We propose a new estimator of low-frequency skewness (monthly) that exploits high-frequency data (5 min) through a direct functional mapping consisting of layers of Convolutional Neural Networks followed by Multi Layer Perceptrons. Monte Carlo experiments involving stochastic volatility models, with and without jumps, show that the estimator reduces finite-sample bias relative to existing realized-skewness estimators and remains accurate under model misspecification. Empirically, our estimator exhibits temporal stability and delivers cross-sectional performance in actual skewness-sorted portfolios. We characterize the finite-sample bias of conventional plug-in skewness estimators and establish risk consistency properties of the proposed NN estimator under standard regularity conditions.
Large language models (LLMs) require substantial memory, motivating low-bit weight quantization for efficient deployment. Existing vector quantization (VQ) methods often improve accuracy by increasing the effective coding dimension, which can complicate independent lookup and local codeword updates. We propose CoS-VQ (Coordinated Shared-Scale Vector Quantization), which preserves low-dimensional codewords while jointly optimizing hard indices and their shared scale across positions. The key challenge is scale-induced coupling: the optimal scale depends on the entire codeword combination and, in turn, changes candidate rankings across positions, so pointwise updates can stall even after scale re-optimization. CoS-VQ collects candidates at multiple probe scales and constructs a tangent separable upper bound for the residual-aware quadratic objective. By reducing candidate comparisons to lower envelopes of lines over positive scales, it identifies finitely many representative intervals for joint index--scale updates without exhaustively enumerating codeword combinations. On Qwen3.8-27B, CoS-VQ outperforms QTIP and LLVQ on the evaluated language modeling, coding, and reasoning benchmarks. Ablations from the same initialization further show larger gains from joint updates than from scale-only refinement, highlighting joint selection as an alternative to increasing codeword dimensionality. The code is available at https://github.com/xzktx003/Cos_VQ.