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Found 11 papers, 1 papers with code
Kernel Methods and Multi-layer Perceptrons Learn Linear Models in High Dimensions
Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization properties of neural networks.
Asymptotics of Ridge Regression in Convolutional Models
We show the double descent phenomenon in our experiments for convolutional models and show that our theoretical results match the experiments.
Implicit Bias of Linear RNNs
The degree of this bias depends on the variance of the transition kernel matrix at initialization and is related to the classic exploding and vanishing gradients problem.
Low-Rank Nonlinear Decoding of $μ$-ECoG from the Primary Auditory Cortex
This decoding problem is particularly challenging due to the complexity of neural responses in the auditory cortex and the presence of confounding signals in awake animals.
Generalization Error of Generalized Linear Models in High Dimensions
We provide a general framework to characterize the asymptotic generalization error for single-layer neural networks (i. e., generalized linear models) with arbitrary non-linearities, making it applicable to regression as well as classification problems.
Inference in Multi-Layer Networks with Matrix-Valued Unknowns
We consider the problem of inferring the input and hidden variables of a stochastic multi-layer neural network from an observation of the output.
Inference with Deep Generative Priors in High Dimensions
This paper presents a novel algorithm, Multi-Layer Vector Approximate Message Passing (ML-VAMP), for inference in multi-layer stochastic neural networks.
High-Dimensional Bernoulli Autoregressive Process with Long-Range Dependence
We derive precise upper bounds on the mean-squared estimation error in terms of the number of samples, dimensions of the process, the lag $p$ and other key statistical properties of the model.
Rigorous Dynamics and Consistent Estimation in Arbitrarily Conditioned Linear Systems
We show that the parameter estimates and mean squared error (MSE) of x in each iteration converge to deterministic limits that can be precisely predicted by a simple set of state evolution (SE) equations.
Joint Dictionary Learning for Example-based Image Super-resolution
Using the sparse representation coefficients of these LR patches over the LR dictionary, the high-resolution (HR) dictionary is trained by minimizing the reconstruction error of HR sample patches.
Expectation Consistent Approximate Inference: Generalizations and Convergence
Approximations of loopy belief propagation, including expectation propagation and approximate message passing, have attracted considerable attention for probabilistic inference problems.
