1
|
Cassella G, Sutterud H, Azadi S, Drummond ND, Pfau D, Spencer JS, Foulkes WMC. Discovering Quantum Phase Transitions with Fermionic Neural Networks. Phys Rev Lett 2023; 130:036401. [PMID: 36763402 DOI: 10.1103/physrevlett.130.036401] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2022] [Accepted: 11/18/2022] [Indexed: 06/18/2023]
Abstract
Deep neural networks have been very successful as highly accurate wave function Ansätze for variational Monte Carlo calculations of molecular ground states. We present an extension of one such Ansatz, FermiNet, to calculations of the ground states of periodic Hamiltonians, and study the homogeneous electron gas. FermiNet calculations of the ground-state energies of small electron gas systems are in excellent agreement with previous initiator full configuration interaction quantum Monte Carlo and diffusion Monte Carlo calculations. We investigate the spin-polarized homogeneous electron gas and demonstrate that the same neural network architecture is capable of accurately representing both the delocalized Fermi liquid state and the localized Wigner crystal state. The network converges on the translationally invariant ground state at high density and spontaneously breaks the symmetry to produce the crystalline ground state at low density, despite being given no a priori knowledge that a phase transition exists.
Collapse
Affiliation(s)
- Gino Cassella
- Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Halvard Sutterud
- Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Sam Azadi
- Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - N D Drummond
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - David Pfau
- Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
- DeepMind, London N1C 4DJ, United Kingdom
| | | | - W M C Foulkes
- Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
| |
Collapse
|
2
|
Christensen AC, Lensjø KK, Lepperød ME, Dragly SA, Sutterud H, Blackstad JS, Fyhn M, Hafting T. Perineuronal nets stabilize the grid cell network. Nat Commun 2021; 12:253. [PMID: 33431847 PMCID: PMC7801665 DOI: 10.1038/s41467-020-20241-w] [Citation(s) in RCA: 238] [Impact Index Per Article: 79.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2019] [Accepted: 11/16/2020] [Indexed: 11/29/2022] Open
Abstract
Grid cells are part of a widespread network which supports navigation and spatial memory. Stable grid patterns appear late in development, in concert with extracellular matrix aggregates termed perineuronal nets (PNNs) that condense around inhibitory neurons. It has been suggested that PNNs stabilize synaptic connections and long-term memories, but their role in the grid cell network remains elusive. We show that removal of PNNs leads to lower inhibitory spiking activity, and reduces grid cells' ability to create stable representations of a novel environment. Furthermore, in animals with disrupted PNNs, exposure to a novel arena corrupted the spatiotemporal relationships within grid cell modules, and the stored representations of a familiar arena. Finally, we show that PNN removal in entorhinal cortex distorted spatial representations in downstream hippocampal neurons. Together this work suggests that PNNs provide a key stabilizing element for the grid cell network.
Collapse
Affiliation(s)
- Ane Charlotte Christensen
- Institute of Basic Medical Sciences, University of Oslo, Oslo, Norway
- Department of Biosciences, University of Oslo, Oslo, Norway
- Center for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
| | - Kristian Kinden Lensjø
- Department of Biosciences, University of Oslo, Oslo, Norway
- Center for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
| | - Mikkel Elle Lepperød
- Institute of Basic Medical Sciences, University of Oslo, Oslo, Norway
- Department of Biosciences, University of Oslo, Oslo, Norway
- Center for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
| | - Svenn-Arne Dragly
- Center for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
- Department of Physics, University of Oslo, Oslo, Norway
| | - Halvard Sutterud
- Center for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
- Department of Physics, University of Oslo, Oslo, Norway
| | - Jan Sigurd Blackstad
- Department of Biosciences, University of Oslo, Oslo, Norway
- Center for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
| | - Marianne Fyhn
- Department of Biosciences, University of Oslo, Oslo, Norway
- Center for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
| | - Torkel Hafting
- Institute of Basic Medical Sciences, University of Oslo, Oslo, Norway.
- Center for Integrative Neuroplasticity, University of Oslo, Oslo, Norway.
| |
Collapse
|