Changing concepts of working memory

Journal name:
Nature Neuroscience
Volume:
17,
Pages:
347–356
Year published:
DOI:
doi:10.1038/nn.3655
Received
Accepted
Published online

Abstract

Working memory is widely considered to be limited in capacity, holding a fixed, small number of items, such as Miller's 'magical number' seven or Cowan's four. It has recently been proposed that working memory might better be conceptualized as a limited resource that is distributed flexibly among all items to be maintained in memory. According to this view, the quality rather than the quantity of working memory representations determines performance. Here we consider behavioral and emerging neural evidence for this proposal.

At a glance

Figures

  1. Evidence from delayed estimation challenging the slot model.
    Figure 1: Evidence from delayed estimation challenging the slot model.

    (a) Example of a color delayed-estimation task8. Observers must report the color in memory that matches a probed location by selecting from a color wheel. (b) The distribution of responses relative to the correct (target) color depends on the number of items in the sample display. (c) Recall variability as measured by the standard deviation (SD) of error increases gradually and continuously with set size. In the item-limit (slot) model, this function would be flat up to set size 4. Adapted with permission from ref. 9. (d) Example of an orientation delayed-estimation task with sequential presentation10. Observers must report the orientation in memory that matches a probed color by adjustment of the probe, using a response dial. An item of the cue color (here, green) is more likely to be probed than items of other colors, making it higher priority for accurate storage. (e,f) Response distributions and standard deviation of errors for the orientation estimation task. When an item of the cue color is present in the sequence, it is remembered with enhanced precision (lower standard deviation) compared with other items in the sequence. Comparison with trials on which the cue color is absent (no cue) shows that uncued items are recalled with lower precision when a cued item is present. Adapted with permission from ref. 10.

  2. Models of working memory.
    Figure 2: Models of working memory.

    (a) In the slot (or item limit) model of working memory4, 5, each visual item is stored in one of a fixed number of independent memory slots (here, 3) with high resolution (left, illustrated, by narrow distribution of errors around the true feature value of a tested item). When there are more items than slots, one or more items are not stored and the slot model predicts that errors in report of a randomly chosen item will be composed of a mixture of high-precision responses (right, blue component of distribution corresponds to trials when the chosen item received a slot) and random guesses (green component corresponds to trials where it did not get a slot). (b) Resource models of working memory8, 11, 17 fundamentally differ: they propose a limited supply of representational medium that is shared out between items, without a limit to the number of items that can be stored. Crucially, the precision with which an item can be recalled depends on the quantity of resource allocated to it. If resources are equally distributed between objects, error variability (width of the distribution) increases continuously with the number of items (compare distribution of error for one versus four items), with a normal distribution being commonly assumed. (c) In discrete-representation models19, the working memory medium is divided into a discrete number of quanta, similar to the slot model. However, these slots are shared out between items; in this respect, this type of model is much closer to resource models than the original slot model (a). For low set sizes (for example, one item shown at left), the quanta combine to produce a high-resolution memory of an item. However, for higher set sizes, above the number of slots available (right), all items get either one or zero quanta, predicting a mixture of low-resolution recall and random guesses. Note how this distribution differs from those in a and b. (d) Variable-precision models15, 16 propose that working memory precision varies, from trial to trial and item to item, around a mean that decreases with increasing number of items as a result of limited resources. This model predicts that recall errors will be made up of an infinite mixture of distributions (assumed normal) of different widths. Variability in precision could stem from variability in resource or from bottom-up factors.

