Identifying variables as invariant or constant at compile-time allows the compiler to perform optimizations including constant folding, code specialization, and partial evaluation. Some variables, which cannot be labeled as constants, may exhibit semi-invariant behavior. A semi-invariant variable is one that cannot be identified as a constant at compile-time, but has a high degree of invariant behavior at run-time. If run-time information was available to identify these variables as semi-invariant, they could then benefit from invariant-based compiler optimizations. We examine the invariance found from profiling instruction values, and show that many instructions have semi-invariant values even across different inputs. We also investigate the ability to estimate the invariance for all instructions in a program from only profiling load instructions. In addition, we propose a new type of profiling called convergent profiling. Estimating the invariance from loads and convergent profiling are used to reduce the profiling time needed to generate an accurate value profile. The value profile can then be used to automatically guide code generation for dynamic compilation, adaptive execution, code specialization, partial evaluation and other compiler optimizations.