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)
Compositional sparsity of learnable functions. Bulletin of the American Mathematical Society 61, 438-456 (2024).
Theory II: Landscape of the Empirical Risk in Deep Learning. (2017).
CBMM Memo 066_1703.09833v2.pdf (5.56 MB)
From Associative Memories to Powerful Machines. (2021).
v1.0 (1.01 MB)
v1.3Section added August 6 on self attention (3.9 MB)
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)
On efficiently computable functions, deep networks and sparse compositionality. (2025).
Deep_sparse_networks_approximate_efficiently_computable_functions.pdf (223.15 KB)
Turing++ Questions: A Test for the Science of (Human) Intelligence. AI Magazine 37 , 73-77 (2016).
Turing_Plus_Questions.pdf (424.91 KB)
Notes on Hierarchical Splines, DCLNs and i-theory. (2015).
CBMM Memo 037 (1.83 MB)
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)
Associative Memory as the Core of Intelligence in Technology and Evolution. (2026).
Review_On_Associative_Memories-14.pdf (245.78 KB)
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)
What if.. (2015).
What if.pdf (2.09 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)
Explicit regularization and implicit bias in deep network classifiers trained with the square loss. arXiv (2020). at <https://arxiv.org/abs/2101.00072>
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)
Deep Learning: mathematics and neuroscience. (2016).
Deep Learning- mathematics and neuroscience.pdf (1.25 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)
Visual Cortex and Deep Networks: Learning Invariant Representations. 136 (The MIT Press, 2016). at <https://mitpress.mit.edu/books/visual-cortex-and-deep-networks>
From Marr’s Vision to the Problem of Human Intelligence. (2021).
CBMM-Memo-118.pdf (362.19 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)
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