  3. Neural correlates of storage in working memory.
    Figure 3: Neural correlates of storage in working memory.

    (a) Short-term maintenance of visual information is associated with sustained elevated BOLD signals (hot colors) in prefrontal and posterior parietal regions, whereas the signal in occipital visual cortex is the same or below that observed at rest (but see d). BOLD signals are displayed on an inflated brain surface, showing gyri in light gray and sulci in dark gray. (b) During maintenance, BOLD amplitude in posterior parietal regions varies with the number of features held in memory (data are from ref. 38). A neural capacity limit has typically been inferred by looking for increases in memory load that are not accompanied by a statistically significant (P < 0.05) increase in signal (here, above four items). However, there are many continuously increasing functions (for example, exponential saturation function, dashed line) that would be incorrectly identified as reaching a plateau by this method. (c) In both humans and monkeys, a lateralized EEG signal at posterior electrodes (the CDA) is correlated with precision of recall, as measured by the error in reproducing a single remembered stimulus location. (d) The information content of BOLD signals is dissociated from signal strength during memory maintenance. In occipital areas (left), visual parameters held in memory can be accurately decoded (blue lines) from voxels that are not consistently elevated above baseline during the delay period (red lines). Decoding from these occipital areas is more effective than from prefrontal and posterior parietal voxels (right) that show elevated delay-period responses. Adapted with permission from refs. 51 (a,d), 38 (b) and 46 (c).

  4. Putative neural basis of set size effects in resource models of working memory.
    Figure 4: Putative neural basis of set size effects in resource models of working memory.

    (a) Example displays for an orientation delayed-estimation task with one or two items. (b) Examples of mean firing rate (dashed lines) and activity on a single trial (points) in neural populations responding to the stimuli in a. Neurons are ordered by preferred orientation. At set size 2, gain (population amplitude) per item is reduced compared with set size 1. (c) Error distributions obtained by optimally decoding spike patterns such as those in b. Errors arise because of stochasticity in spike generation. Precision declines with decreasing gain62, 63, leading to wider distributions for more memory items. In this context, the limited resource is the gain of the population activity.

  5. Interpreting the shape and width of working memory error distributions.
    Figure 5: Interpreting the shape and width of working memory error distributions.

    (a) A crucial area of debate concerns how to model the distribution of recall errors (gray histogram, color estimation data from ref. 15, averaged over all subjects and set sizes). A popular analysis method attempts to do this with a mixture of a circular normal distribution (intended to correspond to items in memory) plus a uniform distribution (intended to correspond to items that are not stored)19. The red line depicts this fit, also averaged over all subjects and set sizes. Note that the circular standard deviation of the normal component in the mixture, SDnormal (average value given) is much lower than that of the raw data (compare actual standard deviation (actual SD) with SDnormal). The mixture does not fit human recall data well, and the interpretation of the two mixture components has therefore been called into question15, 16. (b) Actual SD and SDnormal as a function of set size. SDnormal substantially underestimates the level of noise in memory, which, if all items are stored, is simply the actual SD. An apparent plateau in SDnormal (red symbols) at higher set sizes has been used to argue for slot models19, 21, but such a plateau is not present in the raw data (black symbols). Data are from ref. 15. Error bars represent s.e.m. (c) A resource model in which all items are stored with variable precision accurately accounts for both actual SD and SDnormal. Thus, SDnormal by itself cannot serve to distinguish between slot and resource models69. Adapted from ref. 15; shaded areas are s.e.m. of model fits.

  6. Modes of failure in working memory retrieval.
    Figure 6: Modes of failure in working memory retrieval.

    (a) The working memory representation of a colored square can be decomposed into the location of the object in an internal representation of physical space (for example, in posterior parietal cortex; green), the location of the object's color in an internal 'color space' (for example, in area V4; blue), and 'binding' information that associates the position and color (illustrated here by a spring). (b,c) Increasing working memory load may degrade the quality with which each of the three classes of information is maintained: increasing variability in both color and space representations and making binding information more fragile. (d) To report the color in memory belonging to a given position, the relevant location in internal position space is interrogated, leading via binding information to the corresponding representation in color space. This process can fail in at least three ways. First, variability in position space may cause the wrong position representation to be selected, leading to incorrect report of the color of one of the other objects in memory. Second, binding failure may prevent access to the corresponding color; in this case, a forced response may lead to a random guess from any of the colors in memory. Third, variability in color space may lead to incorrect report of a similar, neighboring color in the internal space. (e) In human data, incorrect reports of non-target objects as a result of the first or second possible sources of failure will produce responses that appear randomly (uniformly) distributed when plotted relative to the target feature value. (f) However, such incorrect reports can be directly observed as a central peak when responses are plotted relative to non-target feature values: if errors were solely a result of variability in the reported feature, this distribution would be flat (data replotted from ref. 9).

