Neural dynamics implement a flexible decision bound with a fixed firing rate for choice: a model-based hypothesis

Decisions are faster and less accurate when conditions favour speed, and are slower and more accurate when they favour accuracy. This speed-accuracy trade-off (SAT) can be explained by the principles of bounded integration, where noisy evidence is integrated until it reaches a bound. Higher bounds reduce the impact of noise by increasing integration times, supporting higher accuracy (vice versa for speed). These computations are hypothesized to be implemented by feedback inhibition between neural populations selective for the decision alternatives, each of which corresponds to an attractor in the space of network states. Since decision-correlated neural activity typically reaches a fixed rate at the time of commitment to a choice, it has been hypothesized that the neural implementation of the bound is fixed, and that the SAT is supported by a common input to the populations integrating evidence. According to this hypothesis, a stronger common input reduces the difference between a baseline firing rate and a threshold rate for enacting a choice. In simulations of a two-choice decision task, we use a reduced version of a biophysically-based network model (Wong & Wang, 2006) to show that a common input can control the SAT, but that changes to the threshold-baseline difference are epiphenomenal. Rather, the SAT is controlled by changes to network dynamics. A stronger common input decreases the model’s effective time constant of integration and changes the shape of the attractor landscape, so the initial state is in a more error-prone position. Thus, a stronger common input reduces decision time and lowers accuracy. The change in dynamics also renders firing rates higher under speed conditions at the time that an ideal observer can make a decision from network activity. The difference between this rate and the baseline rate is actually greater under speed conditions than accuracy conditions, suggesting that the bound is not implemented by firing rates per se

Gain Modulation by an Urgency Signal Controls the Speed–Accuracy Trade-Off in a Network Model of a Cortical Decision Circuit

The speed–accuracy trade-off (SAT) is ubiquitous in decision tasks. While the neural mechanisms underlying decisions are generally well characterized, the application of decision-theoretic methods to the SAT has been difficult to reconcile with experimental data suggesting that decision thresholds are inflexible. Using a network model of a cortical decision circuit, we demonstrate the SAT in a manner consistent with neural and behavioral data and with mathematical models that optimize speed and accuracy with respect to one another. In simulations of a reaction time task, we modulate the gain of the network with a signal encoding the urgency to respond. As the urgency signal builds up, the network progresses through a series of processing stages supporting noise filtering, integration of evidence, amplification of integrated evidence, and choice selection. Analysis of the network's dynamics formally characterizes this progression. Slower buildup of urgency increases accuracy by slowing down the progression. Faster buildup has the opposite effect. Because the network always progresses through the same stages, decision-selective firing rates are stereotyped at decision time

Calcium-dependent calcium decay explains STDP in a dynamic model of hippocampal synapses.

It is widely accepted that the direction and magnitude of synaptic plasticity depends on post-synaptic calcium flux, where high levels of calcium lead to long-term potentiation and moderate levels lead to long-term depression. At synapses onto neurons in region CA1 of the hippocampus (and many other synapses), NMDA receptors provide the relevant source of calcium. In this regard, post-synaptic calcium captures the coincidence of pre- and post-synaptic activity, due to the blockage of these receptors at low voltage. Previous studies show that under spike timing dependent plasticity (STDP) protocols, potentiation at CA1 synapses requires post-synaptic bursting and an inter-pairing frequency in the range of the hippocampal theta rhythm. We hypothesize that these requirements reflect the saturation of the mechanisms of calcium extrusion from the post-synaptic spine. We test this hypothesis with a minimal model of NMDA receptor-dependent plasticity, simulating slow extrusion with a calcium-dependent calcium time constant. In simulations of STDP experiments, the model accounts for latency-dependent depression with either post-synaptic bursting or theta-frequency pairing (or neither) and accounts for latency-dependent potentiation when both of these requirements are met. The model makes testable predictions for STDP experiments and our simple implementation is tractable at the network level, demonstrating associative learning in a biophysical network model with realistic synaptic dynamics

Trading speed and accuracy by coding time: a coupled-circuit cortical model.

Our actions take place in space and time, but despite the role of time in decision theory and the growing acknowledgement that the encoding of time is crucial to behaviour, few studies have considered the interactions between neural codes for objects in space and for elapsed time during perceptual decisions. The speed-accuracy trade-off (SAT) provides a window into spatiotemporal interactions. Our hypothesis is that temporal coding determines the rate at which spatial evidence is integrated, controlling the SAT by gain modulation. Here, we propose that local cortical circuits are inherently suited to the relevant spatial and temporal coding. In simulations of an interval estimation task, we use a generic local-circuit model to encode time by 'climbing' activity, seen in cortex during tasks with a timing requirement. The model is a network of simulated pyramidal cells and inhibitory interneurons, connected by conductance synapses. A simple learning rule enables the network to quickly produce new interval estimates, which show signature characteristics of estimates by experimental subjects. Analysis of network dynamics formally characterizes this generic, local-circuit timing mechanism. In simulations of a perceptual decision task, we couple two such networks. Network function is determined only by spatial selectivity and NMDA receptor conductance strength; all other parameters are identical. To trade speed and accuracy, the timing network simply learns longer or shorter intervals, driving the rate of downstream decision processing by spatially non-selective input, an established form of gain modulation. Like the timing network's interval estimates, decision times show signature characteristics of those by experimental subjects. Overall, we propose, demonstrate and analyse a generic mechanism for timing, a generic mechanism for modulation of decision processing by temporal codes, and we make predictions for experimental verification