Sloppy Spectra

Here we provide eigenvalues for the cost Hessian (in statistics, the eigenvalues of $\chi^2$) at the best fit, for a series of models. (For probabilistic models like the Ising model and the &Lambda CDM model for the cosmic microwave background radiation, these are eigenvalues of the Fisher Information matrix, a generalization of the cost Hessian to probabilistic models.)

• Cell signaling
• Radioactive decay (sums of exponentials)
• Variational wavefunction for Quantum Monte Carlo
• Cosmic microwave background radiation
• Discrete diffusion model
• 2D Ising model
• Meat oxidation model
• Model for particle accelerator
• Neural network number 1
• van der Pol oscillator
• Circadian clock
• Combustion network
• Neural network number 2
• Stock price time series distribution
• Model for particle accelerator (Energy Recovery Linac)
• Hessian for the emittance (not a least-squares cost) for the CESR particle accelerator (CESR), and the Hessian.
• Model of the H2/O2 combustion mechanism
• Neuroscience Hodgkin Huxley model of action potential
• Power systems model of the IEEE 14-bus test system
• Stillinger-Weber interatomic potential for a monolayer of MoS2
• Bryan Daniels' model of gravity generated by SirIsaac
• Transmission loss in an underwater environment with a clay bottom

More on sloppiness:

• Sloppy Models
  • A sloppy systems biology model
  • What is Sloppiness?
  • What are Sloppy Models?
  • Fitting Exponentials: Prediction without parameters
  • Fitting Polynomials: Where is sloppiness from?
  • Why sloppiness? The Sloppy Universality Class
  • Differential Geometry and Sloppy Models (Transtrum)
    • The Model Manifold and Hyperribbons (Transtrum)
    • Sloppy Curvature (Transtrum)
  • Why is science possible? Sloppy models in Physics.
    • Jessie Silverberg's Huffington Post article and Katheryn McGill's vlog Interview from The Physics Factor.
    • Unedited workshop interview by Steven Reiner, Stony Brook School of Journalism; Mobile version.
    • News article on our paper showing physics is sloppy too
• Sloppy model applications
  • Do parameters matter? Fits versus measurements.
  • Experimental design in sloppy systems
  • Robustness and sloppiness
    • Parameter robustness and sloppiness
    • Environmental robustness and sloppiness: Circadian rhythms
    • Evolvability, robustness, and sloppiness
  • Estimating systematic errors for interatomic potentials and for density functional theory.
  • Learning digits with InPCA
  • Visualizing the learning trajectories of deep neural networks using InPCA

James P. Sethna, sethna@lassp.cornell.edu; This work supported by the Division of Materials Research of the U.S. National Science Foundation, through grant DMR-070167.

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).