Techniques for Fine-Tuning Large Language Models

Implementing LoRA from Scratch

Low-Rank Adaptation (LoRA) reduces the number of trainable parameters by decomposing weight matrices into low-rank approximations. This implementation demonstrates the core mathematics behind LoRA using NumPy, focusing on the fundamental matrix operations and rank decomposition.

import numpy as np

class LoRA:
    def __init__(self, input_dim, output_dim, rank=4):
        # Initialize matrices A and B for low-rank decomposition
        self.A = np.random.randn(input_dim, rank) / np.sqrt(rank)
        self.B = np.random.randn(rank, output_dim) / np.sqrt(rank)
        self.alpha = 8  # Scaling factor
        
    def forward(self, x):
        # Compute LoRA transformation: x → x + α(BA)x
        delta = self.alpha * (x @ self.A @ self.B)
        return x + delta

    def get_effective_weights(self):
        return self.alpha * (self.A @ self.B)

# Example usage
lora = LoRA(input_dim=768, output_dim=768, rank=8)
x = np.random.randn(1, 768)
output = lora.forward(x)
print(f"Input shape: {x.shape}")
print(f"Output shape: {output.shape}")
print(f"Effective weights shape: {lora.get_effective_weights().shape}")

Matrix Decomposition in LoRA

The effectiveness of LoRA lies in its ability to approximate large weight matrices through low-rank decomposition. This implementation showcases the mathematical foundation using SVD decomposition and demonstrates parameter reduction calculations.

import numpy as np
from scipy.linalg import svd

def compute_rank_reduction(original_dim, rank):
    """Calculate parameter reduction from LoRA"""
    original_params = original_dim * original_dim
    lora_params = original_dim * rank * 2
    reduction = (1 - lora_params/original_params) * 100
    return original_params, lora_params, reduction

def low_rank_approximation(W, rank):
    """Compute low-rank approximation using SVD"""
    U, S, Vt = svd(W, full_matrices=False)
    # Keep only top-k singular values
    U_k = U[:, :rank]
    S_k = np.diag(S[:rank])
    Vt_k = Vt[:rank, :]
    
    # Reconstruct approximated matrix
    W_approx = U_k @ S_k @ Vt_k
    error = np.linalg.norm(W - W_approx, 'fro')
    return W_approx, error

# Example usage
dim = 768
rank = 8
W = np.random.randn(dim, dim)
W_approx, error = low_rank_approximation(W, rank)
orig, lora, reduction = compute_rank_reduction(dim, rank)

print(f"Original parameters: {orig:,}")
print(f"LoRA parameters: {lora:,}")
print(f"Parameter reduction: {reduction:.2f}%")
print(f"Approximation error: {error:.4f}")

Delta LoRA Implementation

Delta LoRA enhances the standard LoRA by incorporating dropout mechanisms and adaptive scaling. This implementation demonstrates the key modifications that improve model robustness and generalization capabilities.

import numpy as np

class DeltaLoRA:
    def __init__(self, input_dim, output_dim, rank=4, dropout_rate=0.1):
        self.A = np.random.randn(input_dim, rank) / np.sqrt(rank)
        self.B = np.random.randn(rank, output_dim) / np.sqrt(rank)
        self.dropout_rate = dropout_rate
        self.alpha = 8
        self.scaling_vector = np.ones(rank)
        
    def dropout_mask(self, shape):
        return np.random.binomial(1, 1-self.dropout_rate, shape)
    
    def forward(self, x, training=True):
        if training:
            mask = self.dropout_mask(self.A.shape[1])
            A_dropped = self.A * mask[:, np.newaxis]
            delta = self.alpha * (x @ (A_dropped * self.scaling_vector) @ self.B)
        else:
            delta = self.alpha * (x @ (self.A * self.scaling_vector) @ self.B)
        return x + delta

# Example usage
delta_lora = DeltaLoRA(input_dim=768, output_dim=768, rank=8)
x = np.random.randn(1, 768)
train_output = delta_lora.forward(x, training=True)
eval_output = delta_lora.forward(x, training=False)

print(f"Training output shape: {train_output.shape}")
print(f"Evaluation output shape: {eval_output.shape}")

Prefix Tuning Architecture

Prefix tuning optimizes a small set of continuous task-specific vectors while keeping the main model parameters frozen. This implementation showcases the prefix embedding generation and integration with the main model's hidden states.

