相关论文: Under-approximation of the Greatest Fixpoint in Re…

For a continuous function $f$ defined on a closed and bounded domain, there is at least one maximum and one minimum. First, we introduce some preliminaries which are necessary through the paper. We then present an algorithm, which is…

The robustness of deep neural networks (DNNs) is crucial to the hosting system's reliability and security. Formal verification has been demonstrated to be effective in providing provable robustness guarantees. To improve its scalability,…

We prove that any extended formulation that approximates the matching polytope on $n$-vertex graphs up to a factor of $(1+\varepsilon)$ for any $\frac2n \le \varepsilon \le 1$ must have at least $\binom{n}{{\alpha}/{\varepsilon}}$ defining…

Optimizing non-convex functions is a fundamental challenge across machine learning and combinatorial optimization. We introduce and study $\gamma$-weakly $\theta$-up-concavity, a novel first-order condition that characterizes a broad class…

When facing time-variant problems in analog computing, the desirable RNN design requires finite-time convergence and robustness with respect to various types of uncertainties, due to the time-variant nature and difficulties in…

We study the sign problem in lattice field theory with a $\theta$ term. We apply the maximum entropy method (MEM) to flattening phenomenon of the free energy density $f(\theta)$, which originates from the sign problem. In our previous…

Fast weight architectures offer a promising alternative to attention-based transformers for long-context modeling by maintaining constant memory overhead regardless of context length. However, their potential is limited by the next-token…

Large language models (LLMs) often generate code that is functionally correct but inefficient in runtime and memory. Prior approaches to improving code efficiency typically rely on absolute execution feedback, such as profiling a single…

While test-time scaling with verification has shown promise in improving the performance of large language models (LLMs), the role of the verifier and its imperfections remain underexplored. The effect of verification manifests through…

Large Language Models (LLMs) generate functionally correct solutions but often fall short in code efficiency, a critical bottleneck for real-world deployment. In this paper, we introduce a novel test-time iterative optimization framework to…

Large language models (LLMs) are increasingly explored for NP-hard combinatorial optimization problems, but most existing methods emphasize feasible-instance solution generation and do not explicitly address infeasibility detection. We…

As the usage of theorem prover technology expands, so too does the reliance on correctness of the tools. Metamath Zero is a verification system that aims for simplicity of logic and implementation, without compromising on efficiency of…

Many important hyperproperties, such as refinement and generalized non-interference, fall into the class of $\forall\exists$ hyperproperties and require, for each execution trace of a system, the existence of another trace relating to the…

Conformal Prediction (CP) is a widely used technique for quantifying uncertainty in machine learning models. In its standard form, CP offers probabilistic guarantees on the coverage of the true label, but it is agnostic to sensitive…

Natural Language Inference (NLI) models have been used in various ways to improve the factuality of LLM outputs. This is typically done by applying an NLI model to judge whether the model output is entailed from the supposed evidence,…

In logics for the strategic reasoning the main challenge is represented by their verification in contexts of imperfect information and perfect recall. In this work, we show a technique to approximate the verification of Alternating-time…

Techniques for runtime verification often utilise specification languages that are (i) reasonably expressive, and (ii) relatively abstract (i.e. they operate on a level of abstraction that separates them from the system being monitored).…

We study local computation algorithms (LCA) for maximum matching. An LCA does not return its output entirely, but reveals parts of it upon query. For matchings, each query is a vertex $v$; the LCA should return whether $v$ is matched -- and…

By algorithmic metatheorems for a model checking problem P over infinite-state systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a…

Thresholding based iterative algorithms have the trade-off between effectiveness and optimality. Some are effective but involving sub-matrix inversions in every step of iterations. For systems of large sizes, such algorithms can be…