Lee and David Mumford's model. The latter focused on the visual system in the necortex. It was in effect a. Bayesian inference for reasoning about a visual scene.
10th WSEAS Int. Conf. on AUTOMATIC CONTROL, MODELLING & SIMULATION (ACMOS'08), Istanbul, Turkey, May 27-30, 2008
What a memory looks like in the brain? Towards the modeling and simulation of a partial software neocortex for learning THANG N. NGUYEN Department of Information Systems California State University Long Beach Long Beach, California USA
Abstract: - This paper addresses the basic question “What a memory looks like in the brain?” It is with the hope that if a possible answer can be framed and hypothesized, a suitable description of a memory will give insights into the modeling and simulation of a partial software neocortex model for potential learning. The paper discusses prior findings and hypotheses on memory by researchers at three levels of abstraction: cellular (middle), network (higher) and molecular (lower) levels. The paper attempts to combine them, together with the author’s own hypothesis on what a memory looks like, to suggest an integrated view of memory. The paper then suggests an approach towards a software memory model based on an (arguably) observable parallelism between (1) the natural hierarchy and (2) the software hierarchy, ultimately to be simulated for potential learning as does a human newborn. It is realized that there are questionable items in this initial formulation, which are subject to future investigation. Key-Words. AI, biologically-inspired systems, software neocortex, learning, memory, neural nets.
1
and suggested that memory is everywhere, not just restricted to the brain, while others who looked at memory in the context of learning, considered memory as a product of learning, or a basis for learning. On the biology side, common upper class and graduate-level biology textbooks do not address the questions asked, nor offer any direct answer to them. These textbooks include, to name only a few, “Neurobiology" by Gordon M. Shepherd in 1997, "Fundamental Neuroscience" by Michael J. Zigmond in 1999, “Principle of Neural Science by Eric Kandel (ed.) et al., and "From Neuron to Brain" by John G. Nicholls (ed.) et al. in 2001. In artificial intelligence (AI), robotics and other disciplines such as psychology and cross-disciplines such as cognitive science, cognitive neuroscience and others, no direct answers to the questions asked are given either. These include Pitts-McCullough’s model of a single neuron in 1943 [1], various perceptron models, Hebbian cell assembly proposed in 1949 [2], connectionism theory and/or associationism theory (associative memory), and recent artificial neural networks (ANN), in the investigation of memory and learning. Even recently from the 90’s to the present, the work on the neocortex models of T.S. Lee and D. Mumford [3], and that of Thomas Dean [4] as well as the memory-prediction model of Jeff Hawkins [5] do not offer any direct answers. On the medical side, this is not different. Neurosurgeons and physicians have been rather busy
Introduction
When John Von Neumann used the human brain and memory as metaphors and analogies for the development of the stored program concept in computers some sixty years ago, he’d have, arguably, thought of human memory as a physical organ, just as any other organs in the human body. Along the same line of thinking, I asked myself the basic question, “What a memory, then, looks like in the brain?” I soon found out that no textbooks and/or other sources which I have been able to access, have provided a direct answer to “What is memory?” let alone “What a memory looks like?” To the question “What is memory”, the answers are commonly defined as “types” or “kind”, such as “sensory, short-term, working or long-term memory” or “episodic, declarative, explicit or implicit memory”. One of the most direct answers I accidentally found was given, not in a research journal or conference article, but in the National Geographic, November 2007 issue in an article called “Remember this” where it is defined simply as “Memory is a stored pattern of connections formed by the brain’s neurons”. Another definition, given by Yadin Dudai in his book “Memory from A to Z” as an “enduring change in behavior”, and as the “retention over time of learned information, of experience”, is at much higher abstraction level which would not help me much to my intention of mimicking the brain for software build. Some researchers then focused on memory location instead ISBN: 978-960-6766-63-3
348
ISSN: 1790-5117
10th WSEAS Int. Conf. on AUTOMATIC CONTROL, MODELLING & SIMULATION (ACMOS'08), Istanbul, Turkey, May 27-30, 2008
