Thread by @VenkRamaswamy

Excited to share a new (& possibly contrarian) preprint !

“ An Algorithmic Barrier to Neural Circuit Understanding "
biorxiv.org/content/10.110…

Suggests that non-existence of tractable circuit-interrogation algorithms could be a roadblock to neural circuit understanding

(THREAD)

2/ Classically, Neuroscience at the circuit level (at cellular resolution) has largely been correlational, where one finds neurons whose activity is correlated w/ aspects of stimulus/behavior. We’ve learned a great deal by doing this for over half a century.

3/ More recently, we’ve been able to do this at ever-increasing scales, including whole-brain imaging at cellular res. already in C. elegans, hydra, larval zebrafish & adult drosophila.
(e.g. a video below of hydra from cell.com/current-biolog… )

4/ Such incredible neurotechnological advances have upended a lot of classical thinking, data analysis & theory, which was premised on the assumption that one could only access a small # of neurons.

5/ The new challenge for theory is to determine what we can understand from experiments that yield such massive data. Specifically, how do we go about designing such experiments and analyzing data so produced.

6/ Now, finding correlated activity is great, but it doesn’t tell us if that activity is meaningfully responsible for the behavior in question. e.g. people have been finding place-like cells in several regions; it’s largely unclear which are used, when.

https://twitter.com/VenkRamaswamy/status/1064853907963166722

7/ The next frontier in neural circuits is to understand precisely how individual neurons work together to *cause* specific behaviors in specific individuals. This needs perturbational experiments, wherein one perturbs chosen subsets of neurons and sees how it affects behavior.

8/ Technical advances, e.g. 2-photon optogenetics & newer holographic techniques, allow us to perturb activity of arbitrary subsets of neurons. Already, this has been done with concurrent whole-brain imaging in Zebrafish larva.@MishaAhrens
See nature.com/articles/s4159…

9/ Now, it appears necessary to perform multiple perturbation experiments, in general, to understand such causal substrates. It is as yet unclear *how many* experiments are so needed & how this number scales with the size of the nervous system in question.

10/ The other way to look at it is that efficient algorithms are needed that will seek to prescribe the smallest number of experiments necessary to obtain such understanding. How efficient can the most efficient algorithms be?

11/ So, an experiment might entail perturbing activity of a chosen subset of neurons, while concurrently imaging neural circuit activity & attempting to elicit behavior. The specifics of the next experiment so prescribed could depend on the outcome of the current experiment.

12/ We are thus treating the problem of experiment design/execution as an *algorithmic* problem, invoking tools from Computer Science. Note that this is *not* a simplifying assumption. Algorithmic constraints apply not just to computers but also to humans that design experiments.

13/ Now, before devising or analyzing algorithms, we need to define what it means to *understand* mechanistic circuit computation that causes behavior.

14/ There is, as yet, no standard definition of understanding in this context & conceivably, there exist multiple concomitant descriptions constituting notions of understanding that might, for example, include details spanning different spatial/temporal scales.

15/ One way is to say that you won’t define it precisely, but that you want to identify subsets of neurons that *participate* in computations causing behavior. Surely, any detailed account should let you to extract this info easily. (This argument is made rigorous in the work).

16/ What I do in the paper, is precisely define 6 such questions about participation. The first 3 correspond to *sufficient* sub-circuits to evoke the said behavior & the next three are about *necessary* circuits

(These terms however are deprecated. See tandfonline.com/doi/abs/10.108… )

17/ The algorithmic problem, then, is to prescribe experiments to determine each of these 6 types of sub-circuits. The question is how many experiments do you need & how that number scales with the # of neurons in the nervous system.

18/ What I prove, mathematically, is that none of these six problems have algorithms that can answer said question with sub-exponential # of experiments in the # of neurons, in general, unless P=NP. This uses techniques from Theoretical Computer Science.

19/ Performing exponentially-many experiments in the number of neurons would lead one to require more experiments than the estimated number of atoms in the observable universe, even for modest-sized nervous systems – rendering it an impracticable undertaking.

20/ If, remarkably, P=NP were true, it would mean that hundreds of computational problems – many of them commercially important & extensively studied for decades – would have sub-exponential algorithms, where none have been found to date.

See en.wikipedia.org/wiki/P_versus_…

21/ A caveat: The above type of “NP-hardness” result is a worst-case result. It shows that there is a sub-class of circuits which require exponentially-many experiments in the number of neurons.

22/ So, how many experiments *can* we do in practice (& how does this scale w/ # of neurons)?

One way is to ask, well, how many can you do in the average lifespan of an individual animal? Suppose each experiment is a second (behavioral timescale) & you lay them back-to-back.

23/ So, I plotted, for many organisms, estimated avg lifespans as a fn of the estimated # of neurons in their nervous system. Turns out most of them have more neurons than the # of seconds they live. So, you can usually run *less than linear* # of experiments in the # of neurons.

24/ Even if you had neural proxies of behavior that manifested in 100 ms, so you could cut each experiment short to a 100ms, the situation does not dramatically improve.

25/ So, the “NP-hardness” results show examples of circuits that provably need exponentially-many experiments to answer said questions (unless P=NP).
And, you can typically *not even run a linear number*, in practice !

26/ This is a *huge* gap, in that, even for circuits that don’t fall in those “exponential” classes, they have to need *less than linear* # of experiments to feasibly answer. Thus, many neural circuit questions may often not be answerable with a tractable # of experiments.

27/ In closing, the work suggests that in addition to current technological barriers, there exists another barrier — an algorithmic one — to understanding neural circuits comprehensively at resolution. This is a different beast from the technological barriers.

28/ Going forward, it suggests that causal understanding of neural circuits will likely be frequently driven by algorithmic constraints, rather than limitations in experimental methods.

In short, this is a serious issue that needs serious work.

29/ So, what can be done? (1) In the short term, ask what are questions that can always be answered w/ a tractable # of experiments. (2) What questions can be answered w/ a small # of experiments for specific circuit-classes, even if the question isn't so answerable, in general?

30/ Apropos (1), as an example, I introduce one such type of circuit, an instance of which can be determined with log n # of experiments. For an organism w/ 100 billion neurons, this is 37 experiments — quite tractable. (2) above, might need a lot of theory.

31/ Lastly, the work has many more moving parts than could be covered in a tweetstorm, so I invite you to take a look.
biorxiv.org/content/10.110…

Also, happy to address questions here.

/END

Cc: @hardmaru

Special shout-out to @parenthetical_e for detailed comments on an earlier draft of this paper !