Deep learning, part IV (2): Compressing the dynamic range in raw audio signals

In a recent blog post about deep learning based on raw audio waveforms, I showed what effect a naive linear dynamic range compression from 16 bit (65536 possible values) to 8 bit (256 possible values) has on audio quality: Overall perceived quality is low, mostly because silence and quiet parts of the audio signal will get squished. The Wavenet network by Deepmind, however, uses a non-linear compression of the audio amplitude that allowed to map the signal to 8 bit without major losses. In the next few lines, I will describe what this non-linear compression is, and how well it performs on real music.

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Preamplifier bandwidth & two ways of counting photons

For two-photon point scanning microscopy, the excitation laser is typically pulsing at a repetition rate of 80 MHz, that is one pulse each 12.5 ns. To avoid aliasing, it was suggested to synchronize the sampling clock to laser pulses. For this, it is important to know over how much time the signal is smeared, that is, to measure the duration of the transient.

The device that smooths the PMT signal over time is the current-to-voltage amplifier. As far as I know, the two most commonly used ones are the Femto DHPCA-100 (variable gain, although mostly used with the 80 MHz bandwidth setting) and the Thorlabs model (60 MHz fixed bandwidth).

Observing single transients for different preamplifiers

However, 80 MHz bandwidth does not mean that everything below 80 MHz is transmitted and everything beyond suppressed. The companies provied frequency response curves, but in order to get a better feeling, I measured the transients of the above-mentioned preamplifiers when they amplified a single photon detected by a PMT. All transients are rescaled in y-direction (left-hand plot). I also determined a sort of gain for the single events by measuring the amplitude (right-hand plot). I also used two preamplifiers for each model, but could not make out any performance difference between two of the same kind.


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Deep learning, part IV: Deep dreams of music, based on dilated causal convolutions

As many neuroscientists, I’m also interested in artificial neural networks and am curious about deep learning networks. I want to dedicate some blog posts to this topic, in order to 1) approach deep learning from the stupid neuroscientist’s perspective and 2) to get a feeling of what deep networks can and can not do. Part I, Part II, Part III, Part IVb.

One of the most fascinating outcomes of the deep networks has been the ability of the deep networks to create ‘sensory’ input based on internal representations of learnt concepts. (I’ve written about this topic before.) I was wondering why nobody tried to transfer the deep dreams concept from image creation to audio hallucinations. Sure, there are some efforts (e.g. this python project; the Google project Magenta, based on Tensorflow and also on Github; or these LSTM blues networks from 2002). But to my knowledge no one had really tried to apply convolutional deep networks on raw music data.

Therefore I downsampled my classical piano library (44 kHz) by a factor of 7 in time (still good enough to preserve the musical structure) and cut it into some 10’000 fragments of 10 sec, which yields musical pieces each with 63’000 data points – this is slightly fewer datapoints than are contained by 256^2 px images, which are commonly used as training material for deep convolutional networks. So I thought this could work as well. However, I did not manage to make my deep convolutional network classify any of my data (e.g., to decide whether a sample was Schubert or Bach), nor did the network manage to dream creatively of music. As most often with deep learning, I did not know the reasons why my network failed.

Now, Google Deepmind has published a paper that is focusing on a text-to-speech system based on a deep learning architecture. But it can also be trained using music samples, in order to lateron make the system ‘dream’ of music. In the deepmind blog entry you can listen to some 10 sec examples (scroll down to the bottom).

As key to their project, they used not only convolutional filters, but so-called dilated convolutions, thereby being able to span more length-(that is: time-)scales with fewer layers – this really makes sense to me and explains to some extent why I did not get anything with my normal 1d convolutions. (Other reasons why Deepmind’s net performs much better include more computational power, feedforward shortcut connections, non-linear mapping of the 16bit-resolved audio to 8bit for training and possibly other things.)

The authors also mention that it is important to generate the text/music sequence point by point using a causal cut-off for the convolutional filter. This is intuitively less clear to me. I would have expected that musical structure at a certain point in time could very well be determined also by future musical sequences. But who knows what happens in these complex networks and how convergence to a solution looks like.

Another remarkable point is the short memory of the musical hallucinations linked above. After 1-3 seconds, a musical idea is faded because of the exponential decaying memory; a bigger structure is therefore missing. This can very likely be solved by using networks with dilated convolutions that span 10-100x longer timescales and by subsampling the input data (they apparently did not do it for their model, probably because they wanted to generate naturalistic speech, and not long-term musical structure). With increasing computational power, these problems should be overcome soon. Putting all this together, it seems very likely that in 10 years you can feed the full Bach piano recordings into a deep network, and it will start composing like Bach afterwards, probably better than any human. Or, similar to algorithms for paintings, it will be possible to input a piano piece written by Bach and let a network which has learned different musical styles continuously transform it into Jazz.

