ACT-R Tutorial Unit5

Activation and Context

1. Spreading Activation

$B_i = A_i = B_i + \sum_{k}{\sum_j{}{W_{kj}S_{ji}+\epsilon}}$
$S_{ji} = S-ln(fan_i)$
$S$ : the maximum associative strength ( set with :mas parameter)
- by default :mas = nil to disable spreading activation
- enable spreading activation , set :mas to a positive value
- commonly, set high enough to make sure all of the $S_{ij}>0$
default, only imaginal buffer serves as a source of activation
- $W_{imaginal}=1$ , set with :imaginal-activation
- for other buffers :set with :[bufferName]-activation

2.The Fan Effect

study the following:
- studied sentence : targets
- new sentence : foils
- findings:
  - more fan , more respond time
  - foil take longer to respond than target

3.Fan Effect Model

fan-model.lisp (experiment code : fan.lisp)
test for 1 sentence :
- ? (fan-sentence ‘lawyer’ ‘store’ t ‘person’)
test for the whole experiment :
- ? (fan-experiment)
fitted parameter:
- latency factor (:lf) = 0.63
- maximum associative strength (:max) = 1.6
- W = 1.0
compare the result with human data
- R = 0.864 after parameter tuning
Model Representations
- words : ( base-level activation = 10 )
- sentence : ( base-level activation = 0 )
Perceptual Encoding
- the study of fan effect verified that participants only fixate those two words from the sentence (person and location)
- so the model is also modeled to only reads the 2 words and keep simple
- find-person
- ↓
- attend-visual-location
- ↓
- retrieve-meaning
- ↓
- encode-person
- ↓
- attend-visual-location
- ↓
- retrieve-meaning
- ↓
- encode-location
Determining the Response
- after encoding, the imaginal buffer will have a representation for the sentence:
  - Imaginal :
    - ISA = comprehend-sentence
    - arg1 = Lawyer
    - arg2 = Store
- then retrieve a knowledge from DM according to the info in imaginal buffer
  - 根据人物回忆和根据地点回忆，两个production competing with each other and one would be randomly selected
  - 这样做是为了，当屏幕上出现的是 foil 的时候，总是会想起一个事实，而不是返回failure
  - 如果根据buffer failure判定foil，则respond time will only depend on retrieve threshold
  - in fact, human data clearly shows that the fan of the items affects the time to respond to both targets and foils
  - 简化模型：
    - 只运行 retrieve-from-person 数次
    - 只运行 retrieve-from-location 数次
    - 平均结果
      (P retrieve-from-person =imaginal> ISA comprehend-sentence arg1 =person arg2 =location ?retrieval> state free buffer empty ==> =imaginal> ; prevent strict harvesting +retrieval> ISA comprehend-sentence arg1 =person ;!!!!!!!!!!!!!!!!!!!!!!only retrieve one slot
respond : 3 productions
- yes
- mismatch-person
- mismatch-location

4.Analyzing the Retrieval of the Critical Study Chunk in the Fan model

按理说，production只检测了某一个属性，如person或者location
- 因此会有多个chunk符合条件
- 但是根据spreding activation，两个属性都符合的chunk拥有更高的activation
A note on chunks in buffers and the :dcnn parameter
- :ncnar normalize chunk names after run
- :dcnn dynamic chunk name normalizing
- oftern both set to t
- sometimes it may be useful to debug for tracking chunks before merging
A simple target trial
- laywer is in the store
- location : 1fan , person : 1fan
- :act (activation trace parameter ) enabled to see the activation values when retrieve
- $A_i = B_i + \sum_{k}{\sum_j{}{W_{kj}S_{ji}+\epsilon}}$
- $B_i = 0$ , $S=1.6$
- $S_{ji} = S-ln(fan_i)=1.6 - ln(2) = 0.907$
- $W_{i1} = 0.5 , W_{i2} =0.5$
- $A_i = 0 + 0.5 * 0.907 + 0.5 * 0.907 + 0 = 0.907$
- Time to retrieval the i-th chuk is :
  - $Time = Fe^{-A_i} = 0.63 * exp(-0.907) = 0.254$ (s)
A different target trial
- The hippie is in the bank
- location : 2 fan, person : 3 fan
- it will take longer to respond ! (because s is lower, spreding activation is less)
- $S_{hippie} = 1.6 -ln(4) = 0.214$
- $S_{bank} = 1.6 - ln(3) = 0.501$
A foil trial
- The giant is in the bank
- person fan = 3 , location fan = 2
- use retrieval-from-person:
  - matched studied sentences (3) only receive spread activation from “giant”
  - thus activation is less than target
  - thus it takes longer to respond for foils than targets
- use retrieval-from-location:
  - different respond time
- Use 2 productions and average the result is necessary! 不然模型的结果将会局限于只是用某一个item来搜索记忆的策略

