: `mask = grad.abs() > eps`
   - Apply mask to gradients: `grad = grad * mask`
7. **Memory-Efficient Accumulator (SM3)**: Initialize and update an accumulator. For 2D+ tensors, use dimension-wise reduction (e.g., `grad.square().mean(dim=0)`) to minimize memory footprint. Update using `beta_decay` logic. This reflects SM3's O(n+m) philosophy.
8. **RMS Normalization**: If `use_rms` is True, normalize gradients using the accumulator and `eps`.
9. **Momentum**: Implement momentum using `momentum_beta`. Update a `momentum_buffer` state variable.
10. **Weight Decay**: Apply weight decay if `Lambda` is not zero: `p.data.mul_(1 - lr * Lambda)`.
11. **Parameter Update**: Apply the update: `p.data.add_(grad_normalized, alpha=-lr)`.

# Anti-Patterns
- Do not omit the `closure` argument or its handling.
- Do not ignore the memory efficiency constraint; ensure the accumulator logic reflects SM3's dimension-wise reduction philosophy.
- Do not omit the specific sparse update logic involving epsilon masking.
- Do not omit gradient centralization.
- Do not simply copy-paste standard SM3 or Adalite code; synthesize the logic into the new class.
- Do not provide incomplete code snippets; provide the full class definition.

## Triggers

- implement fusedbun optimizer
- implement fusion optimizer from adalite and sm3
- write optimizer with hessian approximation
- pytorch optimizer sparse update mechanism
- memory efficient optimizer for fine-tuning