When you look at the edge of a table, there is a neuron in your head that goes from silence to pop pop pop. As you extend your arm, a nerve commanding the muscle does the same thing. Your retina has neurons whose firing rate goes up or down depending on whether it detects a light spot or a dark spot. The traditional view of the nervous system descends from experiments that have supported this view of neural activity. And perhaps it is true at the outer edges of the nervous system, near the sensory inputs and the motor outputs. But things get murkier once you get inside.
Historically, people began thinking about the brain in terms of how single neurons represent the physical world. The framework they settled on had neurons responding to a specific set of things out in the world, with the activity of those neurons increasing when they saw those specific things and decreasing when they saw their opposite. As time flowed by, this neural picture became jumbled up with questions about whether overall activity level or specific timing of an individual spike was what was important.
When it comes to multiple neurons, a similar view has generally prevailed: activity levels go up or down. Perhaps each neuron has some (noisy) preference for something in the world; now just think of the population as the conjunction of each of their activity. Then the combination of all of the neurons is less noisy than any individual. But still: it’s all about activity going up or down. Our current generation of tools for manipulating neural activity unconsciously echoes this idea of how the nervous system functions. Optogenetics cranks the activity of cells – though often specific subpopulations of cells – to move their activity up or down in aggregate.
An alternate view which I has been pushed primarily by Krishna Shenoy and Mark Churchland takes a dynamic perspective of neural activity, and I think comes from taking a premotor view of the nervous system. Generally, nervous activity is designed to control our physical behavior: moving, shouting, breathing, looking, remaining silent. But that is a lot to have to control, and selection of the correct set of behaviors has to take a huge numbers of factors into account and has a lot to prepare for. What have I seen? How much do I like that? What am I afraid of? How hungry am I? This means that premotor cortical activity is probably representing many things simultaneously in order to choose among them.
The problem can be approached by looking at the population of activity and asking how many different things it could represent, without necessarily knowing what those are. Perhaps the population is considering six different things at the same time (a noted mark of genius)! Now that’s a slightly different perspective: it’s not about the up or down of overall activity, but how that activity flows through possibilities on the level of the whole population.
These streams of possible action must converge into a river somewhere. There are many possible options for how this could happen. They could be lying in wait, just below threshold, building up until they overcome the dam holding their behavior at bay. They could also be gated off, allowed to turn on when some other part of the system decides to allow movement.
But when we stop and consider the dynamics required in movement, in behavior, another possibility emerges. Perhaps there is just a dynamical system churning away, evolving to produce some reaching or jumping. Then these streams of preparatory activity could be pushing the state of the dynamical system in one direction or another to guide its later evolution. Its movement, its decision.
Churchland and Shenoy have worked on providing evidence for this happening in motor cortex as well as prefrontal cortex: neurons there may be tuned to move their activity in some large space, where only the joint activity of all the neurons is meaningful. In this context, we cannot think usefully about the individual neuron but instead must consider the whole population simultaneously. It is not the cog that matters, but the machine.
References
Kaufman MT, Churchland MM, Ryu SI, & Shenoy KV (2014). Cortical activity in the null space: permitting preparation without movement. Nature neuroscience, 17 (3), 440-8 PMID: 24487233
Mante V, Sussillo D, Shenoy KV, & Newsome WT (2013). Context-dependent computation by recurrent dynamics in prefrontal cortex. Nature, 503 (7474), 78-84 PMID: 24201281
Churchland, M., Cunningham, J., Kaufman, M., Foster, J., Nuyujukian, P., Ryu, S., & Shenoy, K. (2012). Neural population dynamics during reaching Nature DOI: 10.1038/nature11129
Shenoy KV, Sahani M, & Churchland MM (2013). Cortical control of arm movements: a dynamical systems perspective. Annual review of neuroscience, 36, 337-59 PMID: 23725001
Ames KC, Ryu SI, & Shenoy KV (2014). Neural dynamics of reaching following incorrect or absent motor preparation. Neuron, 81 (2), 438-51 PMID: 24462104
Churchland, M., Cunningham, J., Kaufman, M., Ryu, S., & Shenoy, K. (2010). Cortical Preparatory Activity: Representation of Movement or First Cog in a Dynamical Machine? Neuron, 68 (3), 387-400 DOI: 10.1016/j.neuron.2010.09.015
neuroecology 
One of the things I’ve found inspiring about Churchland’s work isn’t merely how the neural decoding problem is cast from a univariate up-vs-down metric to a multivariate one – which in the popular understanding is really just a vector of up-vs-down metrics anyway – but rather the notion that higher-order moments, even the humble standard deviation, should also be evaluated for their information content. This resonates both with developing views of the importance of noise and variability in the brain (e.g., W. Maas, 2014), current & historical breakthroughs in artificial neural network algorithms (e.g., dropout [Hinton 2012], reservoir computing, simulated annealing, and even plain-old initial weight randomization), and fascinating work in the biomechanics of expertise, where noise is not reduced by expertise but rather *rotated* in multidimensional movement space (can dig this up if interested – blanking on researcher’s name).
On another note, it’s an almost ironic revelation that, given the perennial struggle of fMRI users against variance in parameter estimate images, the variance *itself* might be carrying information about cognitive processing. Maybe an era of variance contrasts is about to begin.
Biomechanical data I refer to is by Dagmar Sternad, e.g., as discussed in this chapter: http://www.northeastern.edu/actionlab/Action%20Lab%20Publications/Sternad-Abe.BookChapter.pdf
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