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A dynamic normalization model of temporal attention

Abstract

Vision is dynamic, handling a continuously changing stream of input, yet most models of visual attention are static. Here, we develop a dynamic normalization model of visual temporal attention and constrain it with new psychophysical human data. We manipulated temporal attention—the prioritization of visual information at specific points in time—to a sequence of two stimuli separated by a variable time interval. Voluntary temporal attention improved perceptual sensitivity only over a specific interval range. To explain these data, we modelled voluntary and involuntary attentional gain dynamics. Voluntary gain enhancement took the form of a limited resource over short time intervals, which recovered over time. Taken together, our theoretical and experimental results formalize and generalize the idea of limited attentional resources across space at a single moment to limited resources across time at a single location.

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Fig. 1: Behavioural protocol and data.
Fig. 2: Static R&H normalization model of attention equation.
Fig. 3: Model architecture and example simulated time series.
Fig. 4: Voluntary attention as a limited but recoverable resource.
Fig. 5: Model fits to perceptual sensitivity data.
Fig. 6: Generalization to independent datasets.

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Data availability

All behavioural data are publicly available on the Open Science Framework (OSF) (https://osf.io/dkx7n).

Code availability

All custom code for the model is publicly available on OSF (https://osf.io/dkx7n). Code for the behavioural experiments is available on GitHub (https://github.com/racheldenison/temporal-attention).

References

  1. Carandini, M. & Heeger, D. J. Normalization as a canonical neural computation. Nat. Rev. Neurosci. 13, 51–62 (2012).

    Article  CAS  Google Scholar 

  2. Heeger, D. J. Normalization of cell responses in cat striate cortex. Vis. Neurosci. 9, 181–197 (1992).

    Article  CAS  PubMed  Google Scholar 

  3. Bonin, V., Mante, V. & Carandini, M. The suppressive field of neurons in lateral geniculate nucleus. J. Neurosci. 25, 10844–10856 (2005).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  4. Busse, L., Wade, A. R. & Carandini, M. Representation of concurrent stimuli by population activity in visual cortex. Neuron 64, 931–942 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  5. Carandini, M. & Heeger, D. J. Summation and division by neurons in primate visual cortex. Science 264, 1333–1336 (1994).

    Article  CAS  PubMed  Google Scholar 

  6. Ni, A. M. & Maunsell, J. H. R. Spatially tuned normalization explains attention modulation variance within neurons. J. Neurophysiol. 118, 1903–1913 (2017).

    Article  PubMed  PubMed Central  Google Scholar 

  7. Li, H.-H., Carrasco, M. & Heeger, D. J. Deconstructing interocular suppression: attention and divisive normalization. PLoS Comput. Biol. 11, e1004510 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  8. Li, H.-H., Rankin, J., Rinzel, J., Carrasco, M. & Heeger, D. J. Attention model of binocular rivalry. Proc. Natl Acad. Sci. USA 114, E6192–E6201 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  9. Ling, S. & Blake, R. Normalization regulates competition for visual awareness. Neuron 75, 531–540 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. Louie, K., LoFaro, T., Webb, R. & Glimcher, P. W. Dynamic divisive normalization predicts time-varying value coding in decision-related circuits. J. Neurosci. 34, 16046–16057 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  11. Ohshiro, T., Angelaki, D. E. & Deangelis, G. C. A normalization model of multisensory integration. Nat. Neurosci. 14, 775–782 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  12. Reynolds, J. H. & Heeger, D. J. The normalization model of attention. Neuron 61, 168–185 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  13. Boynton, G. M. A framework for describing the effects of attention on visual responses. Vis. Res. 49, 1129–1143 (2009).

    Article  PubMed  Google Scholar 

  14. Lee, J. & Maunsell, J. H. R. A normalization model of attentional modulation of single unit responses. PLoS ONE 4, e4651 (2009).

    Article  PubMed  PubMed Central  Google Scholar 

  15. Maunsell, J. H. R. Neuronal mechanisms of visual attention. Annu. Rev. Vis. Sci. 1, 373–391 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  16. Schwedhelm, P., Krishna, B. S. & Treue, S. An extended normalization model of attention accounts for feature-based attentional enhancement of both response and coherence gain. PLoS Comput. Biol. 12, e1005225 (2016).

