A transducer carries both acoustic position and emitted-label history

The encoder produces acoustic state at a time position, the prediction network represents an output prefix, and a joint network produces a distribution over labels plus blank. In a fixed-target training lattice, output position identifies the corresponding target prefix. During decoding, two hypotheses with the same output length can contain different labels and therefore different prediction states. Do not merge them merely because their integer coordinates match. Cached prediction state belongs to a compatible exact history, including the model revision and any conditioning relevant to that state.

In the conventional transducer lattice, blank moves to the next acoustic step and preserves label history; a label stays at the current acoustic position while extending that history. Several labels may therefore be emitted before a blank advances time. The original Graves transduction paper defines this sequence model and its alignment summation. Its objective does not automatically make an encoder causal: a bidirectional or unrestricted future-context encoder still needs future audio. State the permitted right context separately when calling an RNN-T system streaming.

A path score multiplies the relevant joint probabilities, usually accumulated as log probabilities for stability. Several paths can produce the same output prefix at a compatible acoustic position; sum their contributions when the algorithm's equivalence contract permits it. Keeping only the largest path score changes that calculation. External language models, insertion bonuses, or length normalizations can improve a chosen decoding objective but make a resulting beam score different from the original normalized transducer probability. Record those additions and the exact merging rules for reproducibility.

Beam width, score thresholds, and maximum symbols per acoustic step bound work but can discard the ultimately best output. A hard emission cap can prevent an unproductive expansion loop, yet it is a search approximation rather than a theorem that the model would never emit more labels there. Wider beams also increase joint evaluations and state storage; their effect on final error is empirical under the full scoring policy. Compare latency and word error at the same model, context settings, hardware, and workload instead of assuming one beam size is universally better.

A chunk boundary should not reset an active hypothesis's prediction network or advance the acoustic index twice for overlapping encoder context. Define which acoustic frames are new, which caches summarize history, and whether right-context frames are provisional. Hypothesis forks need independent mutable prediction state or a correct immutable sharing scheme. When a branch is pruned, release its private state without invalidating surviving hypotheses. A finalization rule also needs to distinguish a stable prefix from a provisional best path that later acoustic evidence can overturn.

The queue lab shows only the cost of excess hypothetical search work. Reset, explicitly set BOTH arrival λ=4 and service μ=3, predict q(2)=6 from initial backlog four, then Play or Step four times. Reset and re-set BOTH λ=2 and μ=3; predict q(2)=2. Edits retain t and recompute the original constant-rate trajectory. This fluid model has no labels, lattice, beam width, or neural evaluations. It illustrates a service-capacity tradeoff without predicting how any real transducer's search complexity or error changes with pruning.