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A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

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. & Magrini, M. Cervelli menti algoritmi. 272 (Sperling & Kupfer, 2023). at <https://www.sperling.it/libri/cervelli-menti-algoritmi-marco-magrini>

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., 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. 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)

Poggio, T. & Liao, Q. Explicit regularization and implicit bias in deep network classifiers trained with the square loss. arXiv (2020). at <https://arxiv.org/abs/2101.00072>

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. & 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. What if.. (2015).

What if.pdf (2.09 MB)

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. From Marr’s Vision to the Problem of Human Intelligence. (2021).

CBMM-Memo-118.pdf (362.19 KB)

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

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

Poggio, T. A Perspective: Sparse Compositionality and Efficiently Computable Intelligence. (2026).

Perspective_SPCOMP-9.pdf (170.23 KB)

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. & 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. & 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. & Fraser, M. Compositional sparsity of learnable functions. Bulletin of the American Mathematical Society 61, 438-456 (2024).

Poggio, T. A. & Xu, M. On efficiently computable functions, deep networks and sparse compositionality. (2025).

Deep_sparse_networks_approximate_efficiently_computable_functions.pdf (223.15 KB)

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. Associative Memory as the Core of Intelligence in Technology and Evolution. (2026).

Review_On_Associative_Memories-14.pdf (245.78 KB)

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

v1.2 (2.29 MB)