    Article  PubMed  PubMed Central  Google Scholar 

  17. Smith, P. L., Sewell, D. K. & Lilburn, S. D. From shunting inhibition to dynamic normalization: attentional selection and decision-making in brief visual displays. Vis. Res. 116, 219–240 (2015).

    Article  PubMed  Google Scholar 

  18. Ni, A. M. & Maunsell, J. H. R. Neuronal effects of spatial and feature attention differ due to normalization. J. Neurosci. 39, 5493–5505 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Beuth, F. & Hamker, F. H. A mechanistic cortical microcircuit of attention for amplification, normalization and suppression. Vis. Res. 116, 241–257 (2015).

    Article  PubMed  Google Scholar 

  20. Herrmann, K., Heeger, D. J. & Carrasco, M. Feature-based attention enhances performance by increasing response gain. Vis. Res. 74, 10–20 (2012).

    Article  PubMed  Google Scholar 

  21. Herrmann, K., Montaser-Kouhsari, L., Carrasco, M. & Heeger, D. J. When size matters: attention affects performance by contrast or response gain. Nat. Neurosci. 13, 1554–1559 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  22. Zhang, X., Japee, S., Safiullah, Z., Mlynaryk, N. & Ungerleider, L. G. A normalization framework for emotional attention. PLoS Biol. 14, e1002578 (2016).

    Article  PubMed  PubMed Central  Google Scholar 

  23. Carandini, M., Heeger, D. J. & Movshon, J. A. Linearity and normalization in simple cells of the macaque primary visual cortex. J. Neurosci. 17, 8621–8644 (1997).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Reynaud, A., Masson, G. S. & Chavane, F. Dynamics of local input normalization result from balanced short- and long-range intracortical interactions in area V1. J. Neurosci. 32, 12558–12569 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Sit, Y. F., Chen, Y., Geisler, W. S., Miikkulainen, R. & Seidemann, E. Complex dynamics of V1 population responses explained by a simple gain-control model. Neuron 64, 943–956 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  26. Zhou, J., Benson, N. C., Kay, K. N. & Winawer, J. Compressive temporal summation in human visual cortex. J. Neurosci. 38, 691–709 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  27. Heeger, D. J. & Zemlianova, K. O. A recurrent circuit implements normalization, simulating the dynamics of V1 activity. Proc. Natl Acad. Sci. U. S. A. 117, 22494–22505 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  28. Wainwright, M. J., Schwartz, O. & Simoncelli, E. P. in Statistical Theories of the Brain (eds Rao, R. P. et al.) 1–22 (MIT Press, 2002).

  29. Westrick, Z. M., Heeger, D. J. & Landy, M. S. Pattern adaptation and normalization reweighting. J. Neurosci. 36, 9805–9816 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Wilson, H. R. & Humanski, R. Spatial frequency adaptation and contrast gain control. Vis. Res. 33, 1133–1149 (1993).

    Article  CAS  PubMed  Google Scholar 

  31. Wissig, S. C. & Kohn, A. The influence of surround suppression on adaptation effects in primary visual cortex. J. Neurophysiol. 107, 3370–3384 (2012).

    Article  PubMed  PubMed Central  Google Scholar 

  32. Kaliukhovich, D. A. & Vogels, R. Divisive normalization predicts adaptation-induced response changes in macaque inferior temporal cortex. J. Neurosci. 36, 6116–6128 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  33. Smith, P. L. & Sewell, D. K. A competitive interaction theory of attentional selection and decision making in brief, multielement displays. Psychol. Rev. 120, 589–627 (2013).

    Article  PubMed  Google Scholar 

  34. Smith, P. L. & Ratcliff, R. An integrated theory of attention and decision making in visual signal detection. Psychol. Rev. 116, 283–317 (2009).

    Article  PubMed  Google Scholar 

  35. Carrasco, M. Visual attention: the past 25 years. Vis. Res. 51, 1484–1525 (2011).

    Article  PubMed  Google Scholar 

  36. Carrasco, M., Ling, S. & Read, S. Attention alters appearance. Nat. Neurosci. 7, 308–313 (2004).

    Article  CAS  PubMed  Google Scholar 

  37. Liu, T., Stevens, S. T. & Carrasco, M. Comparing the time course and efficacy of spatial and feature-based attention. Vis. Res. 47, 108–113 (2007).

