Recent studies of black hole and neutron star low mass X-ray binaries(LMXBs) show a positive correlation between the X-ray flux at which the low/hard(LH)-to-high/soft(HS) state transition occurs and the peak flux of the following HS state.By analyzing the data from the All Sky Monitor(ASM) onboard the Rossi X-ray Timing Explorer(RXTE),we show that the HS state flux after the source reaches its HS flux peak still correlates with the transition flux during soft X-ray transient(SXT) outbursts.By studying large outbursts or flares of GX 339-4,Aql X-1 and 4U 1705-44,we have found that the correlation holds up to 250,40,and 50 d after the LH-to-HS state transition,respectively.These time scales correspond to the viscous time scale in a standard accretion disk around a stellar mass black hole or a neutron star at a radius of-104-5 Rg,indicating that the mass accretion rates in the accretion flow either correlate over a large range of radii at a given time or correlate over a long period of time at a given radius.If the accretion geometry is a two-flow geometry composed of a sub-Keplerian inflow or outflow and a disk flow in the LH state,the disk flow with a radius up to-105 Rg would have contributed to the nearly instantaneous non-thermal radiation directly or indirectly,and therefore affects the time when the state transition occurs.