How Matheta Works

Underneath Matheta

  • Matrices model neurons and synapses
  • Unique rules for modifying synaptic efficacies
  • A nervous system architecture based on prototypical emotions (e.g. fear, enjoyment)

Matheta’s Advantages

Using Neurophysiological Information

A Chinese proverb: “If you would carve an axe handle, the model is in your hand.”  This idea guides development at Matheta. We have the whole animal kingdom to examine to discover the ways evolution solved the various problems in making a system that detects, records, and uses information about how the world works so as to survive and prosper. All that science has learned about animal behavior and the neurophysiology behind it is useful to us as this model evolves. First we copy, then we improve.

Behavior and Intelligence

Behavior is the root and purpose of intelligence.  When animals gained the ability to move, they gained the world.  It let them go get food and actively avoid becoming food.  Behavior operates in the world and has effects, consequences in the world that directly affect the animal that emitted (or didn’t emit) them. An animal’s nervous system both emits and directs behavior in a non-random manor. These facts are sometimes unappreciated. As an example, consider a recent article in Science News describing the controversy about whether the comb jellyfish, rather than the sponge, is the closest representative of the first animal. The comb has a nervous system and muscles while sponges have neither so how did the comb start out so advanced? The traditional view states “colonies of single-celled organism called choano-flagellates gave way to multicellular predecessors of sponges; millions of years later, an offshoot of these organisms formed nerve cells. Later on muscles developed.” What we question here is the order of evolution: nerves then muscles. Of what possible use are nerves (information) without muscles (action)? What evolutionary advantage do nerves by themselves bestow? However the converse is clear: Any action, even random movement, has consequences that could work for or against an organism. And once an organism can move, the advantages of directing that movement are so evident they will soon be reflected in the genome. Consider just the simplest example of a reliable rule: move towards smaller organisms and away from bigger.  It is apparent that even such simple rule would confer survival benefits on an organism.  Imagine , also, the thoughts of the smartest sponge in the world: “Oh dear! That Ediacaran is coming to eat me! How I wish I could ru……..” All the modeling done by Matheta is based on the understanding that it is through the ever more sophisticated control of behavior, that is, actions, that intelligence evolves.

Outcome Evaluation

When contingencies are reliable over time they can be built into hardware/biology. Thus, one imagines the directive to move towards the small and away from the large is deep and ancient in animals. But learning is about changes in behavior in the lifetime of a single organism and it must have been a later development because it is a much more complicated problem. Particularly important is the question of how to evaluate the benefit of actions. Every behavior emitted by an organism has a host of consequences. Consider a pigeon pressing a bar: it expended some energy to press it, some heat (more energy) passed through its foot to the metal bar, the bar made a clicking sound, that sound energy dissipated throughout the environment, a food pellet fell out of a chute. Some of those consequences it does (or can) detect: the energy expenditures, the noise, and the food pellet. Others not: the miniscule rise in the temperature in the cage caused by the dissipation of the sound waves. Selecting what to do and not do requires, amongst other things, some kind of system to evaluate events in terms of their impact on an organism’s survivability.   As is evident from the videos, the Matheta system clearly has a system to turn positively (and negatively) evaluated environmental events into appropriate changes in behavior.   But unlike organisms, whose evaluations are based on the particulars of their biochemistry, with Matheta, we are free to define “good” and “bad,”  “positive” or “negative” in whatever way suits our purposes.


You might think that Robby’s observable responses when rewarded or punished (lights, sounds, movements) are mere “eye candy” but that would be a mistake. They are in fact the first manifestations of affect (that is, the biology of emotion). Affect is natural selection’s first take at determining the significance of a stimulus, that is, possible meaning. Affect is inherently built into Matheta. What you see is the forerunner of Matheta’s modeling and display of affect and its internal and external functions. By modeling emotion, Matheta is able to replicate the most powerful force that controls all behavior, even ours. In addition, this will allow systems built using Matheta AI to interact with users in a way that they will feel is naturally rewarding and familiar. For information on new capabilities and potential developmental pathways, please go to “The Way Forward.”


The Arduino is the green circuit board with all the wires sitting on top of the Roomba.  It is a micro controller, a small computer that talks to the outside world through pins on the board.  I have put together a circuit that includes a light sensor, a mini microphone, and a LED beam interrupt (at the base of the funnel that detects when candy drops through it.)  These constitute the sensors of the (incredibly minimal) sensory system of the “artificial organism.”

The Arduino runs a program that mathematically models a simple nervous system, that is, a set of interconnected neurons.  The picture below provides a schematic view of the modeled nervous system.

Mouse's nervous system copy

The nervous system is modeled by using matrices.  One matrix (the Nervous System matrix) is the model of the nervous system where each row is an individual behavior neuron.  The elements of the nervous system matrix indicate the “synaptic efficacy” of the connection between each sensory neuron and each behavior neuron.  The greater the synaptic efficacy, the more the firing of the sensory neuron contributes to the firing of the behavior neuron.

A second matrix (the Stimulus Matrix) sets an element to 1 whenever a sensory neuron “fires” (like it would, say, when the light is on, or a candy drops through).  The image below shows the two matrices.

Synaptic Efficacies My Mod

When the program multiplies these two matrices together (which is what it’s doing most of the time), the effect is to sum up the inputs (some of which may be negative, i.e., inhibitory) on each neuron and “fire” those that exceed a threshold value.  When a behavior neuron fires, the Arduino then simply commands the Roomba to execute the appropriate behavior (turn left, go forward, etc.)

The ONLY other thing the program on the Arduino does is change the “synaptic efficacy” values in the nervous system matrix depending on rules about WHAT IS HAPPENING AT THE SYNAPSE.  This last is important because it is what most distinguishes this from a program anyone could write that would simulate (rather than replicate or model) a nervous system.  That is, a program that says “if x happens then do y.”

That’s why we say that everything you see follows from the actions of the nervous system, why it is indeed an artificial organism only with wires instead of physical neurons, and light sensors instead of eyes, etc.

The most important point being that if you agree that the organism is LEARNING in a way that replicates what is known about animal learning, then it would seem to suggest (strongly, we believe) that the rules that determine the operation of these artificial neurons must have at least SOME resemblance to the rules that determine the functioning of REAL neurons.  And if that is true, why can’t we, given present computer capabilities, eventually replicate the functioning (and hence, learning capability) of any brain, including our own?

To aid understanding, and in the hopes of stimulating interest, below I describe the unique rules of synaptic modification that are at the heart of Matheta’s learning capabilities.

Synaptic Modification Rules

Let the axon of cell A make synaptic connection with the cell body (or dendrites) of cell B:

  1. Whenever cell A fires, all its synapses become temporarily eligible for modification (irrespective of whether they have an excitatory or inhibitory effect on the post-synaptic neuron). The time period here is from a hundred milliseconds to seconds, i.e., that of effective inter-stimulus intervals in classical conditioning.
  2. If the cell B fires during this period of eligibility, the AB synapse efficacy becomes temporarily increased (whether excitatory or inhibitory) This temporary increase lasts on the order of a few seconds to minutes to, i.e., mirroring effective delay times between emission of the operant and reinforcement in operant conditioning.
  3. Whenever the organism ingests something evaluated as food, it produces a hypothesized neuro/chemical, brain-wide process that halts any further decay in the efficacy of any excitatory neurons that are still in a state of temporarily increased efficacy, resulting in a new, higher baseline excitatory efficacy. This is called a positive “fixer.” (As in old-fashioned film development.)
  4. Similarly, an aversive stimulus will result in the production of a negative fixer that halts the decay of any temporarily increased inhibitory synapses.