"Logarithmic Memory Networks (LMNs): Efficient Long-Range Sequence Modeling for Resource-Constrained Environments"

Logarithmic Memory Networks (LMNs) reduce sequence processing complexity from O(n²) to O(log n) using tree-based memory management

LMNs introduce a tree-based memory structure that processes long sequences efficiently while using minimal computational resources, making AI models work better on mobile devices.

https://arxiv.org/abs/2501.07905

🤖 Original Problem:

→ Traditional sequence models like RNNs and Transformers struggle with long sequences due to high computational costs and memory usage

→ Current solutions face quadratic complexity O(n²) with sequence length, making them impractical for resource-constrained environments

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🔧 Solution in this Paper:

→ LMNs use a hierarchical logarithmic tree structure to store and retrieve information efficiently

→ The model employs a single-vector attention mechanism that reduces complexity from O(n²) to O(log n)

→ It features dual operation modes: parallel for training and sequential for inference

→ The architecture eliminates need for explicit positional encoding through implicit path-based encoding

→ Memory blocks use a summarizer layer that condenses information dynamically

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💡 Key Insights:

→ Hierarchical tree structure enables efficient memory management

→ Single-vector attention drastically reduces computational overhead

→ Path-through positional encoding eliminates need for additional encodings

→ Multi-bank memory system allows flexible information storage

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📊 Results:

→ Outperforms GPT-2 with fewer parameters (71,489 vs 71,105) and better validation loss (1.7742 vs 1.9704)

→ Achieves 1,048,576% compression for sequences of length 1024

→ Successfully processes sequences up to 32,768 tokens while traditional attention fails beyond this length