individual neurons may be described as  detectors  ( see oreilly and munakata , 2000 ) . accordingly , the firing of a single neuron announces the presence of ( detects ) some set of input conditions , much like an  idiot light  in a car ( cummins and poirier , 2004 ) . for example , the seat - belt light on a car dashboard is either on or not , indicating that the seat belt is either plugged in or not . the gas light comes on when a certain threshold of fuel level has been crossed . in a home , what an individual neuron detects depends on which neurons it is connected to and at what strength they are connected . in an  integrate - and - fire  neural model , this firing threshold may be implemented by a step activation function ( a sigmoid function is more biologically realistic , but step functions are easier to compute ) . a neuron first sums together all its excitatory and inhibitory inputs ( integrates ) and then passes that sum through an activation function , which determines the output of the neuron . with a step activation function , the neuron will fire if the integration of inputs to the neuron surpasses some threshold , and will not fire otherwise ( in an all - or - none fashion , like an action potential ) . equations 1 and 2 summarize this two - step integrate - and - fire neural model . net represents the net input to an output neuron ( j ) , summing , for all inputs ( i ) , the product of the input activity ( x ) of an i neuron and the weight ( w ) between the i and j neurons . weights correspond to the synaptic strength between two neurons and can range continuously from -1 ( representing a strong inhibitory connection ) to 1 ( representing a strong excitatory connection ) . act takes net as an input , and determines the output based on the threshold value . if  netj < threshold1  if  netj > threshold the particular function ( mapping between input(s ) and output(s ) ) computed by a neural network can be modified by changing the weights between neurons and/or their firing thresholds . by changing the set of neurons whose activity is required for the output to fire , these modifications may alter what an output neuron detects . as a first example , consider a neural network consisting of just three neurons , two constituting an  input layer ,  which both project to a single  output the firing threshold of the output neuron is set at 0.5 , and the weights between each input - output pair are also set to be 0.5 . assume that the activity of input neurons is binary ( 0=off , 1=on ) . with two input units , the conditions under which the output neuron will fire can be determined by constructing a truth table ( table 1 ) . the activation of the output neuron is determined by plugging the activation values of the input neurons into eqs . 1 and 2 . for the particular pattern of weights and threshold in figure 1 , the output neuron will fire whenever any input is on , but will not fire if both inputs are off . this truth table ( table 1 ) can be derived in class by having students enact the neural network in figure 1 . to do this firing is indicated by the student either raising a particular sign , or their hand ( this demonstration will be articulated assuming a sign ) . each student should then be given a single note card with a particular set of instructions and a sign to hold up ( for reasons that will become clear , ask the students to read their instructions , but not the sign they have been given ) : 
 - student 1 ( input layer ) 
 instructions : if your shoulder is tapped , raise your sign and then tap the shoulder of the person directly in front of you.sign:sally had a burger.- student 2 ( input layer ) 
 instructions : if your shoulder is tapped , raise your sign and then tap the shoulder of the person directly in front of you.sign:sally had a coke.- student 3 ( output layer ) 
 instructions : if your shoulder is tapped , raise your sign.sign:sally had a burger or a coke .  - student 1 ( input layer ) 
 instructions : if your shoulder is tapped , raise your sign and then tap the shoulder of the person directly in front of you.sign:sally had a burger . if your shoulder is tapped , raise your sign and then tap the shoulder of the person directly in front of you . - student 2 ( input layer ) 
 instructions : if your shoulder is tapped , raise your sign and then tap the shoulder of the person directly in front of you.sign:sally had a coke . if your shoulder is tapped , raise your sign and then tap the shoulder of the person directly in front of you . - student 3 ( output layer ) 
