Project: 026_SD-LoRA_Scalable_Decoupled_Low-Rank_Adaptation_for | Function: _LoRA_qkv_timm_train.forward (iclr)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
Return **only** the complete Python function code.

user: Complete this Python function:

**DESCRIPTION:** Core SD-LoRA forward computation that implements the decoupled magnitude and direction learning mechanism. This function combines previous LoRA directions with learnable magnitudes and adds the current task's LoRA component.

**KEY TERMS:** {
  "scaling_factor_prev[i]": "αk (LoRA magnitude for previous tasks)",
  "scaling_factor[0]": "αt (LoRA magnitude for current task)",
  "saved_A, saved_B": "{AkBk}t−1k=1 (previously learned directions)",
  "linear_a_q, linear_b_q": "At, Bt (current task LoRA matrices)",
  "qkv": "W0 (original weight matrix)"
}

**CONTEXT CODE:** # Sheng Wang at Feb 22 2023

import math

import timm
import torch
import torch.nn as nn
import torch.nn.functional as F
from einops import rearrange
# from safetensors import safe_open
# from safetensors.torch import save_file
from timm.models.vision_transformer import VisionTransformer as timm_ViT
from torch import Tensor
from torch.nn.parameter import Parameter

from backbone.base_vit import ViT
import os
from backbone.linears import SimpleLinear
import gc
import torch.nn.utils as utils
import copy

class _LoRALayer(nn.Module):
    def __init__(self, w: nn.Module, w_a: nn.Module, w_b: nn.Module):
        raise NotImplementedError("Function implementation has been masked for testing")
    
    def forward(self, x):
        raise NotImplementedError("Function implementation has been masked for testing")
    
class LoRA_ViT(nn.Module):
    """Applies low-rank adaptation to a vision transformer.
    Args:
        vit_model: a vision transformer model, see base_vit.py
        r: rank of LoRA
        num_classes: how many classes the model output, default to the vit model
        lora_layer: which layer we apply LoRA.
    Examples::
        >>> model = ViT('B_16_imagenet1k')
        >>> lora_model = LoRA_ViT(model, r=4)
        >>> preds = lora_model(img)
        >>> print(preds.shape)
        torch.Size([1, 1000])
    """
    def __init__(self, vit_model: ViT, r: int, num_classes: int = 0, lora_layer=None):
        super(LoRA_ViT, self).__init__()

        assert r > 0
        base_vit_dim = vit_model.transformer.blocks[0].attn.proj_q.in_features
        dim = base_vit_dim
        if lora_layer:
            self.lora_layer = lora_layer
        else:
            self.lora_layer = list(range(len(vit_model.transformer.blocks)))
        # create for storage, then we can init them or load weights
        self.w_As = []  # These are linear layers
        self.w_Bs = []
        # lets freeze first
        for param in vit_model.parameters():
            param.requires_grad = False

        # Here, we do the surgery
        for t_layer_i, blk in enumerate(vit_model.transformer.blocks):
            # If we only want few lora layer instead of all
            if t_layer_i not in self.lora_layer:
                continue
            w_q_linear = blk.attn.proj_q
            w_v_linear = blk.attn.proj_v
            w_a_linear_q = nn.Linear(dim, r, bias=False)
            w_b_linear_q = nn.Linear(r, dim, bias=False)
            w_a_linear_v = nn.Linear(dim, r, bias=False)
            w_b_linear_v = nn.Linear(r, dim, bias=False)
            self.w_As.append(w_a_linear_q)
            self.w_Bs.append(w_b_linear_q)
            self.w_As.append(w_a_linear_v)
            self.w_Bs.append(w_b_linear_v)
            blk.attn.proj_q = _LoRALayer(w_q_linear, w_a_linear_q, w_b_linear_q)
            blk.attn.proj_v = _LoRALayer(w_v_linear, w_a_linear_v, w_b_linear_v)

        self.reset_parameters()
        self.lora_vit = vit_model
        if num_classes > 0:
            self.lora_vit.fc = nn.Linear(vit_model.fc.in_features, num_classes)

    def reset_parameters(self) -> None:
        for w_A in self.w_As:
            nn.init.kaiming_uniform_(w_A.weight, a=math.sqrt(5))
        for w_B in self.w_Bs:
            nn.init.zeros_(w_B.weight)

    def forward(self, x: Tensor) -> Tensor:
        return self.lora_vit(x)


class _LoRA_qkv_timm(nn.Module):
    """
    In timm it is implemented as
    self.qkv = nn.Linear(dim, dim * 3, bias=qkv_bias)
    B, N, C = x.shape
    qkv = self.qkv(x).reshape(B, N, 3, self.num_heads, self.head_dim).permute(2, 0, 3, 1, 4)
    q, k, v = qkv.unbind(0)
    """
    def __init__(
        self,
        qkv: nn.Module,
        linear_a_q: nn.Module,
        linear_b_q: nn.Module,
        linear_a_v: nn.Module,
        linear_b_v: nn.Module,
    ):
        super().__init__()
        self.qkv = qkv
        self.linear_a_q = linear_a_q
        self.linear_b_q = linear_b_q
        self.linear_a_v = linear_a_v
        self.linear_b_v = linear_b_v
        # Handle case where qkv might already be replaced by LoRA layer
        if hasattr(qkv, 'in_features'):
            self.dim = qkv.in_features
        elif hasattr(qkv, 'w_qkv'):
            # Already a LoRA layer, get from original
            self.dim = qkv.w_qkv.in_features
        else:
            # Fallback for ViT models (common dimension)
            self.dim = 768
        self.w_identity = torch.eye(qkv.in_features)



Complete the function implementation replacing "raise NotImplementedError".