Inhib conductance into inhib units (g_bar_i.inhib) Strength of feedforward weights to inhib (scale.ff)
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1 1 Networks: Inhibition Controls activity (bidirectional excitation). Inhibition = thermostat-controlled air conditioner inhibitory neurons sample excitatory activity (like a thermostat samples the temperature) more excitatory activity more inhibition to keep the network from getting too hot (active) set point behavior 1. Biology: Feedforward and Feedback. 2. Critical Parameters. 2 Types of Inhibition a) b) Hidden Inhib Anticipates excitation Feed Forward Like having thermostat outside of your house Hidden Feedback Inhib Reacts to excitation Like a normal (indoor) AC thermostat 3. kwta Simplification. 3 Critical Parameters (inhib.proj) 4 Simulations: [amp top down dist.proj; inhib.proj] Feedback a) b) Hidden Inhib Hidden Inhib Feed Forward Inhib conductance into hidden units (g_bar_i.hidden) Inhib conductance into inhib units (g_bar_i.inhib) Strength of feedforward weights to inhib (scale.ff) Strength of feedback weights to inhib (scale.fb) 5 k-winners-take-all (kwta) 6 The function of inhibition is to keep excitatory activity at a rough set point. We can approximate this function by enforcing a max activity level in each layer. kwta: Instead of simulating inhibitory neurons, we choose an inhibitory current g i valuefor each layersuch thatthe specified number k of excitatory neurons are above threshold. Advantages: Much less computationally expensive, avoids oscillations.
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4 kwta: Summary 24 Benefits of Inhibition Simple shortcut we use instead of actual inhibitory interneurons Captures basic idea that inhibition maintains activity at a set point for a given layer Controls activity (bidirectional excitation) Inhibition forces units to compete to represent the input: Only the most appropriate (best-fitting) units survive the competition Specify inhibition valuefor a layersuch thatkunitsareactive k is a parameter: percent activity levels vary across different brain regions! kwta still allows for some wiggle room in overall activation
5 25 Simulations: [inhib.proj] 1. kwta approximates set point behavior. 2. Allows for faster updating. 26 Networks 1. Biology: The cortex 2. Excitation: Unidirectional (transformations) Bidirectional (top-down processing, pattern completion, amplification) 3. Inhibition: Controls bidirectional excitation (feedforward, feedback, set point, kwta approximation) 4. Constraint Satisfaction: Putting it all together. 27 Constraint Satisfaction 28 Harmony Process of trying to satisfy various constraints (from environment, connection weights, activations). Bidirectional excitation and inhibition form part of this larger computational goal. Harmony = extent to which unit activations are consistent with weights H = 2 1 j i a i w ij a j Harmonyis highwhen unitswithstrong (positive) weights are co-active 1. Energy/harmony. 2. AttractorDynamics. 3. Noise. 29 Harmony 30 Harmony John Hopfield showed that harmony tends to increase monotonically as the network settles John Hopfield showed that harmony tends to increase monotonically as the network settles network settling = moving to a more harmonious state
6 31 Attractor Dynamics A network will settle into a stable state over time: the attractor. energy attractor basin Maximize harmony given inputs and weights. 32 Circle Attractor state y state x attractor state Attractor = stable set of states from many starting points. 33 [catsanddogs.proj] 34 Constraint Satisfaction Knowledge is in the weights! (built in here) Harmony as a function of constraints Bidir networks like cats and dogs constitute a content-addressable memory: you can access any part of a memory from any other Who likes to eat grass and play with feathers? In contrast, simple uni-directional nets are more like an address book: you can look up the address from someone s last name, but can t get names from addresses. 35 Constraint Satisfaction 36 Constraint Satisfaction Spontaneous generalization: The network can extract regularities from its base of knowledge What are dogs like? What are medium dogs like? 1. AttractorDynamics. 2. Energy/harmony 3. Noise.
7 37 The Necker Cube a) b) c) Two different interpretations Can t perceive both at once Alternate between perceptions: bistability 38 The Role of Noise Howmight noise beusefulin yourbrain? Local Minimum Global Minimum (local maximum for harmony) 39 [necker cube.proj] 40 Networks Role of noise Accommodation 1. Biology: The cortex 2. Excitation: Unidirectional (transformations) Bidirectional (top-down processing, pattern completion, amplification) 3. Inhibition: Controls bidirectional excitation (feedforward, feedback, set point, kwta approximation) 4. Constraint Satisfaction: Putting it all together.
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