invariants of the said topological space is preserved. In fact, it is known that the four P layers of the LGN as well as those of the P ganglion cells correspond to “input lights of different colors with fine discrimination”. It is also known that axons of M and P neurons of the LGN project to different subdivisions of layer 4 of the primary visual cortex (PVC) or V1 (Step 8). Neurons in the M pathways deal with motion, and are sensitive to differences in contrasts and depth. On the other hand, neurons in P pathways are for recording fine details and color. The cells in V1 are organized as six layers, of which layer 4 receives most inputs. The inputs form a retinotopic map. The six layers are organized into vertical clusters of cells whose functional attributes are similar. Via the simple cells and complex cells, detailed at lower levels are integrated to produce more abstract information at the next higher level. In Step 9, the PVC projects to the association areas (Brodmann areas 18 and 19). This is where information captured from other modalities (such as auditory) is integrated with visual information. Steps 10 and 11 involve integration beyond a single modality. It has been established that whatever modality is involved in perception, being sight, sound, touch, etc, the brain has some sort of an internal neural representation as a map which preserves neighborhood relations well known in topological spaces. The sight has its corresponding retinotopic map and so is the sound. In the case of touch, neural maps of the body surface are located in the primary somatosensory cortex, i.e Broadmann areas 3a, 3b, 1 and 2. Thus, in the perception-to-memory process, we can summarize as follows: • Single modality ends up in primary cortex (visual, auditory, somatosensory, etc.) where the stimuli information is kept topologically • Cross-modality integration is processed in association areas for higher abstraction in shortterm memory (STM) • From STM, encoded information is sent to longterm memory (LTM) via the hippocampus (Steps 12 and 13). Step 14 in Fig 1 connecting the two rectangular boxes at the bottom is a rough formulation of the set of all brain networked patterns as the power set of all neurons, and the intended operations on it, which are to be elaborated in the next three sections. A memory in the brain will be seen as an element of the said power set, and defined as a terminal informationencoded brain network pattern. The operations to be considered included: acquire, consolidate, store, retrieve, and interpret.
studying the brain structure and functions from normal brain, and lesions or injuries of one or more areas of the cerebral cortex caused by trauma, tumor, stroke or surgery in humans or animals. An example is the case of the damaged hippocampus of the H.M. patient causing the loss of long-term memory capability. Also thanks to Golgi staining method used in Ramon y Cajal’s neural work as well as fMRI, PET and/or CAT technologies, investigators have been more concerned with using them for better understanding of brain functions and mechanisms, and apparently careless about what memory is and what it looks like.
2
Perception-to-memory process model abstraction
In this section, I examine and describe the neural process from perception to memory as an abstracted model derived from numerous sources [6-8]. One intention is to possibly recognize and characterize invariants through the process. In visual perception for example, the human perception process starts with sensory stimuli from the object to be seen (Fig. 1). The stimuli in Step 1 are light waves of a wide range of frequencies, carrying information on object form, motion, color and depth, and on the environment. Through layers of transparent cells they reach the photoreceptors in Step 2, according to Ramon de Cajal. The photoreceptors (rods and cones), bipolar cells and ganglion cells together with the horizontal cells and amacrine cells (not listed) make up some well-defined and well-structured layers that capture information as localized graded signals at each respective layer (Steps 3, 4, 5). At the ganglion cell layer, action potentials are created from the collection of localized graded signals and travel along their axons as optic nerves. The action potentials are known as impulses having constant amplitude and duration so the different information they carry are reflected in the frequencies of these impulses. At the next steps (Step 6 and Steps 7a and 7b) the impulses cause the influx of extracellular calcium ions into the presynaptic membranes of the cells. They subsequently cause neurotransmitters to diffuse via the corresponding synaptic clefs and reach the postsynaptic membranes of the lateral geniculate nucleus (LGN). There, the different frequencies would follow two major pathways P and M to the highlystructured six-layer organization of the LGN. One important property is observed: “neighboring regions of the retina make connection to with neighboring geniculate cells”, exhibiting a salient property of topological space of the set of cells in question. Thus, the information on form, movement, color and depth of the object and environment as
ISBN: 978-960-6766-63-3
349
ISSN: 1790-5117
10th WSEAS Int. Conf. on AUTOMATIC CONTROL, MODELLING & SIMULATION (ACMOS'08), Istanbul, Turkey, May 27-30, 2008
Fig. 1: Abstracted neocortex function and process
3 3.1
memory respectively. His model was cleverly devised even before any basic work on molecular neurobiology. One of Hebb rules is best known as “neurons that fire together wire together”, considered as a cell assembly. As a result, many neural nets have been constructed and improved for supervised and unsupervised learning. Applications have been found in many areas, e.g. classification problem, image processing, decision making and optimization, [13-15].