import numpy as np
import torch
import torch.nn as nn

class PrefixTuningModel(nn.Module):
    def __init__(self, hidden_size, prefix_length=10, prefix_projection_size=512):
        super().__init__()
        self.prefix_length = prefix_length
        
        # Prefix embedding layer
        self.prefix_embedding = nn.Sequential(
            nn.Linear(hidden_size, prefix_projection_size),
            nn.Tanh(),
            nn.Linear(prefix_projection_size, hidden_size * 2)  # 2x for key and value
        )
        
        # Initialize prefix tokens
        self.prefix_tokens = nn.Parameter(
            torch.randn(prefix_length, hidden_size)
        )
    
    def forward(self, hidden_states):
        batch_size = hidden_states.shape[0]
        
        # Generate prefix
        prefix = self.prefix_embedding(self.prefix_tokens)
        prefix = prefix.view(self.prefix_length, 2, -1, hidden_size)
        prefix_keys, prefix_values = prefix.split(1, dim=1)
        
        # Reshape for batch processing
        prefix_keys = prefix_keys.squeeze(1).expand(batch_size, -1, -1)
        prefix_values = prefix_values.squeeze(1).expand(batch_size, -1, -1)
        
        # Concatenate with input hidden states
        output = torch.cat([prefix_keys, hidden_states], dim=1)
        return output

# Example usage
hidden_size = 768
model = PrefixTuningModel(hidden_size)
sample_hidden = torch.randn(2, 20, hidden_size)  # Batch x Seq x Hidden
output = model(sample_hidden)
print(f"Input shape: {sample_hidden.shape}")
print(f"Output shape: {output.shape}")

LoRA Feature Augmentation

LoRA-FA extends traditional LoRA by incorporating feature-based decomposition and directional scaling. This implementation demonstrates the enhanced adaptation mechanism with feature-aware weight updates.

import numpy as np
import torch
import torch.nn as nn

class LoRAFeatureAugmentation(nn.Module):
    def __init__(self, input_dim, output_dim, rank=8, num_features=4):
        super().__init__()
        self.rank = rank
        self.num_features = num_features
        
        # Feature-aware decomposition matrices
        self.feature_projector = nn.Linear(input_dim, num_features)
        self.A = nn.Parameter(torch.randn(num_features, input_dim, rank) / np.sqrt(rank))
        self.B = nn.Parameter(torch.randn(num_features, rank, output_dim) / np.sqrt(rank))
        
        # Directional scaling factors
        self.feature_scales = nn.Parameter(torch.ones(num_features))
        self.alpha = 8
        
    def forward(self, x):
        # Extract feature weights
        feature_weights = torch.softmax(self.feature_projector(x), dim=-1)
        
        # Compute feature-weighted adaptation
        delta = torch.zeros_like(x)
        for i in range(self.num_features):
            weight = feature_weights[:, i].unsqueeze(-1)
            feature_delta = x @ self.A[i] @ self.B[i]
            delta += weight * self.feature_scales[i] * feature_delta
            
        return x + self.alpha * delta

# Example usage
model = LoRAFeatureAugmentation(768, 768)
x = torch.randn(2, 768)
output = model(x)
print(f"Input shape: {x.shape}")
print(f"Output shape: {output.shape}")
print(f"Feature scales: {model.feature_scales.data}")

VERA Framework Implementation

VERA (Verification-Enhanced Relevance Adaptation) focuses on maintaining output coherence while fine-tuning. This implementation showcases the verification mechanism and relevance scoring components that ensure high-quality adaptations.

import torch
import torch.nn as nn
import torch.nn.functional as F

class VERAModule(nn.Module):
    def __init__(self, hidden_size, num_heads=8, dropout_rate=0.1):
        super().__init__()
        self.hidden_size = hidden_size
        
        # Relevance scoring components
        self.relevance_scorer = nn.MultiheadAttention(
            hidden_size, num_heads, dropout=dropout_rate
        )
        
        # Verification gate
        self.verification_gate = nn.Sequential(
            nn.Linear(hidden_size * 2, hidden_size),
            nn.LayerNorm(hidden_size),
            nn.ReLU(),
            nn.Linear(hidden_size, 1),
            nn.Sigmoid()
        )
        
    def forward(self, x, context):
        # Compute relevance scores
        relevance_output, attention_weights = self.relevance_scorer(
            x, context, context
        )
        
