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2021
Banburski, A., De La Torre, F., Pant, N., Shastri, I. & Poggio, T. Distribution of Classification Margins: Are All Data Equal?. (2021).PDF icon CBMM Memo 115.pdf (9.56 MB)PDF icon arXiv version (23.05 MB)
Rangamani, A., Xu, M., Banburski, A., Liao, Q. & Poggio, T. Dynamics and Neural Collapse in Deep Classifiers trained with the Square Loss. (2021).PDF icon JMLR__2021-22.pdf (4.61 MB)PDF icon Fixed Appendix (13.31 MB)
2020
Reddy, M. Vuyyuru, Banburski, A., Pant, N. & Poggio, T. Biologically Inspired Mechanisms for Adversarial Robustness. (2020).PDF icon CBMM_Memo_110.pdf (3.14 MB)
Poggio, T., Liao, Q. & Banburski, A. Complexity Control by Gradient Descent in Deep Networks. Nature Communications 11, (2020).PDF icon s41467-020-14663-9.pdf (431.68 KB)
Banburski, A. et al. Dreaming with ARC. Learning Meets Combinatorial Algorithms workshop at NeurIPS 2020 (2020).PDF icon CBMM Memo 113.pdf (1019.64 KB)
Deza, A., Liao, Q., Banburski, A. & Poggio, T. Hierarchically Local Tasks and Deep Convolutional Networks. (2020).PDF icon CBMM_Memo_109.pdf (2.12 MB)
Poggio, T. & Banburski, A. An Overview of Some Issues in the Theory of Deep Networks. IEEJ Transactions on Electrical and Electronic Engineering 15, 1560 - 1571 (2020).
Poggio, T., Banburski, A. & Liao, Q. Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 201907369 (2020). doi:10.1073/pnas.1907369117PDF icon PNASlast.pdf (915.3 KB)
2019
Poggio, T., Kur, G. & Banburski, A. Double descent in the condition number. (2019).PDF icon Fixing typos, clarifying error in y, best approach is crossvalidation (837.18 KB)PDF icon Incorporated footnote in text plus other edits (854.05 KB)PDF icon Deleted previous discussion on kernel regression and deep nets: it will appear, extended, in a separate paper (795.28 KB)PDF icon correcting a bad typo (261.24 KB)PDF icon Deleted plot of condition number of kernel matrix: we cannot get a double descent curve  (769.32 KB)
Banburski, A. et al. Dynamics & Generalization in Deep Networks -Minimizing the Norm. NAS Sackler Colloquium on Science of Deep Learning (2019).
Poggio, T., Banburski, A. & Liao, Q. Theoretical Issues in Deep Networks. (2019).PDF icon CBMM Memo 100 v1 (1.71 MB)PDF icon CBMM Memo 100 v3 (8/25/2019) (1.31 MB)PDF icon CBMM Memo 100 v4 (11/19/2019) (1008.23 KB)
Liao, Q., Banburski, A. & Poggio, T. Theories of Deep Learning: Approximation, Optimization and Generalization . TECHCON 2019 (2019).
Banburski, A. et al. Weight and Batch Normalization implement Classical Generalization Bounds . ICML (2019).
2018
Banburski, A. et al. Theory III: Dynamics and Generalization in Deep Networks. (2018).PDF icon Original, intermediate versions are available under request (2.67 MB)PDF icon CBMM Memo 90 v12.pdf (4.74 MB)PDF icon Theory_III_ver44.pdf Update Hessian (4.12 MB)PDF icon Theory_III_ver48 (Updated discussion of convergence to max margin) (2.56 MB)PDF icon fixing errors and sharpening some proofs (2.45 MB)