Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

# Attractor dynamics gate cortical information flow during decision-making

## Abstract

Decisions are held in memory until enacted, which makes them potentially vulnerable to distracting sensory input. Gating of information flow from sensory to motor areas could protect memory from interference during decision-making, but the underlying network mechanisms are not understood. Here, we trained mice to detect optogenetic stimulation of the somatosensory cortex, with a delay separating sensation and action. During the delay, distracting stimuli lost influence on behavior over time, even though distractor-evoked neural activity percolated through the cortex without attenuation. Instead, choice-encoding activity in the motor cortex became progressively less sensitive to the impact of distractors. Reverse engineering of neural networks trained to reproduce motor cortex activity revealed that the reduction in sensitivity to distractors was caused by a growing separation in the neural activity space between attractors that encode alternative decisions. Our results show that communication between brain regions can be gated via attractor dynamics, which control the degree of commitment to an action.

## Access options

from\$8.99

All prices are NET prices.

## Code availability

The Matlab code for data analyses is available at https://github.com/arsenyf/FinkelsteinFontolan_2021NN. The Matlab code for network models is available at https://github.com/fontolanl/RNN_ALM_gating.

## References

1. 1.

Cole, M. W. et al. Multi-task connectivity reveals flexible hubs for adaptive task control. Nat. Neurosci. 16, 1348–1355 (2013).

2. 2.

Akam, T. & Kullmann, D. M. Oscillatory multiplexing of population codes for selective communication in the mammalian brain. Nat. Rev. Neurosci. 15, 111–122 (2014).

3. 3.

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

4. 4.

Moran, J. & Desimone, R. Selective attention gates visual processing in the extrastriate cortex. Science 229, 782–784 (1985).

5. 5.

Ghose, G. M. & Maunsell, J. H. R. Attentional modulation in visual cortex depends on task timing. Nature 419, 616–620 (2002).

6. 6.

Lennert, T. & Martinez-Trujillo, J. Strength of response suppression to distracter stimuli determines attentional-filtering performance in primate prefrontal neurons. Neuron 70, 141–152 (2011).

7. 7.

Suzuki, M. & Gottlieb, J. Distinct neural mechanisms of distractor suppression in the frontal and parietal lobe. Nat. Neurosci. 16, 98–104 (2013).

8. 8.

Moore, T. & Armstrong, K. M. Selective gating of visual signals by microstimulation of frontal cortex. Nature 421, 370–373 (2003).

9. 9.

McAlonan, K., Cavanaugh, J. & Wurtz, R. H. Guarding the gateway to cortex with attention in visual thalamus. Nature 456, 391–394 (2008).

10. 10.

Wimmer, R. D. et al. Thalamic control of sensory selection in divided attention. Nature 526, 705–709 (2015).

11. 11.

Vogels, T. P. & Abbott, L. F. Gating multiple signals through detailed balance of excitation and inhibition in spiking networks. Nat. Neurosci. 12, 483–491 (2009).

12. 12.

Yu, J., Gutnisky, D. A., Hires, S. A. & Svoboda, K. Layer 4 fast-spiking interneurons filter thalamocortical signals during active somatosensation. Nat. Neurosci. 19, 1647–1657 (2016).

13. 13.

Schneider, D. M., Sundararajan, J. & Mooney, R. A cortical filter that learns to suppress the acoustic consequences of movement. Nature https://doi.org/10.1038/s41586-018-0520-5 (2018).

14. 14.

Fries, P., Reynolds, J. H., Rorie, A. E. & Desimone, R. Modulation of oscillatory neuronal synchronization by selective visual attention. Science 291, 1560–1563 (2001).

15. 15.

Cardin, J. A. et al. Driving fast-spiking cells induces gamma rhythm and controls sensory responses. Nature 459, 663–667 (2009).

16. 16.

Mante, V., Sussillo, D., Shenoy, K. V. & Newsome, W. T. Context-dependent computation by recurrent dynamics in prefrontal cortex. Nature 503, 78–84 (2013).

17. 17.

Carnevale, F., de Lafuente, V., Romo, R., Barak, O. & Parga, N. Dynamic control of response criterion in premotor cortex during perceptual detection under temporal uncertainty. Neuron 86, 1067–1077 (2015).

18. 18.