    Article  PubMed  Google Scholar 

  38. Müller, H. J. & Rabbitt, P. M. Reflexive and voluntary orienting of visual attention: time course of activation and resistance to interruption. J. Exp. Psychol. Hum. Percept. Perform. 15, 315–330 (1989).

    Article  PubMed  Google Scholar 

  39. Nobre, A. C. & van Ede, F. Anticipated moments: temporal structure in attention. Nat. Rev. Neurosci. 19, 34–48 (2018).

    Article  CAS  PubMed  Google Scholar 

  40. Correa, A., Lupiáñez, J. & Tudela, P. Attentional preparation based on temporal expectancy modulates processing at the perceptual level. Psychon. Bull. Rev. 12, 328–334 (2005).

    Article  PubMed  Google Scholar 

  41. Denison, R. N., Heeger, D. J. & Carrasco, M. Attention flexibly trades off across points in time. Psychon. Bull. Rev. 24, 1142–1151 (2017).

    Article  PubMed  PubMed Central  Google Scholar 

  42. Fernández, A., Denison, R. N. & Carrasco, M. Temporal attention improves perception similarly at foveal and parafoveal locations. J. Vis. 19, 12 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

  43. Rohenkohl, G., Gould, I. C., Pessoa, J. & Nobre, A. C. Combining spatial and temporal expectations to improve visual perception. J. Vis. 14, 8 (2014).

    Article  PubMed  PubMed Central  Google Scholar 

  44. Samaha, J., Bauer, P., Cimaroli, S. & Postle, B. R. Top-down control of the phase of alpha-band oscillations as a mechanism for temporal prediction. Proc. Natl Acad. Sci. USA 112, 8439–8444 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  45. Anderson, B. & Sheinberg, D. L. Effects of temporal context and temporal expectancy on neural activity in inferior temporal cortex. Neuropsychologia 46, 947–957 (2008).

    Article  PubMed  Google Scholar 

  46. Correa, A., Lupiáñez, J., Madrid, E. & Tudela, P. Temporal attention enhances early visual processing: a review and new evidence from event-related potentials. Brain Res. 1076, 116–128 (2006).

    Article  CAS  PubMed  Google Scholar 

  47. Coull, J. T. & Nobre, A. C. Where and when to pay attention: the neural systems for directing attention to spatial locations and to time intervals as revealed by both PET and fMRI. J. Neurosci. 18, 7426–7435 (1998).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  48. Miniussi, C., Wilding, E. L., Coull, J. T. & Nobre, A. C. Orienting attention in time. Modulation of brain potentials. Brain 122, 1507–1518 (1999).

    Article  PubMed  Google Scholar 

  49. Denison, R. N., Yuval-Greenberg, S. & Carrasco, M. Directing voluntary temporal attention increases fixational stability. J. Neurosci. 39, 353–363 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  50. Breitmeyer, B. & Ogmen, H. Visual Masking (Oxford Univ. Press, 2006).

    Book  Google Scholar 

  51. Kahneman, D. Method, findings, and theory in studies of visual masking. Psychol. Bull. 70, 404–425 (1968).

    Article  CAS  PubMed  Google Scholar 

  52. Dux, P. E. & Marois, R. The attentional blink: a review of data and theory. Atten. Percept. Psychophys. 71, 1683–1700 (2009).

    Article  PubMed  PubMed Central  Google Scholar 

  53. Raymond, J. E., Shapiro, K. L. & Arnell, K. M. Temporary suppression of visual processing in an RSVP task: an attentional blink? J. Exp. Psychol. Hum. Percept. Perform. 18, 849–860 (1992).

    Article  CAS  PubMed  Google Scholar 

  54. Chun, M. M. & Potter, M. C. A two-stage model for multiple target detection in rapid serial visual presentation. J. Exp. Psychol. Hum. Percept. Perform. 21, 109–127 (1995).

    Article  CAS  PubMed  Google Scholar 

  55. Wyble, B., Potter, M. C., Bowman, H. & Nieuwenstein, M. Attentional episodes in visual perception. J. Exp. Psychol. Gen. 140, 488–505 (2011).