  7. Changing concepts of change detection.
    Figure 7: Changing concepts of change detection.

    (a) Trial procedure in an orientation change detection task13. In contrast with previous studies, the magnitude of the change was varied on a continuum, producing a richer data set. (b) Resource model for change detection. Stimuli in both displays are internally measured in a noisy manner, and an observer applies a decision rule to these measurements to reach a judgment. To maximize accuracy, the decision rule should be based on probabilistic inference. (c) Probabilistic inference in change detection at set size 1 in a resource model, for a circular stimulus variable. The change measured by the observer follows a bell-shaped distribution centered at the true magnitude of change. The observer applies a criterion (green) to decide whether to report a change. At small magnitudes of change, Δ, the miss rate (red shading) might exceed 50%. Both the width of the distribution and the value of the criterion will depend on noise level and thus on set size. At higher N, the measured changes at different locations are combined nonlinearly before a criterion is applied. (d) Proportion of 'change' reports as a function of the magnitude of change, for each set size. Circles and error bars represent data and shaded areas represent variable-precision model with probabilistic inference. In traditional change detection studies, magnitude of change is not varied systematically and these psychometric curves cannot be plotted. (e) Probability distributions over precision in the variable-precision model, as estimated from one subject in a change detection experiment. In the equal-resource model (Fig. 2b), these distributions would be infinitely sharp. All panels except for c are adapted from ref. 13.

