Task: Language Identification
Input (Spanish, English): Overview: This work seems very promising, but I believe it should be compared with more baselines, and more precisely described and explained, from a signal processing point of view.  Pros: New descriptor Fast implementation  Cons: a) Lack of rigor b) Too long accordingly to the content c) The computational gain of the algorithm is not clear d) The work is not compared with its most obvious baseline: a scattering transform  I will detail each cons.  a) Section 1: The author  motivates the use of scattering transform because it defines a contraction of the space that relies on geometric features. " The nonlinearity used in the scattering network is the complex modulus which is piecewise linear." A real modulus is piecewise linear. A complex modulus has a shape of bell when interpreting C as R^2. Could you clarify? \Omega is not introduced.  Could you give a precise reference (page+paper) of this claim: “Higher order nonlinearity refers to |x|^2 instead of |x| as it is usually done in the scattering network.” ?  Section 2: The motivation of the non-linearity is not clear. First, this non-linearity might potentially increase a lot the variance of your architecture since it depends on higher moments(up to 4). I think a fair analysis would be to compute numerically the normalized variance (e.g. divided by the averaged l^2 norm), as a sanity check. Besides, one should prove that the energy is decreasing. It is not possible to argue that this architecture is similar to a scattering transform which has precise mathematical foundations and those results are required, since the setting is different.  Permutation is not a relevant variability.  The notion of sparsity during the whole paper sometimes refers to the number of 0 value, either the l^1 norm. Mathematically, a small value, even 10^-1000 is still a non 0 value.  Did you compute the graph of the figure 4 on the bird dataset? You might use a ratio instead for clarity.   The wavelet that is defined is not a morlet wavelet (
Output (English): en