1-2-AX working memory task
| 1-2-AX working memory task | |
|---|---|
| Purpose | Working memory abilities of long short-term memory |
The 1-2-AX working memory task is a cognitive test which requires working memory to be solved.
It can be used as a test case for
Description
The input of the task is a sequence of the numbers/letters 1, 2, A, X, B and Y, and additional distracting instances of 3, C and Z which should be ignored. For each character of input in sequence, the subject must respond with left (L) or right (R).
The two target sequences that the subject is looking for are A-X and B-Y. When the subject encounters a 1 they must switch to looking for A-X, and when they encounter a 2 they must switch to looking for B-Y.
While looking for A-X, if the subject encounters an X having seen an A previously (and similarly for a Y while looking for B-Y), and where that previous letter was not part of an earlier sequence, they respond R to mark the end of that sequence; their response to all other characters should be L.[2]
Examples
| Input | 2 | 1 | A | A | X | X | Y | A | X |
|---|---|---|---|---|---|---|---|---|---|
| Output | L | L | L | L | R | L | L | L | R |
| Input | 1 | 2 | A | B | X | Y | A | C | Z |
|---|---|---|---|---|---|---|---|---|---|
| Output | L | L | L | L | L | R | L | L | L |
Requirements for algorithms
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.
Solutions
 | This article possibly contains original research. (April 2020) |
Pseudocode
For traditional computer models, both requirements are easy to solve. Here is some Python code (kind of pseudocode but works) where the function next_output gets one single number/letter as input and returns either a letter or nothing. next_outputs is there for convenience to operate on a whole sequence.
last_num = ""
last_letter = ""
def next_output(next_input: str) -> str | None:
"""
Args:
next_input: A string containing a single character.
Returns:
A string containing the letters "L", "R" or None.
Example:
>>> next_output("2")
'L'
"""
global last_num, last_letter
if next_input in ["1", "2"]:
last_num = next_input
last_letter = ""
return "L"
elif next_input in ["A", "B"]:
last_letter = next_input
return "L"
elif next_input in ["X", "Y"]:
seq = last_num + last_letter + next_input
last_letter = next_input
if seq in ["1AX", "2BY"]:
return "R"
return "L"
return None
def next_outputs(next_inputs: str) -> list[str]:
"""
Args:
next_input: A string.
Returns:
A list of strings containing the letters "L" or "R".
Example:
>>> next_outputs("21AAXBYAX")
["L", "L", "L", "L", "R", "L", "L", "L", "R"]
"""
return [next_output(c) for c in next_inputs]
Example:
>>> next_outputs("21AAXBYAX")
['L', 'L', 'L', 'L', 'R', 'L', 'L', 'L', 'R']
>>> next_outputs("12CBZY")
['L', 'L', None, 'L', None, 'R']
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).
Neural network
This task is much more difficult for