Publication
] What if.. (2015).
What if.pdf (2.09 MB)
What if.pdf (2.09 MB) Compositional sparsity of learnable functions. Bulletin of the American Mathematical Society 61, 438-456 (2024).
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) Computational role of eccentricity dependent cortical magnification. (2014). CBMM-Memo-017.pdf (1.04 MB)
CBMM-Memo-017.pdf (1.04 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 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) 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) Deep Learning: mathematics and neuroscience. (2016). Deep Learning- mathematics and neuroscience.pdf (1.25 MB)
Deep Learning- mathematics and neuroscience.pdf (1.25 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) Visual Cortex and Deep Networks: Learning Invariant Representations. 136 (The MIT Press, 2016). at <https://mitpress.mit.edu/books/visual-cortex-and-deep-networks>
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) Notes on Hierarchical Splines, DCLNs and i-theory. (2015). CBMM Memo 037 (1.83 MB)
CBMM Memo 037 (1.83 MB) Deep Leaning: Mathematics and Neuroscience. A Sponsored Supplement to Science Brain-Inspired intelligent robotics: The intersection of robotics and neuroscience, 9-12 (2016).
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)
v1.0 (984.15 KB) v5.7 adding in context learning etc (1.16 MB) From Marr’s Vision to the Problem of Human Intelligence. (2021). CBMM-Memo-118.pdf (362.19 KB)
CBMM-Memo-118.pdf (362.19 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) 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) Compositional Sparsity of Learnable Functions. (2024). This is an update of the AMS paper (230.72 KB)
This is an update of the AMS paper (230.72 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)
Volume Introduction and Preface (232.8 KB) TomasoPoggio.pdf (1.43 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)
PNASlast.pdf (915.3 KB) 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) Cervelli menti algoritmi. 272 (Sperling & Kupfer, 2023). at <https://www.sperling.it/libri/cervelli-menti-algoritmi-marco-magrini>