Gradient Descent
Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent
Jaehoon Lee, Lechao Xiao, Samuel Schoenholz, Yasaman Bahri, Roman Novak, Jascha Sohl-Dickstein, Jeffrey Pennington
Neural Information Processing Systems http://nips.cc/
Appendix of " Complex-valued Neurons Can Learn More but Slower than Real-valued Neurons via Gradient Descent " A Preliminaries
In this section, we first summarize frequently used notations in the following table. Table 4: Frequently used notations.Notation Description C Lemma 7. Let d = 1 . Combining the cases above completes the proof. Subsection B.2 proves several convergence rate lemmas. Subsection B.3 gives some technical We are now ready to prove Theorem 1. Proof of Theorem 1.
How degenerate is the parametrization of neural networks with the ReLU activation function?
Dennis Maximilian Elbrächter, Julius Berner, Philipp Grohs
Neural Information Processing Systems http://nips.cc/
A Guide Through the Zoo of Biased SGD
We also provide examples where biased estimators outperform their unbiased counterparts or where unbiased versions are simply not available. Finally, we demonstrate the effectiveness of our framework through experimental results that validate our theoretical findings.
LocalSignalAdaptivity: ProvableFeatureLearning inNeuralNetworksBeyondKernels
Specifically,we prove that, forasimple data distribution with sparsesignal amidst high-variance noise, a simple convolutional neural network trained using stochastic gradient descent simultaneously learnstothreshold outthenoiseandfindthesignal.
TTOpt: AMaximumVolumeQuantizedTensor Train-basedOptimizationanditsApplicationto ReinforcementLearning
The vital part of every learning-based algorithm is an optimization procedure, e.g., Stochastic Gradient Descent.
Acontrastiveruleformeta-learning
Our rule may be understood as ageneralization of contrastive Hebbian learning to meta-learning and notably, it neither requires computing second derivativesnorgoing backwardsintime,twocharacteristic features of previous gradient-based methods that are hard to conceive in physicalneuralcircuits.
A Proofs of the Main Results
This section describes Stein variational gradient descent (SVGD) by Liu and Wang [19]. The overview is meant as supplementary material for Section 5, where we propose to use SVGD for inferring the DiBS posteriors p(Z | D) and p(Z, Θ | D). In contrast to sampling-based MCMC or optimizationbased variational inference methods, SVGD iteratively transports a fixed set of particles to closely match a target distribution, akin to the gradient descent algorithm in optimization. We refer the reader to Liu and Wang [19] for additional details. Let p(x) with x X be a differentiable density that we want to sample from, e.g., to estimate an expectation.