 instructions : if your shoulder is tapped , raise your sign.sign:sally had a burger or a coke .  if your shoulder is tapped , raise your sign . the instructor can now conduct four tests to see how this student neural network responds . in the first test that student will then raise their sign and tap the student in front of them , who will respond by raising their sign . column , a 0 under the  input2  column , and a 1 under the output column of a truth table on the white board . in the second test , the instructor taps the other input student - neuron , which will have the same effect of producing a response in the output student - neuron . now enter a 0 under input1 , a 1 under input2 , and a 1 under output . in the third test , the instructor taps both input student - neurons , which will also cause an output response . finally , if the instructor does nothing , there should be no output neural activity , and so 0s can be entered under input1 , input2 , and output . for students watching this demonstration , the logical relationship between inputs and output should be fairly clear . the output (  sally had a burger or a coke  ) fires when either one or both of the propositions (  sally had a burger sally had a coke  ) is true ( indicated by the firing of that input neuron ) . however , for the students enacting this computation , they will not know what function they helped implement . since they have not read their signs , they simply raise their sign or do not , depending on if they received a tap . this is appropriate , since no single neuron in the brain  knows  the larger computations in which it participates . asking students to share their instructions with the class , and then questioning them about what they think they were doing will dramatize this point . again , while the student - neurons do not know the information - processing role they played in the large network , the audience will . this demonstrates emergence : clueless neurons following relatively simple instructions were integral to the production of a more complex function . that function is not reducible to the activity of any single neuron , but rather arises because of the coordinated activity of all the components ( that is , the  whole is greater than the sum of its parts ;  there is no  homunculus  in the brain ) . note that the particular values of the weights and threshold are not important , only the relationship between them matters . thus , if the weights were increased to 0.9 , as was the threshold , this network would still compute the inclusive - or function . students often have difficulty appreciating this point initially , and so it may be necessary to repeat it with each demonstration . because information processing in the brain is emergent , note also that this algorithm for computing inclusive - or was implemented with a very different substrate than the brain uses ( tapping people vs. electrochemical neurons ) . indeed , any physical / biological setup in which the relations on the instruction cards obtain can be said to implement the inclusive - or algorithm . if a system could be constructed out of bubble - wrap , whereby the popping of one bubble systematically caused the popping of some other bubble(s ) , then that bubble - wrap system is a type of information processing device . this underscores that the algorithmic level is indeed distinct from the implementational level of analysis . as mapped in table 2 , the output neuron is active here if and only if both inputs are on . to implement this , the threshold of the output neuron is elevated from 0.5 to 1.0 ( figure 2 ) . here again , three students should come to the front of the class and get in the formation depicted in figure 2 . now students receive new instructions and signs : 
 - student 1 ( input layer ) 
 instructions : if your shoulder is tapped , raise your sign and then tap the outside shoulder of the person in front of you.sign:sally had a burger- student 2 ( input layer ) 
 instructions : if your shoulder is tapped , raise you sign and then tap the outside shoulder of the person in front of you.sign:sally had a coke- student 3 ( output layer ) 
 instructions : if both of your shoulders are tapped , raise your sign . otherwise , do nothing.sign:sally had a burger and a cokeby executing the same four combinations of input activity as in demonstration 1 , the rest of the class will clearly see that this network implements the  and  function . once again , the student - neurons will not have much insight into the larger function they enacted . - student 1 ( input layer ) 
 instructions : if your shoulder is tapped , raise your sign and then tap the outside shoulder of the person in front of you.sign:sally had a burger if your shoulder is tapped , raise your sign and then tap the outside shoulder of the person in front of you . - student 2 ( input layer ) 
 instructions : if your shoulder is tapped , raise you sign and then tap the outside shoulder of the person in front of you.sign:sally had a coke  if your shoulder is tapped , raise you sign and then tap the outside shoulder of the person in front of you . - student 3 ( output layer ) 