References

  1. Baddeley, A. Working memory: looking back and looking forward. Nat. Rev. Neurosci. 4, 829839 (2003).
  2. Fuster, J.M. Memory in the Cerebral Cortex: An Empirical Approach to Neural Networks in the Human and Nonhuman Primate (MIT Press, 1999).
  3. Miller, G.A. The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychol. Rev. 63, 8197 (1956).
  4. Cowan, N. The magical number 4 in short-term memory: a reconsideration of mental storage capacity. Behav. Brain Sci. 24, 87114 (2001).
  5. Luck, S.J. & Vogel, E.K. The capacity of visual working memory for features and conjunctions. Nature 390, 279281 (1997).
  6. Pashler, H. Familiarity and visual change detection. Percept. Psychophys. 44, 369378 (1988).
  7. Luck, S.J. & Vogel, E.K. Visual working memory capacity: from psychophysics and neurobiology to individual differences. Trends Cogn. Sci. 17, 391400 (2013).
  8. Wilken, P. & Ma, W.J. A detection theory account of change detection. J. Vis. 4, 11201135 (2004).
  9. Bays, P.M., Catalao, R.F.G. & Husain, M. The precision of visual working memory is set by allocation of a shared resource. J. Vis. 9, 7 (2009).
  10. Gorgoraptis, N., Catalao, R.F., Bays, P.M. & Husain, M. Dynamic updating of working memory resources for visual objects. J. Neurosci. 31, 8502 (2011).
  11. Bays, P.M. & Husain, M. Dynamic shifts of limited working memory resources in human vision. Science 321, 851854 (2008).
  12. Alvarez, G.A. & Cavanagh, P. The capacity of visual short-term memory is set both by visual information load and by number of objects. Psychol. Sci. 15, 106111 (2004).
  13. Keshvari, S., van den Berg, R. & Ma, W.J. No evidence for an item limit in change detection. PLoS Comput. Biol. 9, e1002927 (2013).
  14. Franconeri, S.L., Alvarez, G.A. & Cavanagh, P. Flexible cognitive resources: competitive content maps for attention and memory. Trends Cogn. Sci. 17, 134141 (2013).
  15. van den Berg, R., Shin, H., Chou, W.-C., George, R. & Ma, W.J. Variability in encoding precision accounts for visual short-term memory limitations. Proc. Natl. Acad. Sci. USA 109, 87808785 (2012).
  16. Fougnie, D., Suchow, J.W. & Alvarez, G.A. Variability in the quality of visual working memory. Nat. Commun. 3, 1229 (2012).
  17. Palmer, J. Attentional limits on the perception and memory of visual information. J. Exp. Psychol. Hum. Percept. Perform. 16, 332350 (1990).
  18. Zokaei, N., Gorgoraptis, N., Bahrami, B., Bays, P.M. & Husain, M. Precision of working memory for visual motion sequences and transparent motion surfaces. J. Vis. 11, 2 (2011).
  19. Zhang, W. & Luck, S.J. Discrete fixed-resolution representations in visual working memory. Nature 453, 233235 (2008).
  20. Rademaker, R.L., Tredway, C.H. & Tong, F. Introspective judgments predict the precision and likelihood of successful maintenance of visual working memory. J. Vis. 12, 21 (2012).
  21. Anderson, D.E., Vogel, E.K. & Awh, E. Precision in visual working memory reaches a stable plateau when individual item limits are exceeded. J. Neurosci. 31, 11281138 (2011).
  22. Buschman, T.J., Siegel, M., Roy, J.E. & Miller, E.K. Neural substrates of cognitive capacity limitations. Proc. Natl. Acad. Sci. USA 108, 1125211255 (2011).
  23. Elmore, L.C. et al. Visual short-term memory compared in rhesus monkeys and humans. Curr. Biol. 21, 975979 (2011).
  24. Heyselaar, E., Johnston, K. & Paré, M. A change detection approach to study visual working memory of the macaque monkey. J. Vis. 11, 11 (2011).
  25. Lara, A.H. & Wallis, J.D. Capacity and precision in an animal model of visual short-term memory. J. Vis. 12, 13 (2012).
  26. Bays, P.M., Gorgoraptis, N., Wee, N., Marshall, L. & Husain, M. Temporal dynamics of encoding, storage, and reallocation of visual working memory. J. Vis. 11, 6 (2011).
  27. Desimone, R. & Duncan, J. Neural mechanisms of selective visual attention. Annu. Rev. Neurosci. 18, 193222 (1995).
