Nested-Learning

PyTorch implementation of Google’s Nested Learning & HOPE Architecture

This repository contains a clean, modular, and fully-interpretable implementation of Nested Learning (NL) and the HOPE architecture introduced by Google DeepMind. It includes standalone implementations of:

• CMS (Contextual Multi-Scale Memory)
• Nested Optimizers (GDMemory, MomentumMemory, AdamMemory, DMGD, PreconditionedMomentum)
• Self-Modifying MLP (rank-1 & rank-k)
• HOPE Block (CMS + Self-Modifying MLP + Linear Attention Fast Memory)
• Full HOPE architecture assembly
• Example training on Tiny Shakespeare

This repo aims to make the original research easy to understand and easy to build on.

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🌟 Features

✔ Modular PyTorch implementation of all major components of Nested Learning ✔ Clean code broken into separate notebooks ✔ Implementations match Google’s paper structure ✔ Self-Modifying MLP with low-rank ΔW updates ✔ CMS with parallel multi-timescale memories ✔ Linear Attention with fast KV memory updates ✔ Compare different nested optimizers ✔ Ready for custom tasks and experiments

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📁 Repository Structure

Nested-Learning/
│
├── HOPE-implementation.ipynb # Full HOPE block + assembly
├── cms-implementation.ipynb # CMS multi-level memory
├── nested-optimizer-implementations.ipynb# GD, Momentum, Adam, DMGD, PCM
├── self-modifying-mlp.ipynb # Rank-1 & Rank-k ΔW weight updates
├── tiny-shakespear.ipynb # Example training on Tiny Shakespeare
│
└── NL.pdf # Original Google research paper
└── NL-Handwritten-Notes.pdf # Handwritten notes for mathematical and theoretical reference 

Each component is designed to be independently testable and can be imported into larger models.

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🧠 What is Nested Learning?

Nested Learning introduces a new way for models to:

• learn multi-timescale memory
• perform context-dependent fast learning inside the forward pass
• update their own weights on the fly using low-rank modifications
• combine slow learning (SGD) + fast learning (inner-loop adaptation)

The HOPE architecture is the first fully-scalable implementation of these ideas.

This repo re-creates the core components in a simplified but faithful manner.

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🔩 Implemented Components

1. Nested Optimizers

File: nested-optimizer-implementations.ipynb

• GDMemory
• MomentumMemory
• AdamMemory
• DeepMomentumMemory (DMGD)
• PreconditionedMomentumMemory

These treat optimizer state as differentiable memory.

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2. CMS: Contextual Multi-Scale Memory

File: cms-implementation.ipynb

A stack of memory levels updated at different speeds:

Outputs the aggregated multi-scale context.

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3. Self-Modifying MLP

File: self-modifying-mlp.ipynb

The model predicts a low-rank update to its own weights:

Implemented in:

• Rank-1
• Rank-k (paper-accurate)

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4. Linear Attention Fast Memory

Part of HOPE-implementation.ipynb

A fast KV memory updated with:

Used as a long-term associative memory.

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5. Full HOPE Block

File: HOPE-implementation.ipynb

Combines:

• CMS
• Linear Attention
• Self-Modifying MLP
• FFN + LayerNorm
• Memory dictionary (cms, KV) handling

This is the main unit used to build Nested Learning models.

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6. Example Training: Tiny Shakespeare

File: tiny-shakespear.ipynb

Runs:

• Toy sequence modeling
• Shows how memories evolve over time
• Demonstrates HOPE block in real inference

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🚀 Getting Started

Install dependencies

pip install torch numpy

(Optional Jupyter)

pip install notebook jupyterlab

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🧪 Quick Usage Example

Using HOPE block inside a model:

fromhope_blockimportHOPEBlockblock=HOPEBlock(dim=64, cms_levels=3, rank=4)
x=torch.randn(8, 64)
memories=Noneout, new_memories=block(x, memories)

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📝 Roadmap

• Add full training loop for HOPE-Transformer
• Add memory visualizations
• Add benchmark on character-level tasks
• Add support for multi-head CMS
• Add GPT-style stacked HOPE layers

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🤝 Contributing

Pull requests are welcome. If you extend the architecture (multi-head CMS, recurrent HOPE, etc.), feel free to submit!

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📜 License

MIT License

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🌐 References

• Nested Learning: Scaling Learning with Nested Architectures (Google, 2024–2025)
• Original Paper: Included as NL.pdf

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