Seidemann, E., Zohary, E. & Newsome, W. T. Temporal gating of neural signals during performance of a visual discrimination task. Nature 394, 72–75 (1998).

19. 19.

Fuster, J. M. & Alexander, G. E. Neuron activity related to short-term memory. Science 173, 652–654 (1971).

20. 20.

Tanji, J. & Evarts, E. V. Anticipatory activity of motor cortex neurons in relation to direction of an intended movement. J. Neurophysiol. 39, 1062–1068 (1976).

21. 21.

Erlich, J. C., Bialek, M. & Brody, C. D. A cortical substrate for memory-guided orienting in the rat. Neuron 72, 330–343 (2011).

22. 22.

Fried, I., Mukamel, R. & Kreiman, G. Internally generated preactivation of single neurons in human medial frontal cortex predicts volition. Neuron 69, 548–562 (2011).

23. 23.

Churchland, A. K., Kiani, R. & Shadlen, M. N. Decision-making with multiple alternatives. Nat. Neurosci. 11, 693–702 (2008).

24. 24.

Guo, Z. V. et al. Flow of cortical activity underlying a tactile decision in mice. Neuron 81, 179–194 (2014).

25. 25.

Kaufman, M. T., Churchland, M. M., Ryu, S. I. & Shenoy, K. V. Cortical activity in the null space: permitting preparation without movement. Nat. Neurosci. 17, 440–448 (2014).

26. 26.

Li, N., Daie, K., Svoboda, K. & Druckmann, S. Robust neuronal dynamics in premotor cortex during motor planning. Nature 532, 459–464 (2016).

27. 27.

Inagaki, H. K., Fontolan, L., Romani, S. & Svoboda, K. Discrete attractor dynamics underlies persistent activity in the frontal cortex. Nature 566, 212–217 (2019).

28. 28.

O’Connor, D. H. et al. Neural coding during active somatosensation revealed using illusory touch. Nat. Neurosci. 16, 958–965 (2013).

29. 29.

Hernández, A. et al. Decoding a perceptual decision process across cortex. Neuron 66, 300–314 (2010).

30. 30.

Rajan, K., Harvey, C. D. & Tank, D. W. Recurrent network models of sequence generation and memory. Neuron 90, 128–142 (2016).

31. 31.

Sussillo, D. & Barak, O. Opening the black box: low-dimensional dynamics in high-dimensional recurrent neural networks. Neural Comput. 25, 626–649 (2012).

32. 32.

Ede, F., van, Chekroud, S. R., Stokes, M. G. & Nobre, A. C. Decoding the influence of anticipatory states on visual perception in the presence of temporal distractors. Nat. Commun. 9, 1449 (2018).

33. 33.

Nobre, A., Correa, A. & Coull, J. The hazards of time. Curr. Opin. Neurobiol. 17, 465–470 (2007).

34. 34.

Sussillo, D. & Abbott, L. F. Generating coherent patterns of activity from chaotic neural networks. Neuron 63, 544–557 (2009).

35. 35.

Wang, X.-J. Probabilistic decision making by slow reverberation in cortical circuits. Neuron 36, 955–968 (2002).

36. 36.

Machens, C. K., Romo, R. & Brody, C. D. Flexible control of mutual inhibition: a neural model of two-interval discrimination. Science 307, 1121–1124 (2005).

37. 37.

Lim, S. & Goldman, M. S. Balanced cortical microcircuitry for maintaining information in working memory. Nat. Neurosci. 16, 1306–1314 (2013).

38. 38.

Barak, O. & Tsodyks, M. Working models of working memory. Curr. Opin. Neurobiol. 25, 20–24 (2014).

39. 39.

Wimmer, K., Nykamp, D. Q., Constantinidis, C. & Compte, A. Bump attractor dynamics in prefrontal cortex explains behavioral precision in spatial working memory. Nat. Neurosci. 17, 431–439 (2014).

40. 40.

Kopec, C. D., Erlich, J. C., Brunton, B. W., Deisseroth, K. & Brody, C. D. Cortical and subcortical contributions to short-term memory for orienting movements. Neuron 88, 367–377 (2015).

41. 41.

Kamiński, J. et al. Persistently active neurons in human medial frontal and medial temporal lobe support working memory. Nat. Neurosci. 20, 590–601 (2017).

