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

Perspective_SPCOMP-9.pdf (170.23 KB)

Poggio, T. Is Research in Intelligence an Existential Risk?. (2014).

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

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

Review_On_Associative_Memories-14.pdf (245.78 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. & 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. What if.. (2015).

What if.pdf (2.09 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. & 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., 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. 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)

Poggio, T. & Liao, Q. Explicit regularization and implicit bias in deep network classifiers trained with the square loss. arXiv (2020). at <https://arxiv.org/abs/2101.00072>

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

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

Poggio, T. From Marr’s Vision to the Problem of Human Intelligence. (2021).

CBMM-Memo-118.pdf (362.19 KB)

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. & 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., Anselmi, F. & Rosasco, L. I-theory on depth vs width: hierarchical function composition. (2015).

cbmm_memo_041.pdf (1.18 MB)

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