Functional neural network for decision processing, a racing network of programmable neurons with fuzzy logic where the target operating model relies on the network itself
FFunctional neural network for decision processing, a racing network ofprogrammable neurons with fuzzy logic where the target operating model relies onthe network itself
Frederic Jumelle, Kelvin So, Didan Deng Bright Nation Limited, Smart-Space 3F, Cyberport, Hong Kong Neuromorphic Interactive System Laboratory, Department of Electronic and Computer Engineering, The Hong KongUniversity of Science and Technology, Hong [email protected], [email protected], [email protected]
Abstract
In this paper, we are introducing a novel model of artifi-cial intelligence, the functional neural network for model-ing of human decision-making processes. This neural net-work is composed of multiple artificial neurons racing in thenetwork. Each of these neurons has a similar structure pro-grammed independently by the users and composed of an in-tention wheel, a motor core and a sensory core representingthe user itself and racing at a specific velocity. The mathe-matics of the neuron’s formulation and the racing mechanismof multiple nodes in the network will be discussed, and thegroup decision process with fuzzy logic and the transforma-tion of these conceptual methods into practical methods ofsimulation and in operations will be developed. Eventually,we will describe some possible future research directions inthe fields of finance, education and medicine including theopportunity to design an intelligent learning agent with appli-cation in business operations supervision. We believe that thisfunctional neural network has a promising potential to trans-form the way we can compute decision-making and lead to anew generation of neuromorphic chips for seamless human-machine interactions.
Introduction
Modeling the internal dynamics of human central nervoussystem has been a prominent and significant research prob-lem in artificial intelligence (AI) for decades. Not only issuch knowledge appealing for intellectual purpose, but isalso important for the advance of brain-inspired AI tech-nology and strong AI, i.e. machines that can experienceconsciousness and aim to achieve human cognitive abili-ties (Long and Cotner 2019; Alpcan, Erfani, and Leckie2017; ˇSekrst 2020). However, the major streams of AItechnology focus on weak AI, i.e. the use of machinesfor analysing and accomplishing well-defined and specificproblem solving and reasoning tasks with certain givenrules (Gams et al. 1997; Rajan and Saffiotti 2017). Exam-ples of weak AI include the most common applications ofAI, namely, facial recognition, which analyse human facialimage in a pixel scale and is mostly based on the frameworkof convolutional neural network (CNN) to extract featuresof human faces with trained filters (Sun, Wu, and Hoi 2018;Mahmood et al. 2017). Competency of these models of weak
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AI is further improved by enhancement of computational ef-ficiency than by comprehensive and rigorous understandingof how intelligence is generated or processed in human cen-tral nervous system (Strong 2016).As a recent breakthrough in deep learning, generative ad-versarial network (GAN) suggests a new direction on strongAI research. GAN comprises of two alternating neural net-works, the generator and the discriminator, and attempts tomimic the computing power of the human brain in term oflearning to distinguish real data from fake data (Goodfellow2016; Goodfellow et al. 2014). However, instead of beinginspired from the neuro-biological architectures and trans-mission mechanisms of the central nervous system, the in-trinsic architecture of GAN is based on the CNN framework,making it less appealing for modelling the decision-makingprocess of humans and brings scarce insight into understand-ing the mechanism of human central nervous system. On theother side, Spiking Neural Networks (SNN) are networksthat more closely mimic natural brain networks (Ghosh-Dastidar and Adeli 2009; Wang, Lin, and Dang 2020). Inaddition to neuronal and synaptic state, SNNs incorporatethe concept of time into the operating model. The idea isthat neurons in the SNN do not fire at each propagation cy-cle but fire only when the neuron’s electrical charge reachesa specific value.Decision-making is a complex process with multiple in-puts, a fuzzy logic and an output unique to a person,which requires a computing model capable of operating atimed competition of neurons programmed upon personalattributes such as neuropsychological performance and cen-tral nervous system processing latency. This neuromorphicapproach has been put in place wherein the neurons are pro-grammed by the users to create a racing network for decisionprocessing where the operating model is the network itself.This model refers to the function(s) of learning by accumu-lating try and succeed or try and fail processes such as thosedriven by the urge to execute and those by the urge to en-gage, along with the long short term memory of them. Oneof the assumptions is that decision making involves at least4 components, namely the intention, the reaction time, theemotional response and the velocity of the process, that canbe modelled in a way that computing them becomes pos-sible. The second assumption is that decision-making is alearning process for which reinforcement is a key compo- a r X i v : . [ c s . N E ] F e b ent based on success or failure when the record of theseoutputs can be kept in memory. The third assumption is thathuman logic is fuzzy in which the truth values of variablesmay be any real number between totally true and totallyfalse, between 0 and 1 both inclusive. However, in humansociety a decision