MPO-BMs have NP-hard KL approximation in continuous settings but admit efficient polynomial-bond-dimension approximations with provable KL guarantees for structured targets under locality and spectral-gap conditions.
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ABGD parametrizes piecewise linear functions as difference of max-affine functions and converges linearly to an epsilon-accurate solution with O(d max(sigma/epsilon,1)^2) samples under sub-Gaussian noise, which is minimax optimal up to logs.
RAIC unifies uniform recovery of structured signals from nonlinear observations via PGD, yielding error rates comparable to nonuniform guarantees up to log factors in sparse and 1-bit settings.
Latent diffusion models exhibit geometric decoupling where curvature in out-of-distribution generation is misallocated to unstable semantic boundaries instead of image details, identifying geometric hotspots as the structural cause of editing instability.
citing papers explorer
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On the Approximation Complexity of Matrix Product Operator Born Machines
MPO-BMs have NP-hard KL approximation in continuous settings but admit efficient polynomial-bond-dimension approximations with provable KL guarantees for structured targets under locality and spectral-gap conditions.
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Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions
ABGD parametrizes piecewise linear functions as difference of max-affine functions and converges linearly to an epsilon-accurate solution with O(d max(sigma/epsilon,1)^2) samples under sub-Gaussian noise, which is minimax optimal up to logs.
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Robust Uniform Recovery of Structured Signals from Nonlinear Observations
RAIC unifies uniform recovery of structured signals from nonlinear observations via PGD, yielding error rates comparable to nonuniform guarantees up to log factors in sparse and 1-bit settings.
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Geometric Decoupling: Diagnosing the Structural Instability of Latent
Latent diffusion models exhibit geometric decoupling where curvature in out-of-distribution generation is misallocated to unstable semantic boundaries instead of image details, identifying geometric hotspots as the structural cause of editing instability.