Soft prompts are learned embedding sequences, but nothing guarantees that their token axis behaves like a signal with useful coarse and fine structure. We test that premise with the Discrete Wavelet Transform (DWT), which rewrites a sequence into approximation (coarse, low-frequency) and detail (local, high-frequency) coefficients. Wavelets help images and audio when most squared coefficient mass concentrates in the approximation band and the detail coefficients become sparse. Trained soft prompts meet neither condition. Our primary test decomposes a converged soft prompt into DWT bands, fine-tunes one band or both, and compares against a matched-budget baseline that continues vanilla training with no DWT. A constructed positive control first confirms that the procedure recovers a target displacement when the displacement is confined to the trainable band and rejects it when the required band is frozen. On SST-2 (67K) and AG News (120K) with Haar wavelets, and on an SST-2 check with Daubechies-2, no band-selective mode reliably beats the baseline, and the two bands are interchangeable within 0.2~pts. Direct measurement of the converged prompt finds coefficient mass roughly balanced across the bands and detail coefficients far denser than classical wavelet theory expects. Related variants behave the same way. An end-to-end wavelet prompt tuner does not reliably outperform vanilla, and a token-diversity variant makes prompt tokens more diverse without improving accuracy. On 250 held-out FLAN generation examples, existing Wavelet KD and Standard KD checkpoints are indistinguishable under token F1 and ROUGE-L.

Structured information extraction at small-language-model scale is a routine production workload, yet each new task added to a serving stack can demand new task-specific model state. We propose a schema-hierarchical soft prompt: a small learned prefix, trained on a frozen backbone, that gives every JSON-schema node its own slot, orders the slots by the schema, and marks tree depth with learned embeddings. Used alone on the open USPTO-ORD patent task, it recovers most of a LoRA reference’s extraction quality while training more than an order of magnitude fewer parameters, and ablations attribute the gain to depth and schema order rather than token count. Used with a LoRA adapter on an internal booking task, the same slots stabilize one of two held-out categories, so we report this as a bounded mechanism study rather than a general gain. Inference-time slot replacement indicates that position supplies the schema scaffold while learned content stabilizes generation. Measured serving gives a far smaller task artifact and higher throughput than multi-LoRA as interleaved tasks grow. The soft-prompt module is available at https://github.com/microsoft/Hierarchical-Soft-Prompt.