  In this work we explore the power of future large-scale surveys to constrain
possible deviations from the standard single-field slow-roll inflationary
scenario. Specifically, we parametrize possible fluctuations around the almost
scale-invariant primordial scalar power spectrum in a model independent way. We
then use their imprints on the simulated matter distribution, as observed by
the galaxy clustering and weak lensing probes of Euclid and Square Kilometer
Array, to construct the best constrainable patterns of fluctuations. For
comparison, we make similar forecasts for a futuristic CMB-S4-like survey. The
modes are found to have similar, yet shifted, patterns, with increasing number
of wiggles as the mode number increases. The forecasted constraints are
tightest for CMB anisotropies and galaxy clustering, depending on the details
of the specifications of the survey. As case studies, we explore how two
greatly different physically motivated patterns of primordial power spectrum
are reconstructed by the proposed modes. We propose a figure of merit based on
the amount of information delivered by the modes to truncate the mode hierarchy
which is automatically generated by the analysis.
