Grammars of Formal Uncertainty: When to Trust LLMs in Automated Reasoning Tasks

Large language models (LLMs) show remarkable promise for democratizing automated reasoning by generating formal specifications. However, a fundamental tension exists: LLMs are probabilistic, while formal verification demands deterministic guarantees. This paper addresses this epistemological gap by comprehensively investigating failure modes and uncertainty quantification (UQ) in LLM-generated formal artifacts. Our systematic evaluation of five frontier LLMs reveals Satisfiability Modulo Theories (SMT) based autoformalization's domain-specific impact on accuracy (from +34.8% on logical tasks to -44.5% on factual ones), with known UQ techniques like the entropy of token probabilities failing to identify these errors. We introduce a probabilistic context-free grammar (PCFG) framework to model LLM outputs, yielding a refined uncertainty taxonomy. We find uncertainty signals are task-dependent (e.g., grammar entropy for logic, AUROC>0.93). Finally, a lightweight fusion of these signals enables selective verification, drastically reducing errors (14-100%) with minimal abstention, transforming LLM-driven formalization into a reliable engineering discipline.

Novel adaptation of video segmentation to 3D MRI: efficient zero-shot knee segmentation with SAM2

Intelligent medical image segmentation methods are rapidly evolving and being increasingly applied, yet they face the challenge of domain transfer, where algorithm performance degrades due to different data distributions between source and target domains. To address this, we introduce a method for zero-shot, single-prompt segmentation of 3D knee MRI by adapting Segment Anything Model 2 (SAM2), a general-purpose segmentation model designed to accept prompts and retain memory across frames of a video. By treating slices from 3D medical volumes as individual video frames, we leverage SAM2's advanced capabilities to generate motion- and spatially-aware predictions. We demonstrate that SAM2 can efficiently perform segmentation tasks in a zero-shot manner with no additional training or fine-tuning, accurately delineating structures in knee MRI scans using only a single prompt. Our experiments on the Osteoarthritis Initiative Zuse Institute Berlin (OAI-ZIB) dataset reveal that SAM2 achieves high accuracy on 3D knee bone segmentation, with a testing Dice similarity coefficient of 0.9643 on tibia. We also present results generated using different SAM2 model sizes, different prompt schemes, as well as comparative results from the SAM1 model deployed on the same dataset. This breakthrough has the potential to revolutionize medical image analysis by providing a scalable, cost-effective solution for automated segmentation, paving the way for broader clinical applications and streamlined workflows.

An automated approach for improving the inference latency and energy efficiency of pretrained CNNs by removing irrelevant pixels with focused convolutions

Computer vision often uses highly accurate Convolutional Neural Networks (CNNs), but these deep learning models are associated with ever-increasing energy and computation requirements. Producing more energy-efficient CNNs often requires model training which can be cost-prohibitive. We propose a novel, automated method to make a pretrained CNN more energy-efficient without re-training. Given a pretrained CNN, we insert a threshold layer that filters activations from the preceding layers to identify regions of the image that are irrelevant, i.e. can be ignored by the following layers while maintaining accuracy. Our modified focused convolution operation saves inference latency (by up to 25%) and energy costs (by up to 22%) on various popular pretrained CNNs, with little to no loss in accuracy.