Nonlinear computations in spiking neural networks through multiplicative synapses
Approximate any nonlinear system with spiking artificial neural networks: no training requiredRecommended by Marco Leite based on reviews by 2 anonymous reviewers
Artificial (spiking) neural networks (ANNs) have become an important tool in the modelling of biological neuronal circuits. However, they come with caveats: their typical training can be laborious, and after it is done, the complexity of the connectivity obtained can be almost as daunting as the original biological systems we are trying to model.
In this work , Nardin and colleagues summarize and expand upon the Spike Coding Network (SCN) framework , which originally provides a direct method to derive the connectivity of a spiking ANN representing any given linear system. They generalize this framework to approximate any (non-linear) dynamical system, by yielding the connectivity necessary to represent its polynomial expansion. This is achieved by including multiplicative synapses in their network connections. They show that higher polynomial orders can be efficiently represented with hierarchical network structures. The resulting networks not only enjoy many of the desirable features of traditional ANNs, like robustness to (artificial) cell death and realistic patterns of activity, but also a much more interpretable connectivity. This is promptly leveraged to derive how densely connected a neural network of this type needs to be to be able to represent dynamical systems of different complexities.
The derivations in this work are self-contained and the mathematically inclined neuroscientist can quickly get up to speed with the new multiplicative SCN framework, without the need for prior specific knowledge of SCNs. All the code is available and well commented in https://github.com/michnard/mult_synapses making this introduction even more accessible to its readers. This paper is relevant for those interested in neural representations of dynamical systems and the possible roles for multiplicative synapses and dendritic non-linearities. Those interested in neuromorphic computations will find here an efficient and direct way of representing non-linear dynamical systems (at least those well approximated by low-order polynomials). Finally, those interested in neural temporal pattern generators might find it surprising that only 10 integrate and fire neurons can already very reasonably approximate a chaotic Lorenz system.
 Nardin, M., Phillips, J. W., Podlaski, W. F., and Keemink, S. W. (2021) Nonlinear computations in spiking neural networks through multiplicative synapses. arXiv, ver. 4 peer-reviewed and recommended by Peer Community in Neuroscience. https://arxiv.org/abs/2009.03857v4
 Boerlin, M., Machens, C. K., and Denève, S. (2013). Predictive coding of dynamical variables in
balanced spiking networks. PLoS Comput Biol, 9(11):e1003258. https://doi.org/10.1371/journal.pcbi.1003258
Neurons in the mouse brain correlate with cryptocurrency price: a cautionary tale
Can a mouse understand the crypto market?Recommended by Hernando Martinez Vergara based on reviews by Kenneth Harris, Anirudh Kulkarni and 1 anonymous reviewer
Nowadays it is pretty much accepted that in animals with a nervous system, neural activity leads to behaviour. This framework is very useful to ultimately find a satisfying explanation of how and why animals behave, as it implies that there is a causal relationship between neuronal spiking and muscle and gland activity. In order to get closer to this causation, a common approach in neuroscience is to find correlations between behavioural variables and neuronal activity. Dr. Meijer's manuscript "Neurons in the mouse brain correlate with cryptocurrency price: a cautionary tale"  serves as a proof of concept that neuroscientists need to be careful about the statistical tests they use when looking for these correlations.
In this work, the author considers two recent datasets containing signals that display slow continuous trends over time: neuronal spiking activity from 40,100 neurons, and Bitcoin and Ethereum prices. When testing for correlations between the activity of individual neurons and the simultaneous fluctuations of cryptocurrency prices, he finds that over two thirds of the neurons correlated significantly, and that classical corrective conservative methods still result in one third of the neurons showing correlation. In order to estimate the true false discovery rate of these type of comparissons, the author tested two statistical methods shown to work for simulated data . He shows that also for this large-scale dataset, both the session permutation and the linear shift method manage to reduce the number of correlated neurons to statistically-acceptable levels. Additionaly, the author goes on to show that it is the slow time constant of the crypto prices that are the root for the initial correlations. This work serves as an example for how mislead scientists can be if proper statistical tests are not applied in order to avoid "nonsense correlations" with neuronal data, and it aims to increase awareness about this problem in the neuroscience community.
This rigorous and yet entertaining work can now be added to the collection of cautionary tales that include a dead salmon understanding human emotions  and rat cortical neurons predicting stock market prices . At the very least, it can be a piece of advice for Elon Musk to wait for more evidence before merging two of his new recent interests.
 Meijer, Guido. (2021). Neurons in the Mouse Brain Correlate with Cryptocurrency Price: A Cautionary Tale. PsyArXiv, ver. 3 peer-reviewed and recommended by Peer Community in Circuit Neuroscience. https://doi.org/10.31234/osf.io/fa4wz.
 K. D. Harris. (2020). Nonsense correlations in neuroscience. bioRxiv. 402719. https://doi.org/10.1101/2020.11.29.402719
 T. Marzullo, C. Miller, and D. Kipke. (2016). Stock Market Behavior Predicted by Rat Neurons2. Annals of Improbable Research 12, 401. PDF Link
A quick and easy way to estimate entropy and mutual information for neuroscience
Estimating the entropy of neural data by saving them as a .png fileRecommended by Haudur Freyja Olafsdottir, Mahesh Karnani and Fleur Zeldenrust based on reviews by Federico Stella and 2 anonymous reviewers
Entropy and mutual information are useful metrics for quantitative analyses of various signals across the sciences including neuroscience (Verdú, 2019). The information that a neuron transfers about a sensory stimulus is just one of many examples of this. However, estimating the entropy of neural data is often difficult due to limited sampling (Tovée et al., 1993; Treves and Panzeri, 1995). This manuscript overcomes this problem with a 'quick and dirty' trick: just save the corresponding plots as PNG files and measure the file sizes! The idea is that the size of the PNG file obtained by saving a particular set of data will reflect the amount of variability present in the data and will therefore provide an indirect estimation of the entropy content of the data.