        # Verification gate computation
        combined = torch.cat([x, relevance_output], dim=-1)
        gate_values = self.verification_gate(combined)
        
        # Apply gated adaptation
        output = gate_values * relevance_output + (1 - gate_values) * x
        return output, attention_weights, gate_values

# Example usage
batch_size, seq_length = 2, 10
hidden_size = 768

model = VERAModule(hidden_size)
x = torch.randn(seq_length, batch_size, hidden_size)
context = torch.randn(seq_length, batch_size, hidden_size)

output, attn_weights, gates = model(x, context)
print(f"Output shape: {output.shape}")
print(f"Attention weights shape: {attn_weights.shape}")
print(f"Gate values shape: {gates.shape}")

Performance Metrics Implementation

This implementation provides comprehensive evaluation metrics for fine-tuning techniques, including parameter efficiency, adaptation quality, and computational overhead measurements.

import numpy as np
from typing import Dict, List
import time

class FineTuningMetrics:
    def __init__(self, base_params: int):
        self.base_params = base_params
        self.metrics_history: Dict[str, List[float]] = {
            'parameter_efficiency': [],
            'adaptation_quality': [],
            'compute_overhead': []
        }
    
    def compute_parameter_efficiency(self, adapted_params: int) -> float:
        """Calculate parameter efficiency ratio"""
        efficiency = 1 - (adapted_params / self.base_params)
        self.metrics_history['parameter_efficiency'].append(efficiency)
        return efficiency
    
    def measure_adaptation_quality(self, 
                                 original_output: np.ndarray,
                                 adapted_output: np.ndarray) -> float:
        """Measure output similarity using cosine similarity"""
        orig_flat = original_output.reshape(original_output.shape[0], -1)
        adapt_flat = adapted_output.reshape(adapted_output.shape[0], -1)
        
        similarities = []
        for orig, adapt in zip(orig_flat, adapt_flat):
            sim = np.dot(orig, adapt) / (np.linalg.norm(orig) * np.linalg.norm(adapt))
            similarities.append(sim)
            
        quality = np.mean(similarities)
        self.metrics_history['adaptation_quality'].append(quality)
        return quality
    
    def compute_overhead(self, func, *args) -> float:
        """Measure computational overhead"""
        start_time = time.time()
        func(*args)
        overhead = time.time() - start_time
        self.metrics_history['compute_overhead'].append(overhead)
        return overhead
    
    def get_summary(self) -> Dict[str, float]:
        """Get summary statistics of all metrics"""
        return {
            metric: {
                'mean': np.mean(values),
                'std': np.std(values),
                'min': np.min(values),
                'max': np.max(values)
            }
            for metric, values in self.metrics_history.items()
        }

# Example usage
metrics = FineTuningMetrics(base_params=100_000_000)

# Simulate measurements
adapted_params = 1_000_000
orig_output = np.random.randn(32, 768)
adapted_output = np.random.randn(32, 768)

efficiency = metrics.compute_parameter_efficiency(adapted_params)
quality = metrics.measure_adaptation_quality(orig_output, adapted_output)
overhead = metrics.compute_overhead(np.dot, orig_output, adapted_output.T)

summary = metrics.get_summary()
print("Metrics Summary:")
print(f"Parameter Efficiency: {efficiency:.4f}")
print(f"Adaptation Quality: {quality:.4f}")
print(f"Computational Overhead: {overhead:.4f}s")

Real-world Application - Text Classification

This implementation demonstrates the application of LoRA for fine-tuning a pre-trained model on a text classification task, including data preprocessing, model adaptation, and evaluation metrics tracking.

import torch
import torch.nn as nn
from transformers import AutoTokenizer, AutoModel
from torch.utils.data import Dataset, DataLoader

class CustomDataset(Dataset):
    def __init__(self, texts, labels, tokenizer, max_length=128):
        self.encodings = tokenizer(texts, truncation=True, padding=True,
                                 max_length=max_length, return_tensors='pt')
        self.labels = torch.tensor(labels)
    
    def __len__(self):
        return len(self.labels)
    
    def __getitem__(self, idx):
        return {key: val[idx] for key, val in self.encodings.items()}, self.labels[idx]

class TextClassifierWithLoRA(nn.Module):
    def __init__(self, model_name, num_classes, rank=4):
        super().__init__()
        self.base_model = AutoModel.from_pretrained(model_name)
        hidden_size = self.base_model.config.hidden_size
        
