  Using $\delta N$ formalism, in the context of a generic multi-field inflation
driven on a non-flat field space background, we revisit the analytic
expressions of the various cosmological observables such as scalar/tensor power
spectra, scalar/tensor spectral tilts, non-Gaussianity parameters,
tensor-to-scalar ratio, and the various runnings of these observables. In our
backward formalism approach, the subsequent expressions of observables
automatically include terms beyond the leading order slow-roll expansion
correcting many of the expression at subleading order. To connect our analysis
properly with the earlier results, we rederive the (well) known (single field)
expressions in the limiting cases of our generic formulae. Further, in the
light of PLANCK results, we examine for the compatibility of the consistency
relations within the slow-roll regime of a two-field roulette poly-instanton
inflation realized in the context of large volume scenarios.
