Information processing with population codes

Pouget, A. Dayan, P. Zemel, R. (2000) Information processing with population codes. Nature Reviews Neuroscience 1: 125-132.

Place cells are a population code: Borst, Theunissen (1999). Visual features: orientation, color, direction of motion, depth and many other coded by population code: Usrey & Reid (1999), Zemel, Dayan, Pouget (1998). Motor commands in motor cortex: Tolhurst, Movshon Dean (1982). Leeches and crickets: Salinas & Abbott (1994).

Population codes are robust -- damage to single cell does not catastrophically harm information encoded. Other desirable properties: noise removal, short-term memory, nonlinear function.

Can decode population code with Bayesian maximization like models. Two types of maxima: Maximum a posterior (MAP) estimate: direction with highest probability (Maximize P(s|r)). Maximum likelihood (ML): maximize P(r|s). These are the same if the prior (P(s)) is flat -- i.e. no prior knowledge of s.

ML is optimal decoding method (Seung, Sompolinsky (1993), Deneve, Latham, Pouget (1999) [This will be a good one to do]), but requires substantial data to estimate tuning curves and noise distributions. Can use only preferred direction through 'voting' methods.

Estimation is like template matching MAP is cosine template match, ML template matches with template derived from tuning curve (this is why it is optimal). Neurons that have highest derivative have most influence over the decoding of the population code. Deneve et al 1999 shows how you can implement ML estimator in recurrent neural net.

A population code can form a basis set for all possible non-linear mappings. (basis like sin/cos is basis for fourier transform). Some unsupervised learning algorithms for learning the basis functions from data --  then the needed transformations can be formed from the basis functions. Olshausen & Field (1996), Bishop Svenson Williams (1998), Lewicki, Sejnowski (2000).

Basis function equivalence to population codes is why population codes are so computationally appealing. object recognition: Poggio & Edelman (1990). Object-centered representations: Salinas & Abbott (1997). sensorimotor transformations.

Two directions of motion will yield bimodal bump in population code if the directions are far apart, but only a single bump if motions are close together. ML would fail at decoding the two directions in this case.

Can reformulate population code to be representing a probability density function instead of a specific value. This could allow you to use the code to represent multiple motions by noting that the width of the distribution is wider, also allows for a form of Bayesian inference. However, there is no computational theory based on this idea like the basis function idea.

Gain Modulation in the Central Nervous System: Where Behavior, Neurophysiology, and Computation Meet

Salinas, E. Sejnowski, TJ. (2001) Gain Modulation in the Central Nervous System: Where Behavior, Neurophysiology, and Computation Meet. The Neuroscientist 7(5): 430-440.

Review article by terry.

"Gain modulation is revealed when one input, the modulatory one, affects the gain or the sensitivity of the neuron to the other input, without modifying its selectivity or receptive field properties."

Neurons in parietal area are gain modulated by eye and head position. This creates a "gain-field". The receptive field selectivity is the same -- based on retinal location, but is modulated based on gaze direction.


"Note that although gain-modulated parietal neurons carry information about stimulus location and gaze angle, the response of a single neuron, no matter how reliable, is not enough to determine these quantities; several neurons need to be combined. This is an example of a population code (Pouget and others 2000)."

Dendrites as mechanism for gain modulation: Mel (1993), Mel (1999). Invertebrates: Gabbiani et al (1999).
Recurrent network for gain: Salinas and Abbot (1996)
Synchrony for gain: Salinas and Sejnowski (2000)
Driving and Balanced inputs: Chance and Abbott (2000)

Zipser and Andersen (1988) were first to show computational power of gain modulation. Showed that after learning a coordinate transform hidden units appeared to respond like gain modulated neurons seen in parietal cortex. Xing and Andersen (2000a, 2000b) furthered work to auditory localization. Used gain model of Salinas and Abbot 1996.

Pouget and Sejnowski (1997b) extended results of Salinas and Abbott (1995) by showing that gain modulated neurons could form a "complete set" and create any nonlinear function from a set of synapses.

Information about location originates in eye-centered representation. gain modulation always seems to mediate the generation of the new coordinate representations.

Gain modulation could be used for invariant object recognition. Neurons in V4 are gain modulated by attention. Gain modulation used for size constancy, and motion processing.

Dendritic Properties of Turtle Pyramidal Neurons

Larkum, ME. Watanabe, S. Lasser-Ross, N. Rhodes, P. Ross, WN. (2007) Dendritic Properties of Turtle Pyramidal Neurons. Journal of Neurophysiology 99: 683-694.

