Figures & data: A Generalization Gap Estimation for Overparameterized Models via the Langevin Functional Variance

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Table 1 The generalization gap $Δ (α; X)$ and its estimates (TIC, FV, LFV) with the standard deviations in setting (i) where $s_{i} = n^{1 / 2}$ for $i = 1, 2, \dots, 10$ and 0 otherwise.

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Table 2 The generalization gap $Δ (α; X)$ and its estimates (TIC, FV, LFV) with the standard deviations in setting (ii), where $s_{i} = n^{1 / 2} i^{- 1}$ .

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Table 3 The generalization gap $Δ (α; X)$ and its estimates (TIC, FV, LFV) with the standard deviations in setting (iii), where $s_{i} = n^{1 / 2} i^{- 1 / 2}$ .

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Table 4 The generalization gap and LFV for the NN model with n = 50 and T = 3000.

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Table 5 The generalization gap and LFV for the NN model with n = 500 and T = 3000.

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Table 6 The generalization gap and LFV for the NN model with n = 1000 and T = 3000.

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Table 7 CV statistic and training loss + LFV over 20 different initializations. n denotes the number of samples, and $p = M (d + 2)$ denotes the number of parameters used in NN.

Display Table

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A Generalization Gap Estimation for Overparameterized Models via the Langevin Functional Variance

Table 1 The generalization gap $Δ (α; X)$ and its estimates (TIC, FV, LFV) with the standard deviations in setting (i) where $s_{i} = n^{1 / 2}$ for $i = 1, 2, \dots, 10$ and 0 otherwise.

Table 2 The generalization gap $Δ (α; X)$ and its estimates (TIC, FV, LFV) with the standard deviations in setting (ii), where $s_{i} = n^{1 / 2} i^{- 1}$ .

Table 3 The generalization gap $Δ (α; X)$ and its estimates (TIC, FV, LFV) with the standard deviations in setting (iii), where $s_{i} = n^{1 / 2} i^{- 1 / 2}$ .

Table 4 The generalization gap and LFV for the NN model with n = 50 and T = 3000.

Table 5 The generalization gap and LFV for the NN model with n = 500 and T = 3000.

Table 6 The generalization gap and LFV for the NN model with n = 1000 and T = 3000.

Table 7 CV statistic and training loss + LFV over 20 different initializations. n denotes the number of samples, and $p = M (d + 2)$ denotes the number of parameters used in NN.

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A Generalization Gap Estimation for Overparameterized Models via the Langevin Functional Variance

Figures & data

Table 1 The generalization gap Δ(α;X) and its estimates (TIC, FV, LFV) with the standard deviations in setting (i) where si=n1/2 for i=1,2,…,10 and 0 otherwise.

Table 2 The generalization gap Δ(α;X) and its estimates (TIC, FV, LFV) with the standard deviations in setting (ii), where si=n1/2i−1.

Table 3 The generalization gap Δ(α;X) and its estimates (TIC, FV, LFV) with the standard deviations in setting (iii), where si=n1/2i−1/2.

Table 4 The generalization gap and LFV for the NN model with n = 50 and T = 3000.

Table 5 The generalization gap and LFV for the NN model with n = 500 and T = 3000.

Table 6 The generalization gap and LFV for the NN model with n = 1000 and T = 3000.

Table 7 CV statistic and training loss + LFV over 20 different initializations. n denotes the number of samples, and p=M(d+2) denotes the number of parameters used in NN.

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Table 1 The generalization gap $Δ (α; X)$ and its estimates (TIC, FV, LFV) with the standard deviations in setting (i) where $s_{i} = n^{1 / 2}$ for $i = 1, 2, \dots, 10$ and 0 otherwise.

Table 2 The generalization gap $Δ (α; X)$ and its estimates (TIC, FV, LFV) with the standard deviations in setting (ii), where $s_{i} = n^{1 / 2} i^{- 1}$ .

Table 3 The generalization gap $Δ (α; X)$ and its estimates (TIC, FV, LFV) with the standard deviations in setting (iii), where $s_{i} = n^{1 / 2} i^{- 1 / 2}$ .

Table 7 CV statistic and training loss + LFV over 20 different initializations. n denotes the number of samples, and $p = M (d + 2)$ denotes the number of parameters used in NN.