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Internal representation of task rules by recurrent dynamics: the importance of the diversity of neural responses.

Rigotti M, Ben Dayan Rubin D, Wang XJ, Fusi S - Front Comput Neurosci (2010)

Bottom Line: Specifically, we found that when the inner mental states encoding the task rules are represented by stable patterns of neural activity (attractors of the neural dynamics), the neurons must be selective for combinations of sensory stimuli and inner mental states.A biologically realistic implementation of the model captures several aspects of the activity recorded from monkeys performing context-dependent tasks.Our findings explain the importance of the diversity of neural responses and provide us with simple and general principles for designing attractor neural networks that perform complex computation.

View Article: PubMed Central - PubMed

Affiliation: Center for Theoretical Neuroscience, College of Physicians and Surgeons, Columbia University New York, NY, USA.

ABSTRACT
Neural activity of behaving animals, especially in the prefrontal cortex, is highly heterogeneous, with selective responses to diverse aspects of the executed task. We propose a general model of recurrent neural networks that perform complex rule-based tasks, and we show that the diversity of neuronal responses plays a fundamental role when the behavioral responses are context-dependent. Specifically, we found that when the inner mental states encoding the task rules are represented by stable patterns of neural activity (attractors of the neural dynamics), the neurons must be selective for combinations of sensory stimuli and inner mental states. Such mixed selectivity is easily obtained by neurons that connect with random synaptic strengths both to the recurrent network and to neurons encoding sensory inputs. The number of randomly connected neurons needed to solve a task is on average only three times as large as the number of neurons needed in a network designed ad hoc. Moreover, the number of needed neurons grows only linearly with the number of task-relevant events and mental states, provided that each neuron responds to a large proportion of events (dense/distributed coding). A biologically realistic implementation of the model captures several aspects of the activity recorded from monkeys performing context-dependent tasks. Our findings explain the importance of the diversity of neural responses and provide us with simple and general principles for designing attractor neural networks that perform complex computation.

No MeSH data available.


(A) Minimal scheme of mental states and event-driven transitions for the simplified WCST (same as in Figure 1B). (B) Rule selectivity pattern for 70 simulated cells: for every trial epoch (x-axis) we plotted a black bar when the neuron had a significantly different activity in shape and in color blocks. The neurons are sorted according to the first trial epoch in which they show rule selectivity. (C) Same analysis as in (B), but for spiking activity of single-units recorded in prefrontal cortex of monkeys performing an analog of the WCST (Mansouri et al., 2006). (D) Scheme of mental states and event-driven transitions with multiple states during the inter-trial interval (E) Same as (B), but for the history-dependent scheme in (D). (F) Same as (E), but for the selectivity to the color of the sample (red bars). Short black bars indicate rule selectivity.
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Figure 7: (A) Minimal scheme of mental states and event-driven transitions for the simplified WCST (same as in Figure 1B). (B) Rule selectivity pattern for 70 simulated cells: for every trial epoch (x-axis) we plotted a black bar when the neuron had a significantly different activity in shape and in color blocks. The neurons are sorted according to the first trial epoch in which they show rule selectivity. (C) Same analysis as in (B), but for spiking activity of single-units recorded in prefrontal cortex of monkeys performing an analog of the WCST (Mansouri et al., 2006). (D) Scheme of mental states and event-driven transitions with multiple states during the inter-trial interval (E) Same as (B), but for the history-dependent scheme in (D). (F) Same as (E), but for the selectivity to the color of the sample (red bars). Short black bars indicate rule selectivity.

Mentions: The prescription for building neuronal circuits that implement a given scheme of mental states and event-driven transitions is general, and it can be used for arbitrary schemes provided that there is a sufficient number of RCNs. To test our general theory, we applied our approach to a biologically realistic neural network model designed to perform a rule-based task which is analog to the WCST described in Figure 1 (Mansouri et al., 2006, 2007), whose scheme is reproduced in Figure 7A. We implemented a network of more realistic rate-based model neurons with excitation mediated by AMPA and slow NMDA receptors, and inhibition mediated by GABAA receptors. Figure 6A shows the simulated activities of two rule selective neurons during two consecutive trials after a rule shift. The rule in effect changes from Color to Shape just before the first trial, causing an erroneous response that is corrected in the second trial, after the switch to the alternative rule. Although the two neurons shown in Figure 6A are always selective to the rule, their activity is modulated by other events throughout all the epochs of the trials. This is due to the interaction with the other neurons in the recurrent network and with the RCNs. Figure 6B shows the activity of three RCNs. They typically have a rich behavior exhibiting mixed selectivity that changes depending on the epoch (and hence on the mental state). Two features of the simulated neurons have already been observed in experiments: (1) neurons show rule-selective activity in the inter-trial interval, as observed for a significant fraction of cells in PFC (Mansouri et al., 2006); (2) the selectivity to rules is intermittent, or in other words, neurons are selective to a different extent to the rules depending on the epoch of the trial. This second feature is analyzed in detail in the next section.