Nice intro describing the relation between turtle 3-layer and 6-layer cortex and evolution. Some old-school papers sounds pretty interesting that I should look into. (Connors and Kriegstein (1986), Mulligan and Ulinkski (1990), Reiner (2000)).

Well just look at the difference:

FIG. 1. Dendritic structure of turtle pyramidal neurons. A: schematic diagram of a typical coronal cortical slice positioned over a photograph of the dissected turtle brain. B: diagram of a cortical slice in more detail. The picture of the pyramidal neuron shows the region from which most recordings were made. The thick blue line is the region containing most cell bodies. The main regions of the dorsal cortex are labeled from medial (M) to lateral (L) including the dorsal–medial region (DM) and two dorsal subregions (D1 and D2) from which most of the recordings were made. C and D: outline of turtle and rat L5 pyramidal neurons determined from biocytin fills. Note that that most of the dendrites from the turtle cell are single branches that extend from the somatic region. The L5 neuron has a major apical branch with oblique branches, an apical tuft, and basal dendrites.

Many ephys properties are the same. Active back-propagation of action-potentials is likely. Dendritic APs can grow in size with successive AP initiation. APs initiated closer to the soma, not in the dendrites (Soma electrode AP come before dendrite, even if AP is triggered via dendrite electrode).

Dendritic sodium-spikes can also be initiated similar to hippocampus. Protocol to evoke Ca spikes in rat neocortical pyramids did not evoke Ca spikes in turtle pyramids. Known that Ca spikes can be generated by blocking K channels (Connors & Kriegstein).

"Prepotentials" are small spikelets that Connors & Kriegstein observed. CK thought that these were dendritic in origins, but Larkum says that they are axonal - "prepotentials are axonal spikes that fail to invade the soma and are not dendritic spikes."

Calcium spikes were present. 100 ms time constant. Some cells had calcium waves, where the calcium slowly propagates along the dendrites, likely coming from intracellular stores. Waves not as big as calcium transients in neocortical cells.


"The most obvious consequence of the lack of dendritic Ca2 spikes in reptilian pyramidal neurons
is that dendritic input does not switch the somatic firing pattern from regularly spiking to bursting as in the neocortex (Larkum and Zhu 2002). It has been suggested that the Ca2 spike in neocortical pyramidal neurons serves to associate feedback inputs arriving at the tuft with feedforward inputs in the basal regions (Larkum et al. 1999b, 2007), which clearly is not possible in the turtle cortex."

Abstract Cortex

Perhaps a better way of describing "General Cortex" is to describe it as "Abstract Cortex". Abstract as in computer programming -- a class that can be inherited, but not instantiated itself. All of the different cortical architectures across the brain are serving different functions, and so have slightly different properties. However, they all inherit (literally via evolution) many of their properties from abstract cortex, and then modify to suit their more specific needs.

Abstract cortex is the basis, and the rest of the cortical structures are variations of abstract cortex that are used to solve different problems. Biology has given us a giant tool kit of different cortical structures, which have been adapted to solve different problems. If we can figure out the rules that correspond to the alterations from abstract cortex and the consequences of these alterations on the final output, then we can design cortical structures for handling different types of data.

Evolution has figured out how to make many different variations of abstract cortex in a complementary manner to solve different problems. Vision is not going to be solved with a magic equation that is based on a single optimization, but rather setting up several cortical structures that pay attention to needed information in the visual world. Each of these structures may be driven by their own optimizations, but there will be a cortical structure that is designed to handle motion, one designed to handle faces, etc. To solve vision, there will have to be a lot of complementary cortices all designed to look at the world from different perspectives.

The differences in the cortical structures is partly set up by the type of information that they receive, which is definitely part of the whole process. Each cortical area should be able to handle oddities of the info that it gets, but will be set-up by evolution to transform the information it receives in a specific way. Most of this transformation is described by the general properties of abstract cortex -- i.e. some type of dimensionality reduction and classification. But other properties could emerge that give each cortical area special computational abilities.