5.Partial Matching

modeling errors human make !
- commision (回忆错误) $A_{wrongChunk} > A_{rightChunk}$
- omission (想不起来任何) $RT > A_i$
- A case :
  - probe : The giant is in the bank
  - a studied sentence : The titan is in the bank
- enable partial matching:
  - (sgp :mp t)
  - 模型会自动考虑 buffer中的chunk 和 DM中的chunk的相似程度
  - With partial matching , the chunk might not have the exact slot values as specified in the retrieval request
  - $A_i = B_i + \sum_{k}{\sum_{j}{W_{kj}S_{ji}}} + \sum_{i}{PM_{li}} + \epsilon$
  - specification elements $l$ : over all the slot values
  - Match Scale $P$ : a constant across all slots and is set by :mp = 0
  - Match Similarities $M_{il}$ : similarity between two slot value
    - maximum similarity :ms = 0
    - maximum difference :md = -1.0
  - 实际上的计算：
    - 符合条件：不给惩罚
    - 不符合条件：给予惩罚，降低激活值

6.Grouped Recall

A example for illustrate partial matching
Only use the cognitive part
- no perceptual or motor is used
- is useful when “timing” is not important
- parameters:
  - s = 0.15
  - retrieve threshold = -0.5
  - base-level activation = 0
  - P = 1
  - spreading activation is disabled
Group task
- list should be recalled: 1,2,3,4,5,6,7,8,9
- model response : 1,2,3,4, [~ 6,5], 7,8
- activation is just : sum(similarities ) + noise
Error of Commission
- ```
  +retrieval>
      isa item
      group =group
      position second
      :recently-retrieved nil   ;  not a slot of the chunk  不计算相似度
```
- 搞错5和6的顺序
  - item5 : noise ( - 0.5 ) + similarity (0 ) = -0.5
  - item6 : noise( 0.1 ) + similarity (-0.5) = -0.4
  - 由于noise的影响， [$ A_{item6}] > [$ A_{item5}]
  - similarity is defined:
  - (set-similarities (first second -0.5) (second third -0.5))
  - for those different values that is not specified by “set-similarities” command, will have the default value of maximum difference which is -1.0
Error of Omission
- 没有回忆起9
- due to random noise, $A_{9} < rt$
- 没有其他chunk可以选择，因为item9 是唯一符合 :recently-retrieved nil 这个条件的

7.Simple Addition

human data (respond time) : (4-year-old kids)
- strategy:
  - recall the result
  - if can’t recall, then count
A Modification Request
- ```
  (P harvest-arg2
  =retrieval>
  =imaginal>
      isa  plus-fact
      addend2  nil
  ?imaginal>
      state  free
==>
  *imaginal>     ;// * means  a modification request. does not clear the buffer automatically
      addend2  =retreival
  )
```
- modification request can be done to goal and imaginal module, in the same way
- For goal module:
  - using “ = “ to modify:
    - 0.050 PROCEDURAL MOD-BUFFER-CHUNK GOAL
  - use “*” to modify:
    - 0.050 PROCEDURAL MODULE-MOD-REQUEST GOAL
  - 0.050 GOAL MOD-BUFFER-CHUNK GOAL
    - use “=” , the goal module do modification directly
    - use * , procedule will make a request, then goal module do the modification
if one is trying to compare a model’s actions to human brain activity then knowing “where” an action occurred is important
For imaginal module:
- use * , there will be 200ms time cost to do the request
- The *imaginal action is the recommended way to make changes to the chunk in the imaginal buffer because it includes the time cost for the imaginal module to make the change.

An indirect request

  (P harvest-answer
  =retrieval>
      ISA  	plus-fact
      sum 	=number
  =imaginal>
      ISA 	plus-fact
  ?imaginal>
      state 	free
==>
  *imaginal>
     sum         =number
  +retrieval>    =number   ;!!!! an indirect request 实际上这里是 和=number绑定的chunk整体
)

if the variable =number is bound to the chunk eight
- chunk eight
  - value 8
  - name “eight”
actual request made as the indirect request is:
- +retrieval>
  - value 8
  - name “eight”
Parameters to be adjusted
- retrieval threshold :rt
- activation noise :ans
- match scale :mp
- base-level activation values of the chunks.

