arXiv subjects

Qingjian Ni

Publications and source records attributed to Qingjian Ni.

6 recordsLinked to original sources

arXiv2026

Learning Source Acquisition Policies by Offline Planning

Predicting under an acquisition budget requires choosing feature groups whose value can depend on later queries. O-MPAC transfers finite-horizon risk-cost targets from complete training records into a shared source-action scorer. At inference time, the scorer uses partial observations and source metadata, re-scores after each query, and applies a hard cost mask. We analyze how tied teacher targets and the remaining planning horizon affect the learned decisions. Uniform supervision over tied minima preserves the target distribution under source relabeling. In a five-seed routing experiment, it achieves 0.965 accuracy under both original and context-last orders. On six real tasks, validation selects H1 without action cross-entropy in all thirty splits. O-MPAC has the highest mean budget-integrated accuracy on five tasks against source-adapted GDFS, DIME, AACO+NN and a static policy.

cs.LG↗

arXiv2026

Matched Queries for Curvature and Density at Branching Junctions

At a junction, a score field can reveal weighted tangent rays, yet these first-order quantities do not determine how individual branches bend or how their densities change away from the center. Recovering this missing information is necessary for describing local continuation beyond a single point, but finite observations must separate branchwise second-order effects while allowing error in the estimated center. We address this inverse problem using matched score queries at noise scales $σ$ and $λσ$. For a finite union of $C^{2,α}$ half-branches in $\mathbb{R}^D$, the normalized score has the expansion $F_σ=F_0+σG+O(σ^{1+α})$. Matched subtraction cancels the tangent contribution and exposes $G$, which depends linearly on branchwise curvature and log-density slope. Given tangent directions and weights on distinct rays, $G$ uniquely identifies all $sD$ branch parameters, and $sD$ scalar component observations are necessary. An $O(σ^2)$ center error introduces $D$ translation modes, leading to $(s+1)D$ observations under full-rank calibration, except for a translation-invariant full line. We also establish a perturbation bound and a conditional kernel-density-estimation rate. Experiments reproduce the predicted population and $N^{-1/5}$ trends and remain full rank up to $D=20$ with 16 supplied branches. In end-to-end tests for $D=3$--$5$, a known-count first-order frontend yields full rank in all 135 population systems and a median relative jet error of 0.132. With strong first-order error, matched responses reduce median parameter error by a factor of 49.4 relative to naive tangent subtraction.

stat.ML↗

arXiv2026

Recovering Weighted Tangent Geometry from a Single-Scale Score Field

Near a smooth data manifold, one tangent space summarizes local geometry. At a branch point, the corresponding first-order object is instead a measure over tangent directions, whose normalized masses record the local share of each branch under the chosen data measure. We ask whether a score field at one noise level determines this weighted tangent geometry when the branch center and homogeneity degree $d$ are unknown. In this tangent-measure model, $d$ is the local measure dimension. Gaussian smoothing of a homogeneous tangent measure satisfies an Ornstein--Uhlenbeck eigenfunction equation. Its weak form turns score values---without score derivatives---into a linear system for the center and homogeneity degree, with an explicit rank condition and perturbation bound. After this calibration, the tangential score on one sphere is the spherical log-gradient of a scalar Gaussian--cone transform. Integration recovers that transform up to scale, and all its spherical-harmonic multipliers are positive. Thus one exact shell identifies the normalized angular measure in every ambient dimension $D\geq2$. For at most $K$ positive rays, moments through degree $2K-1$ constructively recover count, directions, and weights in arbitrary dimension. Any fixed observation scheme needs at least $KD-1$ scalar tangential components. In the plane, degree $K$ is both sufficient and necessary, and we give quantitative finite-query certificates. For finite planar $C^{1,β}$ branches with positive $C^{0,β}$ densities, we prove $O(σ^β)$ convergence from the finite-noise score to its tangent model. In controlled experiments, 50k-step training lowers validation normalized-score error across four geometries yet raises angular-moment error, separating ordinary score fit from geometry recovery.

