Does actual inflation converge towards expected inflation or does expected inflation converge towards actual inflation?

There has been a recent divergence between expected inflation in financial markets or inflation expected by households , and actual inflation, especially in the United States. This raises the question of the direction of the convergence: Is actual inflation converging towards expected inflation, as expected inflation is a good predictor of future inflation? Or is expected inflation converging towards actual inflation because financial markets or households are learning and because inflation expectations may be wrong in the short term? We see that: Inflation has a significant impact on expected inflation in the short term; And expected inflation is correlated with future inflation, the cause, but very little: expected inflation is a poor predictor of future inflation.