Cellular level model of memory Single neuron model of Pitts-McCullough and other extended models
One of the earliest models of artificial neuron was due to Walter Pitts and Warren McCullough in 1943. The model has the form of a linear threshold gate, defined mathematically by an activation function y = f (Sum) as a step function at Sum = T where T is the threshold that yields an all-or-none value, and where Sum is ΣakIk with Ik being a set of inputs to the neuron and ak are weight values normalized in the range of (0,1). Since Pitts-McCullough, there have been other non-linear models, such as (1) simple perceptron with one layer by Frank Rosenblatt in 1958 [9] and (2) the multi-layer model in 1960 in which the inputs need not be binary, and the activation function can be more general, thus in effect simulates an associative memory, Other authors extended these models to define training algorithms for the perceptrons until Marvin Minsky and Seymour Papert [10] pointed out the limitation of the models in 1969. This has led to the multi-layer perceptron model with back-propagation algorithm in 1974 by Paul Werbos [11].
3.2
3.3
Thomas Dean proposed his computational framework of the neocortex which was extended from Tai Sing Lee and David Mumford’s model. The latter focused on the visual system in the necortex. It was in effect a Bayesian inference for reasoning about a visual scene via many levels of complexity in a hierarchical organization of visual information captured with interactive cortical computations. Thomas Dean discussed the proposed framework towards graphical models of the neocortex from three aspects: architectural (network of networks), representational (invariants representations) and implementation (hardware processors). In this section, I describe some of the models relevant to my formulation of memory. Except the Pitts-McCullough’s model, the Hebb and other models are classified in the cellular category as a matter of convenience since they all considered and discussed molecular level of neurons in their models. The amazing observation is on Hebb’s model. His cell
Hebbian cell assembly model
The work of Donald Hebb has been known for his prediction of synaptic connection which characterizes the synaptic plasticity as the material basis of mental association. It was summarized by Sebastian Seung [12] and labeled as dual trace mechanism, i.e. reverberatory neural activity and synaptic connection, corresponding to short-term memory and long-term
ISBN: 978-960-6766-63-3
Lee-Mumford’s model and Dean’s model of neocortex
350
ISSN: 1790-5117
10th WSEAS Int. Conf. on AUTOMATIC CONTROL, MODELLING & SIMULATION (ACMOS'08), Istanbul, Turkey, May 27-30, 2008
assembly model in 1949 with prediction on molecular behavior was several years prior to the discovery of DNA by F. Crick and J. Watson in 1953 and almost 10 years before the introduction of the central dogma in 1958, which introduced the discipline of molecular biology. The other observation is that even after the molecular biology was known and actively researched, researchers following Donald Hebb’s formulation did not really incorporate molecular findings and facts in their subsequent models in ANNs. They continued to pursue the cellular aspect of memory and the brain where Bayesian reasoning was the main focus.
4
an axon of the presynpatic cell. The action potential created at the presynaptic cell travels down its axon. In the presence of the action potential the calcium ions outside of the membrane entering the open gated channels on the membrane, allow the vesicles to fuse with the plasma membrane, thereby trigger neurotransmitters to be released into the synaptic cleft and subsequently diffuse through the cleft. The protein receptors at the postsynaptic cell membrane would bind to specific neurotransmitters and open up ion channels on the membrane. Sodium and potassium ions cross the membrane. Depending upon the concentration of the neurotransmitters, and types of receptors, and the number of gated channels, an excitatory or inhibitory effect can drive the postsynaptic cell membrane toward the threshold of an action potential or drive it away from the threshold. Let look at a single neural cell c1 (Fig 2). The cell probably has thousand synapses (axodendritic and/or axosomatic) to other cells. At a particular instant t1, in the presence of action potential a1 from the presynaptic membrane, there will be 1s2 synapses between cell c1 and cell c2 which successfully distribute neurotransmitters across the clefts. After the diffusion, the connection between the presynaptic cell and the postsynaptic cell is broken since the action potential in the presynaptic cell triggering the delivery of neurotransmitters is gone therefore the presynaptic membrane goes back to its resting potential until the next action potential arrives. At the postsynaptic cells, however, the receptors rm of cell c2 are bound to the neurotransmitters to open up voltage-gated channels allowing the exchange of potassium and sodium ions across the post-synaptic membranes. This exchange potentially increases the weighted synaptic potentials such that a postsynaptic action potential is created for some ci of {c2 to ck}. Thus during t1, c2 to ck are fired by c1, resulting in some excitatory cells ep and some ip inhibitory cells where ep+iq = ck. The ep then trigger in the next set of neurons in their neighborhood at their synapses..