stat.ML↗

arXiv2026

When More Generators Hurt: Shellsort on Full Product Grids

Shellsort repeatedly runs insertion sort with decreasing gaps, so its worst-case cost depends on the gap sequence. Pratt's $2^u3^v$ sequence, one of the few systematic constructions with a proven $O(n\log^2 n)$ bound, includes every product below $n$ of two base numbers, or generators. We ask whether adding more base numbers, and thus more intermediate gaps, can improve this full product grid. We show that it cannot when every product is retained and each base is at most a fixed power of the smallest. With $r$ independent bases (different exponent choices give different products) and $Θ(\log n)$ gaps, the best possible worst-case cost is $n\exp(Θ((\log n)^{1-1/r}))$. Thus two bases give the exponent $\sqrt{\log n}$, whereas three give $(\log n)^{2/3}$: more bases are worse. With a budget of $p$ gaps, matching bounds give the factor $\exp(Θ(\log n/p^{1/r}))$ beyond linear cost. The reason is simple. Few products force the smallest base $m$ to be large, and fullness makes $m$ the next-to-last gap. An input built from reversed blocks is already sorted for every earlier gap, forcing $Ω(nm)$ work in the final pass. Powers of distinct primes give a matching construction. For arbitrary gaps, we count current-gap multiples that earlier gaps cannot form. This gives upper and lower bounds for individual passes. A Fourier argument gives necessary conditions for small total cost, while short nonnegative sums give sufficient conditions. In both settings, useful distances must be available before they are needed.

cs.CC↗

arXiv2026

Rectifying Distribution Shift in Cascaded Precipitation Nowcasting

Precipitation nowcasting, which aims to provide high spatio-temporal resolution precipitation forecasts by leveraging current radar observations, is a core task in regional weather forecasting. Recently, the cascaded architecture has emerged as the mainstream paradigm for deep learning-based precipitation nowcasting. This paradigm involves a deterministic model to predict posterior mean, followed by a probabilistic model to generate local stochasticity. However, existing methods commonly overlook the conflation of the systematic distribution shift in deterministic predictions and the local stochasticity. As a result, the distribution shift of the deterministic component contaminates the predictions of the probabilistic component, leading to inaccuracies in precipitation patterns and intensity, particularly over longer lead times. To address this issue, we introduce RectiCast, a two-stage framework that explicitly decouples the rectification of mean-field shift from the generation of local stochasticity via a dual Flow Matching model. In the first stage, a deterministic model generates the posterior mean. In the second stage, we introduce a Rectifier to explicitly learn the distribution shift and produce a rectified mean. Subsequently, a Generator focuses on modeling the local stochasticity conditioned on the rectified mean. Experiments on two radar datasets demonstrate that RectiCast achieves significant performance improvements over existing state-of-the-art methods.

cs.LG↗

arXiv2025

A Multi-scale Representation Learning Framework for Long-Term Time Series Forecasting

Long-term time series forecasting (LTSF) offers broad utility in practical settings like energy consumption and weather prediction. Accurately predicting long-term changes, however, is demanding due to the intricate temporal patterns and inherent multi-scale variations within time series. This work confronts key issues in LTSF, including the suboptimal use of multi-granularity information, the neglect of channel-specific attributes, and the unique nature of trend and seasonal components, by introducing a proficient MLP-based forecasting framework. Our method adeptly disentangles complex temporal dynamics using clear, concurrent predictions across various scales. These multi-scale forecasts are then skillfully integrated through a system that dynamically assigns importance to information from different granularities, sensitive to individual channel characteristics. To manage the specific features of temporal patterns, a two-pronged structure is utilized to model trend and seasonal elements independently. Experimental results on eight LTSF benchmarks demonstrate that MDMixer improves average MAE performance by 4.64% compared to the recent state-of-the-art MLP-based method (TimeMixer), while achieving an effective balance between training efficiency and model interpretability.

cs.LG↗