Year: 2022

EXPONENTIAL INFO STORAGE. “We observe that such a network exhibits a critical state in which a set of would‐be‐high‐threshold neurons becomes effectively gapless. Correspondingly, in this set of neurons the network can store an exponentially large number of patterns within an arbitrarily narrow energy gap.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201800007?casa_token=GdPRXs_tGLEAAAAA%3Ag-pxPMtkcleTYDUNK3mYGfpEzKRyc2LqQknTgFFB7dkYFDL8rDe2s0f4_0Q0oKjXD4_AEgFPGWolVTQ View in LinkedIn

THE GUTS OF THE MACHINE. “The entropy of the resulting micro‐states depends on the symmetry structure of the network. We show that, when we impose a symmetry group of a d‐dimensional sphere, a set of the gapless neurons emerges with their number equal to an area of a ‐dimensional sphere of the same radius.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201800007?casa_token=GdPRXs_tGLEAAAAA%3Ag-pxPMtkcleTYDUNK3mYGfpEzKRyc2LqQknTgFFB7dkYFDL8rDe2s0f4_0Q0oKjXD4_AEgFPGWolVTQ View in LinkedIn

THE IMAGINATIVE LEAP. “Thus, it appears that the neural network – when translated in quantum field theoretic language – can exhibit some intrinsic holographic properties, such as, the emergence of the gapless neurons inhabiting a lower dimensional surface with the resulting micro‐state entropy that scales as the corresponding area. This is something highly reminiscent of gravitational systems, such as, the black holes or the AdS space.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201800007?casa_token=GdPRXs_tGLEAAAAA%3Ag-pxPMtkcleTYDUNK3mYGfpEzKRyc2LqQknTgFFB7dkYFDL8rDe2s0f4_0Q0oKjXD4_AEgFPGWolVTQ View in LinkedIn

“Other ways of being” was how William Wordsworth described other realities in The Prelude, an impressive poem. View in LinkedIn

INEVITABLE QUESTION. “Let us first ask, what are the black holes from the quantum field theoretic point of view?” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201800007?casa_token=GdPRXs_tGLEAAAAA%3Ag-pxPMtkcleTYDUNK3mYGfpEzKRyc2LqQknTgFFB7dkYFDL8rDe2s0f4_0Q0oKjXD4_AEgFPGWolVTQ View in LinkedIn

GIVEN ASSUMPTIONS. “Although a fully‐satisfactory quantum description of black holes is still missing, it is reasonably clear that they represent the states in a Hilbert space of quantized fields. We shall not question this statement.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201800007?casa_token=GdPRXs_tGLEAAAAA%3Ag-pxPMtkcleTYDUNK3mYGfpEzKRyc2LqQknTgFFB7dkYFDL8rDe2s0f4_0Q0oKjXD4_AEgFPGWolVTQ View in LinkedIn

FIRST TASK. “Our task thus boils down to the need of establishing a dictionary between the states of the quantum fields and the states of the quantum neural networks.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201800007?casa_token=GdPRXs_tGLEAAAAA%3Ag-pxPMtkcleTYDUNK3mYGfpEzKRyc2LqQknTgFFB7dkYFDL8rDe2s0f4_0Q0oKjXD4_AEgFPGWolVTQ View in LinkedIn

STARTING AT THE BEGINNING. “In quantum field framework the elementary degrees of freedom are the quantum oscillators describing the different momentum (and spin/helicity) modes of the field.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201800007?casa_token=GdPRXs_tGLEAAAAA%3Ag-pxPMtkcleTYDUNK3mYGfpEzKRyc2LqQknTgFFB7dkYFDL8rDe2s0f4_0Q0oKjXD4_AEgFPGWolVTQ View in LinkedIn

FIRST HOOK. “On the other hand, in a neural network the elementary degrees of freedom are the excitations of neurons.” https://onlinelibrary.wiley.com/doi/full/10.1002/prop.201800007?casa_token=GdPRXs_tGLEAAAAA%3Ag-pxPMtkcleTYDUNK3mYGfpEzKRyc2LqQknTgFFB7dkYFDL8rDe2s0f4_0Q0oKjXD4_AEgFPGWolVTQ View in LinkedIn