Take as a possible (but this is hypothetical) that in MT there are neurons that are more sensitive to the timing of inputs on their dendrites. This makes them do strange computations when there is consistent motion signals -- i.e. if the inputs turn on in order towards the soma, the neuron fires at a higher rate, but if same inputs are turned on in opposite order the neuron fires at a lower rate, ala Bronco, Hausser. These alterations in the dendritic properties make the neurons non-linear with motion signals -- this creates a lot of extra entropy when there is motion in the firing rates of neurons in MT. This extra entropy is used by the abstract cortex algorithm to make useful classifications of motions, and these classifications are useful for the general problem of vision. Thus changes to cellular properties could enable MT to make new transformations of information, which are made useful by the abstract cortex algorithm. The rest of the brain can then use this new information, and if it is useful for survival then it will evolve.

What is value--accumulated reward or evidence? III

Friston, K. Adams, R. Montague, R. (2012) What is value -- accumulated reward or evidence? Frontiers in Neurorobotics 6(11)

The mountain car problem
Need to park up mountain, but car can't make it. Have to climb up opposing valley to gain momentum to reach parking spot. Going to use inference to get it right in 1 trial, instead of learning which is the classic method.

x is the continuous position and velocity (the full state space). a(u) is the real valued action associated with the control state, u. a(u) = [-2, -1 , 0, 1, 2] - can accelerate left (negative) or right (positive) and have strong and moderate acceleration levels.

The state-space was discretized to simulate some noise, so the observed states are the discrete continuous states. Prior beliefs about the final state specify the goal x = (1, 0). The sampling (R(s_{t+1}|s_t, a_t)) probabilities are based on the equations of motion.

the value of an observed state is prescribed by a generative model in terms of the probability a state will be occupied.

valuable behavior simply involves sampling the world to ensure model predictions are fulfilled. prior beliefs about future states have a simple form: future states will minimize uncertainty about our current beliefs.

Perception corresponds to hypothesis testing -- sensory sampling are experiments that generate sensory data. eye movements are optimal experiments to test beliefs about the causes of the data gathered.


Definition: Active inference rests on the tuple (O, X, S, A, R, q, p) that comprises the following:

• A sample space O or non-empty set from which random fluctuations or outcomes ω ∈ O are drawn
• Hidden states X: O × A × → |R—states of the world that cause sensory states and depend on action
• Sensory states S : O × A × → |R—the agent’s sensations that constitute a probabilistic mapping from action and hidden states
• Action A : S × R → |R—an agent’s action that depends on its sensory and internal states
• Internal states R : R × S × O→ |R—the states of the agent that cause action and depend on sensory states
• Generative density p(s, ψ|m)—a probability density function over sensory and hidden states under a generative model denoted by m
• Conditional density q(ψ) := q(ψ|μ)—an arbitrary probability density function over hidden states ψ ∈ X that is parameterized by internal states μ ∈ R

The imperative is to minimize dispersion of sensory and hidden states with respect to action. Don't have access to hidden states, so minimize decomposition of entropy: entropy of the sensory states and conditional entropy of hidden states.

A lot more...

Neurobiological implementations of active inference

• The brain minimizes the free energy of sensory inputs defined by a generative model.
• This model includes prior expectations about hidden controls that maximize salience.
• The generative model used by the brain is hierarchical, non-linear, and dynamic.
• Neuronal firing rates encode the expected state of the world, under this model.

"The third assumption is motivated easily by noting that the world is both dynamic and non-linear and that hierarchical causal structure emerges inevitably from a separation of temproal scales. Finally, the fourth assumption is the Laplace assumption that, in terms of neural codes, leads to the Laplace code that is arguably the simplest and most flexible of all neural codes (Firston, 2009)


This looks a lot like the Maass bayesian stuff in the end. They make a generative model that is hierarchical. Prediction errors are propagated up the hierarchy, while predictions are sent back down.

FIGURE 4 | Schematic detailing the neuronal architecture that might
encode conditional expectations about the states of a hierarchical
model. This shows the speculative cells of origin of forward driving
connections that convey prediction error from a lower area to a higher area
and the backward connections that construct predictions (Mumford, 1992).
These predictions try to explain away prediction error in lower levels. In
this scheme, the sources of forward and backward connections are
superficial and deep pyramidal cells, respectively. The equations represent
a generalized descent on free-energy under the hierarchical models
described in the main text: see also Friston (2008). State-units are in black
and error-units in red. Here, neuronal populations are deployed
hierarchically within three cortical areas (or macro-columns). Within each
area, the cells are shown in relation to cortical layers: supra-granular (I–III),
granular (IV), and infra-granular (V and VI) layers. For simplicity, conditional
expectations about control states had been absorbed into conditional
expectations about hidden causes.