42. 42.

Maimon, G. & Assad, J. A. A cognitive signal for the proactive timing of action in macaque LIP. Nat. Neurosci. 9, 948–955 (2006).

43. 43.

Finnerty, G. T., Shadlen, M. N., Jazayeri, M., Nobre, A. C. & Buonomano, D. V. Time in cortical circuits. J. Neurosci. 35, 13912–13916 (2015).

44. 44.

Najafi, F. et al. Excitatory and inhibitory subnetworks are equally selective during decision-making and emerge simultaneously during learning. Neuron 105, 165–179.e8 (2020).

45. 45.

Kiani, R., Hanks, T. D. & Shadlen, M. N. Bounded integration in parietal cortex underlies decisions even when viewing duration is dictated by the environment. J. Neurosci. 28, 3017–3029 (2008).

46. 46.

Zuo, Y. & Diamond, M. E. Rats generate vibrissal sensory evidence until boundary crossing triggers a decision. Curr. Biol. 29, 1415–1424.e5 (2019).

47. 47.

Peixoto, D. et al. Decoding and perturbing decision states in real time. Nature https://doi.org/10.1038/s41586-020-03181-9 (2021).

48. 48.

Thura, D. & Cisek, P. Deliberation and commitment in the premotor and primary motor cortex during dynamic decision making. Neuron 81, 1401–1416 (2014).

49. 49.

Roitman, J. D. & Shadlen, M. N. Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time task. J. Neurosci. 22, 9475–9489 (2002).

50. 50.

Boucher, L., Palmeri, T. J., Logan, G. D. & Schall, J. D. Inhibitory control in mind and brain: an interactive race model of countermanding saccades. Psychological Rev. 114, 376–397 (2007).

51. 51.

Madisen, L. et al. A robust and high-throughput Cre reporting and characterization system for the whole mouse brain. Nat. Neurosci. 13, 133–140 (2010).

52. 52.

Madisen, L. et al. A toolbox of Cre-dependent optogenetic transgenic mice for light-induced activation and silencing. Nat. Neurosci. 15, 793–802 (2012).

53. 53.

Pluta, S. et al. A direct translaminar inhibitory circuit tunes cortical output. Nat. Neurosci. 18, 1631–1640 (2015).

54. 54.

Liu, L., Finkelstein, A., Chen, S., Li, N. & Svoboda, K. Headbar implantation. Protocols.io https://doi.org/10.17504/protocols.io.bcrsiv6e (2020).

55. 55.

Yatsenko, D. et al. DataJoint: managing big scientific data using MATLAB or Python. Preprint at bioRxiv https://doi.org/10.1101/031658 (2015).

56. 56.

Jun, J. J. et al. Real-time spike sorting platform for high-density extracellular probes with ground-truth validation and drift correction. Preprint at bioRxiv https://doi.org/10.1101/101030 (2017).

## Acknowledgements

We thank D. Hansel and S. Druckmann for discussions; J. Aljadeff, K. Daie, R. Darshan, J. Drugowitsch, H. Inagaki, M. Rozsa and T. Wang for comments on the manuscript; T. Nguyen and other Vathes members for help with DataJoint, and T. Pluntke for animal training. This work was funded by the Howard Hughes Medical Institute and the Simons Foundation. A.F. is a Rothschild Foundation and EMBO Long-Term postdoctoral fellow (ALTF 869-2015).

## Author information

Authors

### Contributions

A.F., M.N.E. and K.S. designed the experiments, with help from N.L. A.F. and M.N.E. collected the experimental data with help from N.L. A.F. analyzed the behavioral and neural data, with input from M.N.E., L.F., S.R. and K.S. L.F. and S.R. conceived the computational models with input from A.F. and K.S. L.F. built the models and performed model simulations. A.F., L.F., S.R. and K.S. wrote the paper, with input from all the authors.

### Corresponding authors

Correspondence to Sandro Romani or Karel Svoboda.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Neuroscience thanks Athena Akrami, Anne Churchland, and Albert Compte 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 Dynamics of putative pyramidal neurons in the basic task.

