Shallow Neural Networks Learn Low-Degree Spherical Polynomials with Learnable Channel Attention
Published:Dec 24, 2025 05:00
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Analysis
This paper presents research on training shallow neural networks with channel attention to learn low-degree spherical polynomials. The core contribution is demonstrating a significantly improved sample complexity compared to existing methods. The authors show that a carefully designed two-layer neural network with channel attention can achieve a sample complexity of approximately O(d^(ℓ0)/ε), which is better than the representative complexity of O(d^(ℓ0) max{ε^(-2), log d}). Furthermore, they prove that this sample complexity is minimax optimal, meaning it cannot be improved. The research involves a two-stage training process and provides theoretical guarantees on the performance of the network trained by gradient descent. This work is relevant to understanding the capabilities and limitations of shallow neural networks in learning specific function classes.
Key Takeaways
- •Shallow neural networks with channel attention can efficiently learn low-degree spherical polynomials.
- •The paper provides improved sample complexity bounds for this learning task.
- •The achieved sample complexity is shown to be minimax optimal.
Reference
“Our main result is the significantly improved sample complexity for learning such low-degree polynomials.”