# Neural Network with incresing number of output and task difficulty

Is it possible to design a network to solve a multiple-output regression task with increasing number of outputs, so the difficulty of the task?

I am trying to solve the problem of frequencies estimation for sum of sine waves with NN. From

$$x(t) = \sum_{k=0}^K a_k sin(2 \pi f_k t) + \text{noise}$$

predict $$a_k$$ and $$f_k$$. However there is an order in the data: $$a_k > a_{k+1}$$ and $$f_k < f_{k+1}$$.

I am familiar with the solution presented in the paper Neural networks for sinusoidal frequency estimation. I implemented it: the input is the signal with $$K$$ sine waves. The output are the $$\{a_k, f_k\}_{k=0}^{K'}$$ with $$K' \leq K$$.

For $$K' = 2$$ is working fine. For $$K' > 2$$ the estimation error is not as good, no metter the architetture (It tried with RNN and CNN or simple Feedforword NN). I noticed that also the prediction of $$a_1, f_1$$ for $$K' > 2$$ is worst then when $$K'=2$$.

The question: is there a DNN technique to start the learning with $$K' = 2$$ and then sequentially increase it?

I was thinking: is it right to use an NN with an output layer of dimension $$2K$$, and predict only 2 values, while $$2K-2$$ are forced to be zeros. So train for some epochs, then unfreeze the next 2 values, then repeat?

• How exactly does your data look like?
– Tim
Commented Jan 17, 2020 at 16:36
• The input consists in a vector 1024 samples matching the observation of 64 milliseconds of waves sampled at 16kHz. The $f_k \in [100, 1000]$ Hz, $a_k \in [0.2, 1]$. Commented Jan 17, 2020 at 17:17
• Have you tried recurrent neural networks?
– Tim
Commented Jan 17, 2020 at 17:52
• Yes and it is slightly better, but still I am more interested in knowing about some techniques for such increasing-difficulty-task. Commented Jan 17, 2020 at 17:59