Hierarchical clustering of trial-averaged PSTHs of putative pyramidal cells recorded in vS1 (a, n = 256 cells) and ALM (b, left ALM n = 1648; right ALM n = 679 cells). a, Average spike rate of vS1 cells in each cluster and percentage of cells in each cluster. Red: trials without photostimulation, (lick-left). Blue: trials with photostimulation (lick-right); Cyan bar indicates the photostimulus. Top, correct trials. Bottom, error trials. Data is presented as trial-averaged activity, then averaged across cells belonging to each cluster ± s.e.m. (across cells, shaded). Cells in vS1 (clusters 1–4) did not switch selectivity on error trials, indicating that they tracked stimulus-related information. b, Same for ALM neurons. Neurons recorded from both hemispheres were clustered together. Bars show the percentage of putative pyramidal cells in left and right ALM that fall within each cluster, mean ± s.e.m across cells. Statistical significance was assessed by Wilcoxon rank sum test (two-sided). Cells in ALM often showed opposite selectivity on error trials (for example, Cluster 1–3), indicating that they tracked choice-related information. Despite the laterality of the movement, trial type selective preparatory activity was similar in left and right ALM (see distribution of cells in clusters 1–3 across hemispheres). Only a minority of cells in ALM did not switch selectivity on error trials – indicating sensory responses (for example, Cluster 4; note that cells in this cluster were more prevalent in left hemisphere). In addition, there was a cluster with neurons exhibiting non-selective ramping responses (Cluster 6), and a cluster with neurons responding to auditory cues that delineated the sample epoch (Cluster 10).

### Extended Data Fig. 2 Dynamics of putative fast-spiking interneurons in the basic task and in the presence of distractors.

Activity of putative fast-spiking interneurons (Methods) recorded in vS1 (n = 92 cells) and ALM (left ALM n = 184; right ALM n = 96 cells). a, Example cells and grand population average (labels as in Fig. 1d-g). b-c, Hierarchical clustering of trial-averaged PSTHs of putative interneurons (labels as in Extended Data. Figure 1a-b, bars indicate mean ± s.e.m across cells). Statistical significance was assessed by Wilcoxon rank sum test (two-sided). Putative interneurons in vS1 and ALM show a diversity of response profiles, suggesting that their activity does not simply reflect average activity of excitatory neurons. d, Session-averaged projections of neural activity of putative fast-spiking interneurons in left ALM on Stimulus, Choice, and Ramping modes (n = 104 cells, distractor trained mice). Red, lick-left trials; blue: lick-right trials. e-f, Trials with distractors projected on Stimulus mode (e, left) and Choice mode (f). Color-code as in Fig. 3 f,h. There was no suppression of distractors in the Stimulus mode during delay (e, right), whereas Choice mode exhibited robustness to distractors at late delay. Error bars, mean ± s.e.m., across sessions. Response size was assessed by repeated measures ANOVA, and also verified by fitting linear regression model. Statistical significance between response size to early- and late-delay distractors was done using two-sided Student t-test with Tukey-Kramer correction for multiple comparison. g, Endpoints of ramping mode of simultaneously recorded putative pyramidal cells versus putative fast-spiking interneurons. Each dot represents the Ramping mode endpoint on a single trial computed for the last 0.2 s of the delay epoch. Endpoints of ramping mode of simultaneously recorded putative fast-spiking (F.S.) interneurons and putative pyramidal neurons were correlated on single trials (r represents the Pearson correlation coefficient).

