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1,321 claims from 825 papers are on the record. 46 have been checked so far; the other 1,275 have no check with a result yet.

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Keyword: generalization error ×Clear all

10 claims from 6 papers

1. Computer Science › Stochastic Gradient Optimization Techniques

   High-dimensional dynamics of generalization error in neural networks

   Advani, Saxe and Sompolinsky · Neural Networks · 2020

   The paper analyses how gradient descent generalises in large neural networks when parameters rival or outnumber examples, finding that learning dynamics naturally guard against overtraining and overfitting.

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   1. UncheckedOvertraining peaks at intermediate network sizes, where free parameters match the number of samples, and falls if the network is made smaller or larger.“Overtraining is worst at intermediate network sizes, when the effective number of free parameters equals the number of samples, and thus can be reduced by making a network smaller or larger.”
   2. UncheckedIn very large (overcomplete) models, some weights stay frozen under gradient descent and input correlations are better conditioned, which guards against overtraining.“We identify two novel phenomena underlying this behavior in overcomplete models: first, there is a frozen subspace of the weights in which no learning occurs under gradient descent; and second, the statistical properties of the high-dimensional regime yield better-conditioned input correlations whi…”
   3. UncheckedWhen a network has as many or more parameters than examples, the paper says good generalisation needs training to start from small initial weights.“Additionally, in the high-dimensional regime, low generalization error requires starting with small initial weights.”

2. Computer Science › Stochastic Gradient Optimization Techniques

   The generalization error of random features regression: Precise asymptotics and double descent curve

   Song and A · arXiv (Cornell University) · 2019

   The paper computes exact large-scale limits of test error for ridge regression on random features, a two-layer network with random first-layer weights, and links the results to the double descent curve.

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   1. UncheckedThe paper presents random features ridge regression as a solvable model that shows all features of double descent without assuming special misspecification structures.“This provides the first analytically tractable model that captures all the features of the double descent phenomenon without assuming ad hoc misspecification structures.”

3. Computer Science › Stochastic Gradient Optimization Techniques

   Scaling description of generalization with number of parameters in deep learning

   Geiger, Jacot, Spigler et al. · Journal of Statistical Mechanics Theory and Experiment · 2020

   The paper explains why test error keeps falling as networks gain parameters, using the Neural Tangent Kernel, and tests its predictions on MNIST and CIFAR images.

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   1. UncheckedUsing the Neural Tangent Kernel, the paper shows that random initialisation makes a neural net's output fluctuate around its average by an amount scaling as N^(-1/4).“We rely on the so-called Neural Tangent Kernel, which connects large neural nets to kernel methods, to show that the initialization causes finite-size random fluctuations $\|f_{N}-\bar{f}_{N}\|\sim N^{-1/4}$ of the neural net output function $f_{N}$ around its expectation $\bar{f}_{N}$.”

4. Computer Science › Neural Networks and Applications

   Spectral bias and task-model alignment explain generalization in kernel regression and infinitely wide neural networks

   Canatar, Bordelon and Pehlevan · Nature Communications · 2021

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   1. Unchecked“We elucidate an inductive bias of kernel regression to explain data with "simple functions", which are identified by solving a kernel eigenfunction problem on the data distribution.”
   2. Unchecked“We show that more data may impair generalization when noisy or not expressible by the kernel, leading to non-monotonic learning curves with possibly many peaks.”

5. Computer Science › Stochastic Gradient Optimization Techniques

   Memorizing without overfitting: Bias, variance, and interpolation in overparameterized models

   Rocks and Mehta · Physical Review Research · 2022

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   1. Unchecked“In both models, increasing the number of fit parameters leads to a phase transition where the training error goes to zero and the test error diverges as a result of the variance (while the bias remains finite).”
   2. Unchecked“We also show that in contrast with classical intuition, over-parameterized models can overfit even in the absence of noise and exhibit bias even if the student and teacher models match.”

6. Computer Science › Stochastic Gradient Optimization Techniques

   Triple descent and the two kinds of overfitting: where and why do they appear?*

   d’Ascoli, Sagun and Biroli · Journal of Statistical Mechanics Theory and Experiment · 2021

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   1. Unchecked“We show that this peak is implicitly regularized by the nonlinearity, which is why it only becomes salient at high noise and is weakly affected by explicit regularization.”