Cross-validation on 7165 molecules yields a mean absolute error of 9.9 kcal/mol, which is an order of magnitude more accurate than counting bonds or semiempirical quantum chemistry. We use the GDB data base, a library of nearly one billion organic molecules that are stable and synthetically accessible according to organic chemistry rules [15]. While potentially applicable to any stoichiometry, as a proof of principle we restrict ourselves to small organic molecules. Specifically, we define a controlled test-bed consisting of all 7165 organic molecules from the GDB data base with up to seven "heavy" atoms that contain C, N, O, or S, being saturated with hydrogen atoms. Atomization energies range from -800 to -2000 kcal/mol.

A framework is introduced for assessing the encoding accuracy and the discriminational ability of a population of neurons upon simultaneous presentation of multiple stimuli. Minimal square estimation errors are obtained from a Fisher information analysis in an abstract compound space comprising the features of all stimuli. Even for the simplest case of linear superposition of responses and Gaussian tuning, the symmetries in the compound space are very different from those in the case of a single stimulus. The analysis allows for a quantitative description of attentional effects and can be extended to include neural nonlinearities such as nonclassical receptive fields.

A framework is introduced for assessing the encoding accuracy and the discriminational ability of a population of neurons upon simultaneous presentation of multiple stimuli. Minimal square estimation errors are obtained from a Fisher information analysis in an abstract compound space comprising the features of all stimuli. Even for the simplest case of linear superposition of responses and Gaussian tuning, the symmetries in the compound space are very different from those in the case of a single stimulus. The analysis allows for a quantitative description of attentional effects and can be extended to include neural nonlinearities such as nonclassical receptive fields.

Bayesian decoding to account for the presentation of multiple objects.