  28. Pertzov, Y., Bays, P.M., Joseph, S. & Husain, M. Rapid forgetting prevented by retrospective attention cues. J. Exp. Psychol. Hum. Percept. Perform. 39, 12241231 (2013).
  29. Melcher, D. & Piazza, M. The role of attentional priority and saliency in determining capacity limits in enumeration and visual working memory. PLoS ONE 6, e29296 (2011).
  30. Shao, N. et al. Saccades elicit obligatory allocation of visual working memory. Mem. Cognit. 38, 629640 (2010).
  31. Bisley, J.W. & Goldberg, M.E. Attention, intention, and priority in the parietal lobe. Annu. Rev. Neurosci. 33, 121 (2010).
  32. Klein, R.M. Inhibition of return. Trends Cogn. Sci. 4, 138147 (2000).
  33. Shibuya, H. & Bundesen, C. Visual selection from multielement displays: measuring and modeling effects of exposure duration. J. Exp. Psychol. Hum. Percept. Perform. 14, 591600 (1988).
  34. Mazyar, H., van den Berg, R. & Ma, W.J. Does precision decrease with set size? J. Vis. 12, 10 (2012).
  35. Emrich, S.M. & Ferber, S. Competition increases binding errors in visual working memory. J. Vis. 12, 12 (2012).
  36. Bundesen, C., Habekost, T. & Kyllingsbæk, S. A neural theory of visual attention: bridging cognition and neurophysiology. Psychol. Rev. 112, 291328 (2005).
  37. Xu, Y. & Chun, M.M. Dissociable neural mechanisms supporting visual short-term memory for objects. Nature 440, 9195 (2006).
  38. Todd, J.J. & Marois, R. Capacity limit of visual short-term memory in human posterior parietal cortex. Nature 428, 751754 (2004).
  39. Linden, D.E.J. et al. Cortical capacity constraints for visual working memory: dissociation of fMRI load effects in a fronto-parietal network. Neuroimage 20, 15181530 (2003).
  40. Vogel, E.K. & Machizawa, M.G. Neural activity predicts individual differences in visual working memory capacity. Nature 428, 748751 (2004).
  41. Leung, H.C., Seelig, D. & Gore, J.C. The effect of memory load on cortical activity in the spatial working memory circuit. Cogn. Affect. Behav. Neurosci. 4, 553563 (2004).
  42. van Dijk, H., van der Werf, J., Mazaheri, A., Medendorp, W.P. & Jensen, O. Modulations in oscillatory activity with amplitude asymmetry can produce cognitively relevant event-related responses. Proc. Natl. Acad. Sci. USA 107, 900905 (2010).
  43. Todd, J.J. & Marois, R. Posterior parietal cortex activity predicts individual differences in visual short-term memory capacity. Cogn. Affect. Behav. Neurosci. 5, 144155 (2005).
  44. Luria, R., Sessa, P., Gotler, A., Jolicøeur, P. & Dell'Acqua, R. Visual short-term memory capacity for simple and complex objects. J. Cogn. Neurosci. 22, 496512 (2010).
  45. Machizawa, M.G., Goh, C.C.W. & Driver, J. Human visual short-term memory precision can be varied at will when the number of retained items is low. Psychol. Sci. 23, 554559 (2012).
  46. Reinhart, R.M.G. et al. Homologous mechanisms of visuospatial working memory maintenance in macaque and human: properties and sources. J. Neurosci. 32, 77117722 (2012).
  47. Logothetis, N.K. What we can do and what we cannot do with fMRI. Nature 453, 869878 (2008).
  48. Wheeler, M.E. & Treisman, A.M. Binding in short-term visual memory. J. Exp. Psychol. Gen. 131, 4864 (2002).
  49. Bays, P.M., Wu, E.Y. & Husain, M. Storage and binding of object features in visual working memory. Neuropsychologia 49, 16221631 (2011).
  50. Umemoto, A., Drew, T., Ester, E.F. & Awh, E. A bilateral advantage for storage in visual working memory. Cognition 117, 6979 (2010).
  51. Riggall, A.C. & Postle, B.R. The relationship between working memory storage and elevated activity as measured with functional magnetic resonance imaging. J. Neurosci. 32, 1299012998 (2012).
  52. Harrison, S.A. & Tong, F. Decoding reveals the contents of visual working memory in early visual areas. Nature 458, 632635 (2009).
  53. Serences, J.T., Ester, E.F., Vogel, E.K. & Awh, E. Stimulus-specific delay activity in human primary visual cortex. Psychol. Sci. 20, 207214 (2009).
