From Blind Solvers to Logical Thinkers: Benchmarking LLMs' Logical Integrity on Faulty Mathematical Problems

Consider the math problem: "Lily received 3 cookies from her best friend yesterday and ate 5 for breakfast. Today, her friend gave her 3 more cookies. How many cookies does Lily have now?" Many large language models (LLMs) in previous research approach this problem by calculating the answer "1" using the equation "3 - 5 + 3." However, from a human perspective, we recognize the inherent flaw in this problem: Lily cannot eat 5 cookies if she initially only had 3. This discrepancy prompts a key question: Are current LLMs merely Blind Solver that apply mathematical operations without deeper reasoning, or can they function as Logical Thinker capable of identifying logical inconsistencies? To explore this question, we propose a benchmark dataset, FaultyMath, which includes faulty math problems of rich diversity: i) multiple mathematical categories, e.g., algebra, geometry, number theory, etc., ii) varying levels of difficulty, and iii) different origins of faultiness -- ranging from violations of common sense and ambiguous statements to mathematical contradictions and more. We evaluate a broad spectrum of LLMs, including open-source, closed-source, and math-specialized models, using FaultyMath across three dimensions: (i) How accurately can the models detect faulty math problems without being explicitly prompted to do so? (ii) When provided with hints -- either correct or misleading -- about the validity of the problems, to what extent do LLMs adapt to become reliable Logical Thinker? (iii) How trustworthy are the explanations generated by LLMs when they recognize a math problem as flawed? Through extensive experimentation and detailed analysis, our results demonstrate that existing LLMs largely function as Blind Solver and fall short of the reasoning capabilities required to perform as Logical Thinker.

Segmenting objects with Bayesian fusion of active contour models and convnet priors

Instance segmentation is a core computer vision task with great practical significance. Recent advances, driven by large-scale benchmark datasets, have yielded good general-purpose Convolutional Neural Network (CNN)-based methods. Natural Resource Monitoring (NRM) utilizes remote sensing imagery with generally known scale and containing multiple overlapping instances of the same class, wherein the object contours are jagged and highly irregular. This is in stark contrast with the regular man-made objects found in classic benchmark datasets. We address this problem and propose a novel instance segmentation method geared towards NRM imagery. We formulate the problem as Bayesian maximum a posteriori inference which, in learning the individual object contours, incorporates shape, location, and position priors from state-of-the-art CNN architectures, driving a simultaneous level-set evolution of multiple object contours. We employ loose coupling between the CNNs that supply the priors and the active contour process, allowing a drop-in replacement of new network architectures. Moreover, we introduce a novel prior for contour shape, namely, a class of Deep Shape Models based on architectures from Generative Adversarial Networks (GANs). These Deep Shape Models are in essence a non-linear generalization of the classic Eigenshape formulation. In experiments, we tackle the challenging, real-world problem of segmenting individual dead tree crowns and delineating precise contours. We compare our method to two leading general-purpose instance segmentation methods - Mask R-CNN and K-net - on color infrared aerial imagery. Results show our approach to significantly outperform both methods in terms of reconstruction quality of tree crown contours. Furthermore, use of the GAN-based deep shape model prior yields significant improvement of all results over the vanilla Eigenshape prior.

Understanding Model Ensemble in Transferable Adversarial Attack

Model ensemble adversarial attack has become a powerful method for generating transferable adversarial examples that can target even unknown models, but its theoretical foundation remains underexplored. To address this gap, we provide early theoretical insights that serve as a roadmap for advancing model ensemble adversarial attack. We first define transferability error to measure the error in adversarial transferability, alongside concepts of diversity and empirical model ensemble Rademacher complexity. We then decompose the transferability error into vulnerability, diversity, and a constant, which rigidly explains the origin of transferability error in model ensemble attack: the vulnerability of an adversarial example to ensemble components, and the diversity of ensemble components. Furthermore, we apply the latest mathematical tools in information theory to bound the transferability error using complexity and generalization terms, contributing to three practical guidelines for reducing transferability error: (1) incorporating more surrogate models, (2) increasing their diversity, and (3) reducing their complexity in cases of overfitting. Finally, extensive experiments with 54 models validate our theoretical framework, representing a significant step forward in understanding transferable model ensemble adversarial attacks.

