The power prior is a popular class of informative priors for incorporating information from historical data. It involves raising the likelihood for the historical data to a power, which acts as discounting parameter. When the discounting parameter is modelled as random, the normalized power prior is recommended. In this work, we prove that the marginal posterior for the discounting parameter for generalized linear models converges to a point mass at zero if there is any discrepancy between the historical and current data, and that it does not converge to a point mass at one when they are fully compatible. In addition, we explore the construction of optimal priors for the discounting parameter in a normalized power prior. In particular, we are interested in achieving the dual objectives of encouraging borrowing when the historical and current data are compatible and limiting borrowing when they are in conflict. We propose intuitive procedures for eliciting the shape parameters of a beta prior for the discounting parameter based on two minimization criteria, the Kullback-Leibler divergence and the mean squared error. Based on the proposed criteria, the optimal priors derived are often quite different from commonly used priors such as the uniform prior.
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Compositional reasoning capabilities are usually considered as fundamental skills to characterize human perception. Recent studies show that current Vision Language Models (VLMs) surprisingly lack sufficient knowledge with respect to such capabilities. To this end, we propose to thoroughly diagnose the composition representations encoded by VLMs, systematically revealing the potential cause for this weakness. Specifically, we propose evaluation methods from a novel game-theoretic view to assess the vulnerability of VLMs on different aspects of compositional understanding, e.g., relations and attributes. Extensive experimental results demonstrate and validate several insights to understand the incapabilities of VLMs on compositional reasoning, which provide useful and reliable guidance for future studies. The deliverables will be updated at //vlms-compositionality-gametheory.github.io/.
Despite being a heavily researched topic, Adversarial Training (AT) is rarely, if ever, deployed in practical AI systems for two primary reasons: (i) the gained robustness is frequently accompanied by a drop in generalization and (ii) generating adversarial examples (AEs) is computationally prohibitively expensive. To address these limitations, we propose SMAAT, a new AT algorithm that leverages the manifold conjecture, stating that off-manifold AEs lead to better robustness while on-manifold AEs result in better generalization. Specifically, SMAAT aims at generating a higher proportion of off-manifold AEs by perturbing the intermediate deepnet layer with the lowest intrinsic dimension. This systematically results in better scalability compared to classical AT as it reduces the PGD chains length required for generating the AEs. Additionally, our study provides, to the best of our knowledge, the first explanation for the difference in the generalization and robustness trends between vision and language models, ie., AT results in a drop in generalization in vision models whereas, in encoder-based language models, generalization either improves or remains unchanged. We show that vision transformers and decoder-based models tend to have low intrinsic dimensionality in the earlier layers of the network (more off-manifold AEs), while encoder-based models have low intrinsic dimensionality in the later layers. We demonstrate the efficacy of SMAAT; on several tasks, including robustifying (i) sentiment classifiers, (ii) safety filters in decoder-based models, and (iii) retrievers in RAG setups. SMAAT requires only 25-33% of the GPU time compared to standard AT, while significantly improving robustness across all applications and maintaining comparable generalization.
The criticality problem in nuclear engineering asks for the principal eigen-pair of a Boltzmann operator describing neutron transport in a reactor core. Being able to reliably design, and control such reactors requires assessing these quantities within quantifiable accuracy tolerances. In this paper we propose a paradigm that deviates from the common practice of approximately solving the corresponding spectral problem with a fixed, presumably sufficiently fine discretization. Instead, the present approach is based on first contriving iterative schemes, formulated in function space, that are shown to converge at a quantitative rate without assuming any a priori excess regularity properties, and that exploit only properties of the optical parameters in the underlying radiative transfer model. We develop the analytical and numerical tools for approximately realizing each iteration step withing judiciously chosen accuracy tolerances, verified by a posteriori estimates, so as to still warrant quantifiable convergence to the exact eigen-pair. This is carried out in full first for a Newton scheme. Since this is only locally convergent we analyze in addition the convergence of a power iteration in function space to produce sufficiently accurate initial guesses. Here we have to deal with intrinsic difficulties posed by compact but unsymmetric operators preventing standard arguments used in the finite dimensional case. Our main point is that we can avoid any condition on an initial guess to be already in a small neighborhood of the exact solution. We close with a discussion of remaining intrinsic obstructions to a certifiable numerical implementation, mainly related to not knowing the gap between the principal eigenvalue and the next smaller one in modulus.
Recent AI systems have shown extremely powerful performance, even surpassing human performance, on various tasks such as information retrieval, language generation, and image generation based on large language models (LLMs). At the same time, there are diverse safety risks that can cause the generation of malicious contents by circumventing the alignment in LLMs, which are often referred to as jailbreaking. However, most of the previous works only focused on the text-based jailbreaking in LLMs, and the jailbreaking of the text-to-image (T2I) generation system has been relatively overlooked. In this paper, we first evaluate the safety of the commercial T2I generation systems, such as ChatGPT, Copilot, and Gemini, on copyright infringement with naive prompts. From this empirical study, we find that Copilot and Gemini block only 12\% and 17\% of the attacks with naive prompts, respectively, while ChatGPT blocks 84\% of them. Then, we further propose a stronger automated jailbreaking pipeline for T2I generation systems, which produces prompts that bypass their safety guards. Our automated jailbreaking framework leverages an LLM optimizer to generate prompts to maximize degree of violation from the generated images without any weight updates or gradient computation. Surprisingly, our simple yet effective approach successfully jailbreaks the ChatGPT with 11.0\% block rate, making it generate copyrighted contents in 76\% of the time. Finally, we explore various defense strategies, such as post-generation filtering and machine unlearning techniques, but found that they were inadequate, which suggests the necessity of stronger defense mechanisms.
