Loop invariant inference is a fundamental yet challenging problem in program verification. Recent LLM-aided guess-and-check techniques have shown strong performance on single-loop programs, but they often struggle with programs containing multiple interacting loops. This paper presents InvWeaver, a neuro-symbolic framework for synthesizing invariants for such programs. The key idea is to expose inter-loop dependencies and propagate proof obligations through a combination of loop-level abstraction, obligation-guided inference, and weakest-precondition-based refinement. We evaluate InvWeaver on a comprehensive benchmark suite, including a newly curated dataset derived from classic algorithms. Experimental results show that InvWeaver substantially outperforms existing invariant inference methods, solving 72 out of 82 multi-loop benchmark problems and maintaining strong performance on single-loop tasks.
A central design principle in modern machine learning and artificial intelligence is to align a model's inductive bias with the structure of its input data. For matrix-valued inputs, relevant matrix-level relationships can be characterised through spectral values and spectral sub…
Automating theoretical research is constrained not only by the generation of candidate results, but also by their reliable evaluation. A common approach is to close the research loop with a large language model (LLM) reviewer. However, such reviewers remain empirically unreliable…
Singular value soft-thresholding can be computed via a reduction to the matrix polar decomposition, which allows one to exploit GPU-friendly algorithms for computing the polar decomposition. Empirically, there is a significant speed-up on GPUs compared to the standard approach us…
In this paper, we propose a new solution for addressing the content cold-start problem in industry-scale search and recommender systems. Compared to prior approaches, we have made the following new contributions: 1) our solution spans the entire multi-stage funnel and generalizes…
Dysphagia is a debilitating late effect of head and neck cancer (HNC) treatment, yet timely identification of at-risk patients remains challenging in survivorship care. Definitive assessment relies on videofluoroscopic imaging, as captured by the Dynamic Imaging Grade of Swallowi…
Electroencephalography (EEG) is widely used to diagnose neurological conditions, but its analysis usually relies on either predefined spectral features or deep neural networks. Predefined features carry a strong bias, since they fix in advance what counts as informative, while de…