Scalar and Grassmann Neural Network Field Theory


Maiti, A. (2024). Scalar and Grassmann Neural Network Field Theory. Perimeter Institute. https://pirsa.org/24020068


Maiti, Anindita. Scalar and Grassmann Neural Network Field Theory. Perimeter Institute, Feb. 16, 2024, https://pirsa.org/24020068


          @misc{ pirsa_PIRSA:24020068,
            doi = {10.48660/24020068},
            url = {https://pirsa.org/24020068},
            author = {Maiti, Anindita},
            keywords = {Other},
            language = {en},
            title = {Scalar and Grassmann Neural Network Field Theory},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {feb},
            note = {PIRSA:24020068 see, \url{https://pirsa.org}}

Anindita Maiti Perimeter Institute for Theoretical Physics

Talk Type Scientific Series


Neural Network Field Theories (NNFTs) are field theories defined via output ensembles of initialized Neural Network (NN) architectures, the backbones of current state-of-the-art Deep Learning techniques. Different limits of NN architectures correspond to free, weakly interacting, and non-perturbative regimes of NNFTs, via central limit theorem and its violations. Nature of field interactions in NNFTs can be controlled by tuning architecture parameters and hyperparameters, systematically, at initialization. I will present a systematic construction of scalar NNFT actions, using various attributes of NN architectures, via a new set of Feynman rules and techniques from statistical physics. Conversely, I will present the construction of a class of NN architectures exactly corresponding to some interacting scalar field theories, via a systematic deformation of NN parameter distributions. As an example of the latter method, I will present the construction of an architecture for $\lambda \phi^4$ scalar NNFT. Lastly, I will introduce Grassmann NNFTs, their free and interacting regimes via central limit theorem for Grassmanns, and construction of an architecture corresponding to free Dirac NNFT. This approach provides us a way to initialize NN architectures exactly representing certain field configurations, and are useful for computing attributes, e.g. correlators, of field theories on lattice.


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