On a different note, I was not really surprised to see some sort of convolutional networks excel at hallucinating musical structure (since convolutional filters are designed to interpret structure), but I am surprised to see that they seem to outperform recurrent networks for generation of natural language (this comparison is made in Deepmind’s paper). Long short-term memory recurrent networks (LSTM RNNs, described e.g. on Colah’s blog, invented by Hochreiter & Schmidhuber in ’97) solve the problem of fast-forgetting that is immanent to regular recurrent neuronal networks. I find it a bit disappointing that these problems can also be overcome by blown-up dilated convolutional feed-forward networks, instead of neuron-intrinsic (more or less) intelligent memory in a recurrent network like in LSTMs. The reason for my disappointment is due the fact that recurrent networks seem to be more abundant in biological brains (although this is not 100% certain), and I would like to see research in machine learning and neuronal networks also focus on those networks. But let’s see what happens next.

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Whole-cell patch clamp, part 1: introductory reading

Ever since I my interested in neuroscience become more serious, I was fascinated by the patch clamp technique, especially applied for the whole cell. Calcium imaging or multi-channel electrophysiology (recent review) is the way to go in order to get an idea what a neuronal population is doing on the single-cell level, but it occludes fast dynamics like bursting, fast oscillations and subthreshold membrane potential dynamics (calcium imaging), or unambiguous assignment of activity to single neurons (multi-channel ephys). That’s exactly what whole-cell patch clamp can do (and much more).

Some months ago, I started using the technique on an adult zebrafish brain ex vivo preparation. This image shows a z-stack of a patched cell that was imaged after the electrical recording. The surrounding cells are labeled with GCaMP; the brighter labeling of the patched neuron was done by a fluorophor inside the pipette that was diffusing into the cell, with which the pipette ideally forms a single electrical compartment. The fluorophor fills up the soma and some of the dendrites. The pipette position is shown as an overlay in the right-hand side image.

Electrophysiology is a very unrewarding and difficult activity, compared to calcium imaging. The typical, old-school electrophysiologist is always alone with his rig, through long nights of a never-ending series of failures, intercepted by few successfully patched and nicely behaving neurons. On average, frustration dominates, no matter how successful he/she is in the end; as a consequence, he fiercely protects his rig from anybody else who wants to touch it and might interfere with the labile stability of his setup. Therefore, over time, he becomes more and more annoyed by any interaction with fellow humans. At least that is what people say about electrophysiologists …

Despite this asocial component, nothing is more encouraging for beginners like me than hearing from others and about their struggles with electrophysiology. I will therefore write about my own experience with electrophysiology so far, and although I’m lacking the year-long experience of older electrophysiologist, I share my experience with the hope to encourage others.

To begin with, here’s a list of useful books and manuals for learning, if one does not have an experienced colleague who shows every single detail:

  • Areles Molleman, Patch Clamping: An Introductory Guide to Patch Clamp Electrophysiology
    A very short book which does not go into the details e.g. of analog electrical circuits of a cell, but gives useful pragmatic advice and how-to-dos for patching (both single channel and whole-cell). Very useful starting point for the beginner.
  • In Labtimes, there’s a 2009 short first-hand report by Steven Buckingham that highlights some of the difficulties of patching and gives precise and concise advice.
  • The Axon Guide for Electrophysiology & Biophysics Laboratory Techniques
    If you have time for 250 pages of technical descriptions, this is your choice. The document might be quite old, but there haven’t been many revolutions to patching anyway. For several troubleshooting issues, I have found good advice in this document.
  • If you are lacking the theoretical background of how neurons, membrane potentials and ions work together, I would recommend online lectures like these slides that have a focus on theoretical underpinnings of measurements and not on measurements and troubleshooting.
  • For a more in-depth description of everything related to membrane potentials and ions: Ion Channels of Excitable Membranes (3rd Ed.) by Bertil Hille. It’s 15 years old, but still the best book that I’ve seen so far. Especially for somebody with a physics background, it is very rewarding to read.
  • For questions related to applications of patching (and other single neuron-specific tools), I can recommend Dendrites  by Stuart, Spruston, Häusser et al., although I have not yet checked the newest, very recent edition (2016)..

Soon, I hope that I will have time to write about some more technical aspects of patching. (Here about how to remove line-frequency noise that stems from the perfusion pump, and about the limitations of quantitative whole cell voltage-clamp recordings, especially in small neurons.)

