Training neural network to implement discrete Fourier transform (DFT/FFT)

readme.md

My third neural network experiment (second was FIR filter). DFT output is just a linear combination of inputs, so it should be implementable by a single layer with no activation function.

Animation of weights being trained:

Red are positive, blue are negative. The black squares (2336 out of 4096) are unused, and could be pruned out to save computation time (if I knew how to do that).

Even with pruning, it would be less efficient than an FFT, so if the FFT output is useful, probably best to do it externally and provide it as separate inputs?

This at least demonstrates that neural networks can figure out frequency content on their own, though, if it's useful to the problem.

The loss goes down for a while but then goes up. I don't know why:

DFT_ANN.py

"""
Train a neural network to implement the discrete Fourier transform
"""
import matplotlib.pyplot as plt
import numpy as np
from tensorflow.keras.layers import Dense
from tensorflow.keras.models import Sequential

N = 32
batch = 10000

# Generate random input data and desired output data
sig = np.random.randn(batch, N) + 1j*np.random.randn(batch, N)
F = np.fft.fft(sig, axis=-1)

# First half of inputs/outputs is real part, second half is imaginary part
X = np.hstack([sig.real, sig.imag])
Y = np.hstack([F.real, F.imag])

# Create model with no hidden layers, same number of outputs as inputs.
# No bias needed.  No activation function, since DFT is linear.
model = Sequential([Dense(N*2, input_dim=N*2, use_bias=False)])
model.compile(loss='mean_squared_error', optimizer='adam')
model.fit(X, Y, epochs=100, batch_size=100)

# Confirm that it works
data = np.arange(N)


def ANN_DFT(x):
    if len(x) != N:
        raise ValueError(f'Input must be length {N}')
    pred = model.predict(np.hstack([x.real, x.imag])[np.newaxis])[0]
    result = pred[:N] + 1j*pred[N:]
    return result


ANN = ANN_DFT(data)
FFT = np.fft.fft(data)
print(f'ANN matches FFT: {np.allclose(ANN, FFT)}')

# Heat map of neuron weights
plt.imshow(model.get_weights()[0], vmin=-1, vmax=1, cmap='coolwarm')

This work is cited here,
https://youtu.be/mYy4Zv80tXQ
@20:21

@ShriAka That's cool, thanks for pointing it out :)

The demo is using random noise data ， if specified data,such as time series data or picture data is used , is it easy to learn the approprate weight?

@Chenhubget It only learns at the frequencies present in the data