DSIRM uses query-bridged contrastive quantization and generative LLMs to create relevance-aware discrete semantic identifiers, reporting +1.54% offline AUC and online lifts on Tmall production data.
Torsion type invariants of singularities
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abstract
Inspired by the LG/CY correspondence, we study the local index theory of the Schr\"odinger operator associated to a singularity defined on ${\mathbb C}^n$ by a quasi-homogeneous polynomial $f$. Under some mild assumption on $f$, we show that the small time heat kernel expansion of the corresponding Schr\"odinger operator exists and is a series of fractional powers of time $t$. Then we prove a local index formula which expresses the Milnor number of $f$ by a Gaussian type integral. Furthermore, the heat kernel expansion provides spectral invariants of $f$. Especially, we define torsion type invariants associated to a singularity. These spectral invariants provide a new direction to study the singularity.
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cs.IR 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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DSIRM: Learning Query-Bridged Discrete Semantic Identifiers for E-commerce Relevance Modeling
DSIRM uses query-bridged contrastive quantization and generative LLMs to create relevance-aware discrete semantic identifiers, reporting +1.54% offline AUC and online lifts on Tmall production data.