In other words, we wish to infer the mapping implied by the data; the cost function is related to the mismatch between our mapping and the data and it implicitly contains prior knowledge about the problem domain.

As the network learns, constantly adjusting and readjusting the strengths of its synapses, it evolves into a device that implicitly contains the phonological rules of English.

The fundamental defect of those theories is that they implicitly contain a negative value for the gravitational energy in the vicinity of matter, which would violate the energy principle.

"This legislation," said Bruce L. Gardner, Assistant Secretary for Economics at the Agriculture Department, "implicitly contains a judgment that food aid is socially twice as valuable as other charitable donations."

The above element, which implicitly requests an assertion containing an authentication statement, was evidently issued by a service provider () and subsequently presented to the identity provider (via the browser).

Gödel's completeness theorem of 1930 implicitly contains a definition of a universal computer, because the logical rules acting on some axioms of arithmetic will eventually prove as a theorem the result of any computation.

Nevertheless, "Rescuing Prometheus" implicitly contains a powerful message.

Steiner later spoke of this book as containing implicitly, in philosophical form, the entire content of what he later developed explicitly as anthroposophy.

Especially in the analysis phase, task models are generated for documentation and user interface generation, which implicitly contains a function model of the process and/or of the machine (Meixner and Goerlich, 2008).

In many cases, the assumption that an element is not equal to zero is insufficient to construct the inverse; the assumption that it is apart from zero implicitly contains the necessary information.