1-2-AX working memory task
The 1-2-AX working memory task is a task which requires working memory to be solved. It can be used as a test case for learning algorithms to test their ability to remember some old data. This task can be used to demonstrate the working memory abilities of algorithms like PBWM or Long short-term memory.
It is an extension of the A-X version of the continuous performance task.
The input of the task is a sequence of the numbers/letters 1, 2, A, X, B, Y. And additional C and Z which should be ignored.
The output is a sequence of the letters L and R — one letter for each input letter (except for C or Z).
The output R should be returned if and only if there is a matching of any trailing part of the input sequence to the regular expression "1[AXBYCZ]*A[CZ]*X" or "2[AXBYCZ]*B[CZ]*Y".
Otherwise (except for C or Z), an L should be returned.
In other words, C and Z are completely ignored. The sequence A-X or B-Y is accepted (with an R) depending if the most recent number was a 1 or a 2. Otherwise, an L is returned.
- "21AAXBYAX" → "LLLLRLLLR"
- "12CBZY" → "LLLR"
To solve this task, an algorithm must be able to both remember the last number 1 or 2 and the last letter A or B independently. We refer to this memory as the working memory. This memory must persist all other input.
In addition, the algorithm must be able to strip out and ignore the letters C and Z.
For traditional computer models, both requirements are easy to solve. Here is some Python code (kind of pseudo code but works) where the function nextOutput gets one single number/letter as input and returns either a letter or nothing. nextOutputs is there for convenience to operate on a whole sequence.
lastNum = "" lastLetter = "" def nextOutput(nextInput): global lastNum, lastLetter if nextInput in ["1","2"]: lastNum = nextInput lastLetter = "" return "L" elif nextInput in ["A","B"]: lastLetter = nextInput return "L" elif nextInput in ["X","Y"]: seq = lastNum + lastLetter + nextInput lastLetter = nextInput if seq in ["1AX","2BY"]: return "R" return "L" return None def nextOutputs(nextInputs): return [ nextOutput(c) for c in nextInputs ]
Finite state machine
Similarly, this task can be solved in a straightforward way by a finite state machine with 7 states (call them ---, 1--, 2--, 1A-, 2B-, 1AX, 2BY).
After all, including working memory into neural networks is a difficult task. There have been several approaches like PBWM or Long short-term memory which have working memory. This 1-2-AX task is good task for these models and both are able to solve the task.
- O'Reilly, R.C. & Frank, M.J (2006). "Making Working Memory Work: A Computational Model of Learning in the Frontal Cortex and Basal Ganglia. Neural". Neural Computation. 18: 283–328. PMID 16378516. doi:10.1162/089976606775093909. Retrieved 2010-05-30.