Data geometry makes time identifiable from noisy interpolants at rate O(1/sqrt(d-k)), rendering the time-blindness gap asymptotically negligible relative to coupling variance.
The local low-dimensionality of natural images
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abstract
We develop a new statistical model for photographic images, in which the local responses of a bank of linear filters are described as jointly Gaussian, with zero mean and a covariance that varies slowly over spatial position. We optimize sets of filters so as to minimize the nuclear norms of matrices of their local activations (i.e., the sum of the singular values), thus encouraging a flexible form of sparsity that is not tied to any particular dictionary or coordinate system. Filters optimized according to this objective are oriented and bandpass, and their responses exhibit substantial local correlation. We show that images can be reconstructed nearly perfectly from estimates of the local filter response covariances alone, and with minimal degradation (either visual or MSE) from low-rank approximations of these covariances. As such, this representation holds much promise for use in applications such as denoising, compression, and texture representation, and may form a useful substrate for hierarchical decompositions.
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SGD on neural network weights induces a BBP phase transition that detaches signal eigenvalues from the random bulk, yielding an analytically solvable phase diagram for trainability in a linear teacher-student model.
citing papers explorer
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What Time Is It? How Data Geometry Makes Time Conditioning Optional for Flow Matching
Data geometry makes time identifiable from noisy interpolants at rate O(1/sqrt(d-k)), rendering the time-blindness gap asymptotically negligible relative to coupling variance.
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Spectral phase transitions and trainability in neural network learning dynamics
SGD on neural network weights induces a BBP phase transition that detaches signal eigenvalues from the random bulk, yielding an analytically solvable phase diagram for trainability in a linear teacher-student model.