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

CBMM-Memo-118.pdf (362.19 KB)

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

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

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

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

Review_On_Associative_Memories-14.pdf (245.78 KB)

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. & 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. What if.. (2015).

What if.pdf (2.09 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. Deep Learning: mathematics and neuroscience. (2016).

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

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

CBMM-Memo-017.pdf (1.04 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., 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. 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. & 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. & Fraser, M. Compositional Sparsity of Learnable Functions. (2024).

This is an update of the AMS paper (230.72 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. 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)