6 ms·

Well the point is that it does not make sense to DFT data before feeding it into a multilayered neural network (or calculating the force generated by mass and a

Well the point is that it does not make sense to DFT data before feeding it into a multilayered neural network (or calculating the force generated by mass and acceleration as you point out). Those formulas make no sense: the network can just learn them on the fly. In fact you'll find that this does not just work for the Fourier transform, but for any FIR filter (and some other classes), and therefore neural networks can deal with signals and construct low-pass filters, high-pass filters, bandgap filters, ... as required for the task at hand without the network (or it's designer) having any idea at all what is happening. I mean there's some basic assumptions these reasonings make (main one is that you need to feed many discretized values from a time window). Of course, a problem remains: local optima. Just because a neural network can construct a filterbank or do a DFT, doesn't mean that it will actually do it when the situation warrants it. If there's a local optimum without filters ... well, you may get unlucky. It there's many local optima without filters ... sucks to be you.

ska 6y ago
> Those formulas make no sense: the network can just learn them on the fly. > Just because [...] can construct a filterbank or do a DFT, doesn't mean that it will actually do it when the situation warrants it. These statements seem in conflict, no?
nonameiguess 6y ago
I don't think I can agree with that. You do a Fourier transform when the data you're working with doesn't admit easily or at all certain operations in the time domain but it does in frequency domain. If you already know that to be the case, preprocessing with a FFT is a better idea than hoping a neural network with enough layers uses a few of those to much less efficiently perform a DFT. Always take advantage of pre-existing knowledge of structure in your data. With the FFT especially, depending on how your data is being ingested, you might be able to use specialized DSPs that implement the FFT directly in hardware. These are cheap and easy to find since they're used in frequency-division multiplexing.
- dkarras 6y ago
  Practically, yes, absolutely! Theoretically, we want the "black box" learning system to do such feature extraction itself. At least, that is the goal.
  - whimsicalism 6y ago
    > does not make sense to DFT data before feeding it into a multilayered neural network is false. "It would be nice if we didn't have to DFT data before feeding it into a multilayered neural network" is true, but a completely different statement.
monocasa 6y ago
Which is weird, because biological neural nets seem to have some evolutionary pressure to do hardware fourier transforms before neurons even get involved. You can see this most clearly in the auditory system where the incoming signal is transformed into the frequency domain by the cochlea before the signal is received by the epithelial cells. Neurons absolutely love working in the frequency domain, but they seem to prefer to not be the ones to do the binning in the first place.
- philipswood 6y ago
  This is probably because the neurons involved can't switch fast enough. Our neural hardware is simply too slow to work in the time domain directly.
  - monocasa 6y ago
    They do just fine with acoustic frequency ranges.
    - philipswood 6y ago
      Firing rates for neurons are in the order of 10hz - under the minimum acoustic frequencies of about 20hz. Peak neuron firing rates basically only touch the lower bounds of frequencies that need to be processed. Without the "hardware acceleration" of the cochlea that preprocesses the time domain signals to frequency domain first, basically our whole audio sensorium is out of processing range. Normal nervous signal transmission speeds are in the order of the speed of sound, switching rates are in Hz range. Voltages are in the 10s of millivolt range.
      - monocasa 6y ago
        Neuron spiking isn't rate encoded, it's temporal encoded. Ie. the distance from the next expected regular interval is the signal, not the spiking interval itself. Additionally there's large variations in neuron spiking rates.

ska 6y ago

> Those formulas make no sense: the network can just learn them on the fly. > Just because [...] can construct a filterbank or do a DFT, doesn't mean that it will actually do it when the situation warrants it. These statements seem in conflict, no?

nonameiguess 6y ago

I don't think I can agree with that. You do a Fourier transform when the data you're working with doesn't admit easily or at all certain operations in the time domain but it does in frequency domain. If you already know that to be the case, preprocessing with a FFT is a better idea than hoping a neural network with enough layers uses a few of those to much less efficiently perform a DFT. Always take advantage of pre-existing knowledge of structure in your data. With the FFT especially, depending on how your data is being ingested, you might be able to use specialized DSPs that implement the FFT directly in hardware. These are cheap and easy to find since they're used in frequency-division multiplexing.

dkarras 6y ago
Practically, yes, absolutely! Theoretically, we want the "black box" learning system to do such feature extraction itself. At least, that is the goal.
- whimsicalism 6y ago
  > does not make sense to DFT data before feeding it into a multilayered neural network is false. "It would be nice if we didn't have to DFT data before feeding it into a multilayered neural network" is true, but a completely different statement.

monocasa 6y ago

Which is weird, because biological neural nets seem to have some evolutionary pressure to do hardware fourier transforms before neurons even get involved. You can see this most clearly in the auditory system where the incoming signal is transformed into the frequency domain by the cochlea before the signal is received by the epithelial cells. Neurons absolutely love working in the frequency domain, but they seem to prefer to not be the ones to do the binning in the first place.

philipswood 6y ago
This is probably because the neurons involved can't switch fast enough. Our neural hardware is simply too slow to work in the time domain directly.
- monocasa 6y ago
  They do just fine with acoustic frequency ranges.
  - philipswood 6y ago
    Firing rates for neurons are in the order of 10hz - under the minimum acoustic frequencies of about 20hz. Peak neuron firing rates basically only touch the lower bounds of frequencies that need to be processed. Without the "hardware acceleration" of the cochlea that preprocesses the time domain signals to frequency domain first, basically our whole audio sensorium is out of processing range. Normal nervous signal transmission speeds are in the order of the speed of sound, switching rates are in Hz range. Voltages are in the 10s of millivolt range.
    - monocasa 6y ago
      Neuron spiking isn't rate encoded, it's temporal encoded. Ie. the distance from the next expected regular interval is the signal, not the spiking interval itself. Additionally there's large variations in neuron spiking rates.