### Extended Data Fig. 3 Transient activity in vS1 and ALM in response to photostimulations in distractor-trained mice.

Spike rate modulation in vS1 (n = 317 cells) and left ALM (n = 1061 cells) of distractor-trained mice in response to strong distractors at different times, computed using all response trials, regardless of the behavioral outcome. Lick-left trials without stimulation (red), with distractors during early-delay (gray), or late-delay (black). Lick-right trials during sample-epoch stimulation (blue). a, Spike rates of example cells. b, Population-averaged responses. c, Quantification of the response size based on the population average (b). There was no reduction of distractor size in vS1 or in ALM of distractor-trained mice as assessed by repeated measures ANOVA, and also verified by fitting linear regression model, despite differences in the effect of distractors on behavior (Fig. 2d). Statistical significance between response size to early- and late-delay distractors was done using two-sided Student t-test with Tukey-Kramer correction for multiple comparison. d, For ALM recordings, we also used targeted dimensionality reduction to extract stimulus-related activity (‘Stimulus mode’, Methods). Throughout the paper, we defined the weights of Stimulus mode based on the difference in firing-rate between trials with and without stimulus, computed during the 0.5 s time-window following stimulus presentation at the Sample epoch (left panel). Here we also calculated the Stimulus mode based on the difference in neural activity following either early- (middle panel) or late-delay distractor (right panel). Neural activity following stimulus or distractors projected on these three modes was rather similar, regardless of what time epoch was used to compute the modes. This indicates that there was no distractor suppression during late-delay regardless of the way the Stimulus mode was computed. f, Correlation between the vectors of neuronal weights for the different definitions of Stimulus modes, showing that these modes were very similar (average Pearson correlation coefficient r = 0.80). Taken together, this suggests that the input channel to ALM (that is the Stimulus mode) does not change substantially through the sample and delay epochs. These results further support our observations that distractors were not suppressed during delay at the level of inputs to ALM. Error bars, mean ± s.e.m., across sessions (n = 17 sessions).

### Extended Data Fig. 4 Dimensionality-reduction on population dynamics in ALM.

a, Targeted dimensionality-reduction to define Stimulus, Choice (trial type selective), and Ramping (non-selective) modes in neural activity space. Modes are defined as one-dimensional subspaces in activity space (arrows) and are orthogonalized with respect to each other (Methods). b, Session-averaged projections of neural activity in left ALM on different modes in distractor-naive (top, n = 1356 cells) and distractor-trained (bottom, n = 1061 cells) mice. Red, lick-left trials; blue: lick-right trials. c, Proportion of trial-to-trial variance explained by different modes in distractor-naive (top) and distractor-trained (bottom) mice. Variance was computed at different time-points along the trial. d, Same as in c, for proportion of trial-averaged variance explained. Trial-averaged variance was computed separately for lick-left and lick-right trials. In all plots, for Choice mode analyses we used correct trials, excluding trials with distractors; for Stimulus and Ramping modes analyses we used correct and error trials, excluding trials with distractors. Shaded area represents the standard error of the mean (s.e.m.), across sessions.

### Extended Data Fig. 5 Robustness of the Choice mode in response to distractors.

Spike rate modulation in left ALM (n = 1061 cells) in response to strong distractors at different trial epochs, in distractor-trained mice. a, Example cells. b, Projection of neural activity on the Choice mode using all cells (left panel) or using only left-preferring cells (right panel). Lick-left trajectory without stimulation (red), with distractors during early-delay (gray), or late-delay (black), computed using correct trials. Lick-right trajectory during sample-epoch stimulation (blue). c, Impact of distractors on the Choice mode. Trajectories were aligned to the onset of each distractor. Data is shown as average across sessions ± s.e.m. (shaded). Data in a-c was computed using correct trials. The effect of distractors on the Choice mode on correct trials was temporary: distractors often resulted in transient change in spike rate of individual cells that contributed to the Choice mode, but their activity later recovered to the unperturbed (red) trajectory, indicating robustness. d, Distribution of Choice mode projections on single trials without distractors, averaged over the last 0.2 s of the delay epoch (end-delay points) for lick-left (red) versus lick-right (blue) trials. e, Distribution of Choice mode projections on trials with early-delay distractor (gray, robust trials; light blue, switching trials). Projections were averaged during mid-delay (left panel) or end-delay (right panel, Methods). Data is expressed as mean ± s.e.m. (shaded) across sessions.

### Extended Data Fig. 6 Distractor-free and distractor-trained RNN models with and without external ramping, comparison with ALM data.

