How important are Undergraduate College Academics after graduation? How much do we actually remember after we leave the college classroom, and for how long? Taking a look at major University ranking methodologies one can easily observe they consistently lack any objective measure of what content knowledge and skills students retain from college education in the long term. Is there any rigorous scholarly published evidence on retention of long-term unused academic content knowledge? We have found no such evidence based on a preliminary literature review. Furthermore, findings in all research papers reviewed in this study were consistent with the following assertion: the Ebbinghaus forgetting curve [Ebbinghaus 1880-1885] is a fundamental law of human nature – in fact, of the whole animal kingdom and applies to memory of all types: verbal, visual, abstract, social and autobiographical. This fundamental law of nature, when examined within the context of academic

learning retention, manifests itself as an exponential curve halving memory saliency about every two years (what we call "Ebbinghaus Speed"). This paper presents the research group’s initial hypothesis and conjectures for college level education programming and curriculum development, suggestions for instructional design enhancing learning durability, as well as future research directions.

http://hdl.handle.net/1721.1/110349

%0 Generic %D 2017 %T Theory of Intelligence with Forgetting: Mathematical Theorems Explaining Human Universal Forgetting using “Forgetting Neural Networks” %A Felipe Cano-Córdoba %A Sanjay Sarma %A Brian Subirana %XIn [42] we suggested that any memory stored in the human/animal brain is forgotten following the Ebingghaus curve – in this follow-on paper, we define a novel algebraic structure, a *Forgetting Neural Network*, as a simple mathematical model based on assuming parameters of a neuron in a neural network are forgotten using the Ebbinghaus forgetting curve. We model neural networks in Sobolev spaces using [35] as our departure point and demonstrate four novel theorems of Forgetting Neural Networks: *theorem of non-instantaneous forgetting, theorem of universal forgetting, curse of forgetting theorem*, and *center of mass theorem*. We also proof the novel *decreasing inference theorem *which we feel is relevant beyond Ebbinghaus forgetting: compositional deep neural networks cannot arbitrarily combine low level “features” – meaning only certain arrangements of features calculated in intermediate levels can show up in higher levels. This proof leads us to present the possibly most efficient representation of neural networks’ *“minimal polynomial basis layer” (MPBL) *since our basis construct can generate n polynomials of order m using only 2m + 1 + n neurons. As we briefly discuss in the conclusion, there are about 10 similarities between forgetting neural networks and human forgetting and our research elicits more questions than it answers and may have implications for neuroscience research including our understanding of how babies learn (or, perhaps, forget), including what we call the *baby forgetting conjecture*.