        # LoRA layers
        self.lora_A = nn.Parameter(torch.randn(hidden_size, rank) / np.sqrt(rank))
        self.lora_B = nn.Parameter(torch.randn(rank, hidden_size) / np.sqrt(rank))
        
        # Classification head
        self.classifier = nn.Linear(hidden_size, num_classes)
        
    def forward(self, input_ids, attention_mask):
        # Get base model outputs
        outputs = self.base_model(input_ids=input_ids, 
                                attention_mask=attention_mask)
        hidden_states = outputs.last_hidden_state[:, 0, :]  # [CLS] token
        
        # Apply LoRA adaptation
        lora_output = hidden_states @ self.lora_A @ self.lora_B
        adapted_hidden = hidden_states + lora_output
        
        # Classification
        logits = self.classifier(adapted_hidden)
        return logits

# Example usage
def train_epoch(model, dataloader, optimizer, criterion):
    model.train()
    total_loss = 0
    correct = 0
    total = 0
    
    for batch in dataloader:
        inputs, labels = batch
        optimizer.zero_grad()
        
        outputs = model(**inputs)
        loss = criterion(outputs, labels)
        
        loss.backward()
        optimizer.step()
        
        total_loss += loss.item()
        _, predicted = outputs.max(1)
        total += labels.size(0)
        correct += predicted.eq(labels).sum().item()
    
    return total_loss / len(dataloader), 100. * correct / total

# Initialize model and training components
model_name = "bert-base-uncased"
num_classes = 2
model = TextClassifierWithLoRA(model_name, num_classes)
tokenizer = AutoTokenizer.from_pretrained(model_name)

# Training setup
optimizer = torch.optim.AdamW(model.parameters(), lr=2e-5)
criterion = nn.CrossEntropyLoss()

Real-world Application Results

# Sample training results
training_metrics = {
    'epoch': [1, 2, 3, 4, 5],
    'train_loss': [0.6932, 0.3845, 0.2756, 0.2134, 0.1876],
    'train_acc': [50.23, 82.45, 89.67, 92.34, 93.56],
    'val_loss': [0.6821, 0.4012, 0.3123, 0.2897, 0.2765],
    'val_acc': [51.12, 80.34, 86.78, 88.92, 89.45]
}

print("Training Results:")
for epoch in range(len(training_metrics['epoch'])):
    print(f"Epoch {training_metrics['epoch'][epoch]}:")
    print(f"  Train Loss: {training_metrics['train_loss'][epoch]:.4f}")
    print(f"  Train Accuracy: {training_metrics['train_acc'][epoch]:.2f}%")
    print(f"  Validation Loss: {training_metrics['val_loss'][epoch]:.4f}")
    print(f"  Validation Accuracy: {training_metrics['val_acc'][epoch]:.2f}%")
    print("-" * 50)

# Parameter efficiency analysis
base_params = sum(p.numel() for p in model.base_model.parameters())
lora_params = sum(p.numel() for p in [model.lora_A, model.lora_B])
reduction = (1 - lora_params/base_params) * 100

print(f"\nParameter Efficiency Analysis:")
print(f"Base Model Parameters: {base_params:,}")
print(f"LoRA Parameters: {lora_params:,}")
print(f"Parameter Reduction: {reduction:.2f}%")

Advanced LoRA Training Strategies

This implementation demonstrates sophisticated training techniques for LoRA, including gradient accumulation, mixed-precision training, and dynamic rank adjustment based on task complexity.

import torch
from torch.cuda.amp import autocast, GradScaler
import numpy as np

class AdvancedLoRATrainer:
    def __init__(self, model, rank_min=2, rank_max=16, 
                 accumulation_steps=4):
        self.model = model
        self.rank_bounds = (rank_min, rank_max)
        self.accumulation_steps = accumulation_steps
        self.scaler = GradScaler()
        
    def dynamic_rank_adjustment(self, validation_loss_history):
        """Adjust LoRA rank based on validation performance"""
        if len(validation_loss_history) < 2:
            return
            
        loss_delta = validation_loss_history[-1] - validation_loss_history[-2]
        current_rank = self.model.lora_A.shape[1]
        
        if loss_delta > 0:  # Validation loss increasing
            new_rank = min(current_rank * 2, self.rank_bounds[1])
        else:
            new_rank = max(current_rank // 2, self.rank_bounds[0])
            
        if new_rank != current_rank:
            self._resize_lora_matrices(new_rank)
    
    def _resize_lora_matrices(self, new_rank):
        """Resize LoRA matrices while preserving learned patterns"""
        with torch.no_grad():
            old_A = self.model.lora_A.data
            old_B = self.model.lora_B.data
            
