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 Čech cohomology theory, can be used to track down attractors in spike train activity in computational neuroscience?