 instructions : if both of your shoulders are tapped , raise your sign . otherwise , do nothing.sign:sally had a burger and a coke  if both of your shoulders are tapped , raise your sign . sally had a burger and a coke  to reiterate the importance of thinking relationally ( and as a test for comprehension ) , students may be asked to come up with a different set of weights and threshold values that would also produce the  and  function . a third neural network demonstration may be conducted to introduce students to two additional elements : inhibitory connections and  hidden  layers . students sometimes have difficulty conceiving what role inhibition might play in the brain ; this demonstration gives an example of one function ,  exclusive - or ,  which requires inhibition . exclusive - oris also a function that can not be computed with just the two layers of neurons used in demonstrations 1 and 2 . incidentally , this limitation of a two - layer network was pointed out in 1969 by marvin minsky and seymour papert , halting much neural network research until the mid-1980s . to compute exclusive - or , three layers of neurons layer ( so - called because the activity of neurons in this layer is not directly manipulated , as with the input neurons , nor is their output activity necessarily visible , as with the output neurons ) , and an output layer . in the exclusive - or function , the output neuron will fire if one of the input neurons is active , but not if both are active ( table 3 ) . for this demonstration , five students need to be organized into the formation illustrated in figure 3 . notice that there are two types of arrows between neurons in figure 3 , representing excitatory and inhibitory connections . to enact these connections , student - neurons in the input layer will produce two types of actions if they are tapped : tapping the student - neuron in front of them ( representing an excitatory connection ) and resting a hand on the shoulder of the person diagonal to them ( representing an inhibitory connection ) . the activity of student - neurons in the hidden layer will , in turn , depend on the type of inputs they receive . the instructions and signs to be given to each student - neuron are as follows : 
 - student 1 ( input layer ) 
 instructions : if your shoulder is tapped : 
 1 ) with your outside hand , tap the shoulder of the person directly in front of you , raise your sign , and then2 ) with your inside hand , rest it on the shoulder of the person diagonal to you and leave it there.sign:sally had a burger- student 2 ( input layer ) 
 instructions : if your shoulder is tapped : 
 3 ) with your outside hand , tap the shoulder of the person directly in front of you , raise your sign , and then4 ) with your inside hand , rest it on the shoulder of the person diagonal to you and leave it there.sign:sally had a coke- students 3 & 4 ( hidden layer ) 
 instructions : you will receive one of three possible signals : a ) you will feel nothing , b ) you will feel a tap on your shoulder , or c ) you will feel a tap on one shoulder and a hand resting on the other shoulder . if you feel nothing , do nothing.if you feel a tap on your shoulder but do not feel a hand resting on the other shoulder ( wait a couple seconds to be sure ) , tap the shoulder of the person in front of you.if you feel a tap on your shoulder and a hand resting on your other shoulder ( wait a couple seconds to be sure ) , do nothing.- student 5 ( output layer ) 
 instructions : if your shoulder is tapped , raise your sign.sign:sally had either a burger or a coke . - student 1 ( input layer ) 
 instructions : if your shoulder is tapped : 
 1 ) with your outside hand , tap the shoulder of the person directly in front of you , raise your sign , and then2 ) with your inside hand , rest it on the shoulder of the person diagonal to you and leave it there.sign:sally had a burger  if your shoulder is tapped : 
 1 ) with your outside hand , tap the shoulder of the person directly in front of you , raise your sign , and then2 ) with your inside hand , rest it on the shoulder of the person diagonal to you and leave it there . 1 ) with your outside hand , tap the shoulder of the person directly in front of you , raise your sign , and then 2 ) with your inside hand , rest it on the shoulder of the person diagonal to you and leave it there . - student 2 ( input layer ) 
 instructions : if your shoulder is tapped : 
 3 ) with your outside hand , tap the shoulder of the person directly in front of you , raise your sign , and then4 ) with your inside hand , rest it on the shoulder of the person diagonal to you and leave it there.sign:sally had a coke if your shoulder is tapped : 
 3 ) with your outside hand , tap the shoulder of the person directly in front of you , raise your sign , and then4 ) with your inside hand , rest it on the shoulder of the person diagonal to you and leave it there . 3 ) with your outside hand , tap the shoulder of the person directly in front of you , raise your sign , and then 4 ) with your inside hand , rest it on the shoulder of the person diagonal to you and leave it there . - students 3 & 4 ( hidden layer ) 
 instructions : you will receive one of three possible signals : a ) you will feel nothing , b ) you will feel a tap on your shoulder , or c ) you will feel a tap on one shoulder and a hand resting on the other shoulder . if you feel nothing , do nothing.if you feel a tap on your shoulder but do not feel a hand resting on the other shoulder ( wait a couple seconds to be sure ) , tap the shoulder of the person in front of you.if you feel a tap on your shoulder and a hand resting on your other shoulder ( wait a couple seconds to be sure ) , do nothing . you will receive one of three possible signals : a ) you will feel nothing , b ) you will feel a tap on your shoulder , or c ) you will feel a tap on one shoulder and a hand resting on the other shoulder . if you feel nothing , do nothing.if you feel a tap on your shoulder but do not feel a hand resting on the other shoulder ( wait a couple seconds to be sure ) , tap the shoulder of the person in front of you.if you feel a tap on your shoulder and a hand resting on your other shoulder ( wait a couple seconds to be sure ) , do nothing . if you feel a tap on your shoulder but do not feel a hand resting on the other shoulder ( wait a couple seconds to be sure ) , tap the shoulder of the person in front of you . if you feel a tap on your shoulder and a hand resting on your other shoulder ( wait a couple seconds to be sure ) , do nothing . - student 5 ( output layer ) 