Network level model of memory
At the network level model of memory which cellular models cited in the previous section are also a part of, the description of memory is more systemic. One can look at the network level of memory as a network of networks, system of networks, network of systems, or system of systems. In this section, I mention only two efforts deemed relevant to my formulation. These include the memory hierarchy hypothesized by Jeff Hawkins and the findings by Albert-Lazslo Barabasi [16] on network biology. In his manuscript “On intelligence”, Hawkins spent 20 pages on features of memory drawn from observations and examples, roughly 15 pages on formulation of a memory framework as a whole (memory hierarchy prediction) and more than 70 pages on how it works. As reviewed by Ben Goertzel [17], Hawkins’s memory-prediction model did not really cover how the brain/mind chooses which predictions are to be made. On the other hand, according to an extensive study by Albert-Lazslo Barabasi and his colleagues on network biology, many properties emerge in the characterization of the networked level of the brain: (1) it’s a scale-free network, (2) it has the small-world effect, (3) it has high clustering, (4) it preserves invariants in the topological sense, and (5) it promotes robustness. Both authors cited above, at the systemic level, have paid little attention to what a memory in the brain in effect is.
5
5.2
Molecular level model of memory
Based on the general process model described in Fig 1, from perception to memory, I now focus on what happens at the synapses, which I claim will give rise to a description of “what memory looks like in the brain”.
5.1
What happens at the synapses?
A typical chemical synapse consists of a presynaptic membrane, the synaptic cleft and a postsynaptic membrane. The presynaptic membrane is at the end of
ISBN: 978-960-6766-63-3
What a memory in the brain looks like?
For the next instant t1+ε, where ε is very small, the process described in (4.1) repeats as explained in the box of Fig.3. A second pattern originated from the object to be seen is generated through the process until it reaches the short-term memory. Thus, during t2-t1 where t2-t1 = m* ε, where m is an integer and ε is a fraction of time, we have a distribution of brain (networked) patterns over time. In the neural space, the distribution looks like a series of networked patterns that are moving from the retina to short-term memory. If each firing was “lighted” and action potentials were “colored”, then one would see the flashing lighted colored patterns moving across the brain areas of the central nervous system, from the 351
ISSN: 1790-5117
10th WSEAS Int. Conf. on AUTOMATIC CONTROL, MODELLING & SIMULATION (ACMOS'08), Istanbul, Turkey, May 27-30, 2008
brain (networked) pattern is also “remembered”. At the next similar stimuli, the percept would go through the same complex process of perception-to-memory in which the memory is reconstructed by the set of neurostransmitters, receptors, influx and outflux of ions through voltage-gated channels where action potentials are created and travel down the series of axons. It is then transferred to long-term memory by the hippocampal system.
retina to STM. If the duration is long enough, the last pattern would be moved from STM to LTM by the hippocampus. We call the last pattern epqr..t reaching the LTM, a terminal brain networked pattern. Its shape in neural space is conditioned by external changes at the source of sight and the attention given by the eyes. If the stimuli stop, all lighted patterns are extinguished but the whole process of firing is “remembered” at the molecular level. The terminal
Fig. 2: Molecular level of memory
Fig. 3: Weak parallelism between the natural hierarchy and software hierarchy In the above sections, I have shown views of memory in the brain at different level of complexity: cellular, molecular and networked. This view suggests a memory can be defined from four aspects. First, as a biological component of the human brain (anatomical), it looks like different “things” (building blocks) at different levels of abstraction (molecular,
ISBN: 978-960-6766-63-3
cellular, and networked). It basically is a stored collection of experienced first messengers and second messengers in neurons involving in the experience. These neurons are not necessarily connected. The same first messengers and second messengers resurface every time a known set of stimuli occur at the sensory system, whether it’s visual, auditory, or else.
352
ISSN: 1790-5117
10th WSEAS Int. Conf. on AUTOMATIC CONTROL, MODELLING & SIMULATION (ACMOS'08), Istanbul, Turkey, May 27-30, 2008
As function (physiological), it does different parts of the entire encoding work. It hypothetically encodes the information in the patterns (sequences) of impulses that travel along the axons to the synapses. When the action potentials terminate at the long-term memory, the last pattern represents an encoded message for the experience. As process, the memory consolidates the collected information and performs the overall storage and recall for use. And lastly, as interpretation-based behavior, it constitutes the basis for learning and other higher mental abilities.
