"Provably Transformers Harness Multi-Concept Word Semantics for Efficient In-Context Learning"

Math cracks how AI understands 'bark' means both tree-skin and dog-sound.

This paper mathematically proves how Transformers use multiple word meanings for in-context learning

https://arxiv.org/abs/2411.02199

🤔 Original Problem:

LLMs show remarkable in-context learning abilities without fine-tuning, but we lack theoretical understanding of how they leverage word semantics across different concepts for this capability.

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🔧 Solution in this Paper:

→ Introduces a concept-based sparse coding prompt model where words and labels have multiple feature embeddings for different concepts

→ Analyzes a two-layer Transformer with softmax attention and ReLU-activated feed-forward network

→ Maintains positive inner products within concepts and orthogonality across concepts

→ Uses cross-entropy loss and stochastic gradient descent for training

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💡 Key Insights:

→ Words can have different semantic meanings across multiple concepts

→ The model achieves exponential convergence despite non-convex optimization

→ Multi-concept encoded linear semantic geometry enables efficient out-of-distribution tasks

→ No requirement on demonstration length or batch size for training

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📊 Results:

→ Achieves Bayes optimal test error with logarithmic number of iterations

→ Proves exponential convergence of 0-1 loss with cross-entropy training

→ First theoretical framework handling softmax attention, ReLU-MLP, and cross-entropy loss simultaneously