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.
Evolutionary game theory shows gradient descent and stochastic gradient descent drive neural networks to distinct stable states favoring shortcut or core subnetworks, with data and optimization noise shaping shortcut bias formation.
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.
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Deciphering Shortcut Learning from an Evolutionary Game Theory Perspective
Evolutionary game theory shows gradient descent and stochastic gradient descent drive neural networks to distinct stable states favoring shortcut or core subnetworks, with data and optimization noise shaping shortcut bias formation.