  54. Ester, E.F., Anderson, D.E., Serences, J.T. & Awh, E. A neural measure of precision in visual working memory. J. Cogn. Neurosci. 25, 754761 (2013).
  55. Emrich, S.M., Riggall, A.C., Larocque, J.J. & Postle, B.R. Distributed patterns of activity in sensory cortex reflect the precision of multiple items maintained in visual short-term memory. J. Neurosci. 33, 65166523 (2013).
  56. Freeman, J., Brouwer, G.J., Heeger, D.J. & Merriam, E.P. Orientation decoding depends on maps, not columns. J. Neurosci. 31, 47924804 (2011).
  57. Lewis-Peacock, J.A., Drysdale, A.T., Oberauer, K. & Postle, B.R. Neural evidence for a distinction between short-term memory and the focus of attention. J. Cogn. Neurosci. 24, 6179 (2012).
  58. Lisman, J.E. & Idiart, M. Storage of 7 ± 2 short-term memories in oscillatory subcycles. Science 267, 15121515 (1995).
  59. Raffone, A. & Wolters, G. A cortical mechanism for binding in visual working memory. J. Cogn. Neurosci. 13, 766785 (2001).
  60. Ma, W.J. & Huang, W. No capacity limit in attentional tracking: Evidence for probabilistic inference under a resource constraint. J. Vis. 9, 130 (2009).
  61. Shafi, M. et al. Variability in neuronal activity in primate cortex during working memory tasks. Neuroscience 146, 10821108 (2007).
  62. Seung, H.S. & Sompolinsky, H. Simple models for reading neuronal population codes. Proc. Natl. Acad. Sci. USA 90, 1074910753 (1993).
  63. Ma, W.J., Beck, J.M., Latham, P.E. & Pouget, A. Bayesian inference with probabilistic population codes. Nat. Neurosci. 9, 14321438 (2006).
  64. Awh, E. & Jonides, J. Overlapping mechanisms of attention and spatial working memory. Trends Cogn. Sci. 5, 119126 (2001).
  65. McAdams, C.J. & Maunsell, J.H.R. Effects of attention on orientation-tuning functions of single neurons in macaque cortical area V4. J. Neurosci. 19, 431441 (1999).
  66. Churchland, A.K., Kiani, R. & Shadlen, M.N. Decision-making with multiple alternatives. Nat. Neurosci. 11, 693702 (2008).
  67. Churchland, A.K. et al. Variance as a signature of neural computations during decision making. Neuron 69, 818831 (2011).
  68. Wei, Z., Wang, X.J. & Wang, D.H. From distributed resources to limited slots in multiple-item working memory: a spiking network model with normalization. J. Neurosci. 32, 1122811240 (2012).
  69. van den Berg, R. & Ma, W.J. 'Plateau'-related summary statistics are uninformative for comparing working memory models. Atten. Percept. Psychophys. (in the press).
  70. van den Berg, R., Awh, E. & Ma, W.J. Factorial comparison of working memory models. Psychol. Rev. (in the press).
  71. Girshick, A.R., Landy, M.S. & Simoncelli, E.P. Cardinal rules: visual orientation perception reflects knowledge of environmental statistics. Nat. Neurosci. 14, 926932 (2011).
  72. Brady, T.F. & Tenenbaum, J.B. A probabilistic model of visual working memory: incorporating higher order regularities into working memory capacity estimates. Psychol. Rev. 120, 85109 (2013).
  73. Bays, P.M. Noise in neural populations accounts for errors in visual working memory. J. Neurosci. (in the press).
  74. Fougnie, D., Asplund, C.L. & Marois, R. What are the units of storage in visual working memory? J. Vis. 10, 27 (2010).
  75. Parra, M.A. et al. Short-term memory binding deficits in Alzheimer's disease. Brain 132, 10571066 (2009).
  76. Brockmole, J.R. & Logie, R.H. Age-related change in visual working memory: a study of 55,753 participants aged 8–75. Front. Psychol. 4, 12 (2013).
  77. Peich, M.-C., Husain, M. & Bays, P.M. Age-related decline of precision and binding in visual working memory. Psychol. Aging 28, 729743 (2013).
  78. Pertzov, Y. et al. Binding deficits in memory following medial temporal lobe damage in patients with voltage-gated potassium channel complex antibody-associated limbic encephalitis. Brain 136, 24742485 (2013).
  79. Eng, H.Y., Chen, D. & Jiang, Y. Visual working memory for simple and complex visual stimuli. Psychon. Bull. Rev. 12, 11271133 (2005).