 instructions : if your shoulder is tapped , raise your sign.sign:sally had either a burger or a coke .  if your shoulder is tapped , raise your sign . sally had either a burger or a coke .  again , the instructor should go through the four combinations of input activity to determine how the output student - neuron responds . as a comprehension test ( either in class or on a test ) , the instructor may  lesion  one of the hidden layer neurons , and ask students to work out how the truth table they previously derived would be changed by this deletion . as a first example , consider a neural network consisting of just three neurons , two constituting an  input layer ,  which both project to a single  output the firing threshold of the output neuron is set at 0.5 , and the weights between each input - output pair are also set to be 0.5 . assume that the activity of input neurons is binary ( 0=off , 1=on ) . with two input units , the conditions under which the output neuron will fire can be determined by constructing a truth table ( table 1 ) . the activation of the output neuron is determined by plugging the activation values of the input neurons into eqs . 1 and 2 . for the particular pattern of weights and threshold in figure 1 , the output neuron will fire whenever any input is on , but will not fire if both inputs are off . this truth table ( table 1 ) can be derived in class by having students enact the neural network in figure 1 . to do this , the instructor should select three students . firing is indicated by the student either raising a particular sign , or their hand ( this demonstration will be articulated assuming a sign ) . each student should then be given a single note card with a particular set of instructions and a sign to hold up ( for reasons that will become clear , ask the students to read their instructions , but not the sign they have been given ) : 
 - student 1 ( input layer ) 
 instructions : if your shoulder is tapped , raise your sign and then tap the shoulder of the person directly in front of you.sign:sally had a burger.- student 2 ( input layer ) 
 instructions : if your shoulder is tapped , raise your sign and then tap the shoulder of the person directly in front of you.sign:sally had a coke.- student 3 ( output layer ) 
 instructions : if your shoulder is tapped , raise your sign.sign:sally had a burger or a coke .  - student 1 ( input layer ) 
 instructions : if your shoulder is tapped , raise your sign and then tap the shoulder of the person directly in front of you.sign:sally had a burger . if your shoulder is tapped , raise your sign and then tap the shoulder of the person directly in front of you . - student 2 ( input layer ) 
 instructions : if your shoulder is tapped , raise your sign and then tap the shoulder of the person directly in front of you.sign:sally had a coke . if your shoulder is tapped , raise your sign and then tap the shoulder of the person directly in front of you . - student 3 ( output layer ) 
 instructions : if your shoulder is tapped , raise your sign.sign:sally had a burger or a coke . the instructor can now conduct four tests to see how this student neural network responds . in the first test that student will then raise their sign and tap the student in front of them , who will respond by raising their sign . column , a 0 under the  input2  column , and a 1 under the output column of a truth table on the white board . in the second test , the instructor taps the other input student - neuron , which will have the same effect of producing a response in the output student - neuron . now enter a 0 under input1 , a 1 under input2 , and a 1 under output . in the third test , the instructor taps both input student - neurons , which will also cause an output response . finally , if the instructor does nothing , there should be no output neural activity , and so 0s can be entered under input1 , input2 , and output . for students watching this demonstration , the logical relationship between inputs and output should be fairly clear . the output (  sally had a burger or a coke  ) fires when either one or both of the propositions (  sally had a burger  ,  sally had a coke  ) is true ( indicated by the firing of that input neuron ) . however , for the students enacting this computation , they will not know what function they helped implement . since they have not read their signs , they simply raise their sign or do not , depending on if they received a tap . this is appropriate , since no single neuron in the brain  knows  the larger computations in which it participates . asking students to share their instructions with the class , and then questioning them about