wiki:box:did-you-know

**Boltzmann machine**, a predecessor of modern machine learning models, is based on a spin-glass model of Sherrington-Kirkpatrick's stochastic Ising Model.*A pair of homologous cycles in a***cellular sheaf**has**effective resistance**as defined via the minimal-norm bounding chain.**Effective resistance**acts as a probability on graph cycles, thus allowing for random sampling to compress a sheaf with control of the eigenspectrum of the sheaf Laplacian. Cellular sheaves thus have natural variational approximations.**Behavior Space**manifold of model parameters as coordinates has simpler models as its**boundaries**with parameters $\theta_\nu = 0, \infty, \theta_\mu$, the model manifold is usually a**hyperribon**.**The loss function**landscape pertaining to can be thought of thermodynamically as an energy function over thermal degrees of freedom? Stochastic gradient descent then acts as a dissipative process introducing self-generated disorder. Furthermore a phase transition occurs at singularity in free energy.*Any real function on a***cotangent bundle**can be interpreted to be a Hamiltonian, so real-valued cotangent bundle is a phase space.*A***more general form**of**Arrow's impossibility theorem**can be shown to be true as a consequence of homotopy.*A recent model called***rapid freeze neuroplasticity**, a phenomenon similar to frozen random patterns in coupled map lattices pertaining to self-organized**quenched disorder**, was proposed as an explanation for neurodynamics of conspiracy theories?*Philip J. Anderson's treated***emergence**centrally through**generalized rigidity**, to be understood as a consequence of broken symmetry and the order parameter.**Nerves**, a construct of Δech cohomology theory, can be used to track down attractors in spike train activity in computational neuroscience?

page revision: 16, last edited: 18 Mar 2024 03:29