arXiv subjects

Ziqian Wu

Publications and source records attributed to Ziqian Wu.

3 recordsLinked to original sources

arXiv2026

FrameOracle: Learning What to See and How Much to See in Videos

Vision-language models (VLMs) advance video understanding but operate under tight computational budgets, making performance dependent on selecting a small, high-quality subset of frames. Existing frame sampling strategies, such as uniform or fixed-budget selection, fail to adapt to variations in content density or task complexity. To address this, we present FrameOracle, a lightweight, plug-and-play module that predicts both (1) which frames are most relevant to a given query and (2) how many frames are needed. FrameOracle is trained via a curriculum that progresses from weak proxy signals, such as cross-modal similarity, to stronger supervision with FrameOracle-41K, the first large-scale VideoQA dataset with validated keyframe annotations specifying minimal sufficient frames per question. Extensive experiments across five VLMs and six benchmarks show that FrameOracle reduces 16-frame inputs to an average of 10.4 frames without accuracy loss. When starting from 64-frame candidates, it reduces inputs to 13.9 frames on average while improving accuracy by 1.5%, achieving state-of-the-art efficiency-accuracy trade-offs for scalable video understanding.

cs.CV↗

arXiv2023

Neural Partial Differential Equations with Functional Convolution

We present a lightweighted neural PDE representation to discover the hidden structure and predict the solution of different nonlinear PDEs. Our key idea is to leverage the prior of ``translational similarity'' of numerical PDE differential operators to drastically reduce the scale of learning model and training data. We implemented three central network components, including a neural functional convolution operator, a Picard forward iterative procedure, and an adjoint backward gradient calculator. Our novel paradigm fully leverages the multifaceted priors that stem from the sparse and smooth nature of the physical PDE solution manifold and the various mature numerical techniques such as adjoint solver, linearization, and iterative procedure to accelerate the computation. We demonstrate the efficacy of our method by robustly discovering the model and accurately predicting the solutions of various types of PDEs with small-scale networks and training sets. We highlight that all the PDE examples we showed were trained with up to 8 data samples and within 325 network parameters.

cs.LG↗

arXiv2012

Additive Relation and Algebraic System of Equations

Additive relations are defined over additive monoids and additive operation is introduced over these new relations then we build algebraic system of equations. We can generate profuse equations by additive relations of two variables. To give an equation with several known parameters is to give an additive relation taking these known parameters as its variables or value and the solution of the equation is just the reverse of this relation which always exists. We show a core result in this paper that any additive relation of many variables and their inverse can be expressed in the form of the superposition of additive relations of one variable in an algebraic system of equations if the system satisfies some conditions. This result means that there is always a formula solution expressed in the superposition of additive relations of one variable for any equation in this system. We get algebraic equations if elements of the additive monoid are numbers and get operator equations if they are functions.

math.GM↗