6
sight and sound. The model needs a minimum of both modalities to incorporate the integration beyond the primary cortices (visual and auditory, etc.). It is hypothesized the software neocortex model will enable learning as a newborn does. The author realizes there are questionable items in this initial formulation, which are subject to be further investigated. Future work will also include the consideration of the mathematics of representing spoken language to be paired with the topological mathematics representing brain network patterns. References: [1] Pitts, W.H. and W.S. McCullough. A logical calculus of the ideas immanent in nervous activity”, Bulletin of Mathematical Biophysics, Vol. 7, 1943. [2] Hebb, Donald O. The Organization of Behavior. New York: Wiley. 1949. [3] Lee, T.S and D. Mumford. Hierarchical Bayesian Inference in the Visual Cortex. Journal of the Optical Society of America Vol. 2(7). 2003 [4] Dean, Thomas. A computational model of the cerebral cortex. In the Proceedings of Twentieth National Conference on Artificial Intelligence (AAAI-05), pages 938-943, Cambridge, Massachusetts. MIT Press. 2005 [5] Hawkins, Jeff with Sandra Blakeslee. On Intelligence, Henry Holt and Co., 2004 [6] Kandel, Eric R., James H. Schwartz and Thomas M. Jessell. Principles of Neural Science, 4th edition. McGraw-Hill, 2000. [7] Fox, S. I. Human Physiology. Boston: Wm.C. Brown Publishers. 1996 [8] Fitzgerald, M.J.T and Jean Folan-Curran, Clinical Neuroanatomy and Related Neuroscience, 4e, W. B. Saunders, 2002 [9] Rosenblatt, Frank. The Perceptron: A Theory of Statistical Separability in Cognitive Systems. Psychological Review, Vol. 65, No. 6, 1958. [10] Minsky, M. and Papert, S. Perceptrons. MIT Press, Cambridge. 1969. [11] Werbos, Paul. The roots of backpropagation, John Wiley and Sons, 1974. [12] Seung, Sabastian. Half a century of Hebb. Nature Neurosci. 3, 1 (2000) [13] Forbes, Nancy, Imitation of Life: How Biology Is Inspiring Computing, The MIT Press, Cambridge, MA, 2004. [14] Mitchell, Melanie. “Life and evolution in computers”, http://web.cecs.pdx.edu/~mm/lifeand-evolution.pdf [15] de Castro, Leandro Nunes and Fernando J. Von Zuben. Recent developments in biologicallyinspired computing, Ideas Group. 2004 [16] Barabasi, Albert-Laszlo, Network Biology. Nature Review. Volume 5, Feb 2004. [17] Goertzel, Ben. On Biological and Digital Intelligence, http://goertzel.org/dynapsyc/2004/OnBiologicalA ndDigitalIntelligence.htm, 2004. [18] Nguyen, Thang N. The software coninuum concept: Towards a biologically inspired model for robust e-business Software automation, Comm AIS, Vol. 15, article 15, February 2005.
Towards a partial software neocortex model for learning
The ultimate objective of this work is to prototype an evolving software such that it learns simple objects and develops some simple concepts as well as recognizing simple words and phrases as do a human newborn. The idea is based on similarities between the natural spectrum (particle, atoms, molecules, etc.) and the software spectrum (bits, simple data structures, complex data structures, etc.) as shown in Fig. 3. In previous investigations [18], it was reported that there exists a striking parallelism between the natural hierarchy (levels of organization from particles to organisms, as indicated in Figure 3 (left side), and what we labeled as the software hierarchy (from bits to application systems) in the right side. As one may observe, some similarities between corresponding constituents express strong resemblance, others weaker. Also many differences exist. The parallelism is not perfect however, if we focus on the similarities, homeomorphisms between them can be drawn. It is claimed that further investigations can be conducted for prototyping with the use of (1) definition and description of memory as a terminal brain (networked) pattern (Fig. 2) in long-term memory from the (topological) power set of neurons where topological invariants are identified, (2) operations to be defined on the set as listed at the bottom of Fig. 1, (3) well-known visual and auditory perception in computer vision and speech recognition research, (4) mapping of brain functions as sketched in perceptionto-memory process (Fig.1) to the software hierarchy (Fig. 3) where OOP classes on the top of OOP foundation classes are defined to reflect biological entity counterparts and their relationships as methods and operations.
7
Concluding remarks
The sketchy framework in Section 6 will be used as a basis for evolutionary prototyping of a partial software neocortex for potential learning with two modalities:
ISBN: 978-960-6766-63-3
353
ISSN: 1790-5117