what they think they were doing will dramatize this point . again , while the student - neurons do not know the information - processing role they played in the large network , the audience will . this demonstrates emergence : clueless neurons following relatively simple instructions were integral to the production of a more complex function . that function is not reducible to the activity of any single neuron , but rather arises because of the coordinated activity of all the components ( that is , the  whole is greater than the sum of its parts ;  there is no  homunculus  in the brain ) . note that the particular values of the weights and threshold are not important , only the relationship between them matters . thus , if the weights were increased to 0.9 , as was the threshold , this network would still compute the inclusive - or function . students often have difficulty appreciating this point initially , and so it may be necessary to repeat it with each demonstration . because information processing in the brain is emergent , note also that this algorithm for computing inclusive - or was implemented with a very different substrate than the brain uses ( tapping people vs. electrochemical neurons ) . indeed , any physical / biological setup in which the relations on the instruction cards obtain can be said to implement the inclusive - or algorithm . if a system could be constructed out of bubble - wrap , whereby the popping of one bubble systematically caused the popping of some other bubble(s ) , then that bubble - wrap system is a type of information processing device . this underscores that the algorithmic level is indeed distinct from the implementational level of analysis . a second neural network demonstration enacts the  and  function . as mapped in table 2 , the output neuron is active here if and only if both inputs are on . to implement this , the threshold of the output neuron is elevated from 0.5 to 1.0 ( figure 2 ) . here again , three students should come to the front of the class and get in the formation depicted in figure 2 . now students receive new instructions and signs : 
 - student 1 ( input layer ) 
 instructions : if your shoulder is tapped , raise your sign and then tap the outside shoulder of the person in front of you.sign:sally had a burger- student 2 ( input layer ) 
 instructions : if your shoulder is tapped , raise you sign and then tap the outside shoulder of the person in front of you.sign:sally had a coke- student 3 ( output layer ) 
 instructions : if both of your shoulders are tapped , raise your sign . otherwise , do nothing.sign:sally had a burger and a cokeby executing the same four combinations of input activity as in demonstration 1 , the rest of the class will clearly see that this network implements the  and  function . once again , the student - neurons will not have much insight into the larger function they enacted . - student 1 ( input layer ) 
 instructions : if your shoulder is tapped , raise your sign and then tap the outside shoulder of the person in front of you.sign:sally had a burger  if your shoulder is tapped , raise your sign and then tap the outside shoulder of the person in front of you . - student 2 ( input layer ) 
 instructions : if your shoulder is tapped , raise you sign and then tap the outside shoulder of the person in front of you.sign:sally had a coke  if your shoulder is tapped , raise you sign and then tap the outside shoulder of the person in front of you . - student 3 ( output layer ) 
 instructions : if both of your shoulders are tapped , raise your sign . otherwise , do nothing.sign:sally had a burger and a coke  if both of your shoulders are tapped , raise your sign . sally had a burger and a coke  to reiterate the importance of thinking relationally ( and as a test for comprehension ) , students may be asked to come up with a different set of weights and threshold values that would also produce the  and  function . a third neural network demonstration may be conducted to introduce students to two additional elements : inhibitory connections and  hidden  layers . students sometimes have difficulty conceiving what role inhibition might play in the brain ; this demonstration gives an example of one function ,  exclusive - or ,  which requires inhibition . exclusive - oris also a function that can not be computed with just the two layers of neurons used in demonstrations 1 and 2 . incidentally , this limitation of a two - layer network was pointed out in 1969 by marvin minsky and seymour papert , halting much neural network research until the mid-1980s . to compute exclusive - or , three layers of neurons are required : an input layer , a  hidden layer ( so - called because the activity of neurons in this layer is not directly manipulated , as with the input neurons , nor is their output activity necessarily visible , as with the output neurons ) , and an output layer . in the exclusive - or function , the output neuron will fire if one of the input neurons is active , but not if both are active ( table 3 ) . for this demonstration , notice that there are two types of arrows between neurons in figure 3 , representing excitatory and inhibitory connections . to enact these connections , student - neurons in the input layer will produce two types of actions if they are tapped : tapping the student - neuron in front of them ( representing an excitatory connection ) and resting a hand on the shoulder of the person diagonal to them ( representing an inhibitory connection ) . the activity of student - neurons in the hidden layer will , in turn , depend on the type of inputs they receive . the instructions and signs to be given to each student - neuron are as follows : 
