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About this paper
Yichuan Deng, Zhihang Li, Zhao Song
A theoretical investigation establishes that an attention-inspired softmax regression problem is convex and features a Lipschitz continuous Hessian. The research introduces a randomized approximate Newton method, achieving an epsilon-accurate solution in logarithmic iterations with near input-sparsity time complexity.
Key insights
- The attention-inspired softmax regression problem, when appropriately regularized, is convex and its Hessian is Lipschitz continuous, making it amenable to efficient optimization.
- The complex Hessian of the softmax regression loss function can be systematically decomposed, facilitating both theoretical analysis and practical approximation via sketching.
- Approximate Newton methods, combined with sketching, can achieve provably fast (logarithmic) convergence rates and near input-sparsity time complexity for non-linear, high-dimensional problems.
Summary by alphaXiv.
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