Advantages of the value as evidence formalism:

• A tractable approximate solution to any stochastic, non-
linear optimal control problem to the extent that stan-
dard (variational) Bayesian procedures exist. Variational or
approximate Bayesian inference is well-established in statis-
tics and data assimilation because it finesses many of
the computational problems associated with exact Bayesian
inference.
• The opportunity to learn and infer environmental constraints
in a Bayes-optimal fashion; particularly the parameters of
equations of motion and amplitudes of observation and hidden
state noise.
• The formalism to handle system or state noise: currently, opti-
mal control schemes are restricted to stochastic control (i.e.,
random fluctuations on control as opposed to hidden states).
One of the practical advantages of active inference is that
fluctuations in hidden states are modeled explicitly, rendering
control robust to exogenous perturbations.
• The specification of control costs in terms of priors on control,
with an arbitrary form: currently, most approximate stochas-
tic optimal control schemes are restricted to quadratic control
costs. In classical schemes that appeal to path integral solutions
there are additional constraints that require control costs to be
a function of the precision of control noise; e.g., Theodorou
et al. (2010) and Braun et al. (2011). These constraints are not
necessary in active inference.

What is value--accumulated reward or evidence? II

Friston, K. Adams, R. Montague, R. (2012) What is value -- accumulated reward or evidence? Frontiers in Neurorobotics 6(11)

Bayes-optimal control without cost functions
Hidden states are extended to include hidden (control) states that model action. Must have a generative model of agency or control. agent infers its future action via Bayesian updates of posterior beliefs about the future.

Control states are not action. They can be regarded as fictive action that gives the generative model extra degrees of freedom to model state transitions under prior beliefs. "This means they only exist in the mind (posterior beliefs) of the agent." [This is why you would feel like you have agency, but you don't in reality].

Hmm... yeah this is complicated. Hopefully the examples will make it a little more clear.

What is value -- accumulated reward or evidence? I

Friston, K. Adams, R. Montague, R. (2012) What is value -- accumulated reward or evidence? Frontiers in Neurorobotics 6(11)

This is a reformulation of reinforcement learning, not as a maximization of integrated reward, but as a process of minimizing the error of a generative model. Thus optimal behavior is purely cast in terms of inference--policies are replaced by inferences.

basic principles of self-organization: minimize surprise (maximize evidence) associated with sensory states, minimize uncertainty about inferred causes of input. This makes value become log-evidence or negative surprise.

Hierarchical perspective on optimization is implicit in this account of optimal behavior. Hierarchical Bayesian inference: optimization at one level is constrained by empirical priors from a higher level. Yuille and Kersten: hierarchical aspect to inference emerges naturally from a separation of temporal scales.

Markovian formulations of value and optimal control.
Begin with Markov decision processes. Linking "free energy minimization" (active inference) and optimial decision theory (reinforcement learning(ish), optimizing policies). Create future states that entails a model of agency to link the two into one. From the text:


"The key distinction between optimal control and active infer-
ence is that in optimal control, action optimizes the expected cost
associated with the hidden states a system or agent visits. In con-
trast, active inference requires action to optimize the marginal
likelihood (Bayesian model evidence) of observed states, under
a generative model. This introduces a distinction between cost-
based optimal control and Bayes-optimal control that eschews
cost. The two approaches are easily reconciled by ensuring the
generative model embodies prior beliefs about state transitions
that minimize expected cost. Our purpose is therefore not to
propose an alternative implementation of optimal control but
accommodate optimal control within the larger framework of
active inference."

The set up for markov decision processes is to maximize cumulative reward. The solutions can be divided into reinforcement learning schemes that compute the value function explicitly and direct policy searches that find the optimal policy directly. The best answers depend on how complex the value funciton is, and how complex the state-space is (i.e. is it possible to visit all states?).

Cannot always know the current state - extension of MDP is partially observed MDP (POMDP). Cannot perform reinforcement learning directly on POMDP, but POMDP can be converted to MDP using beliefs about the current state. Replace reward with its expected value based on current belief state.

Initial approaches: replace reward with desired observations. They will show that any optimal control problem can be formulated as a Bayesian inference problem, within the active inference framework. Action does not minimize cumulative cost, but maximizes the marginal likelihood of observations, under a generative model that entails an optimal policy.

Active inference
"In active inference, action elicits observations that are the most plausible under beliefs about (future) states. This is in contrast to conventional formulations, in which actions are chosen to elicit (valuable) states."


