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excitation inhibition loss Quiz 3 2. Decision making in the honey bee model A) Some'mes is exactly equivalent to the op'mal On optimal decision-making J. A. R. Marshall et al. 3 Figure 2. In the Usher–McClelland model of decision-making diffusion model of decision making n the primate visual cortex, neural populations represent ; accumulated evidence for each of the alternatives. TheseB) Always is exactly equivalent to the opEmal diffusion . excitation populations y1 and y2 integrate noisy inputs I1 and I2, but leak model of decision making g inhibition accumulated evidence at rate k. Each population also inhibits loss e he other in proportion to its own activation level, at rate w.C) Never is exactly equivalent to the opEmal diffusion n When wZk and both are large, the Usher–McClelland model e model of decision making, but can be asymptoEcally Peduces to the diffusion model of decision-making (figure 3). opEmal Figure 2. In the Usher–McClelland model of decision-making e in the16primate visual cortex, neural populations represent s accumulated evidence for each of the alternatives. These g 14 populations y and y integrate noisy inputs I and I , but leak 3. Decision making in the ant models e accumulated evidence at rate k. Each population also inhibits 12 the other in proportion to its own activation level, at rate w. t A) SomeEmes is exactly equivalent to the opEmal When wZk and both are large, the Usher–McClelland model s 10 reduces to the diffusion model of decision-making (figure 3). s diffusion model of decision making 8 16 B) Always is exactly equivalent to the opEmal diffusion 6 14 model of decision making 4 12 C) Never is exactly equivalent to the op'mal diffusion 2 10 y model of decision making, but can be asympto'cally 8 e 0 2 4 6 8 10 12 14 16 d 6 op'mal e 4 t Figure 3. The expected dynamics of the Usher–McClelland 0. G ive y our n ame 2 f model, plotted as the activation of population y1 against the t etypublishing.org on 14 April 2009 1 2 1 2 activation of population When decay 0 what 2 this 4 y2.l6ower 8 fi 10gure 12 equals 16inhibition s14hows in 2 sentences - 1. Explain wZk), the system converges to a line (bold arrow) and a (y1 and y2 are the same as in the figure above): diffuses along it, until a movable decision threshold is reached e Figure 3. The expected dynamics of the Usher–McClelland lines). Along the attracting line, the Usher–McClelland The n egaEve elaEonship between the athe cEvaEon of y1 and the acEvaEon of y2 indicates inhibiEon tdashed model, plotted asrthe activation of population y1 against model is equivalent to the optimal diffusion model of decisionr activation of population y2.yWhen decay equals inhibition between psystem opulaEon 1 and populaEon y2. The solid line is the result of decay equal to inhibiEon (k making (figure s (wZk), the1). converges to a line (bold arrow) and c = w , in along which case the m odel threshold is equivalent diffuses it, until a movable decision is reached to the opEmal diffusion model of decision making.) Usher-‐McClelland Model Leaky inhibitory integraEon Change in acEvaEon of a populaEon of neurons = input signal + noise – decay – inhibiEon from alternaEve populaEon Eqn 4.2 transforms Eqn 4.1 to decouple the Eqns and show the UM model approximates diffusion model & opEmal decision making when w = k & both are large How your brain makes decisions MoEon discriminaEon h[p://www.youtube.com/watch?v=hpvbZxDtXSY (1:40) Siegel et al FronEers in Human NeuroScience 5 (2011) h[p://www.economicswiki.com/economics-‐tutorials/ pareto-‐efficient-‐pareto-‐opEmal-‐tutorial/ Bee decision-‐making model Downloaded from rsif.royalsocietypublishing.org on 14 April 2009 On optimal decision-making gradually increase their firing rate (Schall 2001; Shadlen & Newsome 2001; Roitman & Shadlen 2002). Detailed studies of their activity provide strong evidence that the LIP neurons integrate input from the corresponding MT neurons over time (Huk & Shadlen 2005; Hanks et al. 2006). Hence, as time progresses in the task, the sensory evidence accumulated in the LIP neurons becomes more and more accurate. It has been observed that when the activity of the LIP neurons exceeds a certain threshold, the decision is made and an eye movement in the corresponding direction is initiated (Schall 2001; Shadlen & Newsome 2001; Roitman & Shadlen 2002). This arrangement of neural populations with decision thresholds lends itself to representation through a simple model, as described in §4. J. A. R. Marshall et al. 3 excitation inhibition loss Figure 2. In the Usher–McClelland model of decision-making in the primate visual cortex, neural populations represent accumulated evidence for each of the alternatives. These populations y1 and y2 integrate noisy inputs I1 and I2, but leak accumulated evidence at rate k. Each population also inhibits the other in proportion to its own activation level, at rate w. When wZk and both are large, the Usher–McClelland model reduces to the diffusion model of decision-making (figure 3). 16 14 4. THE USHER–MCCLELLAND MODEL 12 The Usher–McClelland model represents decisionmaking using neural populations that act as mutually inhibitory, leaky integrators of incoming evidence (figure 2). In the moving-dots decision task described above, these integrator populations would represent the LIP neural populations corresponding to the different possible eye movement decisions. Each population of integrator neurons receives a noisy input signal that it integrates, subject to some constant loss. Each population also inhibits the activation of the other to a degree proportional to its own activation. So, as one 10 8 6 4 2 0 2 4 6 8 10 12 14 16 Figure 3. The expected dynamics of the Usher–McClelland Ants: no direct switching Undecided Scouts choose y2 y2 commiCed scouts recruit new scouts y2 scouts decay from y2 Bee decision-‐making model Undecided Scouts choose y2 y2 commiCed scouts recruit new scouts y2 scouts decay from y2 Y2 scouts directly switch to y1 InformaEon gathering, evaluaEon, deliberaEon, consensus, choice, implementaEon • • • • • Bees commit all at once; waggle dances are broadcast in a crowded hive (only a few see it at at Eme) Ants go one at a Eme with no opportunity (usually) to assess mulEple nests; commit based on a quorum at one nest site How ants assess nest size: Ant lays a trail; leaves, returns, counts number of Emes it crosses its trail Ants show preferences, consistent rankings, transiEvity, weighing of all a[ributes Ants use a 'weighted addiEve Strategy' prefer bright, thick and narrow over dark thin and wide (with constant area) even though dark is most important Pra[ showed quorum sensing -‐-‐-‐switch from tandem running to carrying (full commitment) once a (changeable) threshold # of ants have chosen to stay in a nest