Amft Meta Learning Alignment

AMFT: Aligning LLM Reasoners by Meta-Learning Imitation-Exploration

Core Concept

Traditional LLM alignment pipelines follow two distinct stages: Supervised Fine-Tuning (SFT) for imitation, then Reinforcement Learning (RL) for exploration. This separation creates problems—catastrophic forgetting during RL and suboptimal trade-offs between following human demonstrations and discovering novel solutions.

AMFT (Adaptive Meta Fine-Tuning) reframes SFT and RL as complementary reward signals within a single training framework. Using meta-learning, the system automatically discovers the optimal balance between imitation and exploration without manual tuning of mixture weights.

Architecture Overview

• Implicit Rewards Framework: Treats SFT loss and RL loss as two reward signals to be optimally balanced
• Meta-Gradient Controller: Uses meta-learning to compute adaptive weights that balance imitation vs. exploration
• Single-Stage Training: Merges SFT and RL into one unified objective with learnable interpolation
• Entropy Regularization: Stabilizes training by constraining policy entropy to prevent divergence
• Dynamic Weighting: Adapts the imitation-exploration balance based on training dynamics

Implementation Steps

1. Define SFT and RL Objectives

Set up both objectives as separate loss components that will be weighted and combined.

import torch
import torch.nn.functional as F
from torch.optim import Adam

def compute_sft_loss(model, batch):
    """
    Supervised Fine-Tuning loss: standard next-token prediction
    Encourages the model to match human demonstrations
    """
    input_ids = batch['input_ids']
    labels = batch['labels']

    logits = model(input_ids).logits
    sft_loss = F.cross_entropy(
        logits.view(-1, model.config.vocab_size),
        labels.view(-1),
        reduction='mean'
    )
    return sft_loss

def compute_rl_loss(model, batch, reward_model):
    """
    Reinforcement Learning loss: policy gradient with reward signal
    Encourages the model to maximize external reward (e.g., correctness)
    """
    prompts = batch['prompts']
    responses = model.generate(prompts, max_length=256, num_return_sequences=4)

    # Compute rewards for generated responses
    rewards = reward_model.score(responses)

    # Policy gradient: negative log-likelihood weighted by rewards
    log_probs = model.compute_log_probs(responses)
    rl_loss = -(log_probs * rewards).mean()

    return rl_loss

2. Compute Entropy Regularization

Add entropy regularization to prevent the policy from collapsing to a deterministic policy during RL.

def compute_entropy_regularization(model, prompts, target_entropy=0.5):
    """
    Entropy regularization: encourages diverse generations
    Prevents policy collapse and stabilizes training
    """
    logits = model(prompts).logits
    probs = F.softmax(logits, dim=-1)

    # Shannon entropy
    entropy = -(probs * torch.log(probs + 1e-8)).sum(dim=-1).mean()

    # Regularization term: penalize if entropy drops below target
    entropy_loss = (target_entropy - entropy).clamp(min=0)
    return entropy_loss, entropy

3. Initialize Meta-Learning Controller

Create a learnable meta-parameter that controls the balance between SFT and RL losses.

class AdaptiveWeightController(torch.nn.Module):
    """
    Meta-learner that computes adaptive weights for SFT vs RL balance
    """
    def __init__(self, hidden_size=64):
        super().__init__()
        self.hidden_size = hidden_size

        # Meta-network: maps training statistics to weights
        self.meta_net = torch.nn.Sequential(
            torch.nn.Linear(4, hidden_size),
            torch.nn.ReLU(),
            torch.nn.Linear(hidden_size, 2),  # Output 2 weights: w_sft, w_rl
            torch.nn.Softmax(dim=-1)  # Normalize to sum to 1
        )

        self.optimizer = Adam(self.meta_net.parameters(), lr=1e-4)

    def forward(self, training_stats):
        """
        Compute adaptive weights based on training statistics
        training_stats: [sft_loss, rl_loss, entropy, gradient_norm]
        """
        # Normalize statistics to prevent scale issues
        normalized_stats = torch.log(training_stats + 1e-8)
        weights = self.meta_net(normalized_stats)
        return weights

    def update(self, sft_loss, rl_loss, entropy):
        """
        Meta-gradient step: optimize weights to balance objectives
        """
        # Meta-objective: minimize weighted sum, but adapt weights based on loss ratio
        loss_ratio = rl_loss / (sft_loss + 1e-8)
        meta_loss = loss_ratio.detach()  # Stop gradient for meta-optimization

        self.optimizer.zero_grad()
        meta_loss.backward()
        self.optimizer.step()

4. Unified Training Objective

Combine SFT and RL losses using the adaptive weights, with entropy regularization.

def compute_amft_loss(model, batch, reward_model, weight_controller,
                     entropy_weight=0.1, entropy_target=0.5):
    """
    AMFT combined loss: adaptive weighted sum of SFT and RL
    """
    # Compute individual loss components
    sft_loss = compute_sft_loss(model, batch)
    rl_loss = compute_rl_loss(model, batch, reward_model)
    entropy_reg, entropy = compute_entropy_regularization(
        model, batch['prompts'], target_entropy=entropy_target
    )

    # Compute gradient norms for meta-learning
    sft_grads = torch.autograd.grad(sft_loss, model.parameters(),
                                    retain_graph=True, create_graph=False)
    sft_grad_norm = sum((g ** 2).sum() for g in sft_grads) ** 0.5

    rl_grads = torch.autograd.grad(rl_loss, model.parameters(),
                                   retain_graph=True, create_graph=False)
    rl_grad_norm = sum((g ** 2).sum() for g in rl_grads) ** 0.5

