Post-publication review: The geometry of robustness in spiking neural networks

Selected paper: Calaim, Dehmelt, Gonçalves and Machens, The geometry of robustness in spiking neural networks, eLife (2022)

The main message: This theoretical neuroscience paper describes an intuitive way how to think about the effect of single spikes in a network where the output and its error is closely monitored and used as feedback. This intuition is best illustrated by the video below. The video shows how the activity of a network tries to trace a target (in this case a sinus wave). Each neuron defines a boundary (the differently colored lines in the video in the 2D case). If the output of the network exceeds one such boundary surface, a corrective spike of the respective neuron is emitted. The signal is therefore kept in the target zone by being bounced back once it becomes incorrect. This enables us for example to think about cases where single neurons are perturbed – when they are excited, inhibited or when they die – in an intuitive and geometric way in terms of single spikes.

Video 1 from Calaim, Dehmelt, Gonçalves and Machens, eLife (2022), reproduced here under the CC BY 4.0 license.

The strong points:

  • This visualization of the spiking dynamics in a neuronal network makes several points intuitively clear. For example, why such networks are robust to deletion or inhibition but not excitation of a single neuron (this is illustrated by deformations of the bounding box).
  • More generally, the visualization makes it intuitive how neurons might be able to cooperate when taking advantage of such specific and fast feedback loops.
  • This sort of simulated network tends to produce unphysiological or at least undesired behavior (discussed as “ping-pong” effect in the paper). This behavior becomes quite apparent and understandable due to the intuitive visualization.
  • Finally, it is simply really cool to use this visualization tool and to think about redundant neurons as those neurons where the boundary surfaces in this bounding box have similar locations/orientations.

The weak points:

  • The first weak point is that the presentation, despite the nice and intuitive video above, does not seem, from my perspective, accessible for everybody. Here, the task of the presented network is to approximate an externally supplied function (e.g., a sinus function). While many other neuroscientists, also many theoretical neuroscientists, think about neuronal networks as devices to represent information and to transform it, this paper therefore rather aims for a “control” approach. In my opinion, it is reasonable to think about the brain as a control device (to control the environment), but I feel that many readers might be already lost because they don’t understand why such an approach is taken. Only when reading the related work by the group (for an introduction, check out Boerlin et al., PLoS Comp Biol (2013) or Denève and Machens, Nat Neuro (2016)), one understands that this property of function approximation could also be a useful model of normal operation of the brain, where the task is to react towards the environment and not to approximate a god-given function. I feel that the authors introduce their idea not in an ideal way to reach a broader audience, especially since I the general idea could in principle be understood by a broader audience.
  • It is not clear how the intuition about the effect of single spikes and the target zone in the bounding box would translate to other network architectures that do not follow the rather specific designs. These network designs were described in previous work by Christian Machens and Sophie Denève and feature a specific excitatory/inhibitory connectivity. A core feature of such networks is that the voltages of neurons are largely synchronized but their spiking is not, resulting in a seemingly asynchronous firing regime as found in the cortex, despite redundancy at the voltage behavior of single neurons.
    This limitation also came up during the review process. The authors try to discuss these questions in detail and to address some of them, as much as possible, with additional analyses and models. Check out the open reviews (which are always accessible for eLife papers)!

Conclusion: I like the paper because it comes up with a surprising, new and maybe even useful idea. It attempts to think about the consequences and circumstances of a single neuron’s spike, and how the effect of this single spike on other neurons can be understood. As a caveat, all these intuitions come with the assumption that there is a closely monitored error of the output signal, which in turn is fed back into the system in a very precise manner. This assumption might seem very strong in the beginning. However, in order to understand things, we have to make some assumptions, and even from wrong assumptions, we might be able to develop first intuitions about what is going on. I would be curious whether and how this bounding box picture could be applied to other network architectures.

This entry was posted in Network analysis, Neuronal activity, Reviews and tagged . Bookmark the permalink.

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