Publication
Evolving Images for Visual Neurons Using a Deep Generative Network Reveals Coding Principles and Neuronal Preferences. Cell 177, 1009 (2019).
Author's last draft (20.26 MB)
Deep Leaning: Mathematics and Neuroscience. A Sponsored Supplement to Science Brain-Inspired intelligent robotics: The intersection of robotics and neuroscience, 9-12 (2016).
An Overview of Some Issues in the Theory of Deep Networks. IEEJ Transactions on Electrical and Electronic Engineering 15, 1560 - 1571 (2020).
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)
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)
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)
Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 201907369 (2020). doi:10.1073/pnas.1907369117
PNASlast.pdf (915.3 KB)
I-theory on depth vs width: hierarchical function composition. (2015).
cbmm_memo_041.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)
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)
Compositional Sparsity of Learnable Functions. (2024).
This is an update of the AMS paper (230.72 KB)
Cervelli menti algoritmi. 272 (Sperling & Kupfer, 2023). at <https://www.sperling.it/libri/cervelli-menti-algoritmi-marco-magrini>
Computational role of eccentricity dependent cortical magnification. (2014).
CBMM-Memo-017.pdf (1.04 MB)
Is Research in Intelligence an Existential Risk?. (2014).
Is Research in Intelligence an Existential Risk.pdf (571.42 KB)
Theory II: Landscape of the Empirical Risk in Deep Learning. (2017).
CBMM Memo 066_1703.09833v2.pdf (5.56 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)
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)
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)
Notes on Hierarchical Splines, DCLNs and i-theory. (2015).
CBMM Memo 037 (1.83 MB)
Implicit dynamic regularization in deep networks. (2020).
v1.2 (2.29 MB)
v.59 Update on rank (2.43 MB)
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)
Turing++ Questions: A Test for the Science of (Human) Intelligence. AI Magazine 37 , 73-77 (2016).
Turing_Plus_Questions.pdf (424.91 KB)
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)
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