Problem
Research questions and friction points this paper is trying to address.
representation learning
quantum signal processing
quantum neural tangent kernel
training dynamics
data geometry
Representation Learning with Quantum Signal Processing
🤖 AI Summary
该研究通过量子信号处理(QSP)解决了表示学习中的特征变化问题，揭示了输入依赖的几何结构，并证明了全非线性梯度流的稀疏数据保证。
📝 Abstract
Representation learning begins when training changes the features that define similarity between data. A frozen-kernel model only reweights a fixed geometry. We establish quantum signal processing (QSP) as a solvable quantum model of the representation-learning regime. At arbitrary depth, we compute the exact mean and variance of its quantum neural tangent kernel, revealing an input-dependent angular geometry whose diagonal remains non-self-averaging even when the underlying unitary approaches Haar randomness. We also prove a sparse-data guarantee for the full nonlinear gradient flow without freezing or ensemble-averaging the kernel: the realized dynamics converges to an integrable scalar flow with a time-dependent kernel closure and explicit convergence times. A finite-depth speed limit holds for every data set and trajectory. At higher data density, numerical results show coupled evolution beyond both the scalar and frozen-kernel descriptions. These results give a controlled theory of learned quantum data geometry with provable training dynamics beyond the frozen limit.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Quantum Signal Processing
Representation Learning
Quantum Neural Tangent Kernel
Non-self-averaging Diagonal
Sparse-data Guarantee
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