Brain Building Kit™

Mathematics of the Brain
artificial brain assembly tools
with sample neuron and brain libraries




A tool DARPA uses to evaluate proposals:

"Heilmeier Catechism."

As director of ARPA George Heilmeier had a set of questions he expected every proposal for a new research program to answer

Responses to the Heilmeier catechism:

What is the problem, why is it hard? [top]

Useful synthetic neurons, neuropils, and brains cannot be built from currently available computer resources and theories.

Paraphrasing Santiago Ramón y Cajal (Nobel Medicine 1906), three basic questions must be answered:

  1. What advantages do neuron shapes confer?
  2. How are signals formed, sent, and used?
  3. What rules are used to grow shapes?

The literature on nervous systems is large, fragmented, and contentious. Neurologists say one thing while neuroscientists say another. There is no consensus on answers to any of Cajal's questions. A simple brain exhibiting published paradoxical perception could be evidence of success, but one cannot build simple brains from available theoretical models, and no such simple brain has been sustained against its critics. Even the C. Elegans nervous system, with 302 neurons, has not been modelled successfully despite plentiful computer memory and speed.

I am inclined to believe clinical neurologist observations. These are more often in conflict with scientific theory than is generally known. Neurologists use words like "aura" and "premonition" within their community. not as mysticism, but as code words for observations that cannot be explained and for which there are no more comfortable words. Specifically, the nervous system will respond to events that have not yet happened.

The degree of disparity in neuroscientist discussions makes it difficult to conceive of a single clean model that is consistent with the physics, chemistry, and histology of an entire neuron, that can be combined as many neurons in aggregates to solve specific problems. It is difficult to decide that a specific proposed abstraction deviates from the real brain in an insignificant way, or rather in a manner that fundamentally breaks the model.

The continuing lack of consensus indicates that the only valid test one can make of a model is to ask; "does the structure look like the histology, are internal signals consistent with the nanoscale chemistry, and do signal outputs resemble those known from observations of a living brain or part being modelled?"

A Brain Building Kit™ must be constructed such that a competent engineer could sketch out the known connections in a real brain, drive signals into it, generate output more useful than the input, and cause reflex actuation suited to the context of the signal. To make such a kit, one would have to have a single clean baseline model of a neuron from which specialized neurons can inherit, rules for aggregating neurons into neuropils, rules for adapting neurons and neuropils, and examples of applying signals to neuropils and their expected output.

That is the chief problem. From that point on, the problem degenerates to choosing best practices and interfaces, and decoding higher brain structures based on what is learned by decoding sensory/motor neuropils.

How is it solved today? [top]

Much research has been funded to identify "interesting" features in a scene. "Mathematical Physiology (Keener and Sneyd, Springer 2001)" documents the state of the art in understanding living systems. "Introduction to the Mathematics of Medical Imaging (Epstein, Prentice Hall 2003)" documents one branch of image processing. Too numerous books and papers have been written on "machine vision". Standard methods of image processing bank heavily on spatial frequency transforms, wavelet transforms, or heuristics like the "Sombrero" convolution.

A variety of technologies exists for imitating various scales of neural processing. Jeff Hawkins and his team do some notable work on cortical functions. Carver Meade and his several teams produce useful engineering. Teams like irobot develop ever-improving decision and actuation technologies. Michael F. Deering examines the engineering limitations of vision. Teams at a variety of universities develop neural nets, neuromimetics. John Moore and his team at Duke have detailed conventional membrane models of neurons. There are a number of odd-ball theories that respond to unanswered paradoxes.

The key thing to note is that, although problems are partially solved and models work to some limited degree, no clearly winning general basis for constructing brains is found in any of these. Yet, it is clear that neurons are simply ordinary cells with some useful adaptations.

What is the new technical idea; Why can we succeed now? [top]

All my solutions use simple math on discrete arrays (highly parallelizable). Spatial frequency transforms are absent in these solutions. Neurons are modeled as simple bundled signal carriers. Dendrites organize coincidences of received signals. Neurons have local cytoskeletal states depending on historical signals. To start a dendritic signal, a specific condition must occur. Axon pulses are formed from integrated dendritic signals. Axons project and dendrites collect using simple clear rules. Transduction into and out of neurons solve some paradoxes. Topological transfer functions solve some paradoxes. Layered transfer functions solve some paradoxes.

The brain can be viewed as having layers within structures. The dense interdigitation of axons with dendrites in a layer is called a neuropil. Some example structures and neuropils, imitating visual pathways, have been tested, and work. The rules I use for producing neurons, neuropils, and structures seem consistent with natural brains.