    Article  PubMed  PubMed Central  Google Scholar 

  56. Potter, M. C., Chun, M. M., Banks, B. S. & Muckenhoupt, M. Two attentional deficits in serial target search: the visual attentional blink and an amodal task-switch deficit. J. Exp. Psychol. Learn. Mem. Cogn. 24, 979–992 (1998).

    Article  CAS  PubMed  Google Scholar 

  57. Auksztulewicz, R., Myers, N. E., Schnupp, J. W. & Nobre, A. C. Rhythmic temporal expectation boosts neural activity by increasing neural gain. J. Neurosci. 39, 9806–9817 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  58. Cravo, A. M., Rohenkohl, G., Wyart, V. & Nobre, A. C. Temporal expectation enhances contrast sensitivity by phase entrainment of low-frequency oscillations in visual cortex. J. Neurosci. 33, 4002–4010 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  59. Rohenkohl, G., Cravo, A. M., Wyart, V. & Nobre, A. C. Temporal expectation improves the quality of sensory information. J. Neurosci. 32, 8424–8428 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  60. Desimone, R. & Duncan, J. Neural mechanisms of selective visual attention. Annu. Rev. Neurosci. 18, 193–222 (1995).

    Article  CAS  PubMed  Google Scholar 

  61. Giordano, A. M., McElree, B. & Carrasco, M. On the automaticity and flexibility of covert attention: a speed–accuracy trade-off analysis. J. Vis. 9, 30.1–10 (2009).

    Article  Google Scholar 

  62. Luck, S. J., Hillyard, S. A., Mouloua, M. & Hawkins, H. L. Mechanisms of visual–spatial attention: resource allocation or uncertainty reduction? J. Exp. Psychol. Hum. Percept. Perform. 22, 725–737 (1996).

    Article  CAS  PubMed  Google Scholar 

  63. Pestilli, F. & Carrasco, M. Attention enhances contrast sensitivity at cued and impairs it at uncued locations. Vis. Res. 45, 1867–1875 (2005).

    Article  PubMed  Google Scholar 

  64. Gold, J. I. & Shadlen, M. N. The neural basis of decision making. Annu. Rev. Neurosci. 30, 535–574 (2007).

    Article  CAS  PubMed  Google Scholar 

  65. Ratcliff, R., Smith, P. L., Brown, S. D. & McKoon, G. Diffusion decision model: current issues and history. Trends Cogn. Sci. 20, 260–281 (2016).

    Article  PubMed  PubMed Central  Google Scholar 

  66. Cheal, M., Lyon, D. R. & Hubbard, D. C. Does attention have different effects on line orientation and line arrangement discrimination? Q. J. Exp. Psychol. A, Hum. Exp. Psychol. 43, 825–857 (1991).

    Article  CAS  Google Scholar 

  67. Hein, E., Rolke, B. & Ulrich, R. Visual attention and temporal discrimination: differential effects of automatic and voluntary cueing. Vis. Cogn. 13, 29–50 (2006).

    Article  Google Scholar 

  68. Ling, S. & Carrasco, M. Sustained and transient covert attention enhance the signal via different contrast response functions. Vis. Res. 46, 1210–1220 (2006).

    Article  PubMed  Google Scholar 

  69. Nakayama, K. & Mackeben, M. Sustained and transient components of focal visual attention. Vis. Res. 29, 1631–1647 (1989).

    Article  CAS  PubMed  Google Scholar 

  70. Remington, R. W., Johnston, J. C. & Yantis, S. Involuntary attentional capture by abrupt onsets. Percept. Psychophys. 51, 279–290 (1992).

    Article  CAS  PubMed  Google Scholar 

  71. Ma, W. J., Husain, M. & Bays, P. M. Changing concepts of working memory. Nat. Neurosci. 17, 347–356 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  72. Reeves, A. & Sperling, G. Attention gating in short-term visual memory. Psychological Rev. 93, 180–206 (1986).

    Article  CAS  Google Scholar 

  73. Sperling, G. & Weichselgartner, E. Episodic theory of the dynamics of spatial attention. Psychol. Rev. 102, 503–532 (1995).

