  Simultaneous Machine Translation (SiMT) generates target outputs while
receiving stream source inputs and requires a read/write policy to decide
whether to wait for the next source token or generate a new target token, whose
decisions form a \textit{decision path}. Existing SiMT methods, which learn the
policy by exploring various decision paths in training, face inherent
limitations. These methods not only fail to precisely optimize the policy due
to the inability to accurately assess the individual impact of each decision on
SiMT performance, but also cannot sufficiently explore all potential paths
because of their vast number. Besides, building decision paths requires
unidirectional encoders to simulate streaming source inputs, which impairs the
translation quality of SiMT models. To solve these issues, we propose
\textbf{S}elf-\textbf{M}odifying \textbf{S}tate \textbf{M}odeling (SM$^2$), a
novel training paradigm for SiMT task. Without building decision paths, SM$^2$
individually optimizes decisions at each state during training. To precisely
optimize the policy, SM$^2$ introduces Self-Modifying process to independently
assess and adjust decisions at each state. For sufficient exploration, SM$^2$
proposes Prefix Sampling to efficiently traverse all potential states.
Moreover, SM$^2$ ensures compatibility with bidirectional encoders, thus
achieving higher translation quality. Experiments show that SM$^2$ outperforms
strong baselines. Furthermore, SM$^2$ allows offline machine translation models
to acquire SiMT ability with fine-tuning.
