For a concrete example (happens less nowadays with bigger models, but it still happens, especially later into a context window), models hate long json strings. It's very easy to get a json output like
{"name": "Bob", "biography": "Bob is a fantastic builder, having ...
Critically, the ellipses terminate the JSON. With schema-constrained decoding, you _must_ eventually terminate that broken string, and it'll typically terminate it right after the ellipses. Basically, by the point you got to the first period the output was borked. You were backed into a corner. Retry as a strategy fixes that.
As another example failure mode that's a bit more subtle, you might have a set of "correct" tokens early on in the output which get the KV cache into a bit of a wonky state, causing it to have worse outputs toward the end of your output. Disallowing invalid next states forces you to generate tokens in that worse-output state. Retry lets you fail more often and then hopefully not have those wonky-state early tokens. It's not really that you were backed into a bad state as a hard rule, but that you were backed into a bad state as a probabilistic statement.
For a toy model to think about, suppose the entire grammar is [ab, ba], and the LLM's universe of training data is [ab, ab, ba, bb]. The "right" distribution (retry on failure) is {ab: 67%, ba: 33%}. The schema-constrained distribution is {ab: 50%, ba: 50%}.
i.e. it might be that a particular model may need some additional conditioning, or perhaps adjusting the order of the json output affects it to produce lower-quality results.
You have to remember that the LLM will be expected to generate 10s of thousands of tokens on a single turn, where things like quantization noise lead to cascading error further on. So when you can, you really want to stay within the model's distribution.
I have a reasonably strong prior that it should be better though. That comes from my observations that whenever I notice the difference in distribution the retry method is better (obvious sampling bias, but what kind of person ignores their own experiences). As a stronger piece of evidence and intuition, the entire goal of these systems is to reproduce a certain distribution. If that distribution says that you should use ripgrep 10x as often as you should use grep then that's a signal you probably don't want to throw away. Constrained decoding might very well do so and place them on even footing or skew 10x the other direction. Retry faithfully captures that original distribution. I'm skeptical of solutions which want to shy too far away from it (similarly with most applications of changing the model's temperature).
The more important point is just that they're different, so we should probably measure the impact.
The order of the output fields can actually be used to tune performance of the outputs. It can be helpful to force the LLM to reason about specific fields first if later fields benefit from seeing those earlier fields' output. You have to test it because some times the results are surprising in directions you didn't expect.
XGrammar has an option somewhere to allow fields to appear in any order but I don't know if vLLM exposes it. There are some tradeoffs and limitations for allowing fields to show up in any order because there is some complexity in schema parsing like that.
When you know enough about the JSON structure to understand how to set a decoding order, then you can simply break the problem into smaller parts so it's more manageable.
Otherwise, you have these solutions: - GEPA-style prompt optimization for simple agents - If working with large models, you can just have them do step-by-step problem solving & relying on their CoT for accuracy. - A small model can simply be trained to do what you want
And if those don't work, I would be extremely surprised.