 - student 1 ( input layer ) 
 instructions : if your shoulder is tapped : 
 1 ) with your outside hand , tap the shoulder of the person directly in front of you , raise your sign , and then2 ) with your inside hand , rest it on the shoulder of the person diagonal to you and leave it there.sign:sally had a burger- student 2 ( input layer ) 
 instructions : if your shoulder is tapped : 
 3 ) with your outside hand , tap the shoulder of the person directly in front of you , raise your sign , and then4 ) with your inside hand , rest it on the shoulder of the person diagonal to you and leave it there.sign:sally had a coke- students 3 & 4 ( hidden layer ) 
 instructions : you will receive one of three possible signals : a ) you will feel nothing , b ) you will feel a tap on your shoulder , or c ) you will feel a tap on one shoulder and a hand resting on the other shoulder . if you feel nothing , do nothing.if you feel a tap on your shoulder but do not feel a hand resting on the other shoulder ( wait a couple seconds to be sure ) , tap the shoulder of the person in front of you.if you feel a tap on your shoulder and a hand resting on your other shoulder ( wait a couple seconds to be sure ) , do nothing.- student 5 ( output layer ) 
 instructions : if your shoulder is tapped , raise your sign.sign:sally had either a burger or a coke .  - student 1 ( input layer ) 
 instructions : if your shoulder is tapped : 
 1 ) with your outside hand , tap the shoulder of the person directly in front of you , raise your sign , and then2 ) with your inside hand , rest it on the shoulder of the person diagonal to you and leave it there.sign:sally had a burger  if your shoulder is tapped : 
 1 ) with your outside hand , tap the shoulder of the person directly in front of you , raise your sign , and then2 ) with your inside hand , rest it on the shoulder of the person diagonal to you and leave it there . 1 ) with your outside hand , tap the shoulder of the person directly in front of you , raise your sign , and then 2 ) with your inside hand , rest it on the shoulder of the person diagonal to you and leave it there . - student 2 ( input layer ) 
 instructions : if your shoulder is tapped : 
 3 ) with your outside hand , tap the shoulder of the person directly in front of you , raise your sign , and then4 ) with your inside hand , rest it on the shoulder of the person diagonal to you and leave it there.sign:sally had a coke  if your shoulder is tapped : 
 3 ) with your outside hand , tap the shoulder of the person directly in front of you , raise your sign , and then4 ) with your inside hand , rest it on the shoulder of the person diagonal to you and leave it there . 3 ) with your outside hand , tap the shoulder of the person directly in front of you , raise your sign , and then 4 ) with your inside hand , rest it on the shoulder of the person diagonal to you and leave it there . - students 3 & 4 ( hidden layer ) 
 instructions : you will receive one of three possible signals : a ) you will feel nothing , b ) you will feel a tap on your shoulder , or c ) you will feel a tap on one shoulder and a hand resting on the other shoulder . if you feel nothing , do nothing.if you feel a tap on your shoulder but do not feel a hand resting on the other shoulder ( wait a couple seconds to be sure ) , tap the shoulder of the person in front of you.if you feel a tap on your shoulder and a hand resting on your other shoulder ( wait a couple seconds to be sure ) , do nothing . you will receive one of three possible signals : a ) you will feel nothing , b ) you will feel a tap on your shoulder , or c ) you will feel a tap on one shoulder and a hand resting on the other shoulder . if you feel nothing , do nothing.if you feel a tap on your shoulder but do not feel a hand resting on the other shoulder ( wait a couple seconds to be sure ) , tap the shoulder of the person in front of you.if you feel a tap on your shoulder and a hand resting on your other shoulder ( wait a couple seconds to be sure ) , do nothing . if you feel a tap on your shoulder but do not feel a hand resting on the other shoulder ( wait a couple seconds to be sure ) , tap the shoulder of the person in front of you . if you feel a tap on your shoulder and a hand resting on your other shoulder ( wait a couple seconds to be sure ) , do nothing . - student 5 ( output layer ) 