is expected to be made in terms of a sim-plistic yes or no. This extreme bipolarity is quite challengingand can throw light onto what researchers have called themirror neuron system in the learning process especially inaction observation and action execution (Shillcock, Thomas,and Bailes 2019; Zhang et al. 2018), which could be playinga significant role in human decision making process such asin the case of moral dilemma (Christov-Moore, Conway, andIacoboni 2017). This observation makes the invention of anovel neural network architecture with the insight of the hu-man mirror neuron system (Kilroy and Aziz-Zadeh 2017), akeen step towards understanding the central nervous systemand computing artificial intelligence.In this paper, we are proposing a novel artificial gen-eral intelligence model, the Functional Neural Network(FNN), which refers to the capacity of a neuron to be-come part of a neural network through temporal synchro-nization. FNN is made of programmable neurons based ona 3-dimensional profile (using attributes such as biological-metrics, neuropsychological-metrics and chrono-metrics) ofeach user generated from a neuropsychological performancetest taking inputs from the user’s mobile camera for facialattributes recognition and emotional state capture. The Arti-ficial Mirror Neuron (AMN) is a single hybrid neuron cre-ated upon the user’s profile scores which comprises a mir-ror structure articulated between a motor core and a sensorycore, and determines the velocity of a user’s neuron in anetwork of multiple users represented by other neurons ina race. This competition is used for modelling the decision-making process of each user as seen in a group of other usersof similar, competitive, or challenging nature which dependson the type of their individual request for decision process-ing. Decision types can be simple binary choice or reactionalto sentiment analysis or a probabilistic response to a specificmarket signal whether social, industrial, or financial. Givensufficient training by a variety of users under a wide set ofrequests that are kept in memory, the FNN is able to gen-erate a prescription to a user’s question or dilemma, upongroup consensus and/or expert consensus for the user’s ref-erence and trigger an executive decision. Group consensusand expert consensus are a breakthrough from existing arti-ficial intelligence techniques and offer a new perspective inunderstanding the importance of synchronicity in human de-cision processing with potential application in industry sec-tors where rational decision-making matters greatly. Methodology
Artificial Mirror Neuron (AMN) of the FunctionalNeural Network
Artificial Mirror Neuron (AMN) is a hybrid structure serv-ing as the fundamental building block of the FunctionalNeural Network (FNN). A single functional network com-prises a large network of mirror neurons. Each of them is a programmable single unit which has multiple inputs. Theinputs of each neuron are obtained at the time of launch-ing a new request by using a simple cognitive test thatcan quantify the subject’s reaction time, combined with theMIMAMO-net (Deng et al. 2019) that can qualify the sub-ject’s emotional response by facial emotion recognition. Inother words, FNN is an AI model based on a network ofspecialized neurons, i.e. AMN, to simulate some user brainfunctions, obtain a reaction and generate a prescription use-ful to the user.Each neuron is made of 3 basic elements: the intentionwheel (large circle above the axis x with the green hypocy-cloid with 3 cusps), the motor core inside (small circle insidethe intention wheel and above the axis x) and its counterpartthe sensory core (small circle and below the axis x with thered epicycloid with one cusp). The neuron moves dynami-cally from left to right in a calculated velocity depending onthe age of the user.A schematic structural view of an AMN is presented inFigure 1.The 4 featured components of AMN includes:• Size of intention wheel R : the intention wheel is a fic-titious component of an intention-based decision since itis hardly measurable, it only refers to the initial driver ofa decision for which the size is apprehended by a coef-ficient, usually 3 in reference to the triangle made of theoccipital lobe, the frontal cortex and the thalamus, appliedto the motor core;• Radius of the motor core r : the motor core refers to thereaction time of the user in the programming test, whichdepends on the relative cognitive velocity of the subject ina range of 1 to 5. This score sets the radius of the motorcore;• Radius of the sensory core r : the sensory core refers tothe emotional response of the user in the same test mir-roring the reaction time, which depends on the valence-arousal status of the user in a range of 1 to 5. This scoresets the radius of the sensory core:• Velocity of the feed forward system v : the velocity of thefeed forward system is the motor’s velocity and inverselyproportional to the age of the user, i.e. the decision maker.To initialize a mirror neuron, the inputs are:• the size of the intention wheel R • the motor core’s radius r • the sensory core’s radius r • the velocity of the motor core v The internal dynamic of each Artificial Mirror Neuron istri-cycloid whereas the intention wheel takes the form of ahypocycloid, the motor core describes a cycloid and the sen-sory core an epicycloid. When these 3 elements are com-bined and put in motion, they can compute the behavior’scomplexity of a single unit of the natural architecture in-volved in functional decision processing. They can also beused to construct a model of acquisition of social skills suchas inter-personal communication of information whether byimitation or reprocessing.igure 1: Tri-cycloid structure of the artificial mirror neuron.
