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Found 7 papers, 0 papers with code
A theory of data variability in Neural Network Bayesian inference
Using our formalism on a synthetic task and on MNIST we obtain a homogeneous kernel matrix approximation for the learning curve as well as corrections due to data variability which allow the estimation of the generalization properties and exact results for the bounds of the learning curves in the case of infinitely many training data points.
Optimal signal propagation in ResNets through residual scaling
We here derive a systematic finite-size theory for ResNets to study signal propagation and its dependence on the scaling for the residual branch.
Decomposing neural networks as mappings of correlation functions
Understanding the functional principles of information processing in deep neural networks continues to be a challenge, in particular for networks with trained and thus non-random weights.
Unified field theoretical approach to deep and recurrent neuronal networks
Bayesian inference on Gaussian processes has proven to be a viable approach for studying recurrent and deep networks in the limit of infinite layer width, $n\to\infty$.
Unfolding recurrence by Green’s functions for optimized reservoir computing
Cortical networks are strongly recurrent, and neurons have intrinsic temporal dynamics.
Unfolding recurrence by Green's functions for optimized reservoir computing
Cortical networks are strongly recurrent, and neurons have intrinsic temporal dynamics.
Capacity of the covariance perceptron
Closed-form expressions reveal superior pattern capacity in the binary classification task compared to the classical perceptron in the case of a high-dimensional input and low-dimensional output.