Expansive Supervision for Neural Radiance Field

Neural Radiance Fields have achieved success in creating powerful 3D media representations with their exceptional reconstruction capabilities. However, the computational demands of volume rendering pose significant challenges during model training. Existing acceleration techniques often involve redesigning the model architecture, leading to limitations in compatibility across different frameworks. Furthermore, these methods tend to overlook the substantial memory costs incurred. In response to these challenges, we introduce an expansive supervision mechanism that efficiently balances computational load, rendering quality and flexibility for neural radiance field training. This mechanism operates by selectively rendering a small but crucial subset of pixels and expanding their values to estimate the error across the entire area for each iteration. Compare to conventional supervision, our method effectively bypasses redundant rendering processes, resulting in notable reductions in both time and memory consumption. Experimental results demonstrate that integrating expansive supervision within existing state-of-the-art acceleration frameworks can achieve 69% memory savings and 42% time savings, with negligible compromise in visual quality.

Test-time adaptation for geospatial point cloud semantic segmentation with distinct domain shifts

Domain adaptation (DA) techniques help deep learning models generalize across data shifts for point cloud semantic segmentation (PCSS). Test-time adaptation (TTA) allows direct adaptation of a pre-trained model to unlabeled data during inference stage without access to source data or additional training, avoiding privacy issues and large computational resources. We address TTA for geospatial PCSS by introducing three domain shift paradigms: photogrammetric to airborne LiDAR, airborne to mobile LiDAR, and synthetic to mobile laser scanning. We propose a TTA method that progressively updates batch normalization (BN) statistics with each testing batch. Additionally, a self-supervised learning module optimizes learnable BN affine parameters. Information maximization and reliability-constrained pseudo-labeling improve prediction confidence and supply supervisory signals. Experimental results show our method improves classification accuracy by up to 20\% mIoU, outperforming other methods. For photogrammetric (SensatUrban) to airborne (Hessigheim 3D) adaptation at the inference stage, our method achieves 59.46\% mIoU and 85.97\% OA without retraining or fine-turning.

A Radiometric Correction based Optical Modeling Approach to Removing Reflection Noise in TLS Point Clouds of Urban Scenes

Point clouds are vital in computer vision tasks such as 3D reconstruction, autonomous driving, and robotics. However, TLS-acquired point clouds often contain virtual points from reflective surfaces, causing disruptions. This study presents a reflection noise elimination algorithm for TLS point clouds. Our innovative reflection plane detection algorithm, based on geometry-optical models and physical properties, identifies and categorizes reflection points per optical reflection theory. We've adapted the LSFH feature descriptor to retain reflection features, mitigating interference from symmetrical architectural structures. By incorporating the Hausdorff feature distance, the algorithm enhances resilience to ghosting and deformation, improving virtual point detection accuracy. Extensive experiments on the 3DRN benchmark dataset, featuring diverse urban environments with virtual TLS reflection noise, show our algorithm improves precision and recall rates for 3D points in reflective regions by 57.03\% and 31.80\%, respectively. Our method achieves a 9.17\% better outlier detection rate and 5.65\% higher accuracy than leading methods. Access the 3DRN dataset at (https://github.com/Tsuiky/3DRN).

SPABA: A Single-Loop and Probabilistic Stochastic Bilevel Algorithm Achieving Optimal Sample Complexity

While stochastic bilevel optimization methods have been extensively studied for addressing large-scale nested optimization problems in machine learning, it remains an open question whether the optimal complexity bounds for solving bilevel optimization are the same as those in single-level optimization. Our main result resolves this question: SPABA, an adaptation of the PAGE method for nonconvex optimization in (Li et al., 2021) to the bilevel setting, can achieve optimal sample complexity in both the finite-sum and expectation settings. We show the optimality of SPABA by proving that there is no gap in complexity analysis between stochastic bilevel and single-level optimization when implementing PAGE. Notably, as indicated by the results of (Dagr\'eou et al., 2022), there might exist a gap in complexity analysis when implementing other stochastic gradient estimators, like SGD and SAGA. In addition to SPABA, we propose several other single-loop stochastic bilevel algorithms, that either match or improve the state-of-the-art sample complexity results, leveraging our convergence rate and complexity analysis. Numerical experiments demonstrate the superior practical performance of the proposed methods.

