13 accepted papers
Automating formal proofs of combinatorial identities is challenging for LLM-based provers, as long-horizon proof planning is required and unconstrained search quickly explodes. Symbolic methods such as the Wilf--Zeilberger (WZ) method can achieve a mechanized proof of combinatorial identities by con…
Automated proving of polynomial inequalities is a fundamental challenge in automated mathematical reasoning, where rich algebraic structure and a rapidly growing certificate search space hinder scalability. Purely symbolic approaches provide strong guarantees but often scale poorly as the number of …
Neural algorithmic reasoning has recently emerged as a popular research direction. It aims to train neural networks to mimic the step-by-step behavior of classical rule-based algorithms. More specifically, the execution of such algorithms can be abstracted as a sequence of states, where each state
Polynomial inequality proving is fundamental to many mathematical disciplines and finds wide applications in diverse fields. Current traditional algebraic methods are based on searching for a polynomial positive definite representation over a set of basis. However, these methods are limited by trunc…
Polynomial Lyapunov function \mathcal V (x) provides mathematically rigorous that converts stability analysis into efficiently solvable optimization problem. Traditional numerical methods rely on user-defined templates, while emerging neural \mathcal V (x) offer flexibility but exhibit poor generali…
Automated Theorem Proving is an important and challenging task. Although large language models (LLMs) have demonstrated remarkable potential in mathematical reasoning, their performance in formal theorem proving remains constrained by the scarcity of high-quality supervised fine-tuning (SFT) data. T…
The paper studies sequential reasoning over graph-structured data, which stands as a fundamental task in various trending fields like automated math problem solving and neural graph algorithm learning, attracting a lot of research interest. Simultaneously managing both sequential and graph-structure…
Neural algorithmic reasoning is an emerging area of machine learning that focuses on building neural networks capable of solving complex algorithmic tasks. Recent advancements predominantly follow the standard supervised learning paradigm -- feeding an individual problem instance into the network ea…
Deep convolutional neural networks (CNNs) have achieved unprecedented success in single image super-resolution over the past few years. Meanwhile, there is an increasing demand for single image super-resolution with arbitrary scale factors in real-world scenarios. Many approaches adopt scale-specifi…
In recent years, there has been an increasing demand for real-time super-resolution networks on mobile devices. To address this issue, many lightweight super-resolution models have been proposed. However, these models still contain time-consuming components that increase inference latency, limiting…
Blind super-resolution, different from conventional non-blind super-resolution based on the assumption of fixed degradation, handles various unknown Gaussian blur kernels, and thus is closer to real-world application. The accuracy of kernel estimation and deconvolution directly influences the perfor…
Bayesian neural networks (BNNs) retain NN structures with a probability distribution placed over their weights. With the introduced uncertainties and redundancies, BNNs are proper choices of robust controllers for safety-critical control systems. This paper considers the problem of verifying the saf…
There is a pressing need to verify robustness of classification deep neural networks (CDNNs) as they are embedded in many safety-critical applications. Existing robustness verification approaches rely on computing the over-approximation of the output set, and can hardly scale up to practical CDNNs,…