Shujian Li | Searcharxiv

arXiv2026

Moment-based linear programming bounds for locally recoverable codes

In this paper we derive new Delsarte-type linear programming bounds for $q$-ary $(r,\delta)$-locally recoverable codes (LRCs) with three attributes: first, the variable set is comparable in size to that of the classical Delsarte LP; second, our LP exploits the higher-order information forced by the local-distance condition through order $\delta-2$, in the sense that for nondegenerate linear codes, its balanced base part gives exactly the same dimension bound as the symmetrized refined-weight LP of Gruica, Jany, and Ravagnani, while the additional constraints, nonvacuous whenever $\delta \ge 3$, give a further strengthening; and third, it applies to general $(r,\delta)$-LRCs, linear and nonlinear alike. Extensive computations over binary and ternary alphabets show that the convex-hull LP yields improvements not captured by the previous LP and often sharpens the shortening and generalized Singleton bounds.

cs.IT↗

arXiv2025

GPS: Distilling Compact Memories via Grid-based Patch Sampling for Efficient Online Class-Incremental Learning

Online class-incremental learning aims to enable models to continuously adapt to new classes with limited access to past data, while mitigating catastrophic forgetting. Replay-based methods address this by maintaining a small memory buffer of previous samples, achieving competitive performance. For effective replay under constrained storage, recent approaches leverage distilled data to enhance the informativeness of memory. However, such approaches often involve significant computational overhead due to the use of bi-level optimization. Motivated by these limitations, we introduce Grid-based Patch Sampling (GPS), a lightweight and effective strategy for distilling informative memory samples without relying on a trainable model. GPS generates informative samples by sampling a subset of pixels from the original image, yielding compact low-resolution representations that preserve both semantic content and structural information. During replay, these representations are reassembled to support training and evaluation. Experiments on extensive benchmarks demonstrate that GRS can be seamlessly integrated into existing replay frameworks, leading to 3%-4% improvements in average end accuracy under memory-constrained settings, with limited computational overhead.

cs.CV↗