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tokens: only the two-point statistic is insufficient to probe all the effects of different cosmological parameters on the evolution of the overall cosmological field. This motivates the need for considering other summary statistics in the analysis of clustering on smaller scales. Since the total information available in a survey scales with the number of independent modes (Tegmark 1997 ), and given that there are many more independent modes on small scales, it is important to develop these new statistical methods, that better extract information from small scales, to make optimal use of data from ongoing and future cosmological surveys. Various approaches towards harnessing information beyond that contained in the two-point statistics have been explored in the literature. One method is consider the higher N -point functions in the analysis – the three-point function and its Fourier transform, the bispectrum (e.g. Scoccimarro et al. 1998 ; Takada Jain 2004 ; Sefusatti et al. 2006 ), or the four-point function and its Fourier transform, the trispectrum (e.g. Verde Heavens 2001 ). While these additional statistics can be highly informative about small-scale clustering, and promise to yield significantly tighter constraints on some cosmological parameters (Coulton et al. 2019 ; Hahn et al. 2020 ), one drawback is that they generally entail much higher computational costs to measure either from simulations, or from data. The computational complexity rises with N – the order of the highest connected correlation function considered, while keeping the data size fixed. Further, the noise properties for these higher order estimators often make it difficult to obtain good signal-to-noise ratio (SNR) over a wide range of scales. In spite of these issues, analyses including higher order correlations, especially the bispectrum, have successfully been applied to certain cosmological data sets (Gil-Marín et al. 2015 ; Slepian et al. 2017 ; Gualdi et al. 2019 ). In this context, there also exist approaches which attempt to undo the non-linear effects of gravitational clustering on various cosmological fields. Once this procedure is applied, the analysis proceeds with the measurement of the two-point function of the linearized field. This approach has already been applied specifically to the reconstruction of the Baryon Acoustic Oscillation (BAO) signal (Eisenstein et al. 2007 ; Padmanabhan, White Cohn 2009 ; Padmanabhan et al. 2012 ). Schmittfull et al. ( 2015 ) showed that the reconstruction process can be interpreted as the transfer of information from the higher connected N -point functions in the observed field into the reconstructed two-point function. More recently, methods have been proposed for the full reconstruction of the initial linear modes from non-linear observables at low redshift (Baldauf et al. 2010 ; Seljak et al. 2017 ; Modi, Feng Seljak 2018 ; Horowitz, Seljak Aslanyan 2019 ). There is also a large body of literature investigating the one point