Mathematical Formulations of AMN
Now we present the mathematical formulations of AMN andoutline the formulas governing the dynamics of the intentionwheel, motor core and sensory core.
Motor core
The trajectory of the motor is a cycloid, whichis the curve traced by a point of the rim of a circular wheelas the wheel rolls along a straight line without slipping.The cycloid (motor core) runs through the origin, with ahorizontal base given by the x-axis, generated by a circle ofradius r rolling over the positive side of the base ( y ≥ ). Itstrajectory consists of the points ( x, y ) , with x = r ( θ − sin θ ) (1) y = r (1 − cos θ ) (2)where θ is a real parameter, corresponding to the anglethrough which the rolling circle has rotated. (See figure 3).For given θ , the circle’s center lies at ( x, y ) = ( rθ, r ) .Solving for θ and replacing, the Cartesian equation of themotor core is found to be: x = r cos − (cid:16) − yr (cid:17) − (cid:112) y (2 r − y ) (3)On the other hand, when y is viewed as a function of x ,the cycloid is differentiable everywhere except at the cusps,where it hits the x -axis, with the derivative tending toward inf or − inf as one approaches a cusp. The map from θ to ( x, y ) is a differentiable curve, and the singularity where thederivative is is an ordinary cusp.A cycloid segment from one cusp to the next is called anarch of the cycloid. The first arch of the cycloid consists ofpoints such that ≤ θ ≤ π . All in all, the equation of thecycloid (motor core) satisfies the differential equation: (cid:18) dydx (cid:19) = 2 ry − (4) Sensory core
Sensory core is an epicycloid, which is aplane curve produced by tracing the path of a chosen pointon the circumference of a circle – called an epicycle – whichrolls without slipping around a fixed circle.If the small cycle has radius r, and the larger circle hasradius R=kr, then the parametric equations for the trajectoryof the epicycloid (sensory core) is given by either: x = ( R + r ) cos θ − r cos (cid:18) R + rr θ (cid:19) (5) y = ( R + r ) sin θ − r sin (cid:18) R + rr θ (cid:19) (6)or x = r ( k + 1) cos θ − r cos (( k + 1) θ ) (7) y = r ( k + 1) sin θ − r sin (( k + 1) θ ) (8)where θ can be referred to in figure 3.We can observe that if k is an integer, then the curve isclosed, and has k cusps. If k is a rational number, say k = p/q expressed in simplest terms, then the curve has p cusps.If k is an irrational number, then the curve never closes, andforms a dense subset of the space between the larger circleand a circle of the radius R + 2 r . Intention wheel
An intention wheel is a hypocycloid,which is a special plane curve generated by the trace of afixed point on a small circle that rolls within a larger circle.In AMN, the hypocycloid of the intention wheel dependscompletely on the cycloid of the motor core.If the small cycle has radius r, and the larger circle hasradius R=kr, then the parametric equations for the trajectoryof the hypocycloid (intention wheel) is given by either: x = ( R − r ) cos θ + r cos (cid:18) R − rr θ (cid:19) (9) y = ( R − r ) sin θ − r sin (cid:18) R − rr θ (cid:19) (10)igure 2: Structural view of the racing mechanics of a Func-tional Network of 8 competing neurons which can stop at apreset deadline whether set in time or distance.or x = r ( k −
1) cos θ + r cos (( k − θ ) (11) y = r ( k −
1) sin θ − r sin (( k − θ ) (12)We can observe that if k is an integer, then the curve isclosed, and has k cusps. If k is a rational number, say k = p/q expressed in simplest terms, then the curve has p cusps.If k is an irrational number, then the curve never closes, andfills the space between the larger circle and a circle of radius R − r .Lastly, the area enclosed by the hypocycloid and the arclength of the hypocycloid are given by: A = ( k − k − k πR = ( k − k − πr (13)and s = 8( k − k πR = 8( k − r (14)respectively. Functional Neural Network (FNN) and FuzzyLogic