 instructions : if your shoulder is tapped , raise your sign.sign:sally had either a burger or a coke .  if your shoulder is tapped , raise your sign . sally had either a burger or a coke .  again , the instructor should go through the four combinations of input activity to determine how the output student - neuron responds . as a comprehension test ( either in class or on a test ) , the instructor may  lesion  one of the hidden layer neurons , and ask students to work out how the truth table they previously derived would be changed by this deletion . the preceding demonstrations are rooted in the work of mcculloch and pitts ( 1943 ) , who first articulated how small networks of neurons may implement logical functions . logical functions form the basis of modern computing . while computers and brains clearly have significant differences , pointing out this parallel to students may help them better understand how neurons could participate in computationally sophisticated processes . these demonstrations begin with the metaphor of a neuron as detector , and enact how relatively simple two and three - layer networks of neurons implement a few logical functions . since mcculloch and pitts pioneering work , it has been shown that a three - layer neural network ( consisting of input , hidden , and output layers ) can compute any continuous function , and a four - layer network ( with two hidden layers ) can compute any computable function ( cybenko , 1988 ) . thus , most neural networks , like standard computers , are so - called  universal computers .  with the  exclusive - or network , students are brought up to the level of architectural complexity that can compute most functions . this parallel between the brain and the computer can help students conceptually bridge the implementation level ( e.g. , neurons , electronic components ) with the computational level ( e.g. , object recognition , excel ) . while computers may be technically mysterious , they are not usually considered to be metaphysically mysterious . linking the information processing of neurons , as demonstrated above , to computers in this way , for example , real neurons are noisy , not perfectly silent in the absence of stimulation . a sigmoid function is also a more realistic activation function than a step - function . in a sigmoid function , increasing excitatory input above threshold will increase the rate of action potentials , until some upper - limit of saturation is reached . simulations with a high degree of neurophysiological realism require significant computational resources ( in terms of memory and processing time ) , which severely limits the ability to also explore interactions between neurons . nonetheless , to the extent that any model is useful , key processes hypothesized to be responsible for the overall functional dynamics of a system will be extracted and explored . for neurons , non - linearity enables neurons to be effective detectors , and non - linearity underlies the complex information processing that can emerge from collections of interacting neurons . while the specific algorithm executed by an actual neural network in the brain is an empirical question ( see oreilly and munakata , 2000 for many examples ) , the three demonstrations detailed here provide a minimal set with which to bridge the implementational and computational levels of the brain . these three demonstrations have been used in several classes , ranging from an introductory psychology class to an upper level neuroscience class . in all cases , they also engage students in material that many ( particularly in an introductory class ) may not find very interesting . in an upper - level class , however , students usually require a fair amount of repetition and practice manipulating networks ( e.g. , by changing weight and threshold values , and determining the consequences of lesioning ) before they are able to fully comprehend and articulate its dynamics . students typically have little history in thinking about neurons from an information - processing perspective , and often need time to appreciate the importance of relationships between neurons . nonetheless , these relatively simple demonstrations provide a vehicle to teach students how the electrochemical processing of neurons relates to the information processing dynamics of the brain . the amount of time an instructor chooses to spend on the demonstrations depends on his / her goal . one or more of them can be done very quickly as a simple demonstration , or they could serve as the centerpiece for a larger discussion spanning several class periods . through them , students should come to have a better understanding and appreciation of how neurophysiology connects with the high - level descriptions of brain processing given in cognitive and systems neuroscience .
david marr famously proposed three levels of analysis ( implementational , algorithmic , and computational ) for understanding information processing systems such as the brain . 
 while two of these levels are commonly taught in neuroscience courses ( the implementational level through neurophysiology and the computational level through systems / cognitive neuroscience ) , the algorithmic level is typically neglected . 
 this leaves an explanatory gap in students understanding of how , for example , the flow of sodium ions enables cognition . 
 neural networks bridge these two levels by demonstrating how collections of interacting neuron - like units can give rise to more overtly cognitive phenomena . the demonstrations in this paper 
 are intended to facilitate instructors introduction and exploration of how neurons  process information .