The method the study employs is based on Shannon’s Source Coding Theorem - an approach used in the field of compressed sensing - which is still not widely used in neuroscience. The resulting algorithm is very straightforward, essentially consisting of just saving a figure of your data as a PNG file. Therefore it provides a useful tool for a fast and computationally efficient evaluation of the information content of a signal, without having to resort to more math-heavy methods (as the computation is done “for free” by the PNG compression software). It also opens up the possibility to pursue a similar strategy with other (than PNG) image compression software. The main limitation is that the PNG conversion method presented here allows only a relative entropy estimation: the size of the file is not the absolute value of entropy, due to the fact that the PNG algorithm also involves filtering for 2D images.
The study comprehensively reviews the use of entropy estimation in circuit neuroscience, and then tests the PNG method against other math-heavy methods, which have also been made accessible elsewhere (Ince et al., 2010). The study demonstrates use of the method in several applications. First, the mutual information between stimulus and neural response in whole-cell and unit recordings is estimated. Second, the study applies the method to experimental situations with less experimental control - such as recordings of hippocampal place cells (O’Keefe & Dostrovsky,1971) as animals freely explore an environment. The study shows the method can replicate previously established metrics in the field (e.g. Skaggs information, Skaggs et al. 1993). Importantly, it does this while making fewer assumptions on the data than traditional methods. Third, he study extends the use of the method to imaging data of neuronal morphology, such as charting the growth stage of neuronal cultures. However, the radial entropy of a dendritic tree seems at first more difficult to interpret than the common Sholl analysis of radial crossings of dendrite segments (Figure 6Ac of Zbili and Rama, 2021). As the authors note, a similar technique is used in paleobiology to discriminate pictures of biogenic rocks from abiogenic ones (Wagstaff and Corsetti, 2010). Perhaps neuronal subtypes could also be easily distinguished through PNG file size (Yuste et al., 2020). These examples are generally promising and creative applications.The authors used open source software and openly shared their code so anyone can give it a spin (https://github.com/Sylvain-Deposit/PNG-Entropy).
We were inspired by the wide applicability of the presented back-of-the-envelope technique, so we used it in a situation that the study had not tested: namely, the dissection of microcircuits via optogenetic tagging of target neurons. In this process, one is often confronted with the problem that not only the opsin-carrying cells will spike in response to light, but also other nearby neurons which are activated synaptically (via the opto-tagged cell). Separating these two types of responses is typically done using a latency or jitter analysis, which requires the experimenter subjectively searching for detection parameters. Therefore a rapid and objective technique is preferable. The PNG rate difference method on slice whole cell recordings of opsin tagged neurons revealed higher mutual information metrics for direct optogenetic activation than for postsynaptic responses, showing the method can be easily used to objectively segregate different spike triggers.
Figure caption: Using a PNG entropy metric to distinguish between direct optogenetic responses and postsynaptic excitatory responses. Left, PNG rate difference calculated for whole cell recordings of optogenetic activation in brain slices. About 20 consecutive 60ms sweeps were analysed from each of 7 postsynaptic cells and 8 directly activated cells. Analysis was performed as in Fig4B of the preprint (https://doi.org/10.1101/2020.08.04.236174) using code from https://github.com/Sylvain-Deposit/PNG-Entropy/blob/master/BatchSaveAsPNG.py. Right, six example traces from a cell carrying channelrhodopsin (black, top) and a cell that was excited synaptically (gray, bottom).
Ince, R.A.A., Mazzoni, A., Petersen, R.S., and Panzeri, S. (2010). Open source tools for the information theoretic analysis of neural data. Front Neurosci 4. https://doi.org/10.3389/neuro.01.011.2010
O'Keefe, J., & Dostrovsky, J. (1971). The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely-moving rat. Brain Research, 34(1), 171-175. https://doi.org/10.1016/0006-8993(71)90358-1
Skaggs, M. E., McNaughton, B. L., Gothard, K. M., and Markus, E. J. (1993). An information-theoretic approach to deciphering the hippocampal code. Adv. Neural Inform. Process Syst. 5, 1030-1037.
Tovée, M.J., Rolls, E.T., Treves, A., and Bellis, R.P. (1993). Information encoding and the responses of single neurons in the primate temporal visual cortex. J Neurophysiol 70, 640-654. https://doi.org/10.1152/jn.1922.214.171.1240
Treves, A., and Panzeri, S. (1995). The Upward Bias in Measures of Information Derived from Limited Data Samples. Neural Computation 7, 399-407. https://doi.org/10.1162/neco.19126.96.36.1999
Verdú, S. (2019). Empirical Estimation of Information Measures: A Literature Guide. Entropy (Basel) 21. https://doi.org/10.3390/e21080720
Wagstaff, K.L., and Corsetti, F.A. (2010). An evaluation of information-theoretic methods for detecting structural microbial biosignatures. Astrobiology 10, 363-379. https://doi.org/10.1089/ast.2008.0301
Yuste, R., Hawrylycz, M., Aalling, N., Aguilar-Valles, A., Arendt, D., Armañanzas, R., Ascoli, G.A., Bielza, C., Bokharaie, V., Bergmann, T.B., et al. (2020). A community-based transcriptomics classification and nomenclature of neocortical cell types. Nat Neurosci 23, 1456-1468. https://doi.org/10.1038/s41593-020-0685-8
Zbili, M., and Rama, S. (2021). A quick and easy way to estimate entropy and mutual information for neuroscience. BioRxiv 2020.08.04.236174. https://doi.org/10.1101/2020.08.04.236174