The mechanics of the Functional Mirror Network is basedon a pool of competing mirror neurons made of neurons in Figure 3: Value of the angle θ at the deadline determines thestate of the neuron and the output value.memory (memorial) and a new neuron (request neuron), thatmove forward until they reach a preset deadline where thestate of each individual neuron is determined by the valueof the angle θ (see figure 3) and will qualify the networkfor a sum state and deliver a prescription to make a decisionregarding the request. Figure 2 shows a structural view ofthe racing mechanics.The FNN model is an intention-based decision processingsystem that delivers an output in the form of a sum of states.The competing neurons are reaching the deadline in differentstates and the network is deemed to deliver a prescription ac-cording to the sum of states at the deadline. Then the outputresult can trigger a near-natural decision such as buy or sell,yes or no on behalf of the user. In other words, this personalneural network has a human fuzzy logic effect and the ideaof extending each personal neural network to other personalnetworks of similar structure is only logical and the sum ofall these networks can help to understand synchronicity inhuman societies, organized markets and crowd psychologyregarding decision making especially these involved in crisiswhether social, financial, medical or environmental.Modelling human fuzzy logic for decision processingmeans that each neuron has many-valued output. The cy-cloid movement of the motor core along the timeline en-sures that there are 360 values of truth between the 1 orfalse and the 0 or true, both inclusive. Accordingly, the con-fidence score of the result will be 1 minus the value of truthe.g. 0% at 1 (false) and 100% at 0 (true). This output modeldelivers a binary response with confidence score. Figure 3illustrates the correspondence between angle degree in thecycloid movement and output value.In terms of formulas, we can express the binary responseand confidence score for motor core of a node asBinary response = ( v m t )%(2 πr )2 πr Confidence score (in %) = (1 − ( v m t )%(2 πr )2 πr ) · where v m will be the velocity of the motor core.imilarly, we can express the binary response and confi-dence score for sensory core of a node asBinary response = ( v s t )%(2 πr )2 πr Confidence score (in %) = (1 − ( v s t )%(2 πr )2 πr ) · where v s will be the velocity of the sensory core.For the FNN, we can define also the concept of groupbinary response and confidence score of the motor cores andthe sensory cores in the network respectively. In terms offormulas, we can express them as follows. For motor coresof N nodes we have,Group binary response = 1 N N (cid:88) i =1 (cid:20) ( v mi t )%(2 πr i )2 πr i (cid:21) Group confidence score (in %) = (cid:32) − N N (cid:88) i =1 (cid:20) ( v mi t )%(2 πr i )2 πr i (cid:21)(cid:33) · where v mi are be the velocity of the i -th motor core. On theother hand, for sensory cores of N nodes we have,Group binary response = 1 N N (cid:88) i =1 (cid:20) ( v si t )%(2 πr i )2 πr i (cid:21) Group confidence score (in %) = (cid:32) − N N (cid:88) i =1 (cid:20) ( v si t )%(2 πr i )2 πr i (cid:21)(cid:33) · where v si are be the velocity of the i -th sensory core.From the group binary response and confidence score ofthe motor cores and sensory cores, we can deduce and ana-lyze the expert consensus and group consensus and derivethe various additional functions based on these computa-tions, for example, after finding the best performers in termsof the binary response, we can compute the ideal velocitiesfor those low performers to boost in order to achieve the per-formance of the best performers. We are going to layout thewhole framework in the following sections.In our FNN model, the loss function is based on the binaryresponse of the nodes. The loss function captures the differ-ence between the predicted binary response and the correctdecision. Loss function = (cid:107) y predicted − y (cid:107) where y predicted is the predicted binary response, which canbe in terms of individual or group, and y is the correct deci-sion. Important algorithms and methods of FNN
The functional mirror network for decision processing is acognitive computing design that aims to describe the follow-ing mechanisms of the brain in reference to two distinctive groups of algorithms and new methods regarding the execu-tive decision and/or the intuitive decision including calculat-ing the time response of a single neuron, finding the expertconsensus in the network, boosting the velocity of certainneurons based on the preset deadline, anticipating the bestperformer, the best result, the best performance and plan-ning for boosting reward.