Internal representation of task rules by recurrent dynamics: the importance of the diversity of neural responses.

Rigotti M, Ben Dayan Rubin D, Wang XJ, Fusi S - Front Comput Neurosci (2010)

(A) Minimal scheme of mental states and event-driven transitions for the simplified WCST (same as in Figure 1B). (B) Rule selectivity pattern for 70 simulated cells: for every trial epoch (x-axis) we plotted a black bar when the neuron had a significantly different activity in shape and in color blocks. The neurons are sorted according to the first trial epoch in which they show rule selectivity. (C) Same analysis as in (B), but for spiking activity of single-units recorded in prefrontal cortex of monkeys performing an analog of the WCST (Mansouri et al., 2006). (D) Scheme of mental states and event-driven transitions with multiple states during the inter-trial interval (E) Same as (B), but for the history-dependent scheme in (D). (F) Same as (E), but for the selectivity to the color of the sample (red bars). Short black bars indicate rule selectivity.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2967380&req=5

Figure 7: (A) Minimal scheme of mental states and event-driven transitions for the simplified WCST (same as in Figure 1B). (B) Rule selectivity pattern for 70 simulated cells: for every trial epoch (x-axis) we plotted a black bar when the neuron had a significantly different activity in shape and in color blocks. The neurons are sorted according to the first trial epoch in which they show rule selectivity. (C) Same analysis as in (B), but for spiking activity of single-units recorded in prefrontal cortex of monkeys performing an analog of the WCST (Mansouri et al., 2006). (D) Scheme of mental states and event-driven transitions with multiple states during the inter-trial interval (E) Same as (B), but for the history-dependent scheme in (D). (F) Same as (E), but for the selectivity to the color of the sample (red bars). Short black bars indicate rule selectivity.
Mentions: The prescription for building neuronal circuits that implement a given scheme of mental states and event-driven transitions is general, and it can be used for arbitrary schemes provided that there is a sufficient number of RCNs. To test our general theory, we applied our approach to a biologically realistic neural network model designed to perform a rule-based task which is analog to the WCST described in Figure 1 (Mansouri et al., 2006, 2007), whose scheme is reproduced in Figure 7A. We implemented a network of more realistic rate-based model neurons with excitation mediated by AMPA and slow NMDA receptors, and inhibition mediated by GABAA receptors. Figure 6A shows the simulated activities of two rule selective neurons during two consecutive trials after a rule shift. The rule in effect changes from Color to Shape just before the first trial, causing an erroneous response that is corrected in the second trial, after the switch to the alternative rule. Although the two neurons shown in Figure 6A are always selective to the rule, their activity is modulated by other events throughout all the epochs of the trials. This is due to the interaction with the other neurons in the recurrent network and with the RCNs. Figure 6B shows the activity of three RCNs. They typically have a rich behavior exhibiting mixed selectivity that changes depending on the epoch (and hence on the mental state). Two features of the simulated neurons have already been observed in experiments: (1) neurons show rule-selective activity in the inter-trial interval, as observed for a significant fraction of cells in PFC (Mansouri et al., 2006); (2) the selectivity to rules is intermittent, or in other words, neurons are selective to a different extent to the rules depending on the epoch of the trial. This second feature is analyzed in detail in the next section.

Bottom Line: Specifically, we found that when the inner mental states encoding the task rules are represented by stable patterns of neural activity (attractors of the neural dynamics), the neurons must be selective for combinations of sensory stimuli and inner mental states.A biologically realistic implementation of the model captures several aspects of the activity recorded from monkeys performing context-dependent tasks.Our findings explain the importance of the diversity of neural responses and provide us with simple and general principles for designing attractor neural networks that perform complex computation.

View Article: PubMed Central - PubMed

Affiliation: Center for Theoretical Neuroscience, College of Physicians and Surgeons, Columbia University New York, NY, USA.

ABSTRACT
Neural activity of behaving animals, especially in the prefrontal cortex, is highly heterogeneous, with selective responses to diverse aspects of the executed task. We propose a general model of recurrent neural networks that perform complex rule-based tasks, and we show that the diversity of neuronal responses plays a fundamental role when the behavioral responses are context-dependent. Specifically, we found that when the inner mental states encoding the task rules are represented by stable patterns of neural activity (attractors of the neural dynamics), the neurons must be selective for combinations of sensory stimuli and inner mental states. Such mixed selectivity is easily obtained by neurons that connect with random synaptic strengths both to the recurrent network and to neurons encoding sensory inputs. The number of randomly connected neurons needed to solve a task is on average only three times as large as the number of neurons needed in a network designed ad hoc. Moreover, the number of needed neurons grows only linearly with the number of task-relevant events and mental states, provided that each neuron responds to a large proportion of events (dense/distributed coding). A biologically realistic implementation of the model captures several aspects of the activity recorded from monkeys performing context-dependent tasks. Our findings explain the importance of the diversity of neural responses and provide us with simple and general principles for designing attractor neural networks that perform complex computation.

No MeSH data available.