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)
What if.. (2015).
What if.pdf (2.09 MB)
An Overview of Some Issues in the Theory of Deep Networks. IEEJ Transactions on Electrical and Electronic Engineering 15, 1560 - 1571 (2020).
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. Proceedings of the National Academy of Sciences 201907369 (2020). doi:10.1073/pnas.1907369117
PNASlast.pdf (915.3 KB)
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)
Deep Learning: mathematics and neuroscience. (2016).
Deep Learning- mathematics and neuroscience.pdf (1.25 MB)
Theory II: Landscape of the Empirical Risk in Deep Learning. (2017).
CBMM Memo 066_1703.09833v2.pdf (5.56 MB)
I-theory on depth vs width: hierarchical function composition. (2015).
cbmm_memo_041.pdf (1.18 MB)
Visual Cortex and Deep Networks: Learning Invariant Representations. 136 (The MIT Press, 2016). at <https://mitpress.mit.edu/books/visual-cortex-and-deep-networks>
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)
Deep Leaning: Mathematics and Neuroscience. A Sponsored Supplement to Science Brain-Inspired intelligent robotics: The intersection of robotics and neuroscience, 9-12 (2016).
Compositional Sparsity of Learnable Functions. (2024).
This is an update of the AMS paper (230.72 KB)
How Deep Sparse Networks Avoid the Curse of Dimensionality: Efficiently Computable Functions are Compositionally Sparse. (2022).
v1.0 (984.15 KB)
v5.7 adding in context learning etc (1.16 MB)
Explicit regularization and implicit bias in deep network classifiers trained with the square loss. arXiv (2020). at <https://arxiv.org/abs/2101.00072>
Computational role of eccentricity dependent cortical magnification. (2014).
CBMM-Memo-017.pdf (1.04 MB)
Cervelli menti algoritmi. 272 (Sperling & Kupfer, 2023). at <https://www.sperling.it/libri/cervelli-menti-algoritmi-marco-magrini>
From Marr’s Vision to the Problem of Human Intelligence. (2021).
CBMM-Memo-118.pdf (362.19 KB)
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)
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)
Notes on Hierarchical Splines, DCLNs and i-theory. (2015).
CBMM Memo 037 (1.83 MB)
Complexity Control by Gradient Descent in Deep Networks. Nature Communications 11, (2020).
s41467-020-14663-9.pdf (431.68 KB)
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