Modeling executive decision, new methods and algo-rithms for the motor core: • MOTOR TIME RESPONSE: to compute the average an-gle θ (see figure 3) and the group binary response and con-fidence score of the motor cores in the network accordingto the rule of the fuzzy logic with preset time deadline;• MOTOR DISTANCE RESPONSE: to compute the aver-age angle θ (see figure 3) and the group binary responseand confidence score of the motor cores in the network ac-cording to the rule of the fuzzy logic with preset distancedeadline;• MOTOR NET COMPETE: to select the best performersbased on their motor cores performance in the networkaccording to the rule of the fuzzy logic with a preset timedeadline. This method can contribute to building an “ex-pert mirror network”;• MOTOR BOOST REQUEST: to boost the velocity of lowperformers motor core according to the ratio of the bestperformers. In other words, to compute how much the ve-locity (in %) of low performance motor cores should beincreased to meet the performance of the best performers.• MOTOR BOOST REWARD: to call both the MOTORNET COMPETE and MOTOR BOOST REQUEST in or-der to anticipate reward. Based on the new average binaryresponse and confidence score computed in the networkfor a specific request, this method combines the expertmirror network (best performers per request type) withboost request (increased velocities) to anticipate perfor-mance and reward.• IDEAL TIME: to predict best results according to a timedeadline comparatively to the function of best performers.• IDEAL DISTANCE: to predict best results according toa distance deadline comparatively to the function of bestperformance. Modeling intuitive decision, new methods and algo-rithms for the sensory core: • The SENSORY TIME RESPONSE: to compute the an-gle θ (see figure 3) angle and the group binary responseand confidence score of the sensory cores in the networkaccording to the rule of the fuzzy logic with preset timedeadline;• SENSORY DISTANCE RESPONSE: to compute the an-gle θ (see figure 3) angle and the group binary responseand confidence score of the sensory cores in the networkaccording to the rule of the fuzzy logic with preset dis-tance deadline;igure 4: The velocity and radius of motor core and sensorycore can be different.• SENSORY NET COMPETE: to select the best perform-ers based on the sensory cores in the network accordingto the rule of the fuzzy logic with a preset time deadline;• SENSORY BOOST REQUEST: to boost the velocity oflow performers of sensory core according to the ratioof the best performers. In other words, to compute howmuch the velocity (in %) of low performance motor coresshould be increased to meet the performance of the bestperformers.• SENSORY BOOST REWARD: to call both the SEN-SORY NET COMPETE and MOTOR BOOST RE-QUEST to anticipate reward. Based on the new averagebinary response and confidence score computed in thenetwork for a specific request, this method combines theexpert mirror network (best performers per request type)with boost request (increased velocities) to anticipate per-formance and reward. Future research directions and applications
Simulations in Finance
One of the key parameters of the FNN is the velocity of thecores of different nodes competing against a preset deadline.In the current configuration, we are assuming that all veloc-ities are set when the nodes are initialized. Based on thisinitial setup, we have developed some core functions suchas NET COMPETE, BOOST REQUEST and BOOST RE-WARD. But we are keen to extend the concept of velocity toallow acceleration and deceleration of the nodes to simulatescenarios closer to real life such as fast-cycling markets riskmanagement and high frequency trading. This research di-rection can not only lead to testing new models of decisionmaking for the actors of financial markets, but also enablemore accurate simulations in finance and trading that canalso be applied to the supply chain in anticipation of the de-mand.
