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Dynamics & Generalization in Deep Networks -Minimizing the Norm. NAS Sackler Colloquium on Science of Deep Learning (2019).
Classical generalization bounds are surprisingly tight for Deep Networks. (2018).
CBMM-Memo-091.pdf (1.43 MB) CBMM-Memo-091-v2.pdf (1.88 MB)
CBMM-Memo-091.pdf (1.43 MB) CBMM-Memo-091-v2.pdf (1.88 MB) Theory III: Dynamics and Generalization in Deep Networks. (2018). Original, intermediate versions are available under request (2.67 MB) CBMM Memo 90 v12.pdf (4.74 MB) Theory_III_ver44.pdf Update Hessian (4.12 MB) Theory_III_ver48 (Updated discussion of convergence to max margin) (2.56 MB) fixing errors and sharpening some proofs (2.45 MB)
Original, intermediate versions are available under request (2.67 MB) CBMM Memo 90 v12.pdf (4.74 MB) Theory_III_ver44.pdf Update Hessian (4.12 MB) Theory_III_ver48 (Updated discussion of convergence to max margin) (2.56 MB) fixing errors and sharpening some proofs (2.45 MB) Musings on Deep Learning: Properties of SGD. (2017). CBMM Memo 067 v2 (revised 7/19/2017) (5.88 MB) CBMM Memo 067 v3 (revised 9/15/2017) (5.89 MB) CBMM Memo 067 v4 (revised 12/26/2017) (5.57 MB)
CBMM Memo 067 v2 (revised 7/19/2017) (5.88 MB) CBMM Memo 067 v3 (revised 9/15/2017) (5.89 MB) CBMM Memo 067 v4 (revised 12/26/2017) (5.57 MB) Theory of Deep Learning IIb: Optimization Properties of SGD. (2017). CBMM-Memo-072.pdf (3.66 MB)
CBMM-Memo-072.pdf (3.66 MB) Theory of Deep Learning III: explaining the non-overfitting puzzle. (2017). CBMM-Memo-073.pdf (2.65 MB) CBMM Memo 073 v2 (revised 1/15/2018) (2.81 MB) CBMM Memo 073 v3 (revised 1/30/2018) (2.72 MB) CBMM Memo 073 v4 (revised 12/30/2018) (575.72 KB)
CBMM-Memo-073.pdf (2.65 MB) CBMM Memo 073 v2 (revised 1/15/2018) (2.81 MB) CBMM Memo 073 v3 (revised 1/30/2018) (2.72 MB) CBMM Memo 073 v4 (revised 12/30/2018) (575.72 KB) Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review. International Journal of Automation and Computing 1-17 (2017). doi:10.1007/s11633-017-1054-2 art%3A10.1007%2Fs11633-017-1054-2.pdf (1.68 MB)
art%3A10.1007%2Fs11633-017-1054-2.pdf (1.68 MB) Theory I: Why and When Can Deep Networks Avoid the Curse of Dimensionality?. (2016). CBMM-Memo-058v1.pdf (2.42 MB) CBMM-Memo-058v5.pdf (2.45 MB) CBMM-Memo-058-v6.pdf (2.74 MB) Proposition 4 has been deleted (2.75 MB)
CBMM-Memo-058v1.pdf (2.42 MB) CBMM-Memo-058v5.pdf (2.45 MB) CBMM-Memo-058-v6.pdf (2.74 MB) Proposition 4 has been deleted (2.75 MB)