arXiv:2606.09731v1 Announce Type: new Abstract: We tightly characterize the VC dimension of depth-$L$ Transformers with a total of $W$ parameters, mapping an input sequence of length $T$ to a single output, establishing an upper bound of $O(L W \log (T W))$ and a nearly matching lower bound of $\Omega(L W \log (T W / L))$. We further tightly characterize the sample complexity of chain-of-thought learning using such a Transformer, showing teacher forcing (i.e. selecting a predictor consistent with the entire chain-of-thought on training data) learns with sample complexity $O\left(L W \log \left
This paper provides foundational theoretical work for understanding the learning capabilities and limitations of Transformer models, which are central to current AI advancement.
A strategic reader should care because this research offers critical insights into the efficiency of Transformer training, paving the way for more robust and resource-optimized AI systems.
By tightly characterizing the VC dimension and sample complexity, this research provides a theoretical basis for optimizing Transformer architectures and training data requirements, potentially accelerating AI development.
- · AI researchers
- · Machine learning startups
- · Cloud AI providers
- · Compute hardware manufacturers
- · Inefficient AI training practices
- · Compute-intensive AI development without optimized models
Improved theoretical understanding of Transformer capabilities and training requirements.
More efficient design and training of large language models and other Transformer-based AI systems, leading to reduced compute costs and faster development cycles.
Accelerated deployment of advanced AI applications across various industries due to better efficiency and predictability of model performance.
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