Publication

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2023
Xu, M., Rangamani, A., Liao, Q., Galanti, T. & Poggio, T. Dynamics in Deep Classifiers trained with the Square Loss: normalization, low rank, neural collapse and generalization bounds. Research (2023). doi:10.34133/research.0024PDF icon research.0024.pdf (4.05 MB)
2020
Poggio, T., Liao, Q. & Banburski, A. Complexity Control by Gradient Descent in Deep Networks. Nature Communications 11, (2020).PDF icon s41467-020-14663-9.pdf (431.68 KB)
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>
Deza, A., Liao, Q., Banburski, A. & Poggio, T. Hierarchically Local Tasks and Deep Convolutional Networks. (2020).PDF icon CBMM_Memo_109.pdf (2.12 MB)
Poggio, T., Liao, Q. & Xu, M. Implicit dynamic regularization in deep networks. (2020).PDF icon v1.2 (2.29 MB)PDF icon v.59 Update on rank (2.43 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.1907369117PDF icon PNASlast.pdf (915.3 KB)
2019
Xiao, W., Chen, H., Liao, Q. & Poggio, T. Biologically-plausible learning algorithms can scale to large datasets. International Conference on Learning Representations, (ICLR 2019) (2019).PDF icon gk7779.pdf (721.53 KB)
Banburski, A. et al. Dynamics & Generalization in Deep Networks -Minimizing the Norm. NAS Sackler Colloquium on Science of Deep Learning (2019).
Poggio, T., Banburski, A. & Liao, Q. Theoretical Issues in Deep Networks. (2019).PDF icon CBMM Memo 100 v1 (1.71 MB)PDF icon CBMM Memo 100 v3 (8/25/2019) (1.31 MB)PDF icon CBMM Memo 100 v4 (11/19/2019) (1008.23 KB)
Liao, Q., Banburski, A. & Poggio, T. Theories of Deep Learning: Approximation, Optimization and Generalization . TECHCON 2019 (2019).
Banburski, A. et al. Weight and Batch Normalization implement Classical Generalization Bounds . ICML (2019).
2018
Xiao, W., Chen, H., Liao, Q. & Poggio, T. Biologically-plausible learning algorithms can scale to large datasets. (2018).PDF icon CBMM-Memo-092.pdf (1.31 MB)
Liao, Q., Miranda, B., Hidary, J. & Poggio, T. Classical generalization bounds are surprisingly tight for Deep Networks. (2018).PDF icon CBMM-Memo-091.pdf (1.43 MB)PDF icon CBMM-Memo-091-v2.pdf (1.88 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).PDF icon 02_761-774_00966_Bpast.No_.66-6_28.12.18_K1.pdf (1.18 MB)
Poggio, T. & Liao, Q. Theory II: Deep learning and optimization. Bulletin of the Polish Academy of Sciences: Technical Sciences 66, (2018).PDF icon 03_775-788_00920_Bpast.No_.66-6_31.12.18_K2.pdf (5.43 MB)
Banburski, A. et al. Theory III: Dynamics and Generalization in Deep Networks. (2018).PDF icon Original, intermediate versions are available under request (2.67 MB)PDF icon CBMM Memo 90 v12.pdf (4.74 MB)PDF icon Theory_III_ver44.pdf Update Hessian (4.12 MB)PDF icon Theory_III_ver48 (Updated discussion of convergence to max margin) (2.56 MB)PDF icon fixing errors and sharpening some proofs (2.45 MB)
2017
Chandrasekhar, V. et al. Compression of Deep Neural Networks for Image Instance Retrieval. (2017). at <https://arxiv.org/abs/1701.04923>PDF icon 1701.04923.pdf (614.33 KB)
Zhang, C. et al. Musings on Deep Learning: Properties of SGD. (2017).PDF icon CBMM Memo 067 v2 (revised 7/19/2017) (5.88 MB)PDF icon CBMM Memo 067 v3 (revised 9/15/2017) (5.89 MB)PDF icon CBMM Memo 067 v4 (revised 12/26/2017) (5.57 MB)
Liao, Q. & Poggio, T. Object-Oriented Deep Learning. (2017).PDF icon CBMM-Memo-070.pdf (963.54 KB)
Poggio, T. & Liao, Q. Theory II: Landscape of the Empirical Risk in Deep Learning. (2017).PDF icon CBMM Memo 066_1703.09833v2.pdf (5.56 MB)
Zhang, C. et al. Theory of Deep Learning IIb: Optimization Properties of SGD. (2017).PDF icon CBMM-Memo-072.pdf (3.66 MB)
Poggio, T. et al. Theory of Deep Learning III: explaining the non-overfitting puzzle. (2017).PDF icon CBMM-Memo-073.pdf (2.65 MB)PDF icon CBMM Memo 073 v2 (revised 1/15/2018) (2.81 MB)PDF icon CBMM Memo 073 v3 (revised 1/30/2018) (2.72 MB)PDF icon CBMM Memo 073 v4 (revised 12/30/2018) (575.72 KB)
Leibo, J. Z., Liao, Q., Anselmi, F., Freiwald, W. A. & Poggio, T. View-Tolerant Face Recognition and Hebbian Learning Imply Mirror-Symmetric Neural Tuning to Head Orientation. Current Biology 27, 1-6 (2017).
Mhaskar, H., Liao, Q. & Poggio, T. When and Why Are Deep Networks Better Than Shallow Ones?. AAAI-17: Thirty-First AAAI Conference on Artificial Intelligence (2017).
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/s11633-017-1054-2PDF icon art%3A10.1007%2Fs11633-017-1054-2.pdf (1.68 MB)

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