Moreau Envelope for Nonconvex Bi-Level Optimization: A Single-loop and Hessian-free Solution Strategy

This work focuses on addressing two major challenges in the context of large-scale nonconvex Bi-Level Optimization (BLO) problems, which are increasingly applied in machine learning due to their ability to model nested structures. These challenges involve ensuring computational efficiency and providing theoretical guarantees. While recent advances in scalable BLO algorithms have primarily relied on lower-level convexity simplification, our work specifically tackles large-scale BLO problems involving nonconvexity in both the upper and lower levels. We simultaneously address computational and theoretical challenges by introducing an innovative single-loop gradient-based algorithm, utilizing the Moreau envelope-based reformulation, and providing non-asymptotic convergence analysis for general nonconvex BLO problems. Notably, our algorithm relies solely on first-order gradient information, enhancing its practicality and efficiency, especially for large-scale BLO learning tasks. We validate our approach's effectiveness through experiments on various synthetic problems, two typical hyper-parameter learning tasks, and a real-world neural architecture search application, collectively demonstrating its superior performance.

A sustainable development perspective on urban-scale roof greening priorities and benefits

Greenspaces are tightly linked to human well-being. Yet, rapid urbanization has exacerbated greenspace exposure inequality and declining human life quality. Roof greening has been recognized as an effective strategy to mitigate these negative impacts. Understanding priorities and benefits is crucial to promoting green roofs. Here, using geospatial big data, we conduct an urban-scale assessment of roof greening at a single building level in Hong Kong from a sustainable development perspective. We identify that 85.3\% of buildings reveal potential and urgent demand for roof greening. We further find green roofs could increase greenspace exposure by \textasciitilde61\% and produce hundreds of millions (HK\$) in economic benefits annually but play a small role in urban heat mitigation (\textasciitilde0.15\degree{C}) and annual carbon emission offsets (\textasciitilde0.8\%). Our study offers a comprehensive assessment of roof greening, which could provide reference for sustainable development in cities worldwide, from data utilization to solutions and findings.

UB-FineNet: Urban Building Fine-grained Classification Network for Open-access Satellite Images

Fine classification of city-scale buildings from satellite remote sensing imagery is a crucial research area with significant implications for urban planning, infrastructure development, and population distribution analysis. However, the task faces big challenges due to low-resolution overhead images acquired from high altitude space-borne platforms and the long-tail sample distribution of fine-grained urban building categories, leading to severe class imbalance problem. To address these issues, we propose a deep network approach to fine-grained classification of urban buildings using open-access satellite images. A Denoising Diffusion Probabilistic Model (DDPM) based super-resolution method is first introduced to enhance the spatial resolution of satellite images, which benefits from domain-adaptive knowledge distillation. Then, a new fine-grained classification network with Category Information Balancing Module (CIBM) and Contrastive Supervision (CS) technique is proposed to mitigate the problem of class imbalance and improve the classification robustness and accuracy. Experiments on Hong Kong data set with 11 fine building types revealed promising classification results with a mean Top-1 accuracy of 60.45\%, which is on par with street-view image based approaches. Extensive ablation study shows that CIBM and CS improve Top-1 accuracy by 2.6\% and 3.5\% compared to the baseline method, respectively. And both modules can be easily inserted into other classification networks and similar enhancements have been achieved. Our research contributes to the field of urban analysis by providing a practical solution for fine classification of buildings in challenging mega city scenarios solely using open-access satellite images. The proposed method can serve as a valuable tool for urban planners, aiding in the understanding of economic, industrial, and population distribution.