Self-organization, and transitions from reversible to irreversible behaviour, of interacting particle assemblies driven by externally imposed stresses or deformation is of interest in comprehending diverse phenomena in soft matter. They have been investigated in a wide range of systems, such as colloidal suspensions, glasses, and granular matter. In different density and driving regimes, such behaviour is related to yielding of amorphous solids, jamming, and memory formation, emph{etc.} How these phenomena are related to each other has not, however, been much studied. In order to obtain a unified view of the different regimes of behaviour, and transitions between them, we investigate computationally the response of soft sphere assemblies to athermal cyclic shear deformation over a wide range of densities and amplitudes of shear deformation. Cyclic shear deformation induces transitions from reversible to irreversible behaviour in both unjammed and jammed soft sphere packings. Well above isotropic jamming density ($bf{phi_J}$), this transition corresponds to yielding. In the vicinity of the jamming point, up to a higher density limit we designate ${bf phi_J^{cyc}}$, an unjammed phase emerges between a localised, emph{absorbing} phase, and a diffusive, {emph irreversible} phase. The emergence of the unjammed phase signals the shifting of the jamming point to higher densities as a result of annealing, and opens a window where shear jamming becomes possible for frictionless packings. Below $bf{phi_J}$, two distinct localised states, termed point and loop reversibile, are observed. We characterise in detail the different regimes and transitions between them, and obtain a unified density-shear amplitude phase diagram.
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