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Poggio, T. & Anselmi, F. Visual Cortex and Deep Networks: Learning Invariant Representations. 136 (The MIT Press, 2016). at <https://mitpress.mit.edu/books/visual-cortex-and-deep-networks>
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)
Poggio, T. From Marr’s Vision to the Problem of Human Intelligence. (2021).PDF icon CBMM-Memo-118.pdf (362.19 KB)
Poggio, T., Anselmi, F. & Rosasco, L. I-theory on depth vs width: hierarchical function composition. (2015).PDF icon cbmm_memo_041.pdf (1.18 MB)
Poggio, T. & Liao, Q. Theory II: Landscape of the Empirical Risk in Deep Learning. (2017).PDF icon CBMM Memo 066_1703.09833v2.pdf (5.56 MB)
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)
Poggio, T. & Fraser, M. Compositional Sparsity of Learnable Functions. (2024).PDF icon This is an update of the AMS paper (230.72 KB)
Poggio, T. Deep Learning: mathematics and neuroscience. (2016).PDF icon Deep Learning- mathematics and neuroscience.pdf (1.25 MB)
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)

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