    Article  Google Scholar 

  74. Reeves, A. Attention as a unitary concept. Vision 4, 48 (2020).

    Article  PubMed Central  Google Scholar 

  75. Bundesen, C. A theory of visual attention. Psychol. Rev. 97, 523–547 (1990).

    Article  CAS  PubMed  Google Scholar 

  76. Bundesen, C., Habekost, T. & Kyllingsbæk, S. A neural theory of visual attention: bridging cognition and neurophysiology. Psychol. Rev. 112, 291–328 (2005).

    Article  PubMed  Google Scholar 

  77. Bundesen, C., Vangkilde, S. & Petersen, A. Recent developments in a computational theory of visual attention (TVA). Vis. Res. 116, 210–218 (2015).

    Article  PubMed  Google Scholar 

  78. Jones, M. R. Time Will Tell: A Theory of Dynamic Attending (Oxford Univ. Press, 2019).

    Book  Google Scholar 

  79. Large, E. W. & Jones, M. R. The dynamics of attending: how people track time-varying events. Psychol. Rev. 106, 119–159 (1999).

    Article  Google Scholar 

  80. Vangkilde, S., Coull, J. T. & Bundesen, C. Great expectations: temporal expectation modulates perceptual processing speed. J. Exp. Psychol. Hum. Percept. Perform. 38, 1183–1191 (2012).

    Article  PubMed  Google Scholar 

  81. Vangkilde, S., Petersen, A. & Bundesen, C. Temporal expectancy in the context of a theory of visual attention. Philos. Trans. R. Soc. B 368, 20130054 (2013).

    Article  Google Scholar 

  82. Anton-Erxleben, K. & Carrasco, M. Attentional enhancement of spatial resolution: linking behavioural and neurophysiological evidence. Nat. Rev. Neurosci. 14, 188–200 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  83. Carrasco, M. & Barbot, A. How attention affects spatial resolution. Cold Spring Harb. Symp. Quant. Biol. 79, 149–160 (2015).

    Article  PubMed Central  Google Scholar 

  84. Lawrence, M. A. & Klein, R. M. Isolating exogenous and endogenous modes of temporal attention. J. Exp. Psychol. Gen. 142, 560–572 (2013).

    Article  PubMed  Google Scholar 

  85. McCormick, C. R., Redden, R. S., Lawrence, M. A. & Klein, R. M. The independence of endogenous and exogenous temporal attention. Atten. Percept. Psychophys. 80, 1885–1891 (2018).

    Article  CAS  PubMed  Google Scholar 

  86. Moon, J., Choe, S., Lee, S. & Kwon, O. S. Temporal dynamics of visual attention allocation. Sci. Rep. 9, 3664 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

  87. Nieuwenstein, M., Van der Burg, E., Theeuwes, J., Wyble, B. & Potter, M. Temporal constraints on conscious vision: on the ubiquitous nature of the attentional blink. J. Vis. 9, 18.11–14 (2009).

    Article  Google Scholar 

  88. Wyart, V., de Gardelle, V., Scholl, J. & Summerfield, C. Rhythmic fluctuations in evidence accumulation during decision making in the human brain. Neuron 76, 847–858 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  89. Hilkenmeier, F. & Scharlau, I. Rapid allocation of temporal attention in the attentional blink paradigm. Eur. J. Cogn. Psychol. 22, 1222–1234 (2010).

    Article  Google Scholar 

  90. Martens, S. & Johnson, A. Timing attention: cuing target onset interval attenuates the attentional blink. Mem. Cogn. 33, 234–240 (2005).

    Article  Google Scholar 

  91. Visser, T. A. W., Tang, M. F., Badcock, D. R. & Enns, J. T. Temporal cues and the attentional blink: a further examination of the role of expectancy in sequential object perception. Atten. Percept. Psychophys. 76, 2212–2220 (2014).

    Article  PubMed  Google Scholar 

  92. Di Lollo, V., Kawahara, J.-I., Shahab Ghorashi, S. M. & Enns, J. T. The attentional blink: resource depletion or temporary loss of control? Psychol. Res. 69, 191–200 (2005).

    Article  PubMed  Google Scholar 

  93. Shapiro, K. L., Hanslmayr, S., Enns, J. T. & Lleras, A. Alpha, beta: the rhythm of the attentional blink. Psychon. Bull. Rev. 34, 1472–1478 (2017).

