Why Does Deep and Cheap Learning Work So Well?
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Every Gaussian transformation on N modes can be decomposed into a CV circuit containing only the basic Gaussian gates (rotation, displacement, squeezing, and beamsplitter).
“Every Gaussian transformation on N modes [Eq.( 7)] can be decomposed into a CV circuit containing only the basic gates mentioned above.”
From Continuous-variable quantum neural networks (2019) · cites this paper as [49]
Deeper neural networks can be more powerful and more efficient than shallower networks with the same number of parameters.
“While the original theorems showed that two layers were sufficient for universal function approximation, deeper networks can be more powerful and more efficient than shallower networks with the same number of parameters [57][58][59].”
From Continuous-variable quantum neural networks (2019) · cites this paper as [59]
The connection between translationally invariant Hamiltonians and convolutional networks was also noted in Ref. [59].
“The connection between translationally invariant Hamiltonians and convolutional networks was also noted in Ref. [59].”
From Continuous-variable quantum neural networks (2019) · cites this paper as [59]
In the phase space picture, the symplectic transformation M H generated by H is obtained via the rule M H = exp( H ), where is the symplectic form from Eq. (8).
“In the phase space picture, the symplectic transformation M H generated by H is obtained via the rule [49] M H = exp( H ),”
From Continuous-variable quantum neural networks (2019) · cites this paper as [49]
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Solving the quantum many-body problem with artificial neural networks
Carleo, G., & Troyer, M. (2017) · Science · doi:10.1126/science.aag2302 · Cited by 2,215 · see citing works
Dimensionless constants, cosmology, and other dark matters
Tegmark, M., Aguirre, A., Rees, M. J., & Wilczek, F. (2006) · Physical Review D · doi:10.1103/physrevd.73.023505 · Cited by 401 · cited 2× · see citing works
“Taken together, the constraints on locality, symmetry and polynomial order reduce the number of continuous parameters in the Hamiltonian of the standard model of physics to merely 32 [13].”
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Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019) · Journal of Computational Physics · doi:10.1016/j.jcp.2018.10.045 · Cited by 20,384 · see citing works
Quantum convolutional neural networks
Cong, I., Choi, S., & Lukin, M. D. (2019) · Nature Physics · doi:10.1038/s41567-019-0648-8 · Cited by 1,517 · see citing works
Recent advances and applications of deep learning methods in materials science
Choudhary, K., DeCost, B., Chen, C., Jain, A., Tavazza, F., Cohn, R., Park, C. W., Choudhary, A., Agrawal, A., Billinge, S. J. L., et al. (2022) · npj Computational Materials · doi:10.1038/s41524-022-00734-6 · Cited by 1,172 · see citing works
“However, it is important to note that the theorem doesn ’ t guarantee that the functions can be learnt easily 52 .”
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Safron, A. (2020) · Frontiers in Artificial Intelligence · doi:10.3389/frai.2020.00030 · Cited by 133 · see citing works
Autonomous Molecular Design: Then and Now
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Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines
Cheng, S., Chen, J., & Wang, L. (2018) · Entropy · doi:10.3390/e20080583 · Cited by 104 · see citing works
Degeneracy and Redundancy in Active Inference
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Empirical Asset Pricing via Machine Learning
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- Authors
- Lin, H. W., Tegmark, M., & Rolnick, D.
- Affiliations
- Harvard University (US)
- Massachusetts Institute of Technology (US)
- Corresponding author
- Lin, Henry W.
- Venue
- Journal of Statistical Physics
- Published
- 2017-07-21
- Volume
- 168
- Issue
- 6
- Pages
- 1223-1247
- ISSN
- 0022-4715 (ISSN-L)
- 1572-9613
- OpenAlex
- W2511261638
- Cited by
- 393
- References
- 3
- Citations by year
- 2026: 22 · 2025: 31 · 2024: 29 · 2023: 39 · 2022: 42 · 2021: 49 · 2020: 60 · 2019: 58 · 2018: 52 · 2017: 11
- FWCI
- 29.54
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Statistical Physics (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Stochastic Gradient Optimization Techniques
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Algorithms
- Keywords
- deep learning, neural network efficiency, function approximation, symmetry, locality, compositionality, information theory, renormalization group, linear neural networks
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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