Definition: Active inference rests on the tuple
(X, A, ϑ, P, Q, R, S) comprising:

• A finite set of hidden states X
• Real valued hidden parameters ϑ ∈ Rd
• A finite set of sensory states S
• A finite set of actions A
• Real valued internal states μ ∈ Rd that parameterize a conditional density
• A sampling probability R(s'|s, a) = Pr({st+1 = s |st = s, at = a}) that observation s ∈ S at time t + 1 follows action a ∈ A, given observation s ∈ S at time t
• A generative probability P(s, x, theta|m)
• A conditional probablity Q(x, theta|mu)

(Wait, is mu part of the tuple? Did they just miss it?).

Three distinctions between this and MDP: 1. Agent is equipped with a probabilistic mapping between actions and direct sensory consequences (this is the sampling probability). 2. Hidden states include future and past states, or the agent represents a sequence or trajectory over states. 3. There are no reward or cost functions. Cost functions will be replaced by priors over hidden states and transitions, such that costly states are surprising and are avoided by action.

The goal is to minimize the "free energy": internal states minimize the free energy of currently observed states, while action selects the next observation that, on average, has the smallest free energy. Can express free energy as Gibbs energy (expected under the conditional distribution, Q) minus entropy of the conditional distribution. When free energy is minimized the conditional distribution approximates (Q) the posterior distribution (P). Under some simplifying assumptions this corresponds to predictive coding.

By setting prior beliefs one can generalize the active inference model to any optimal control problem.

General Cortex

Understanding how cortex evolved is seeming like a problem that needs more attention. The story that I imagine is that there must have been a time when there was a "general cortex". This piece of tissue perhaps arose out of a nucleus that was designed for detecting the molecules around early organisms (i.e. smelling). But somehow, the tissue got adapted quickly for other tasks. Cortex got spread around to serve other purposes.

If that is true, that cortex was suddenly spread from one modality to all (suddenly being on evolutionary terms), then take into consideration that the type of information coming from these modalities were greatly different. I mean we're talking about most of cognitive function. The cortex was spread out to start handling all of these functions, taking in different forms of information and organizing them in a useful way.

There was a period of general cortex, where it processed any kind of sensory modality, motor system, cognitive control or any other type of information. Evolution began wiring it up in more complex ways, adding more cells to make it more powerful. The structures started to organize so that more cells could be packed in to the same volume. The connections being most of the volume were scaled back such that only the areas that needed to communicate were available. As evolution raged on, the areas specialized for their functions, learning new tricks to process more and more information.

What general cortex means is that the type of information that we could process may not be limited to naturalistic information. Naturalistic information has a very complex and interesting structure, but it has a particular structure. There are other types of information that likely have structure, but of a different kind than perhaps nature. Can general cortex make sense of all kinds of information structures? So long as there is a signal, cortex will find it?

Perhaps there truly is a similarity between auditory and visual information that our brain receives. In essence you truly are receiving the pixel information coming from the outside world -- this is basically why pixels work. There is a deeper meaning to this information that your brain parses out, but we can control the pixels on a computer screen. I could show you anything in pixel space. Any type of information, even just noise. Would we ever say that your brain was incapable of not seeing anything that we could show it? The brain certainly can be shown illusions, but it still perceives something.

Building a machine that could perceive any type of information as cortex perceives the world is an interesting possibility of general cortex. It is so effortless for our brains to perceive the world, even though this is a remarkably complex and intense operation. We can find ways to manipulate the information that we perceive that we have built this amazing society. Our visual systems were designed to process a three-dimensional world over the course of evolution, but if there was a general cortex, and say the world had been 4-dimensional instead of three, would it be impossible for evolution to come up with cortex that could see in 4-dimensions? Can we find the patterns of how general cortex became neocortex to see how we could make it see it 4-dimensions? (Could we even train our own neocortex to see in 4D?)

Phase Resetting in an Asymptotically Phaseless System: On the Phase Response of Limit Cycles Verging on a Heteroclinic Orbit

Shaw, KM. Park, YM, Chiel, HJ. Thomas, PJ. (2012) Phase Resetting in an Asymptotically Phaseless System: On the Phase Response of Limit Cycles Verging on a Heteroclinic Orbit. Journal of Applied Dynamical Systems 11(1): 350-391.