a, Schematics of inputs to RNN models. Distractor-free RNNs were trained to reproduce stimulus and no-stimulus trials only. Distractor-trained RNNs were trained to additionally reproduce the PSTH of correct early-delay distractor trials. In addition, RNNs could receive a linearly ramping external input (purple, ‘ramping RNN’) or a constant zero input (green, ‘autonomous RNN’). Autonomous RNNs relied solely on internal recurrent (autonomous) dynamics to reproduce the slow ramping observed in the data, while ramping RNNs could make use of both the recurrent dynamics and the ramping input. We trained four networks based on the activity of neurons in left ALM: a distractor-free autonomous RNN (b-d), a distractor-trained autonomous RNN (e-g), a distractor-trained ramping RNN (h-j) and a distractor-free ramping RNN (Figs. 45). b,e,h, Proportion of lick right responses. In the 3 networks shown, the proportion of lick-right distractor-evoked trials was qualitatively similar to those observed in the data (Fig. 2d) and in the distractor-free ramping RNN (Fig. 4c), implying that all RNNs displayed a form of temporal gating. Error bars, mean ± s.e.m across sessions (n = 20, 100 trials per condition). c,f,i, RNNs activity projected on Choice mode for correct stimulus trials (blue), correct no-stimulus trials (red), correct and switching trials evoked by early-delay distractor (full and dotted gray, respectively), correct late-delay distractor trials (black). d,g,j, Fixed-point search results projected onto Choice mode. Green circles, stable fixed points. Purple diamonds, saddle points. Yellow diamonds, slow points (that is points where the network flow was significantly different from zero but much slower than the typical timescale of a single neuron, see Methods). In the autonomous RNNs (d,g), trajectories moved through a number of slow points before reaching either of the two stable-fixed points, in contrast to ramping networks in which, during most of the delay epoch, trajectories remained close to either of the two stable fixed points that were moved by the external ramping input (j, Fig. 5a). Hence, ramping and autonomous networks relied on different mechanism to achieve the slow ramping observed in the data. The fixed-point search revealed a partial difference in the dynamics of distractor-free and distractor-trained ramping networks. In the distractor-free ramping network, trajectories closely followed the moving stable fixed-point during the delay epoch (Fig. 5a). In the distractor-trained ramping network (j), lick-right trajectories (blue) were close to a slow saddle point during the first half of the delay epoch (purple diamonds) and then approached the moving stable fixed points during the second part of the delay. From the offset of the early-delay distractor until the end of the delay epoch the dynamics of the distractor-trained ramping network was qualitatively similar to that of the distractor-free ramping network. In addition, both the saddle point (present in the first part of the delay epoch) and the stable fixed-points (present in the second part of the delay epoch) were moving because of the external ramping stimulus, confirming that the ramping stimulus drives the dynamics in the distractor-trained ramping network. k (top), Trial-averaged trajectories of stimulus-evoked correct trials (blue) and early-distractor evoked (gray) switching trials, aligned to stimulus/distractor onset for all trained RNNs and for ALM data. k (bottom), Slopes of stimulus-evoked correct trials (blue) and early-distractor-evoked (gray) switching trials trajectories. Error bars, mean ± s.d. across trials (RNNs, 400 trials per condition) or mean ± s.e.m. across sessions (ALM data from distractor-trained mice only, n = 17 sessions). Statistical significance between stimulus-evoked and early-delay distractor-evoked slopes was assessed by Student t-test (two-sided, no corrections were made for multiple comparisons); from left to right: P=0.0074, P <0.0001, P <0.0001, P<0.0001, P=0.0003. Switching trajectories evoked by early-delay distractor in ALM data (rightmost panels) exhibited a steeper slope compatible with trajectories generated by the RNN models with external ramping input, but not with trajectories generated by the autonomous RNNs.

### Extended Data Fig. 7 Recurrent neural network trained on ALM data from the left and right hemispheres.

a, RNN trained to reproduce the PSTHs of recorded putative excitatory neurons from left ALM (n = 668 units) and right ALM (n = 351 units), during correct lick-right trials and correct lick-left trials. A linear ramping input (black) was delivered to units belonging to both hemispheres during sample and delay epochs. Stimuli and distractors were delivered to units belonging to left ALM, but not to units belonging to the right ALM, to conform with the experimental design according to which photostimulation was delivered to the left hemisphere. b, Proportion of right outputs generated by the two-hemisphere RNN model with ramping input, in response to stimulus (blue), and distractors during early (gray) and late (black) delay. The network outcome (left/right) was defined by whether the activity along the Choice mode (computed in activity space of left hemisphere RNN units) crossed the choice boundary at the end of the delay (Methods). Error bars, mean ± s.e.m. across sessions (n = 20, 100 trials per condition). c-d, Two-hemisphere RNN activity projected on Choice mode (c, computed using units belonging to left ALM (c) or right ALM (d) for correct trials (solid lines) and trials with early-delay distractor that resulted in right response (‘switching trials’, dashed lines); color scheme as in Fig. 3h. e-f, Neural activity recorded from ALM on left (e) and right hemisphere (f), projected onto Choice mode; color scheme as in panel c-d. The dynamics of the two-hemisphere network exhibited gating of distractors during late-delay, similarly to the dynamics observed in ALM in both hemispheres.

