Publications

CBMM Memos were established in 2014 as a mechanism for our center to share research results with the wider scientific community. Click here to read more about the memos and to see a full list of the memos.

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Pouncy, T. & Gershman, S. J. Inductive biases in theory-based reinforcement learning. Cognitive Psychology 138, 101509 (2022).

Pouncy, T., Tsividis, P. & Gershman, S. J. What Is the Model in Model‐Based Planning?. Cognitive Science 45, (2021).

Ponce, C. R. et al. 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)

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

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

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. & 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. 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. 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. & Fraser, M. Compositional Sparsity of Learnable Functions. (2024).

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

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

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

CBMM-Memo-017.pdf (1.04 MB)

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)

Added result about square loss and min norm (898.03 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., Liao, Q. & Banburski, A. Complexity Control by Gradient Descent in Deep Networks. Nature Communications 11, (2020).

s41467-020-14663-9.pdf (431.68 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., 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. & 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. Is Research in Intelligence an Existential Risk?. (2014).

Is Research in Intelligence an Existential Risk.pdf (571.42 KB)

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

Perspective_SPCOMP-9.pdf (170.23 KB)

Poggio, T. From Associative Memories to Powerful Machines. (2021).

v1.0 (1.01 MB)

v1.3Section added August 6 on self attention (3.9 MB)

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., 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)

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