            # SVD for rank reduction/expansion
            U, S, V = torch.svd(old_A @ old_B)
            
            # Initialize new matrices
            new_A = torch.randn(old_A.shape[0], new_rank) / np.sqrt(new_rank)
            new_B = torch.randn(new_rank, old_B.shape[1]) / np.sqrt(new_rank)
            
            # Copy existing patterns
            min_rank = min(new_rank, old_A.shape[1])
            new_A[:, :min_rank] = U[:, :min_rank] @ torch.diag(
                torch.sqrt(S[:min_rank]))
            new_B[:min_rank, :] = torch.diag(
                torch.sqrt(S[:min_rank])) @ V[:min_rank, :]
            
            # Update model parameters
            self.model.lora_A = torch.nn.Parameter(new_A)
            self.model.lora_B = torch.nn.Parameter(new_B)
    
    def train_step(self, batch, optimizer, criterion):
        """Training step with mixed precision and gradient accumulation"""
        optimizer.zero_grad()
        accumulated_loss = 0
        
        for micro_batch in torch.split(batch, batch.shape[0] // 
                                     self.accumulation_steps):
            with autocast():
                outputs = self.model(micro_batch)
                loss = criterion(outputs) / self.accumulation_steps
                
            self.scaler.scale(loss).backward()
            accumulated_loss += loss.item()
            
        self.scaler.step(optimizer)
        self.scaler.update()
        
        return accumulated_loss

# Example usage
model = TextClassifierWithLoRA("bert-base-uncased", num_classes=2)
trainer = AdvancedLoRATrainer(model)

# Training loop with metrics
validation_losses = []
batch = torch.randn(32, 512)  # Example batch
optimizer = torch.optim.AdamW(model.parameters())
criterion = torch.nn.CrossEntropyLoss()

loss = trainer.train_step(batch, optimizer, criterion)
validation_losses.append(loss)
trainer.dynamic_rank_adjustment(validation_losses)

Optimization Techniques in LoRA

This implementation focuses on advanced optimization strategies for LoRA, including adaptive learning rates, weight decay scheduling, and gradient clipping mechanisms.

import torch
import math
from torch.optim import Optimizer

class LoRAOptimizer(Optimizer):
    def __init__(self, params, lr=1e-3, betas=(0.9, 0.999),
                 weight_decay=0.01, warmup_steps=1000):
        defaults = dict(lr=lr, betas=betas, weight_decay=weight_decay)
        super().__init__(params, defaults)
        self.warmup_steps = warmup_steps
        self.current_step = 0
        
    def step(self, closure=None):
        loss = None
        if closure is not None:
            loss = closure()
            
        for group in self.param_groups:
            for p in group['params']:
                if p.grad is None:
                    continue
                    
                # Compute warmup factor
                warmup_factor = min(1.0, self.current_step / self.warmup_steps)
                
                # Parameter-specific learning rate
                if hasattr(p, 'is_lora'):
                    effective_lr = group['lr'] * math.sqrt(warmup_factor)
                else:
                    effective_lr = group['lr'] * warmup_factor
                
                # Gradient clipping
                torch.nn.utils.clip_grad_norm_(p, max_norm=1.0)
                
                # Weight decay with scheduling
                if group['weight_decay'] > 0:
                    p.data.mul_(1 - effective_lr * group['weight_decay'])
                
                # Update parameters
                p.data.add_(p.grad, alpha=-effective_lr)
                
        self.current_step += 1
        return loss

# Example usage
def configure_optimizer(model, lr=2e-5):
    # Separate LoRA and non-LoRA parameters
    lora_params = []
    base_params = []
    
    for name, param in model.named_parameters():
        if 'lora' in name:
            param.is_lora = True
            lora_params.append(param)
        else:
            base_params.append(param)
    
    optimizer = LoRAOptimizer([
        {'params': base_params},
        {'params': lora_params, 'lr': lr * 10}  # Higher LR for LoRA
    ], lr=lr)
    
    return optimizer

# Initialize and use optimizer
model = TextClassifierWithLoRA("bert-base-uncased", num_classes=2)
optimizer = configure_optimizer(model)

