Publication
] Deep Learning: mathematics and neuroscience. (2016).
Deep Learning- mathematics and neuroscience.pdf (1.25 MB)
Deep Learning- mathematics and neuroscience.pdf (1.25 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)
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) From Associative Memories to Powerful Machines. (2021). v1.0 (1.01 MB) v1.3Section added August 6 on self attention (3.9 MB)
v1.0 (1.01 MB) v1.3Section added August 6 on self attention (3.9 MB) Notes on Hierarchical Splines, DCLNs and i-theory. (2015). CBMM Memo 037 (1.83 MB)
CBMM Memo 037 (1.83 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)
art%3A10.1007%2Fs11633-017-1054-2.pdf (1.68 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)
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) Cervelli menti algoritmi. 272 (Sperling & Kupfer, 2023). at <https://www.sperling.it/libri/cervelli-menti-algoritmi-marco-magrini>
What if.. (2015). What if.pdf (2.09 MB)
What if.pdf (2.09 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)
03_775-788_00920_Bpast.No_.66-6_31.12.18_K2.pdf (5.43 MB) An Overview of Some Issues in the Theory of Deep Networks. IEEJ Transactions on Electrical and Electronic Engineering 15, 1560 - 1571 (2020).
Computational role of eccentricity dependent cortical magnification. (2014). CBMM-Memo-017.pdf (1.04 MB)
CBMM-Memo-017.pdf (1.04 MB) Deep Leaning: Mathematics and Neuroscience. A Sponsored Supplement to Science Brain-Inspired intelligent robotics: The intersection of robotics and neuroscience, 9-12 (2016).
Complexity Control by Gradient Descent in Deep Networks. Nature Communications 11, (2020). s41467-020-14663-9.pdf (431.68 KB)
s41467-020-14663-9.pdf (431.68 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)
v1.0 (984.15 KB) v5.7 adding in context learning etc (1.16 MB) Is Research in Intelligence an Existential Risk?. (2014). Is Research in Intelligence an Existential Risk.pdf (571.42 KB)
Is Research in Intelligence an Existential Risk.pdf (571.42 KB) 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)
02_761-774_00966_Bpast.No_.66-6_28.12.18_K1.pdf (1.18 MB) Implicit dynamic regularization in deep networks. (2020). v1.2 (2.29 MB) v.59 Update on rank (2.43 MB)
v1.2 (2.29 MB) v.59 Update on rank (2.43 MB) On efficiently computable functions, deep networks and sparse compositionality. (2025). Deep_sparse_networks_approximate_efficiently_computable_functions.pdf (223.15 KB)
Deep_sparse_networks_approximate_efficiently_computable_functions.pdf (223.15 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)
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) 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)
Volume Introduction and Preface (232.8 KB) TomasoPoggio.pdf (1.43 MB) Explicit regularization and implicit bias in deep network classifiers trained with the square loss. arXiv (2020). at <https://arxiv.org/abs/2101.00072>
Turing++ Questions: A Test for the Science of (Human) Intelligence. AI Magazine 37 , 73-77 (2016). Turing_Plus_Questions.pdf (424.91 KB)
Turing_Plus_Questions.pdf (424.91 KB) 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)
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) 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)
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. Bulletin of the American Mathematical Society 61, 438-456 (2024).