This article proposes a conceptual framework to guide research in neural computation by relating it to mathematical progress in other fields and to examples illustrative of biological networks. The goal is to provide insight into how biological networks, and possibly large artificial networks such as foundation models, transition from analog computation to an analog approximation of symbolic computation. From the mathematical perspective, I focus on the development of consistent symbolic representations and optimal policies for action selection within network settings. From the biological perspective, I give examples of human and animal social network behavior that may be described using these mathematical models.

We propose that many human behaviors can be accurately described as a set of dynamic models (e.g., Kalman filters) sequenced together by a Markov chain. We then use these dynamic Markov models to recognize human behaviors from sensory data and to predict human behaviors over a few seconds time. To test the power of this modeling approach, we report an experiment in which we were able to achieve 95% accuracy at predicting automobile drivers' subsequent actions from their initial preparatory movements.

Biological systems have a large degree of redundancy, a fact that is usually thought to have little effect beyond providing reliable function despite the death of individual neurons. We have discovered, however, that redundancy can qualitatively change the computations carried out by a network. We prove that for both feedforward and feedback networks the simple duplication of nodes and connections results in more accurate, faster, and more stable computation.

A simple neural mechanism that recovers surface shape from image shading is derived from a simplified model of the physics of image formation. The mechanism's performance is surprisingly good even when applied to complex natural images, and is even able to extract significant shape information from some line drawings.

Visual object recognition is a difficult problem that has been solved by biological visual systems. An approach to object recognition is described in which the image is segmented into parts using two simple, biologically-plausible mechanisms: a filtering operation to produce a large set of potential object “parts,” followed by a new type of network that searches among these part hypotheses to produce the simplest, most likely description of the image's part structure.