Detecting and segmenting small objects, such as lung nodules and tumor lesions, remains a critical challenge in image analysis. These objects often occupy less than 0.1% of an image, making traditional transformer architectures inefficient and prone to performance degradation due to redundant attention computations on irrelevant regions. Existing sparse attention mechanisms rely on rigid hierarchical structures, which are poorly suited for detecting small, variable, and uncertain object locations. In this paper, we propose BoltzFormer, a novel transformer-based architecture designed to address these challenges through dynamic sparse attention. BoltzFormer identifies and focuses attention on relevant areas by modeling uncertainty using a Boltzmann distribution with an annealing schedule. Initially, a higher temperature allows broader area sampling in early layers, when object location uncertainty is greatest. As the temperature decreases in later layers, attention becomes more focused, enhancing efficiency and accuracy. BoltzFormer seamlessly integrates into existing transformer architectures via a modular Boltzmann attention sampling mechanism. Comprehensive evaluations on benchmark datasets demonstrate that BoltzFormer significantly improves segmentation performance for small objects while reducing attention computation by an order of magnitude compared to previous state-of-the-art methods.

Large Language Models (LLMs) have shown impressive abilities in many applications.When a concrete and precise answer is desired, it is important to have a quantitative estimation of the potential error rate.However, this can be challenging due to the text-in-text-out nature of generative models.We present a method based on Pareto optimization that generates a risk score to estimate the probability of error in an LLM response by integrating multiple sources of information.We prove theoretically that the error estimator optimized in our framework aligns with the LLM and the information sources in an Pareto optimal manner.Experimental results show that the risk scores estimated by our method are well correlated with the true LLM error rate, thus facilitating error correction.By dynamically combining with prompting strategies such as self-verification and information retrieval, we demonstrate the proposed method can be utilized to increase the performance of an LLM, surpassing state-ofthe-art task specific models.