### Extended Data Fig. 8 External ramping input level determines robustness to distractors.

a, Schematics of distractor-free ramping RNN when an external ramping input of variable slope (purple) was delivered to the network. b, Proportion of distractor-evoked switching trials as a function of the time at which the distractor was delivered and of ramping input strength. Note that i) weaker ramping input induce more errors and ii) distractors delivered late in the delay are gated more efficiently. This suggests that elapsed time and amplitude of the ramping input were directly related: the gating of late distractors could be explained by the increased amplitude of the external ramping compared to earlier times in the delay. c, Assessing the contribution of external ramping input to temporal gating of distractors in the distractor-free ramping network. Left panel: To dissociate the impact on RNN dynamics of the external ramping input (which progressively increased during sample and delay epochs) from the effects of passage of time per se (that is regardless of the ramping), we clamped the external ramping input at the level it reached at the offset of the early-delay distractor (t = −1.2 s, black vertical line). Right panel: Proportion of switching trials for early- (gray) and late-delay (black) distractors: unlike the case examined in Fig. 4 (in which, for the same RNN, the external input kept ramping throughout the delay epoch), the proportion of switching trials evoked by late-delay distractor when the ramping input was clamped was similar to that of early-delay distractor. This indicates that temporal gating is regulated by the external ramp level and not by the passage of time per se. d, Relaxation time constants of distractor-free ramping network as a function of time at which the perturbation was delivered. In this test, the ramping input was set to the value it had reached at time ti in the delay (left panel), and, for each ramping input level, a perturbation of amplitude 0.2 a.u. along the Choice mode was delivered to the RNN during lick-left trials (middle panel). We then measured the time it took the network activity to drift back towards the lick left trajectory, that is the relaxation constant τ, by fitting a single exponential decay function $$f\left( t \right) = A\exp \left( { - \frac{t}{\tau }} \right) + B$$ to the decaying trajectories. The relaxation time constant decreased as ramping slope increased (right panel), suggesting a deepening of the lick-left attraction basin with increased ramping (which corresponds, equivalently, to later times in the delay).

