Chain model training diverges after switching from lattice-free MMI to standard MMI in Kaldi nnet3

Question

We run Kaldi nnet3 chain training on a mid-size corpus and are evaluating the two documented MMI variants: lattice-free MMI (the default in most chain recipes) and standard MMI with pre-generated lattices. After switching the training objective while keeping the same acoustic model topology, iVector input, and learning-rate schedule, the objective function oscillates and WER on the dev set regresses compared to the lattice-free baseline.

The relevant constraints: lattice-free MMI avoids the lattice-generation and lattice-alignment overhead, but the Kaldi documentation and recipe comments note it uses a different denominator graph construction (a phone-level decoding graph rather than utterance-specific lattices). Standard MMI depends on lattice quality from a prior alignment model, so a weak aligner could poison the denominator. We are unsure whether the divergence reflects a hyperparameter mismatch (e.g., the learning rate or l2-regularize settings tuned for LF-MMI) or a genuine lattice-quality problem.

Should learning-rate and regularization settings be re-tuned when moving from lattice-free to standard MMI in nnet3, or are the chain recipe defaults expected to transfer?
Is there a documented way to diagnose whether divergence comes from poor denominator lattices versus optimization instability?
Does Kaldi expose any objective-level logging that distinguishes numerator versus denominator instability during chain training?

Tasadduq Burney · Answer

Kaldi nnet3 Chain Training Divergence When Switching from Lattice-Free to Standard MMI

Switching the training objective from lattice-free MMI (LF-MMI) to standard MMI in Kaldi nnet3 changes the objective landscape because standard MMI relies on utterance-specific lattices generated from a prior alignment model. When the same acoustic model topology, iVector input, and learning-rate schedule are kept, the objective function often oscillates and dev-set WER regresses relative to the LF-MMI baseline.

Learning-rate and l2-regularize values tuned for LF-MMI often destabilize standard MMI. The objective scales differ, and the denominator construction (utterance lattices vs phone-level graphs) shifts the curvature of the optimization surface.
Standard MMI's denominator marginalizes over generated lattices. If the prior aligner produced sparse or biased alignments, the denominator likelihood can be silently degraded, pulling the objective off course even if the numerator fits well.

The Kaldi nnet3 chain training log reports per-iteration mmi.num.llik (numerator acoustic likelihood) and mmi.den.llik (denominator marginal likelihood). These separate terms isolate whether divergence originates from the acoustic model update or the denominator lattice marginalization.

Inspect per-iteration logs for mmi.num.llik and mmi.den.llik. If the numerator oscillates while the denominator remains stable, the instability is optimization-driven; reduce the learning rate (e.g., 0.5x-2x the LF-MMI value) and consider increasing l2-regularize into the 0.01-0.1 range.
If the denominator likelihood is low, unstable, or shows a downward trend across iterations, the problem likely originates from lattice quality. Inspect alignment diagnostics from the prior model and verify that the generated lattices cover the expected phone sequence with consistent log-likelihoods.
Re-train with adjusted hyperparameters and, if needed, regenerate the alignment lattice set using a more robust aligner or additional training iterations before switching to standard MMI.

To determine whether hyperparameter re-tuning or lattice validation should be the immediate next step, please share the per-iteration mmi.den.llik trend from a failing run. That single detail will clarify whether the denominator is the primary driver of divergence.

Note: Log tag names and hyperparameter optima can vary across Kaldi nnet3 releases; the ranges cited are representative recommendations from documented recipes.

Chain model training diverges after switching from lattice-free MMI to standard MMI in Kaldi nnet3

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Kaldi nnet3 Chain Training Divergence When Switching from Lattice-Free to Standard MMI

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