Memory-Efficient LoRA Implementation

This implementation showcases advanced memory optimization techniques for LoRA, utilizing gradient checkpointing and efficient memory management strategies for handling large models with limited resources.

import torch
import torch.nn as nn
from torch.utils.checkpoint import checkpoint
import gc

class MemoryEfficientLoRA(nn.Module):
    def __init__(self, base_model, rank=8, chunk_size=1024):
        super().__init__()
        self.base_model = base_model
        self.hidden_size = base_model.config.hidden_size
        self.chunk_size = chunk_size
        
        # Initialize LoRA matrices with memory-efficient storage
        self.lora_A = nn.Parameter(
            torch.empty(self.hidden_size, rank, dtype=torch.float16)
        )
        self.lora_B = nn.Parameter(
            torch.empty(rank, self.hidden_size, dtype=torch.float16)
        )
        self.reset_parameters()
        
    def reset_parameters(self):
        nn.init.normal_(self.lora_A, std=0.02)
        nn.init.normal_(self.lora_B, std=0.02)
        
    def chunked_forward(self, hidden_states):
        batch_size = hidden_states.shape[0]
        output = torch.zeros_like(hidden_states)
        
        for i in range(0, batch_size, self.chunk_size):
            chunk = hidden_states[i:i + self.chunk_size]
            
            def custom_forward(x):
                return x @ self.lora_A @ self.lora_B
                
            output[i:i + self.chunk_size] = checkpoint(
                custom_forward, chunk, preserve_rng_state=False
            )
            
            # Explicit memory cleanup
            if i % (self.chunk_size * 4) == 0:
                torch.cuda.empty_cache()
                gc.collect()
                
        return output
    
    def forward(self, input_ids, attention_mask=None):
        base_output = self.base_model(
            input_ids=input_ids,
            attention_mask=attention_mask
        )
        hidden_states = base_output.last_hidden_state
        
        # Apply LoRA with memory optimization
        lora_output = self.chunked_forward(hidden_states)
        
        return base_output.last_hidden_state + lora_output

# Example usage with memory monitoring
def train_with_memory_tracking(model, dataloader, epochs=1):
    model = model.cuda()
    optimizer = torch.optim.AdamW(model.parameters(), lr=1e-4)
    
    for epoch in range(epochs):
        for batch in dataloader:
            # Track memory usage
            torch.cuda.reset_peak_memory_stats()
            initial_mem = torch.cuda.memory_allocated()
            
            inputs = {k: v.cuda() for k, v in batch.items()}
            outputs = model(**inputs)
            loss = outputs.mean()  # Example loss
            
            loss.backward()
            optimizer.step()
            optimizer.zero_grad()
            
            final_mem = torch.cuda.memory_allocated()
            peak_mem = torch.cuda.max_memory_allocated()
            
            print(f"Memory Usage:")
            print(f"Initial: {initial_mem/1e6:.2f}MB")
            print(f"Final: {final_mem/1e6:.2f}MB")
            print(f"Peak: {peak_mem/1e6:.2f}MB")

# Create sample data and model
sample_data = [
    {"input_ids": torch.randint(0, 1000, (16, 512)),
     "attention_mask": torch.ones(16, 512)}
]
sample_dataloader = torch.utils.data.DataLoader(sample_data)

base_model = AutoModel.from_pretrained("bert-base-uncased")
efficient_model = MemoryEfficientLoRA(base_model)

# Train with memory tracking
train_with_memory_tracking(efficient_model, sample_dataloader)

Additional Resources

• ArXiv Papers and References:
  • LoRA: Low-Rank Adaptation of Large Language Models https://arxiv.org/abs/2106.09685
  • Efficient Fine-Tuning of Language Models https://arxiv.org/abs/2312.15685
  • Memory-Efficient Fine-Tuning of Large Language Models https://arxiv.org/abs/2303.16742
  • Optimal Transport for Parameter-Efficient Fine-Tuning https://arxiv.org/abs/2310.12962
  • A Survey of Deep Learning Approaches for Parameter-Efficient Transfer Learning https://arxiv.org/abs/2311.11017

For further research and implementation details, consider searching:

• "Parameter-efficient fine-tuning techniques"
• "Memory optimization in language models"
• "Low-rank adaptation methods"
• "Efficient transfer learning approaches"