    # Get adaptive weights from meta-controller
    training_stats = torch.tensor(
        [sft_loss.item(), rl_loss.item(), entropy.item(), sft_grad_norm.item()],
        device=model.device
    )
    w_sft, w_rl = weight_controller(training_stats)

    # Combined loss
    amft_loss = w_sft * sft_loss + w_rl * rl_loss + entropy_weight * entropy_reg

    return amft_loss, {
        'sft_loss': sft_loss,
        'rl_loss': rl_loss,
        'entropy': entropy,
        'w_sft': w_sft,
        'w_rl': w_rl
    }

5. Main Training Loop

Implement the unified training with both model updates and meta-controller updates.

def train_amft(model, reward_model, train_loader, num_epochs=10):
    """
    Main AMFT training loop: single-stage imitation + exploration
    """
    model_optimizer = Adam(model.parameters(), lr=5e-5)
    weight_controller = AdaptiveWeightController()

    for epoch in range(num_epochs):
        for step, batch in enumerate(train_loader):
            # Forward pass: compute combined loss
            amft_loss, stats = compute_amft_loss(
                model, batch, reward_model, weight_controller,
                entropy_weight=0.1, entropy_target=0.6
            )

            # Model update
            model_optimizer.zero_grad()
            amft_loss.backward()
            torch.nn.utils.clip_grad_norm_(model.parameters(), max_norm=1.0)
            model_optimizer.step()

            # Meta-update: adjust weights based on loss dynamics
            weight_controller.update(
                sft_loss=stats['sft_loss'],
                rl_loss=stats['rl_loss'],
                entropy=stats['entropy']
            )

            if step % 100 == 0:
                print(f"Epoch {epoch}, Step {step}")
                print(f"  AMFT Loss: {amft_loss:.4f}")
                print(f"  SFT Loss: {stats['sft_loss']:.4f}, "
                      f"RL Loss: {stats['rl_loss']:.4f}")
                print(f"  Weights: w_sft={stats['w_sft']:.3f}, "
                      f"w_rl={stats['w_rl']:.3f}")
                print(f"  Entropy: {stats['entropy']:.4f}")

    return model, weight_controller

6. Inference and Evaluation

Use the trained model for generation and evaluate on both imitation and exploration metrics.

def evaluate_amft_model(model, test_prompts, reward_model, reference_answers):
    """
    Evaluate AMFT model on both imitation and exploration quality
    """
    model.eval()

    imitation_score = 0  # How well it matches SFT training
    exploration_score = 0  # How well it maximizes reward

    with torch.no_grad():
        for prompt, reference in zip(test_prompts, reference_answers):
            response = model.generate(prompt, max_length=256)

            # Imitation quality: BLEU/exact match with reference
            imitation = compute_similarity(response, reference)

            # Exploration quality: external reward
            exploration = reward_model.score(response)

            imitation_score += imitation
            exploration_score += exploration

    avg_imitation = imitation_score / len(test_prompts)
    avg_exploration = exploration_score / len(test_prompts)

    print(f"Imitation Score: {avg_imitation:.4f}")
    print(f"Exploration Score: {avg_exploration:.4f}")
    print(f"Combined: {0.5 * avg_imitation + 0.5 * avg_exploration:.4f}")

    return avg_imitation, avg_exploration

Practical Guidance

Hyperparameters & Configuration

• Entropy Target: 0.5-0.8 (depends on vocabulary size; higher for larger vocabularies)
• Entropy Weight: 0.05-0.2 (balance between diversity and accuracy)
• Meta Learning Rate: 1e-4 to 1e-3 (much slower than main model learning rate)
• Model Learning Rate: 5e-5 to 1e-4 (typical LLM fine-tuning rates)
• Gradient Clipping: max_norm=1.0 recommended for stability
• Weight Update Frequency: Every 10-50 model steps

When to Use AMFT

• You want unified imitation + exploration training (avoid two-stage pipeline)
• Catastrophic forgetting is an issue when transitioning from SFT to RL
• You need automatic balancing without manual mixture weight tuning
• You have strong reward signals that complement human demonstrations
• You want dynamic adaptation as training progresses

When NOT to Use AMFT

• Your task only needs imitation (SFT is sufficient)
• You lack a good reward model (RL component would be noisy)
• You need strict control over imitation vs. exploration balance
• Training budget is very limited (meta-learning adds overhead)
• Your base model is already well-aligned (fine-tuning not needed)

Common Pitfalls

1. Unstable Meta-Learning: If weight controller learns too quickly, training becomes unstable. Use conservative meta learning rates (1e-4).
2. Insufficient Entropy Regularization: Without entropy constraints, policy collapses to deterministic outputs. Always include regularization term.
3. Poor Reward Signal: If reward model is noisy or misaligned, RL component becomes harmful. Validate reward model quality first.
4. Imbalanced Data: If SFT batch and RL batch have different distributions, weighting becomes harder. Use balanced sampling.
5. No Baseline Model: Compare against pure SFT to ensure AMFT actually helps; sometimes simpler approaches suffice.

Reference

AMFT (2508.06944): https://arxiv.org/abs/2508.06944

Note: This paper has been withdrawn from arXiv due to potential academic misconduct concerns. The skill documents the core technical approach but use with awareness of the paper's disputed status.

Single-stage unified training of imitation and exploration using meta-learned weight balancing achieves better performance than traditional two-stage SFT+RL pipelines.