Joint KL yields horizon-free approximation but an information-theoretic lower bound of order Omega(H) for estimation error in autoregressive learning, with matching computationally efficient upper bounds.
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Proposes pointwise Riemannian Dimension from feature eigenvalues to derive tighter, representation-aware generalization bounds for deep networks in the nonlinear regime.
Nonconvex projected gradient descent for noisy inductive matrix completion achieves linear convergence and order-optimal error at sample complexity scaling with side-information dimension a instead of ambient dimension n.
Stationary duality reduces composite cardinality optimization to simple cardinality, yielding dual problems with equivalent local solutions and global solutions under appropriate parameter selection.
citing papers explorer
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Autoregressive Learning in Joint KL: Sharp Oracle Bounds and Lower Bounds
Joint KL yields horizon-free approximation but an information-theoretic lower bound of order Omega(H) for estimation error in autoregressive learning, with matching computationally efficient upper bounds.
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Pointwise Generalization in Deep Neural Networks
Proposes pointwise Riemannian Dimension from feature eigenvalues to derive tighter, representation-aware generalization bounds for deep networks in the nonlinear regime.
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Sample efficient inductive matrix completion with noise and inexact side information
Nonconvex projected gradient descent for noisy inductive matrix completion achieves linear convergence and order-optimal error at sample complexity scaling with side-information dimension a instead of ambient dimension n.
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On the Stationary Duality of Structural Composite Cardinality Optimization
Stationary duality reduces composite cardinality optimization to simple cardinality, yielding dual problems with equivalent local solutions and global solutions under appropriate parameter selection.