Initial model
- make sure the model can do the task perfectly with subsymbolic components diabled
- assumptions:
  - know numbers of 0-9
  - have encountered the addition facts for problems with addends from 0 to 5.
  - do not try problem solving strategy, only recall the addition facts
  - it is important ： specific strategy or include different strategies sometimes
  - 对于某个人，这个模型最好和这个人采取相同的解决问题的策略，才能更好的建模
Making errors
- retrieve incorrect number ❌
- retrieve incorrect additional fact or fail to ✅
  - +retrieval>
    - ISA　　　　　plus-fact
    - addend1　　 =val1
    - addend2 =val2
Setting similarities
- it is not a reasonable paramter to be fit
- similarity between numbers :
  - $similarity(a,b) = - 0.1 * |a-b|$
- chose match scale:
  - make sure that we pick a value here which ensures that the similarity will make a difference in the activation values.
  - :mp=5
Activation noise
- The more noise , there is the less likely to respond correctly
- experience of the auther:
  - an activation noise value in the range of 0.0-1.0 has been a good setting
  - for most of those the value tends to fall somewhere between 0.2 and 0.5.
- :ans = 0.5
Retrieval threshold and base-levels
- base level activation of the number facts should be set high enough
  - 不然在encode阶段就会失败，这显然不合理
- (set-base-levels (zero 10) (one 10) (two 10) (three 10) (four 10) (five 10) (six 10) (seven 10) (eight 10) (nine 10) )
Adjusting the parameters
- search on only one parameter at a time.
- mp = 16
- ans = 0.7
Adjusting the model
- a fact of children
  - correct on small problem
  - when they respond incorrectly, the answers are more often smaller than the correct answer
    - 2+5 = 6 is more often than 2+5 = 8
    - 一般来说会少数，不会多数
  - There seems to be a bias for the smaller answers.
- solution : increase base level activation of small adiition facts (sum < 4)
  - (set-base-levels (f00 .1)(f01 .1)(f02 .1)(f03 .1)(f04 .1) (f10 .1)(f11 .1)(f12 .1)(f13 .1) (f20 .1)(f21 .1)(f22 .1) (f30 .1)(f31 .1) (f40 .1))
  - fitted value = 0.65
other things can do :
- modifying the similarities used to something other than linear

8. Learning from experience

1-hit Blackjack
- card : 1 ~ 10
- How to win : collect cards whose sum is less than or equal to 21 and greater than the sum of the opponent’s cards.
- 合計が21に近いカード，相手より大きい
- 特殊规则：card 1
  - if sum < 21 , then it can be counted as 11
  - else, counted as 1
- hit ： add a card
- stay : not add a card
- without knowing opponent’s choice, act as quickly
- 相手：a fixed strategy , but is not known by the model
General modeling task description
- no visual and aural, all game state is in goal buffer
- 10 seconds to decide “S” or “H”
  - if no key is pressed, considered as stay
- after 10sec, the goal buffer is updated to refect game’s action and the outcome of the game
- use the info to decide if it should be learned
Goal chunk specifics
- start:
- after 10 sec:
- play 100 times
- wining rate in each 5 hand group is computed
Starting model
- simple strategy of learning:
  - recall a similar experience
  - if a similar chunck and wined , recall the action
  - based on the feedback , create a chunk that holds the learned info for this hand
- an overwritten action using “@”
- ```
  (p remember-game
  =goal>
  isa game-state
   	state retrieving
 =retrieval>
  isa learned-info
   	action =act
 ?manual>
   state free
 ==>
 =goal>
   state nil
 +manual>
   cmd press-key
   key =act
 @retrieval>   ;//  "@" : overwrite action  ,  erase and do not sent to DM
 ;=retrieval>
 ;  mc1 nil
 ;  action nil    ;// prevent merging and strengthen the bad play
 )
```
- modification action using “=” , erase all
- only the slots and values specified in the overwrite action will remain in the chunk in the buffer , all other slots and values are erased.
- When it is used without any modifications,
  - the buffer will be empty
  - the chunk which was there is not cleared and sent to declarative memory
- To prevent that chunk from merging back into DM and strengthening the chunk which was retrieved.
  - the chunk retrieved may not be the best choice (noise or have not enough experience)
  - so , it should be erased and the model should wait for the feedback before creating a new chunk
    - win : create
    - lose : not create
- set similarity: use hook function
  - $similartiy(a,b) = -\frac{abs(a-b)}{max(a,b)}$
  - 该公式符合人类心理
  - less difference more similar.
  - larger numbers are more similar than smaller numbers for a given difference.
- 2 set of parameters:
  - control how the model is configured
    (sgp :esc t ; enable subsymbolic component :bll .5 ; base level learning with a decay rate of 0.5 :ol t ;optimized learning equation to speed up :sim-hook "1hit-bj-number-sims" ;hook function of calculating similarities scores :cache-sim-hook-results t ; to cache the similarity values :er t ; Randomness is enabled :lf 0) ; latency factor. all retrievals complete immediately becase we have a time limit of 10 sec but do not have to fit latency data.
- how the mechanisms used in the model
  - (sgp :v nil :ans .2 :mp 10.0 :rt -60)
  - rt is very low and match scale is high (10) so that the model should always be able to retrieve some relevant chunk if there are any