These are Brain Building Kit™ goals in the proposal for DARPA-BAA-09-865

  • 10X sub-pixel resolution for 20X or higher diffractive blur radius
  • Color correction in color-cast images
  • Contrast improvement
  • Simultaneous noise reduction with feature enhancement
  • Simple object recognition through rotation, translation, scale, tilt, and warp

I conclude that a general basis for constructing brains is possible. Preliminary experimental results have proven fruitful. A number of perceptual paradoxes are completely solved. A number of deviations from convention are necessary to enable these solutions. These solutions seem to arise out of sheer mathematical necessity and do not depend critically on the specifics of the underlying materials so much as on an average range of behaviors of one material upon another. It has been unnecessary to invent unrealistic scenarios.

What is the impact if successful? [top]

A general BBK (Brain Building Kit™) has enormous consequences. Where electronic spreadsheets revolutionized the financial world, a BBK enables engineers to capture and employ many other economies. Simple example neuropils with explanations of input and output signals can be used to train novice BBK engineers to identify opportunites.

In a similar manner to electronic spreadsheets the community of BBK support can be layered with core engineers working on improving the BBK engine including growth rules, interface engineers working on improving the BBK usability, internal application engineers developing a library of "known" neuron topologies, external expert engineers developing libraries of industry specific brains, external application engineers refining brains to their specific devices, and end users whose responses to the brain-enabled device cause it to regrow.

Sir Charles Sherrington (Nobel Medicine 1932) once said "The brain is the crowning achievement of the reflex system." By this, I believe he meant that there is nothing but reflex in a brain's structure and function. As such, it is important to consider the reflex arc as the primary goal of all brain building. Devices can be built with reflexes more appropriate to the user than the cleverest engineer can ever hard-code in a program.

The world of smart devices could be deeply affected by substituting appropriate-to-use topological reflex primitives for expert system code.

How will the program be organized? [top]
Personnel (Rough Draft)
Preference for those familiar with discrete manifolds and APL or J
Project management
Preference for familiarity with XP ("Extreme Programming")
Preference for established expert in Science/Technology/User integration
Preference for XP experienced math-adept physics-adept people with interest in neural signal processing
Preference for experience in military technologies, processes, and projects
Preference for gifted polymath
Chief Scientist/Team Lead
My role
Milestones (Rough Draft)
Transduction/Topology Prototyping
BBK Visualization/Construction
Test Suite
Tasks (Rough Draft)
Team Recruitment
Unit-Tested Primitives Resource Development
Visualization/Construction Tools Development
Test Suite Assembly/Development
System Design Documentation
Consolidate Methods into a generic BBK
Specialization to Device
Test Device
Presentation Development
Schedule (Rough Draft)

How will intermediate results be generated? [top]

The first stage of development will focus on visual processing. This is convenient due to the great volume of histological literature on visual brain. Within this stage, there are many intermediate goals. The final product will be a processor to perform reliable object identification including IFF.

My approach to this is so-called "bottom-up". First perform transductions properly (new material), then early perceptual transforms, and finally, using a new form of memory, predictive modeling to confirm identification. Each intermediate goal is an autonomous sub-project subject to integration. Each sub-project will be managed under Extreme Programming rules. Nevertheless, a "top-down" architecture will guide all sub-projects towards integration.

The Extreme Programming methodology is particularly suited to this project due to the large number of innovations to be managed and the unmanageably large scale of documentation required were more traditional design methods used.

Using the disciplined software development practices of Extreme Programming, the team will generate new "iterations" each month. This process will include training and discussion time for the new methods. Every month, a report will be generated documenting what the final status of the current iteration is and what specific goals are to be met in the next.

Amongst the goals to be met by early development are:

Contrast Invariance
Color Constancy
Hyperacute (sub-pixel) imaging
Feature recovery in noise-reduced image
Feature prediction
Shape discrimination

How will you measure progress? [top]

Extreme Programming practices address this. For each iteration, specific goals are written as "User Stories". Probability of success within the iteration is evaluated. Developers commit to the level of effort required. Programming pairs implement unit tests, code for the user stories, and document. This material is assembled into a monthly progress report. In this report will be lists and charts for:

  • unit test results documentation
  • code coverage
  • performance
  • code internal documentation completeness
  • system documentation
  • operational capabilities
  • signal input/output test suites compliance test results
  • project status

What will it cost? [top]

With exceptionally talented contributors, a full staff could be as small as 5 people. Fully loaded, and with equipment purchases, my rough estimate is approximately $2M in the first year.

Copyright(c)2009 Jonathan D. Lettvin, All Rights Reserved October 22, 2017, 11:46 am Contact: (617) 600-4499 email