Paper:
Spike-sorting is of central importance for neuroscience research. We introduce a novel spike-sorting method comprising a deep autoencoder trained end-to-end with a biophysical generative model, biophysically motivated priors, and a selfsupervised loss function to training a deep autoencoder. The encoder infers the action potential event times for each source, while the decoder parameters represent each source's spatiotemporal response waveform. We evaluate this approach in the context of real and synthetic multi-channel surface electromyography (sEMG) data, a noisy superposition of motor unit action potentials (MUAPs). Relative to an established spike-sorting method, this autoencoder-based approach shows superior recovery of source waveforms and event times. Moreover, the biophysical nature of the loss functions facilitates interpretability and hyperparameter tuning.
Overall, these results demonstrate the efficacy and motivate further development of self-supervised spike sorting techniques.

Review:
This paper describes a machine learning model for learning spiking representations from EMG (electromyography) like data. The basic model is an autoencoder, where the bottleneck layer is designed to project the waveform inputs into "spike" representations. Specifically, there is a DSD (Deep Spike Decoder) encoder and decoder, where the encoder is implemented as either a DenseNet[1]-like or Tiramisu[2]-like architecture. The bottleneck seems to be implemented by a linear layer binarized with a Gumbel-Softmax activation. The decoder is a linear layer. Several losses are considered, including a L4-norm (!), a sparsity loss, a parsimony loss, a uniqueness loss, and a refractory period loss. The model is validated qualitatively on real EMGs, and quantitatively on synthetic data.
The strengths of the paper are the following:
- Spiking models are very interesting class of models, which if attained would have a great impact on several other areas of machine learning. 
- I like the straightforward design that is fit to the purpose of generating spiking representations. A Gumbel-Softmax has proven its validity and is a logical fit to the problem setup.
- I like the simpler setup the paper chooses.
  -- First, the paper chooses not to take the route of trying to learn backpropagation through infinite time steps, as often happens in spiking methods. This is a beast on each own, which would be nice to set as an ultimate goal (in my opinion). For now, however, it's ok if we forego this requirement.
  -- Second, the paper chooses not to assume that signals come asynchronously, which again makes things unnecessarily complex, given the state of the field.
The weaknesses of the paper:
- While the problem setup is simple, perhaps it makes some assumptions that are too strong. In my opinion, the strongest one is that of batch-learning (for the lack of a better name). Often, spiking models are studied in an online setup where the data comes online (continuously), and then spikes are generated when sufficient changes in the inputs warrant a delta-difference (spike). When in batch mode, however, it should be quite much easier to obtain spikes that lead to good reconstructions, as there is no much need for a "memory" mechanism. While one could argue whether an online setup is necessary or not, in my opinion it is necessary and would make a spiking model challenging and interesting to learn. Otherwise, it looks like a conventional autoencoder, only with spikes instead of dense representations.
- The model is unclear and writing vague.
- First of all, after reading the abstract and the introduction I get the feeling that the model is probabilistic, as there is mention of priors and autoencoders. Also, later on a Gumbel-Softax is mentioned for binarization. Gumbel-Softmax is a continuous function and binarization makes sense when sampling, that is when assuming a generative process. However, the rest of the paper seems not to explain a probabilistic or generative model. There is no explicit prior discussed. There is no sampling procedure discussed. The losses are explained but not within a particular probabilistic or stochastic framework. If the model is not stochastic, one way or the other, how are the discrete spikes obtained and how is the system is trained?
- All the loss functions, albeit logical when taken one by one, they do look ad hoc and appearing out of the blue. This perhaps relates to the previous point, where it is not clear if the model is stochastic or deterministic. If it is deterministic, it is ok to have all the loss functions appearing like that, but I would expect some more explanation on what purpose do they fill w.r.t. the spiking model. In the end, what does the deep spiker model try to achieve? Learn spikes as representations? Recover the original spikes? Be sparse? If yes, why and how sparse? Be energy-efficient?
- Some design choices are quite unclear. Generally, it is fair to say that the experimental and design setups are rather simple: multiple 1-D waveforms and not much noise (from what I get). In that context, it is not clear why DenseNets, or even Tiramisu-Nets are used as an encoder; especially when the decoder is a simple linear model. 
- Also, phrases like "what good combinations are useful ... the hyperparametres of DSD" do not add to the clarity. There is no exploration of hyperparameters in the experiments and no individual examination of the contribution of each loss (unless I missed it somewhere).
- Similarly, what does "For the DSD ... between 10 minutes to an hour depending on ...".  Such statements should be more precise, for instance plotting wall clock time vs training loss.
All in all, while I like the motivation and the original direction, I believe there exist a lot of questions  unanswered before acceptance.