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Assumption violations in causal discovery and the robustness of score matching. 37th Conference on Neural Information Processing Systems (NeurIPS 2023) (2024). at <https://proceedings.neurips.cc/paper_files/paper/2023/file/93ed74938a54a73b5e4c52bbaf42ca8e-Paper-Conference.pdf>
Estimating Koopman operators with sketching to provably learn large scale dynamical systems. 37th Conference on Neural Information Processing Systems (NeurIPS 2023) (2023). at <https://proceedings.neurips.cc/paper_files/paper/2023/file/f3d1e34a15c0af0954ae36a7f811c754-Paper-Conference.pdf>
Heteroscedastic Gaussian Processes and Random Features: Scalable Motion Primitives with Guarantees. 7th Conference on Robot Learning (CoRL 2023 (2023). at <https://proceedings.mlr.press/v229/caldarelli23a/caldarelli23a.pdf>
The Janus effects of SGD vs GD: high noise and low rank. (2023).
Updated with appendix showing empirically that the main results extend to deep nonlinear networks (2.95 MB) Small updates...typos... (616.82 KB)
Updated with appendix showing empirically that the main results extend to deep nonlinear networks (2.95 MB) Small updates...typos... (616.82 KB) An Optimal Structured Zeroth-order Algorithm for Non-smooth Optimization. 37th Conference on Neural Information Processing Systems (NeurIPS 2023) (2023). at <https://proceedings.neurips.cc/paper_files/paper/2023/file/7429f4c1b267cf619f28c4d4f1532f99-Paper-Conference.pdf>
Scalable Causal Discovery with Score Matching. NeurIPS 2022 (2022). at <https://openreview.net/forum?id=v56PHv_W2A>
For interpolating kernel machines, the minimum norm ERM solution is the most stable. (2020). CBMM_Memo_108.pdf (1015.14 KB) Better bound (without inequalities!) (1.03 MB)
CBMM_Memo_108.pdf (1015.14 KB) Better bound (without inequalities!) (1.03 MB) Beating SGD Saturation with Tail-Averaging and Minibatching. Neural Information Processing Systems (NeurIPS 2019) (2019). 9422-beating-sgd-saturation-with-tail-averaging-and-minibatching.pdf (389.35 KB)
9422-beating-sgd-saturation-with-tail-averaging-and-minibatching.pdf (389.35 KB) Dynamics & Generalization in Deep Networks -Minimizing the Norm. NAS Sackler Colloquium on Science of Deep Learning (2019).
Implicit Regularization of Accelerated Methods in Hilbert Spaces. Neural Information Processing Systems (NeurIPS 2019) (2019). 9591-implicit-regularization-of-accelerated-methods-in-hilbert-spaces.pdf (451.14 KB)
9591-implicit-regularization-of-accelerated-methods-in-hilbert-spaces.pdf (451.14 KB) Theory III: Dynamics and Generalization in Deep Networks. (2018). Original, intermediate versions are available under request (2.67 MB) CBMM Memo 90 v12.pdf (4.74 MB) Theory_III_ver44.pdf Update Hessian (4.12 MB) Theory_III_ver48 (Updated discussion of convergence to max margin) (2.56 MB) fixing errors and sharpening some proofs (2.45 MB)
Original, intermediate versions are available under request (2.67 MB) CBMM Memo 90 v12.pdf (4.74 MB) Theory_III_ver44.pdf Update Hessian (4.12 MB) Theory_III_ver48 (Updated discussion of convergence to max margin) (2.56 MB) fixing errors and sharpening some proofs (2.45 MB) Computational and Cognitive Neuroscience of Vision 85-104 (Springer, 2017).
Symmetry Regularization. (2017). CBMM-Memo-063.pdf (6.1 MB)
CBMM-Memo-063.pdf (6.1 MB) 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) 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) Holographic Embeddings of Knowledge Graphs. Thirtieth AAAI Conference on Artificial Intelligence (AAAI-16) (2016). 1510.04935v2.pdf (360.65 KB)
1510.04935v2.pdf (360.65 KB) On invariance and selectivity in representation learning. Information and Inference: A Journal of the IMA iaw009 (2016). doi:10.1093/imaiai/iaw009 imaiai.iaw009.full_.pdf (267.87 KB)
imaiai.iaw009.full_.pdf (267.87 KB) 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)
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) Deep Convolutional Networks are Hierarchical Kernel Machines. (2015). CBMM Memo 035_rev5.pdf (975.65 KB)
CBMM Memo 035_rev5.pdf (975.65 KB) Discriminative Template Learning in Group-Convolutional Networks for Invariant Speech Representations. INTERSPEECH-2015 (International Speech Communication Association (ISCA), 2015). at <http://www.isca-speech.org/archive/interspeech_2015/i15_3229.html>
Holographic Embeddings of Knowledge Graphs. (2015). holographic-embeddings.pdf (677.87 KB)
holographic-embeddings.pdf (677.87 KB) On Invariance and Selectivity in Representation Learning. (2015). CBMM Memo No. 029 (812.07 KB)
CBMM Memo No. 029 (812.07 KB) I-theory on depth vs width: hierarchical function composition. (2015). cbmm_memo_041.pdf (1.18 MB)
cbmm_memo_041.pdf (1.18 MB)