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Complexity Control by Gradient Descent in Deep Networks. Nature Communications 11, (2020). s41467-020-14663-9.pdf (431.68 KB)
Explicit regularization and implicit bias in deep network classifiers trained with the square loss. arXiv (2020). at <https://arxiv.org/abs/2101.00072>
Hierarchically Local Tasks and Deep Convolutional Networks. (2020). CBMM_Memo_109.pdf (2.12 MB)
Implicit dynamic regularization in deep networks. (2020). v1.2 (2.29 MB) v.59 Update on rank (2.43 MB)
Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 201907369 (2020). doi:10.1073/pnas.1907369117 PNASlast.pdf (915.3 KB)
Biologically-plausible learning algorithms can scale to large datasets. International Conference on Learning Representations, (ICLR 2019) (2019). gk7779.pdf (721.53 KB)
Dynamics & Generalization in Deep Networks -Minimizing the Norm. NAS Sackler Colloquium on Science of Deep Learning (2019).
Theoretical Issues in Deep Networks. (2019). CBMM Memo 100 v1 (1.71 MB) CBMM Memo 100 v3 (8/25/2019) (1.31 MB) CBMM Memo 100 v4 (11/19/2019) (1008.23 KB)
Theories of Deep Learning: Approximation, Optimization and Generalization . TECHCON 2019 (2019).
Biologically-plausible learning algorithms can scale to large datasets. (2018). CBMM-Memo-092.pdf (1.31 MB)
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)
Theory I: Deep networks and the curse of dimensionality. Bulletin of the Polish Academy of Sciences: Technical Sciences 66, (2018). 02_761-774_00966_Bpast.No_.66-6_28.12.18_K1.pdf (1.18 MB)
Theory II: Deep learning and optimization. Bulletin of the Polish Academy of Sciences: Technical Sciences 66, (2018). 03_775-788_00920_Bpast.No_.66-6_31.12.18_K2.pdf (5.43 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)
Compression of Deep Neural Networks for Image Instance Retrieval. (2017). at <https://arxiv.org/abs/1701.04923> 1701.04923.pdf (614.33 KB)
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)
Object-Oriented Deep Learning. (2017). CBMM-Memo-070.pdf (963.54 KB)
Theory II: Landscape of the Empirical Risk in Deep Learning. (2017). CBMM Memo 066_1703.09833v2.pdf (5.56 MB)
Theory of Deep Learning IIb: Optimization Properties of SGD. (2017). 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)
View-Tolerant Face Recognition and Hebbian Learning Imply Mirror-Symmetric Neural Tuning to Head Orientation. Current Biology 27, 1-6 (2017).
When and Why Are Deep Networks Better Than Shallow Ones?. AAAI-17: Thirty-First AAAI Conference on Artificial Intelligence (2017).
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)