    Google Scholar 

  94. Nieuwenhuis, S., Gilzenrat, M. S., Holmes, B. D. & Cohen, J. D. The role of the locus coeruleus in mediating the attentional blink: a neurocomputational theory. J. Exp. Psychol. Gen. 134, 291–307 (2005).

    Article  PubMed  Google Scholar 

  95. Denison, R. N., Parker, J. A. & Carrasco, M. Modeling pupil responses to rapid sequential events. Behav. Res. Methods 52, 1991–2007 (2020).

    Article  PubMed  PubMed Central  Google Scholar 

  96. Carrasco, M. in The Oxford Handbook of Attention (eds Kastner S. & Nobre A. C.) 183–230 (Oxford Univ. Press, 2014).

  97. DeValois, R. L. & DeValois, K. K. Spatial Vision (Oxford Univ. Press, 1990).

  98. Brainard, D. H. The Psychophysics Toolbox. Spat. Vis. 10, 433–436 (1997).

    Article  CAS  PubMed  Google Scholar 

  99. Kleiner, M., Brainard, D. H. & Pelli, D. G. What’s new in Psychtoolbox-3? Perception 36, ECVP Abstract Supplement (2007).

  100. Pelli, D. G. The VideoToolbox software for visual psychophysics: transforming numbers into movies. Spat. Vis. 10, 437–442 (1997).

    Article  CAS  PubMed  Google Scholar 

  101. Breitmeyer, B. G. & Ogmen, H. Recent models and findings in visual backward masking: a comparison, review, and update. Percept. Psychophys. 62, 1572–1595 (2000).

    Article  CAS  PubMed  Google Scholar 

  102. Acerbi, L. & Ma, W. J. Practical Bayesian optimization for model fitting with Bayesian adaptive direct search. Proc. Adv. Neural Inform. Process. Syst. 30 (2017).

  103. Burnham, K. P. & Anderson, D. R. Model Selection and Multi-Model Inference: A Practical Information-Theoretic Approach (Springer, 2002).

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Acknowledgements

This research was supported by National Institutes of Health National Eye Institute R01 EY019693 to M.C. and D.J.H., R01 EY027401 to M.C., F32 EY025533 to R.N.D. and T32 EY007136 to NYU. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. The authors thank H.-H. Li for consultation on the model and Carrasco Lab members, especially V. Peña for assistance with data collection and A. Fernández and M. Jigo for their comments on the manuscript.

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R.N.D., M.C. and D.J.H. conceived the project, designed the experiment and interpreted the behavioural results and model findings. R.N.D. and D.J.H. conceived the model. R.N.D. implemented the model, conducted the experiment and analysed the data. R.N.D. wrote and all three authors edited the manuscript.

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Correspondence to Rachel N. Denison.

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The authors declare no competing interests.

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Peer review information Nature Human Behaviour thanks Elkan Akyürek, Benjamin Morillon and Valentin Wyart and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Individual observer data.

Behavioural data for individual observers (data points) at each SOA (separate plots). Valid vs. invalid performance for T1 (purple) and T2 (green). For visualization, individual data across SOAs and cuing conditions were normalized separately for each target by adding a constant to equate the individual target mean with the group mean. This adjusts for individual differences in overall performance for a given target without changing the differences among cueing and SOA conditions, facilitating visualization of the pattern of data across these factors. (a) Perceptual sensitivity (d’). Data points lying above the unity line have a temporal cueing effect: higher d’ for valid than invalid trials. The improvement of d’ with temporal attention specifically for intermediate SOAs was consistent across individual observers. (b) Reaction time (RT). Data points lying below the unity line have a temporal cueing effect: faster RT for valid than invalid trials. Reaction time improvements were consistent across observers.

Extended Data Fig. 2 Behavioural statistics.

Repeated measures ANOVA table for behavioural data. SOA = stimulus onset asynchrony, dfn = degrees of freedom in the numerator, dfd = degrees of freedom in the denominator.

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Denison, R.N., Carrasco, M. & Heeger, D.J. A dynamic normalization model of temporal attention. Nat Hum Behav 5, 1674–1685 (2021). https://doi.org/10.1038/s41562-021-01129-1

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