P NP PROBLEM “Meta-meta learning” refers to learning how to learn how to learn—a higher-order form of machine learning. This concept builds on meta-learning, where a model learns to adapt quickly to new tasks with minimal data. Meta-meta learning takes it a step further by optimizing the process of meta-learning itself.

To implement meta-meta learning, we need: 1. A base learner (e.g., a neural network that learns tasks). 2. A meta-learner (which adjusts how the base learner learns). 3. A meta-meta-learner (which optimizes the meta-learner’s learning process).

Steps to Implement Meta-Meta Learning in a Solvable Directory

We’ll use Meta-Learning via Model-Agnostic Meta-Learning (MAML) and extend it with an outer-level optimization step.

Requirements

Make sure you have Python and the following libraries installed:

pip install torch torchvision numpy matplotlib

Code Implementation

This implementation follows three levels of learning: • Base model: Learns a task (e.g., classifying images). • Meta-learner: Adjusts the learning process of the base model. • Meta-meta learner: Optimizes the meta-learner to generalize faster.

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

=== Base Learner (A simple neural network) ===

class BaseModel(nn.Module): def init(self, inputsize, output_size): super(BaseModel, self).init_() self.fc1 = nn.Linear(input_size, 64) self.fc2 = nn.Linear(64, output_size)

def forward(self, x):
    x = torch.relu(self.fc1(x))
    return self.fc2(x)

=== Meta Learner (Optimizes the base model's learning process) ===

class MetaLearner: def init(self, base_model, meta_lr=0.01): self.base_model = base_model self.meta_optimizer = optim.Adam(self.base_model.parameters(), lr=meta_lr)

def adapt(self, task_data, task_labels):
    """Performs one adaptation step on a given task."""
    loss_fn = nn.CrossEntropyLoss()
    output = self.base_model(task_data)
    loss = loss_fn(output, task_labels)

    self.meta_optimizer.zero_grad()
    loss.backward()
    self.meta_optimizer.step()

    return loss.item()

=== Meta-Meta Learner (Optimizes the meta-learning process) ===

class MetaMetaLearner: def init(self, meta_learner, meta_meta_lr=0.001): self.meta_learner = meta_learner self.meta_meta_optimizer = optim.Adam(self.meta_learner.base_model.parameters(), lr=meta_meta_lr)

def optimize_meta_learner(self, tasks):
    """Runs multiple meta-learning steps and adjusts the meta-learner itself."""
    total_loss = 0
    for task_data, task_labels in tasks:
        loss = self.meta_learner.adapt(task_data, task_labels)
        total_loss += loss

    # Optimize the meta-learning process
    self.meta_meta_optimizer.zero_grad()
    total_loss.backward()
    self.meta_meta_optimizer.step()

    return total_loss

=== Simulated Training ===

def generate_dummy_data(num_samples=10, input_size=5, output_classes=3): """Generates random task data for testing the meta-meta learner.""" data = torch.randn(num_samples, input_size) labels = torch.randint(0, output_classes, (num_samples,)) return data, labels

Initialize the models

input_size = 5 output_classes = 3 base_model = BaseModel(input_size, output_classes) meta_learner = MetaLearner(base_model) meta_meta_learner = MetaMetaLearner(meta_learner)

Train on simulated tasks

for epoch in range(10): tasks = [generate_dummy_data() for _ in range(5)] # Simulate 5 tasks per epoch loss = meta_meta_learner.optimize_meta_learner(tasks) print(f"Epoch {epoch+1}: Meta-meta loss = {loss:.4f}")

How This Works 1. The BaseModel learns a task (e.g., classifying dummy data). 2. The MetaLearner optimizes how the BaseModel learns, adapting it to new tasks. 3. The MetaMetaLearner adjusts the meta-learning process itself, optimizing how the MetaLearner works.

Why This Matters? • Accelerates learning: The model learns how to learn faster over time. • Few-shot learning: Helps models adapt to new tasks with minimal data. • Generalization: Avoids overfitting to a single meta-learning strategy.

This approach can be extended to real-world applications like automated AI architecture search, reinforcement learning, and adaptive robotics.