### Extended Data Fig. 9 Effects of multiple stimulations on behavior and ALM dynamics.

a, Task schematics with additional stimulation on lick-right trials. b, Probability to lick-right after single or multiple vS1 photostimulations. Error bars, Mean ± s.e.m. across sessions (n = 37 sessions). P values indicate statistical significance by a two-sided paired Student t-test. c, ALM neural activity projected on Choice mode on correct lick-right trials with additional stimulation during early delay (light-blue) or late delay (cyan); activity on trials without stimulation (red) or with single stimulation during sample epoch (blue) are shown for comparison. d, Same as in c, for additional stimulation during pre-sample epoch (dark blue). Data was computed based on activity of neurons recorded in left ALM (n = 1061 cells) of distractor-trained mice. To study the effect of additional stimuli on lick-right trials, we first compared a single stimulus during sample-epoch (‘Sample’) to additional identical stimuli during delay (‘Sample + Early Delay’, and ‘Sample + Late Delay’; a). We considered three possible outcomes: 1) Additional stimuli during delay would not affect performance because a lick-right instruction was already provided during sample epoch; 2) Additional stimuli provide additional evidence in favor of lick-right decision, which can be encoded by larger activity along the Choice mode in ALM. In this case, additional stimuli would increase the probability to lick-right regardless of their timing (early or late in the delay); 3) Additional stimuli on lick-right trials could ‘rescue’ neural dynamics on error trials, which would otherwise follow lick-left neural trajectory. Such rescue by an additional stimulus would consist of a switch from the erroneous lick-left trajectory to the correct lick-right trajectory. Stimulus-induced rescue can be expected to occur more often for early- rather than late-delay stimulation, because later in time the two attractors would be further apart from each other and thus less amenable to switching. Also, because in our attractor model selectivity (distance between attractors) is controlled by the non-specific ramping input, trials with multiple stimulations are not expected to result in higher selectivity at the end of the delay epoch. Our results supported the third possibility because: i) Additional stimulation during early delay (‘Sample + Early Delay’) but not late delay (‘Sample + Late Delay’) increased lick-right probability compared to single stimulation during sample (‘Sample’; b); ii) Choice mode trajectories were perturbed by the second stimulation during early or late delay, but then recovered to same level as the trajectory for single stimulation (c). These transient perturbations can be attributed to feedforward inhibition, as we observed that putative fast-spiking interneurons in ALM also responded to stimulation (Extended Data Fig. 2). The eventual recovery of the neural activity to the original lick-right trajectory, further supports the notion that lick-right trajectory was stabilized by attractor dynamics – which made the neural activity robust to transient perturbations. We also tested an experimental condition in which the additional stimulus was given during pre-sample epoch on lick-right trials (‘Pre-sample + Sample’, a). This increased the probability to lick right, and the Choice mode trajectory on these trials started earlier and ramped to a higher level compared to ‘Sample’ trajectory (b,d). The fact that both Pre-Sample stimulation and Early-Delay stimulation increased behavioral performance, but only Pre-Sample stimulation resulted in higher Choice mode activity by the end of the delay, is also consistent with a moving attractor model in which the fixed point corresponding to the lick-right attractor is moved in state-space by the ramping input. In this scenario, an earlier onset of the ramping input (for example during pre-sample) would result in larger separation between attractors by the end of the delay – which would be manifested by larger selectivity along the Choice mode (Supplementary Fig. 6). Taken together, these results showed that ALM dynamic: 1) was robust on lick-right trials, 2) was influenced by the time elapsed from the initiation of preparatory activity, and 3) did not encode the total number of stimuli. More broadly, these results suggest that similarly to frontal cortical regions in rats (Hanks, T. D. et al. 2015, Nature 520, 220–223), ALM activity in mice in this task encodes the categorical choice rather than graded strength of evidence.

### Extended Data Fig. 10 Distractor-impact on persistent activity in ALM is learning-dependent.

Spike rate modulations in left ALM in distractor-naive versus distractor-trained mice, in response to weak-distractors computed using correct trials. a, Spike rates of example cells and b, Activity along the Choice mode in the presence of weak distractors in distractor-naive (top, n = 1356 cells) and distractor trained mice (bottom, n = 1061 cells). Lick-left trajectory without stimulation (red), and with weak distractors during early-delay (gray), or late-delay (black). Lick-right trajectory during sample-epoch stimulation (blue). Note that weak distractors had a persistent effect in ALM of distractor-naive mice. Specifically, distractors shifted the activity from lick-left trajectory towards lick-right trajectory. This was evident from shifts in projections on Choice mode (b) and from activity of individual cells that contributed to this mode (a). In contrast, in distractor-trained mice, the effect of distractors was transient. c, Impact of weak distractors on Choice mode in distractor-naive (gold) and distractor-trained mice (purple). Trajectories were aligned to the onset of each distractor. Data is shown as average across distractors with different onset times and sessions ± s.e.m. (shaded). In distractor-naive mice the effect of distractor persisted for at least 0.8 s (the time interval from the late-delay distractor onset and the Go cue), whereas in distractor-trained mice the activity recovered to the unperturbed trajectory. d, Schematics of putative attraction basins in distractor-naive (left) and distractor-trained (right) mice (cartoon). Shallow basin of attraction in distractor-mice mice allowed sufficiently strong stimuli to switch the neural activity from one basin to another.

## Supplementary information

### Supplementary Information

Supplementary Figs. 1–6.

### Supplementary Math Notes

Supplementary Math Note 1.1, 1.2 and 1.3.

## Rights and permissions

Reprints and Permissions

Finkelstein, A., Fontolan, L., Economo, M.N. et al. Attractor dynamics gate cortical information flow during decision-making. Nat Neurosci (2021). https://doi.org/10.1038/s41593-021-00840-6

• Accepted:

• Published:

• ### Closing the gate to distractors during decision-making

• Edmund Chong
•  & Athena Akrami

Nature Neuroscience (2021)