Simulation in Medicine
In the methodology, we have separated the algorithms andmethods of the FNN into two groups, one of them relates tothe motor core and the other to the sensory core. It is im-portant to note that although motor core and sensory core are both defined on the same x-axis and share some math-ematic properties, they may not be identical as shown infigure 4. Motor core and sensory core are not necessarilysynchronized depending on their respective sizes and veloc-ities. That leads us to introduce the concepts of relative syn-chronicity and true asynchrony between the executive andintuitive parts of a same decision process or between dif-ferent processes regarding the motor and sensory cores’ be-haviors. This research direction opens the way to simulationof the learning process(es) whether by accelerating, slow-ing down, or controlling it with applications in educationsuch as computer-assisted training, enhanced learning, spe-cial needs education for autists, or cognitive behavioral ther-apy (CBT) such as desensitization to control phobias andanxiety, and reconditioning. It could also allow psychiatristsand neuropsychologists to better understand the relationshipbetween disorderly learning and personality disorders, ad-dictions, and criminal misconducts.
Learning agent with application in ArtificialGeneral Intelligence
Apart from the direct applications in the fields of financeand medicine, we can also foresee the potential of the FNNin the design of learning agent for Artificial General Intel-ligence (AGI). AGI is a strong AI that has the capacity tounderstand or learn to execute an intellectual task like a hu-man being. Because FNN has the capacity to process a de-cision, prescribe a decision trend while forcing the feedbackinto a performance memorial, it could act as a cognitive ad-visor rendering cognitive computing services that can me-diate human-machine interactions and enhance significantlythe performance of complex business environments such asregulated financial markets. In this sense, AGI can becomean intelligent regulator for business supervision as shownin Figure 5. In this design, the receptors are a selection ofpre-synaptic neurons running in FNN(s) and the effectorsare post-synaptic neurons that are connected to the FNN bysynaptic gates for performance optimization. The gating andfiring will take advantage of the feedback from the deci-sions made by the user in relation to the FNN prescriptions,whether correct or not, and from the final effect of the deci-sion on real business operations. The feedback will create aretrograde signaling to affect the gates’ subsequent firings.The learning patterns will accumulate in the LSTM perfor-mance memorial to serve as a database of the conduct edge.A conduct edge is a subplot using a database of observedconducts or performance memorial (LSTM) to react to anincoming signal captured by the receptors in the businessenvironment. On the other side of the Learning Element, thePolicy Administrator is another subplot that can cause theGovernance, Risk management and Compliance (GRC) li-brary to trial the conduct notice issued upon reception ofa bad label, and make the Cognitive Expert Advisor learn,concur and effect a decision.
Conclusion
In this paper we have proposed a novel model of ArtificialGeneral Intelligence (AGI), the Functional Neural Networkigure 5: Intelligent Learning Regulator for business operations supervision.(FNN) for modeling of human decision-making processes.The FNN is made of multiple Artificial Mirror Neurons(AMN) racing in the network. Each neuron has the samestructure comprising motor core, sensory core and intentionwheel and a specific velocity. We have discussed the struc-ture of a simple AMN and its mathematical formulation. Wehave illustrated the racing mechanism of multiple nodes inthe FNN, the group decision process using fuzzy logic andhow to transform these conceptual methods into practicalmethods of simulation and in operations. Finally, we havepresented possible future research directions in the fields offinance, education and medicine including the opportunity todesign an intelligent learning agent with application in AGI.We believe that FNN promises to transform the way we cancompute decision-making and lead to a new generation ofAI chips for seamless human-machine interactions.
Acknowledgment.
The theory presented in this paper isbased on three of our patents, namely, ”Method for In-formed Decision Making” and ”System for Informed De-cision Making”, Frederic Andre Jumelle, Yu Zhao and YatWan Lui, Hong Kong short-term patents grant certificateNo. HK30012597A and No. HK30024011A, and ”Methodand System for Informed Decision Making”, Frederic An-dre Jumelle, Yu Zhao and Yat Wan Lui, international patentapplication No. PCT/CN2019/124550.
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