1. The strategies of coding in spatial memory V.A. Lyakhovetskii 1, E.V. Bobrova 2 1 St. Petersburg Electrotechnical University 2 Pavlov Institute of Physiology RAS http://sevolod.narod.ru e-mail: v_la2002@mail.ru

2. Fig. 1. I) Variants of piece transition: move (A), free-form (B); II) Experimental design (one target and three distracters in each slide). Recognition of chess positions Among the most fundamental questions of spatial memory research is what object features are coded. Previously it was shown that chess positions are coded in relative (the move length and its direction) or in absolute (the square’s numbers) coordinates depending on the type of transition by the piece. I)II)

3. Fig. 2. The recognition stage of the experiment. (2- target, 1, 3, 4 - distracters)

4. Fig 3. The distribution of human errors in memorizing chess positions. eP(S, D) - distance between stimulus (S) and chosen distractor (D). Move Free-form transition 27 volunteers (in total 900 positions). Recognition => 18% of errors. Lyakhovetskii et al., ECVP 2006

5. Reproduction of arm movements Fig.4. The memorization (A) and reproduction (B) stages. A B Using a similar paradigm we studied the recall of hand movements. The blindfolded volunteer had to remember and immediately reproduce by pen the sequence of 7 hand positions on a sheet of paper A4. Each of 47 right-handed volunteers completed one run with the right hand and one run with the left hand.

6. Fig. 5. An example of experimental protocol (right hand).

7. Fig. 6. An example of experimental protocol (left hand).

8. Fig 7. The distribution of human errors in memorizing arm movements. eP - distance between correct and chosen hand position. eM - angle between correct and chosen hand direction. 47 volunteers (in total 658 positions). Reproduction => 65% of errors.

9. Fig. 8. Relative accuracy of position- and movement-specific sequence representations. The quantity of cases (3) are lower than the quantity of cases (4) both for the right and for the left hand, but the differences between (3) and (4) are significant for the right hand (p 0.05). The prevalence of movement-specific representation is significant for the right hand only. Bobrova & Lyakhovetskii, EuroCogSci 2007

10. The network model Memorization Reproduction of arm movements (Kosko BAM) The developed neural network, using different coding schemes, reproduced the percentage and the pattern of errors for both experiments. S 1 ->S 2 … S 5 ->S 6 Perception X 1 ->X 2 … X 5 ->X 6 Storage W SiSi Perception XiXi W X’ i+1 X’ i+1 =X i+1 ?eP i, eM i Error Calc Comparison Kosko, 1988

11. Recognition of chess positions (BAM with state-dependent weights) S, X - stimuli and their internal representations, D, Y - distractors and their internal representations, W – weight matrix of neural network, W X, W Yj – adaptive part of weight matrix, ||…|| - Hemming distance, sgn(...) - signum function, i = 1  6, j = 1  3, η = const S i S i+1 D (i+1)j X i X i+1 Y (i+1)j W+ W X X’ i+1 Y’ (i+1)j W+ W Yj ||X’ i+1 -X i+1 || ||Y’ (i+1)j -Y (i+1)j || eP i Comparison X i+1 or Y (i+1)j Perception Error Calc Conclusion Kothari et al., 1998

12. Fig 9. The distribution of model errors in different coding schemes. Coding schemes A. Independent coding. X i+1 = f(S i+1 ) S X and S Y are coded B. Relative coding. X i+1 = f(S i, S i+1 ) Chess:  S X and  S Y are coded Arm movements:  s and  s are coded

13. Fig 10. The distribution of model errors in memorizing chess positions and arm movements. Relative coding - Move, Right hand Relative + independent coding – Free-Form transition + left hand 10000 runs (in total 60000 positions). Recognition => 10-20% of errors. Reproduction => 58-60% of errors.

14. Fig 11. The distribution of model errors in memorizing arm movements.

15. Fig. 12. Relative accuracy of model position- and movement-specific sequence representations. Conclusions a) relative coding is used for memorizing right hand movements but a mixture of relative and absolute coding is used for memorizing left hand movements; b) irrespective of modality (tactile or visual) common principles of spatial coding exist.