  80. Keshvari, S., van den Berg, R. & Ma, W.J. Probabilistic computation in human perception under variability in encoding precision. PLoS ONE 7, e40216 (2012).
  81. Palmer, J., Verghese, P. & Pavel, M. The psychophysics of visual search. Vision Res. 40, 12271268 (2000).
  82. Ma, W.J., Navalpakkam, V., Beck, J.M., Van den Berg, R. & Pouget, A. Behavior and neural basis of near-optimal visual search. Nat. Neurosci. 14, 783790 (2011).
  83. Awh, E., Barton, B. & Vogel, E.K. Visual working memory represents a fixed number of items regardless of complexity. Psychol. Sci. 18, 622628 (2007).
  84. Rouder, J.N., Morey, R., Cowan, N., Morey, C. & Pratte, M. An assessment of fixed-capacity models of visual working memory. Proc. Natl. Acad. Sci. USA 105, 59755979 (2008).
  85. Brady, T.F. & Alvarez, G.A. Hierarchical encoding in visual working memory: ensemble statistics bias memory for individual items. Psychol. Sci. 22, 384392 (2011).
  86. Orhan, A.E. & Jacobs, R.A. A Probabilistic clustering theory of the organization of visual short-term memory. Psychol. Rev. 120, 297328 (2013).
  87. Dyrholm, M., Kyllingsbaek, S., Espeseth, T. & Bundesen, C. Generalizing parametric models by introducing trial-by-trial parameter variability: The case of TVA. J. Math. Psychol. 55, 416429 (2011).
  88. Sims, C.R., Jacobs, R.A. & Knill, D.C. An ideal-observer analysis of visual working memory. Psychol. Rev. 119, 807830 (2012).
  89. Olson, I.R. & Jiang, Y. Is visual short-term memory object based? Rejection of the 'strong-object' hypothesis. Percept. Psychophys. 64, 10551067 (2002).
  90. Xu, Y. Limitations of object-based feature encoding in visual short-term memory. J. Exp. Psychol. Hum. Percept. Perform. 28, 458468 (2002).
  91. Fougnie, D. & Alvarez, G.A. Object features fail independently in visual working memory: evidence for a probabilistic feature-store model. J. Vis. 11, 3 (2011).
  92. Fougnie, D., Cormiea, S.M. & Alvarez, G.A. Object-based benefits without object-based representations. J. Exp. Psychol. Gen. 142, 621626 (2013).
  93. Marshall, L. & Bays, P.M. Obligatory encoding of task-irrelevant features depletes working memory resources. J. Vis. 13, 21 (2013).
  94. Brady, T.F., Konkle, T., Gill, J., Oliva, A. & Alvarez, G.A. Visual long-term memory has the same limit on fidelity as visual working memory. Psychol. Sci. 24, 981990 (2013).
  95. Kumar, S. et al. Resource allocation and prioritization in auditory working memory. Cogn. Neurosci. 4, 1220 (2013).
  96. Vul, E., Frank, M.C., Alvarez, G.A. & Tenenbaum, J.B. Explaining human multiple object tracking as resource-constrained approximate inference in a dynamic probabilistic model. Adv. Neural Inf. Process. Syst. 22, 19551963 (2009).
  97. Holcombe, A.O. & Chen, W.-Y. Exhausting attentional tracking resources with a single fast-moving object. Cognition 123, 218228 (2012).
  98. Chesney, D.L. & Haladjian, H.H. Evidence for a shared mechanism used in multiple-object tracking and subitizing. Atten. Percept. Psychophys. 73, 24572480 (2011).
  99. Burnett Heyes, S., Zokaei, N., van der Staaij, I., Bays, P.M. & Husain, M. Development of visual working memory precision in childhood. Dev. Sci. 15, 528539 (2012).
  100. Noack, H., Lövdén, M. & Lindenberger, U. Normal aging increases discriminal dispersion in visuospatial short-term memory. Psychol. Aging 27, 627637 (2012).

Download references

Author information

Affiliations

  1. Center for Neural Science and Department of Psychology, New York University, New York, New York, USA.

    • Wei Ji Ma
  2. Department of Experimental Psychology and Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, UK.

    • Masud Husain
  3. Institute of Neurology, University College London, London, UK.

    • Paul M Bays
  4. Institute of Cognitive and Brain Sciences, University of California Berkeley, Berkeley, California, USA.

    • Paul M Bays

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Additional data