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The zebrafish, and the other zebrafish

Zebrafish are often used as a model organism for in vivo brain imaging, because they are transparent. Or at least that is what many people think who do not work with zebrafish. In reality, most people use zebrafish larvae for in vivo imaging, typically not older than 5 days (post fertilization). At this developmental stage, the total larval body length is still less than the brain size of the adult fish. After 3-4 weeks, the fish look less like tadpoles and more like fish, measuring 10-15 mm in size (see also video below). They attain the full body length of approx. 25 to 45 mm within 3-4 months.

This video shows a zebrafish larva (7 days old), two adult zebrafish (16 months old) and a juvenile zebrafish (4.5 weeks old).

After 4-5 days, the brain size of larvae exceeds the dimensions that can be imaged with cellular resolution in vivo using light sheet or confocal microscopy when embedded in agarose. After approx. 4 weeks, even for unpigmented fish the thickened skull makes imaging of deeper brain regions very difficult. Superficial brain regions like the tectum are better accessible, but fish of this age are too strong to be restrained by agarose embedding. Brain imaging for adult fish is still possible in ex vivo whole brain preparations [1], but with loss of behavioral readout. Use of toxins for immobilization is an option (e.g. with curare in zebrafish [2] or in other fish species [3]), but not a legal one in some countries, including Switzerland. These are some of the reasons why most people stick to the simple zebrafish larva. My PhD lab is one of the few that does physiology in adult zebrafish.

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Neuroscience on Youtube

Recently, I’ve been to the Basel ICON conference, where the recent Nobel laureate Eric Betzig gave an impressive talk on microscopy techniques (including lattice light sheet, SIM and expansion microscopy). Some days ago, I found a similar talk by Eric Betzig (although with less recent results) simply on youtube.
The advantages of online videos compared to live talks are obvious, and I wonder why people do not use them more often, both to learn about research and to communicate their own research. Additionally, compared to research papers, the personality of a researcher is much more obvious from a talk – which is important to know for students interested in working in his/her lab. Here just a small collection of some good talks by neuroscientists which are not as flashy and fancy as TED talks, but much more informative and interesting.

Here is Eve Marder on central pattern generators in lobsters and crabs. She had been developing experiments and models for this seemingly simply system for more than 40 years, thereby exposing the complexity of a system consisting of only 30 neurons.

Ken Harris, a mathematician by training and now more interested in large-scale brain activity recordings in mice, gives a rather technical, but very understandable talk on advances and problems in spike sorting for multielectrode arrays.

Larry Abbott, one of the most well-known theoreticians in neuroscience, with a very interesting talk about experimental findings in the olfactory system of the fruit fly.

Christof Koch on the search for the neuronal correlates of consciousness. In the late 90s, he was one of the pioneers in this field together with Francis Crick; more recently, he is working together with Giulio Tononi.

Edvard Moser on spatial navigation and place cells/grid cells. For this topic he was awarded the Nobel prize 2014.

Haim Sompolinsky with a theoretical perspective on sensory representations. Coming from physics, Haim Sompolinsky helped transferring the physics of phase transitions to the mathematical modeling of neuronal network models in the late 80s.

Some of the links might be outdated in a couple of years, but I hope that researchers will start uploading more recent and well-prepared talks in the years to come, replacing overcrowded plenary talks by often jet-lagged speakers.

Update [2016-07-20]: Maybe this is the right place to mention a very nice series of podcasts, featuring interviews with leading neuroscientists, e.g. Michael Shadlen or Peter Jonas, or of my thesis supervisor in Basel, Rainer Friedrich. Thanks to Anne Urai who posted a link to this webpage on her blog.

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Large field of view microscopes for mouse brain imaging

For typical confocal or two-photon microscopes that maintain (sub)cellular resolution, a high-magnification objective is needed (typically 16x, 20x or 25x). This in turn limits the field of view (FOV) to ⌀ 1.0-1.5 mm.

For imaging in the mouse brain cortex, which is basically a big unwrinkled surface of a size of the order of 10 mm, a bigger FOV would be nice to have for some applications. Recently, a couple of papers came out that tried to increase the FOV, while using optical engineering to maintain the resolution. (Please don’t hesitate to tell me if I missed a relevant publication.)

Few years ago, I would have expected such papers to be published in Nature Methods, but apparently the time has come where optical engineering and improvement of existing techniques is not considered enough for passing the novelty bar. However, the three papers offer some very interesting lessons on engineering a two-photon microscope, of which I want to pick a few:

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