In the rapidly evolving field of autonomous driving, precise segmentation of LiDAR data is crucial for understanding complex 3D environments. Traditional approaches often rely on disparate, standalone codebases, hindering unified advancements and fair benchmarking across models. To address these challenges, we introduce MMDetection3D-lidarseg, a comprehensive toolbox designed for the efficient training and evaluation of state-of-the-art LiDAR segmentation models. We support a wide range of segmentation models and integrate advanced data augmentation techniques to enhance robustness and generalization. Additionally, the toolbox provides support for multiple leading sparse convolution backends, optimizing computational efficiency and performance. By fostering a unified framework, MMDetection3D-lidarseg streamlines development and benchmarking, setting new standards for research and application. Our extensive benchmark experiments on widely-used datasets demonstrate the effectiveness of the toolbox. The codebase and trained models have been publicly available, promoting further research and innovation in the field of LiDAR segmentation for autonomous driving.
Fairness is a critical objective in policy design and algorithmic decision-making. Identifying the causal pathways of unfairness requires knowledge of the underlying structural causal model, which may be incomplete or unavailable. This limits the practicality of causal fairness analysis in complex or low-knowledge domains. To mitigate this practicality gap, we advocate for developing efficient causal discovery methods for fairness applications. To this end, we introduce local discovery for direct discrimination (LD3): a polynomial-time algorithm that recovers structural evidence of direct discrimination. LD3 performs a linear number of conditional independence tests with respect to variable set size. Moreover, we propose a graphical criterion for identifying the weighted controlled direct effect (CDE), a qualitative measure of direct discrimination. We prove that this criterion is satisfied by the knowledge returned by LD3, increasing the accessibility of the weighted CDE as a causal fairness measure. Taking liver transplant allocation as a case study, we highlight the potential impact of LD3 for modeling fairness in complex decision systems. Results on real-world data demonstrate more plausible causal relations than baselines, which took 197x to 5870x longer to execute.
We consider limit probabilities of first order properties in random graphs with a given degree sequence. Under mild conditions on the degree sequence, we show that the closure set of limit probabilities is a finite union of closed intervals. Moreover, we characterize the degree sequences for which this closure set is the interval $[0,1]$, a property that is intimately related with the probability that the random graph is acyclic. As a side result, we compile a full description of the cycle distribution of random graphs and study their fragment (disjoint union of unicyclic components) in the subcritical regime. Finally, we amend the proof of the existence of limit probabilities for first order properties in random graphs with a given degree sequence; this result was already claimed by Lynch~[IEEE LICS 2003] but his proof contained some inaccuracies.
Reliably measuring the collinearity of bivariate data is crucial in statistics, particularly for time-series analysis or ongoing studies in which incoming observations can significantly impact current collinearity estimates. Leveraging identities from Welford's online algorithm for sample variance, we develop a rigorous theoretical framework for analyzing the maximal change to the Pearson correlation coefficient and its p-value that can be induced by additional data. Further, we show that the resulting optimization problems yield elegant closed-form solutions that can be accurately computed by linear- and constant-time algorithms. Our work not only creates new theoretical avenues for robust correlation measures, but also has broad practical implications for disciplines that span econometrics, operations research, clinical trials, climatology, differential privacy, and bioinformatics. Software implementations of our algorithms in Cython-wrapped C are made available at //github.com/marc-harary/sensitivity for reproducibility, practical deployment, and future theoretical development.
Machine learning models can be trained with formal privacy guarantees via differentially private optimizers such as DP-SGD. In this work, we study such privacy guarantees when the adversary only accesses the final model, i.e., intermediate model updates are not released. In the existing literature, this hidden state threat model exhibits a significant gap between the lower bound provided by empirical privacy auditing and the theoretical upper bound provided by privacy accounting. To challenge this gap, we propose to audit this threat model with adversaries that craft a gradient sequence to maximize the privacy loss of the final model without accessing intermediate models. We demonstrate experimentally how this approach consistently outperforms prior attempts at auditing the hidden state model. When the crafted gradient is inserted at every optimization step, our results imply that releasing only the final model does not amplify privacy, providing a novel negative result. On the other hand, when the crafted gradient is not inserted at every step, we show strong evidence that a privacy amplification phenomenon emerges in the general non-convex setting (albeit weaker than in convex regimes), suggesting that existing privacy upper bounds can be improved.
The number of artificial intelligence algorithms for learning causal models from data is growing rapidly. Most ``causal discovery'' or ``causal structure learning'' algorithms are primarily validated through simulation studies. However, no widely accepted simulation standards exist and publications often report conflicting performance statistics -- even when only considering publications that simulate data from linear models. In response, several manuscripts have criticized a popular simulation design for validating algorithms in the linear case. We propose a new simulation design for generating linear models for directed acyclic graphs (DAGs): the DAG-adaptation of the Onion (DaO) method. DaO simulations are fundamentally different from existing simulations because they prioritize the distribution of correlation matrices rather than the distribution of linear effects. Specifically, the DaO method uniformly samples the space of all correlation matrices consistent with (i.e. Markov to) a DAG. We also discuss how to sample DAGs and present methods for generating DAGs with scale-free in-degree or out-degree. We compare the DaO method against two alternative simulation designs and provide implementations of the DaO method in Python and R: //github.com/bja43/DaO_simulation. We advocate for others to adopt DaO simulations as a fair universal benchmark.
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