Ok, I'm not going to read through this whole paper, but Hillel Chiel and Peter Thomas came and visited our lab yesterday (1/9/13), and I thought they had some interesting things to say about dynamical systems, control, and neural theory.

They were discussing CPGs and noting the interesting fact that if you look at these CPGs they can stall out at certain points during their oscillations. The stalling is driven by other factors, but they were asking the basic question of how to design a dynamical system that could have this kind of property.

Their solution revolves around what is becoming a popular way of making CPG-like control systems, which is to use heteroclinic channels. The idea of heteroclinic channels is that you utilize simple saddle-nodes that have a stable and unstable manifolds. You point one unstable manifold of one node at the stable manifold of another node, and then you arrange several nodes around in a circle. In this configuration you create a stable, heteroclinic orbit. This orbit, however, goes through the equilibrium points of the saddle nodes, which means that the stable orbit has an infinite period. However, you'll never reach the stable orbit, so you slowly go around in circles (with your period increasing in size each time, exponentially).

Their insight was that if you point the manifolds slightly off of, then you can create stable limit cycles that have different oscillatory dynamics. One way they do it is by making the system piece-wise linear, which also allows them to do calculations analytically. It basically works like this:

So, a single paramter varies how much these grids are aligned. Each grid is basically a simple linear system that has a saddle node. You don't have to do it completely piece wise linear, but it  is useful to see. By adjusting the a value, they can alter the dwell time around the limit cycle, which is a hypothesis to suggest how neural systems can produce these CPGs which dwell in certain parts of the rhythm. Sensory feedback etc is modulating the CPG to adjust the dwells.

The other really nice thing about making these heteroclinic orbits is that it could be a useful engineering tool for designing arbitrary oscillatory control systems. Each of the saddle nodes can be placed in various locations and pointed at each other in a pretty simple way. Perhaps instead of being piece-wise linear there are more continuous ways of designing it as well, something like the nodes effect on the system fall of with distance.

It could be interesting just to explore how you could make a neural system that utilizes these properties, and how you could get it to learn certain types of oscillations. There would be some relation between the neural circuitry and the intrinsic neural dynamics that govern the parameters of the saddle nodes, and then you could make a learning rule to relate those parameters to patterns in the system. It would be like motor learning: as you learn to walk you begin by forcing neurons to do the basic pattern, and each time you do the basic pattern the learning adjusts the saddle nodes formed by the system. Eventually the saddle nodes converge to the oscillation that is basically the average.

But how do you craft the nodes? How do you decide, given an oscillation where to place the nodes? How would you learn to place new nodes? Can you adjust the stability of the nodes for more control? How do you make a neural system that has these properties, and can easily manipulate these properties?

Cortical Feedback Control of Olfactory Bulb Circuits

Boyd, AM. Sturgill, JF. Poo, C. Isaacson, JS. (2012) Cortical Feedback Control of Olfactory Bulb Circuits. Neuron 76: 1161-1174.

This is Alison's paper. Cortical feedback to bulb may be like cortex to thalamus. Express ChR2 in olfactory pyramidal cells. Opening paragraph is even about the oddity that olfactory cortex does not have a thalamus, and the bulb may be playing this role.

IPSCs in MT cells when ChR2 axons stimulated. Disynaptic inhibition mediated by AMPARs. NMDA blockers have no effects. No conventional fast excitatory synatpic responses from cortical to mitral (i.e. driving synapses). However, some small inward currents were observed, blocked by NBQX (AMPAR antagonist), but slow and not responsive to changes in holding potential. Also observed in cells in which the primary apical dendrite was severed. These sound like modulatory feedback inputs, but surprising that they go away even when apical tuft is severed--it seems like most feedback inputs go through apical tuft.

Cortical feedback directly excites GCs, which inhibit MTs. Cortex also drives feed-forward inhibition onto GCs. Net effect on a particular GC could be excitatory or inhibitory. Meditated by deep short axon cells (dSACs). dSACs receive higher convergence of cortical feedback projections, but their numbers are lower.

A similar arrangement of cortical feedback projects to neurons near/in the bulb. Cortical feedback mainly drives inhibitory neurons, and avoids the excitatory cells. E summarizes nicely:

In vivo, ramp LED, allows sustained "self-organized" cortical activity. Gamma ensues, spikes coherent with gamma. Odors produce both gamma and beta. Light + Odors abolishes beta, more spiking in cortex ("layer 2/3"). Cortical activation also drove gamma in bulb.