arXiv subjects

Li Zhe

Publications and source records attributed to Li Zhe.

3 recordsLinked to original sources

arXiv2026

Computing the minimal monomial basis for multivariate Birkhoff interpolation

This paper studies algorithms for computing the minimal monomial basis for multivariate Birkhoff interpolation problems. Our approach is built around the notion of a reverse reduced set, which serves as the key tool for bridging the interpolation conditions to the monomial basis, thereby avoiding the construction and evaluation of Vandermonde matrices required in existing algorithms. For the single-node case, we prove that after Gaussian elimination on the incidence matrix, the least monomials of the polynomial set corresponding to the interpolation conditions precisely constitute the minimal monomial basis. To handle the multi-node case, we exploit the one-to-one correspondence between interpolation functionals and formal power series, whereby interpolation conditions at arbitrary nonzero nodes can all be converted to the origin. This provides both a coherent theoretical framework and a constructive algorithm for determining a proper minimal monomial basis for the general multivariate Birkhoff interpolation problem. Numerical examples demonstrate the effectiveness of the proposed algorithm.

math.NA↗

arXiv2021

CPT: A Pre-Trained Unbalanced Transformer for Both Chinese Language Understanding and Generation

In this paper, we take the advantage of previous pre-trained models (PTMs) and propose a novel Chinese Pre-trained Unbalanced Transformer (CPT). Different from previous Chinese PTMs, CPT is designed to utilize the shared knowledge between natural language understanding (NLU) and natural language generation (NLG) to boost the performance. CPT consists of three parts: a shared encoder, an understanding decoder, and a generation decoder. Two specific decoders with a shared encoder are pre-trained with masked language modeling (MLM) and denoising auto-encoding (DAE) tasks, respectively. With the partially shared architecture and multi-task pre-training, CPT can (1) learn specific knowledge of both NLU or NLG tasks with two decoders and (2) be fine-tuned flexibly that fully exploits the potential of the model. Moreover, the unbalanced Transformer saves the computational and storage cost, which makes CPT competitive and greatly accelerates the inference of text generation. Experimental results on a wide range of Chinese NLU and NLG tasks show the effectiveness of CPT.

cs.CL↗

arXiv2014

Primary visual cortex as a saliency map: parameter-free prediction of behavior from V1 physiology

It has been hypothesized that neural activities in the primary visual cortex (V1) represent a saliency map of the visual field to exogenously guide attention. This hypothesis has so far provided only qualitative predictions and their confirmations. We report this hypothesis' first quantitative prediction, derived without free parameters, and its confirmation by human behavioral data. The hypothesis provides a direct link between V1 neural responses to a visual location and the saliency of that location to guide attention exogenously. In a visual input containing many bars, one of them saliently different from all the other bars which are identical to each other, saliency at the singleton's location can be measured by the shortness of the reaction time in a visual search task to find the singleton. The hypothesis predicts quantitatively the whole distribution of the reaction times to find a singleton unique in color, orientation, and motion direction from the reaction times to find other types of singletons. The predicted distribution matches the experimentally observed distribution in all six human observers. A requirement for this successful prediction is a data-motivated assumption that V1 lacks neurons tuned simultaneously to color, orientation, and motion direction of visual inputs. Since evidence suggests that extrastriate cortices do have such neurons, we discuss the possibility that the extrastriate cortices play no role in guiding exogenous attention so that they can be devoted to other functional roles like visual decoding or endogenous attention.

q-bio.NC↗