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)
Author's last draft (20.26 MB) Deep Leaning: Mathematics and Neuroscience. A Sponsored Supplement to Science Brain-Inspired intelligent robotics: The intersection of robotics and neuroscience, 9-12 (2016).
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)
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) Notes on Hierarchical Splines, DCLNs and i-theory. (2015). CBMM Memo 037 (1.83 MB)
CBMM Memo 037 (1.83 MB) Cervelli menti algoritmi. 272 (Sperling & Kupfer, 2023). at <https://www.sperling.it/libri/cervelli-menti-algoritmi-marco-magrini>
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) 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) 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) 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) 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) A Perspective: Sparse Compositionality and Efficiently Computable Intelligence. (2026). Perspective_SPCOMP-9.pdf (170.23 KB)
Perspective_SPCOMP-9.pdf (170.23 KB) Compositional sparsity of learnable functions. Bulletin of the American Mathematical Society 61, 438-456 (2024).
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) 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) 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: 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) Theory II: Landscape of the Empirical Risk in Deep Learning. (2017). CBMM Memo 066_1703.09833v2.pdf (5.56 MB)
CBMM Memo 066_1703.09833v2.pdf (5.56 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) Associative Memory as the Core of Intelligence in Technology and Evolution. (2026). Review_On_Associative_Memories-14.pdf (245.78 KB)
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).
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) 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) I-theory on depth vs width: hierarchical function composition. (2015). cbmm_memo_041.pdf (1.18 MB)
cbmm_memo_041.pdf (1.18 MB)