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Poggio, T., Mutch, J. & Isik, L. Computational role of eccentricity dependent cortical magnification. (2014).

CBMM-Memo-017.pdf (1.04 MB)

Poggio, T., Rosasco, L., Shashua, A., Cohen, N. & Anselmi, F. Notes on Hierarchical Splines, DCLNs and i-theory. (2015).

CBMM Memo 037 (1.83 MB)

Poggio, T., Anselmi, F. & Rosasco, L. I-theory on depth vs width: hierarchical function composition. (2015).

cbmm_memo_041.pdf (1.18 MB)

Poggio, T. & Meyers, E. Turing++ Questions: A Test for the Science of (Human) Intelligence. AI Magazine 37 , 73-77 (2016).

Turing_Plus_Questions.pdf (424.91 KB)

Poggio, T. Is Research in Intelligence an Existential Risk?. (2014).

Is Research in Intelligence an Existential Risk.pdf (571.42 KB)

Poggio, T. What if.. (2015).

What if.pdf (2.09 MB)

Poggio, T. Deep Learning: mathematics and neuroscience. (2016).

Deep Learning- mathematics and neuroscience.pdf (1.25 MB)

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., Mhaskar, H., Rosasco, L., Miranda, B. & Liao, Q. 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)

Poggio, T. Deep Leaning: Mathematics and Neuroscience. A Sponsored Supplement to Science Brain-Inspired intelligent robotics: The intersection of robotics and neuroscience, 9-12 (2016).

Poggio, T., Mhaskar, H., Rosasco, L., Miranda, B. & Liao, Q. 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)

Poggio, T. & Liao, Q. Theory II: Landscape of the Empirical Risk in Deep Learning. (2017).

CBMM Memo 066_1703.09833v2.pdf (5.56 MB)

Poggio, T. et al. 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)

Poggio, T. & Liao, Q. 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)

Poggio, T. & Liao, Q. 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)

Poggio, T., Banburski, A. & Liao, Q. 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)

Poggio, T., Kur, G. & Banburski, A. Double descent in the condition number. (2019).

Fixing typos, clarifying error in y, best approach is crossvalidation (837.18 KB)

Incorporated footnote in text plus other edits (854.05 KB)

Deleted previous discussion on kernel regression and deep nets: it will appear, extended, in a separate paper (795.28 KB)

correcting a bad typo (261.24 KB)

Deleted plot of condition number of kernel matrix: we cannot get a double descent curve (769.32 KB)

Poggio, T. & Squire, L. R. The History of Neuroscience in Autobiography Volume 8 8, (Society for Neuroscience, 2014).

Volume Introduction and Preface (232.8 KB)

TomasoPoggio.pdf (1.43 MB)

Poggio, T., Liao, Q. & Banburski, A. Complexity Control by Gradient Descent in Deep Networks. Nature Communications 11, (2020).

s41467-020-14663-9.pdf (431.68 KB)

Poggio, T. Stable Foundations for Learning: a framework for learning theory (in both the classical and modern regime). (2020).

Original file (584.54 KB)

Corrected typos and details of "equivalence" CV stability and expected error for interpolating machines. Added Appendix on SGD. (905.29 KB)

Edited Appendix on SGD. (909.19 KB)

Deleted Appendix. Corrected typos etc (880.27 KB)

Added result about square loss and min norm (898.03 KB)

Poggio, T., Banburski, A. & Liao, Q. Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 201907369 (2020). doi:10.1073/pnas.1907369117

PNASlast.pdf (915.3 KB)

Poggio, T. & Cooper, Y. Loss landscape: SGD has a better view. (2020).

CBMM-Memo-107.pdf (1.03 MB)

Typos and small edits, ver11 (955.08 KB)

Small edits, corrected Hessian for spurious case (337.19 KB)

Poggio, T., Liao, Q. & Xu, M. Implicit dynamic regularization in deep networks. (2020).

v1.2 (2.29 MB)

v.59 Update on rank (2.43 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. From Associative Memories to Powerful Machines. (2021).

v1.0 (1.01 MB)

v1.3Section added August 6 on self attention (3.9 MB)