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The adele ring of a number field is a central object in modern number theory. Its status as a locally compact topological ring is one of the key reasons why, leading to its widespread use within the Langlands Program. We describe a formal proof that the adele ring of a number field is locally compact in the Lean 4 theorem prover. Our work includes the formalisations of new types, including the completion of a number field at an infinite place and the finite $S$-adele ring, as well as formal proofs that completions of a number field are locally compact and their rings of integers at finite places are compact.

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Linearizability is a commonly accepted correctness criterion for concurrent data structures. However, verifying linearizability of highly concurrent data structures is still a challenging task. In this paper, we present a simple and complete proof technique for verifying linearizability of concurrent stacks. Our proof technique reduces linearizability of concurrent stacks to establishing a set of conditions. These conditions are based on the happened-before order of operations, intuitively express the LIFO semantics and can be proved by simple arguments. Designers of concurrent data structures can easily and quickly learn to use the proof technique. We have successfully applied the method to several challenging concurrent stacks: the TS stack, the HSY stack, and the FA stack, etc.

Despite the success of input transformation-based attacks on boosting adversarial transferability, the performance is unsatisfying due to the ignorance of the discrepancy across models. In this paper, we propose a simple but effective feature augmentation attack (FAUG) method, which improves adversarial transferability without introducing extra computation costs. Specifically, we inject the random noise into the intermediate features of the model to enlarge the diversity of the attack gradient, thereby mitigating the risk of overfitting to the specific model and notably amplifying adversarial transferability. Moreover, our method can be combined with existing gradient attacks to augment their performance further. Extensive experiments conducted on the ImageNet dataset across CNN and transformer models corroborate the efficacy of our method, e.g., we achieve improvement of +26.22% and +5.57% on input transformation-based attacks and combination methods, respectively.

Deep learning-based models are widely deployed in autonomous driving areas, especially the increasingly noticed end-to-end solutions. However, the black-box property of these models raises concerns about their trustworthiness and safety for autonomous driving, and how to debug the causality has become a pressing concern. Despite some existing research on the explainability of autonomous driving, there is currently no systematic solution to help researchers debug and identify the key factors that lead to the final predicted action of end-to-end autonomous driving. In this work, we propose a comprehensive approach to explore and analyze the causality of end-to-end autonomous driving. First, we validate the essential information that the final planning depends on by using controlled variables and counterfactual interventions for qualitative analysis. Then, we quantitatively assess the factors influencing model decisions by visualizing and statistically analyzing the response of key model inputs. Finally, based on the comprehensive study of the multi-factorial end-to-end autonomous driving system, we have developed a strong baseline and a tool for exploring causality in the close-loop simulator CARLA. It leverages the essential input sources to obtain a well-designed model, resulting in highly competitive capabilities. As far as we know, our work is the first to unveil the mystery of end-to-end autonomous driving and turn the black box into a white one. Thorough close-loop experiments demonstrate that our method can be applied to end-to-end autonomous driving solutions for causality debugging. Code will be available at //github.com/bdvisl/DriveInsight.

The proliferation of large language models (LLMs) has sparked widespread and general interest due to their strong language generation capabilities, offering great potential for both industry and research. While previous research delved into the security and privacy issues of LLMs, the extent to which these models can exhibit adversarial behavior remains largely unexplored. Addressing this gap, we investigate whether common publicly available LLMs have inherent capabilities to perturb text samples to fool safety measures, so-called adversarial examples resp.~attacks. More specifically, we investigate whether LLMs are inherently able to craft adversarial examples out of benign samples to fool existing safe rails. Our experiments, which focus on hate speech detection, reveal that LLMs succeed in finding adversarial perturbations, effectively undermining hate speech detection systems. Our findings carry significant implications for (semi-)autonomous systems relying on LLMs, highlighting potential challenges in their interaction with existing systems and safety measures.

The goal of this paper is to investigate the complexity of gradient algorithms when learning sparse functions (juntas). We introduce a type of Statistical Queries ($\mathsf{SQ}$), which we call Differentiable Learning Queries ($\mathsf{DLQ}$), to model gradient queries on a specified loss with respect to an arbitrary model. We provide a tight characterization of the query complexity of $\mathsf{DLQ}$ for learning the support of a sparse function over generic product distributions. This complexity crucially depends on the loss function. For the squared loss, $\mathsf{DLQ}$ matches the complexity of Correlation Statistical Queries $(\mathsf{CSQ})$--potentially much worse than $\mathsf{SQ}$. But for other simple loss functions, including the $\ell_1$ loss, $\mathsf{DLQ}$ always achieves the same complexity as $\mathsf{SQ}$. We also provide evidence that $\mathsf{DLQ}$ can indeed capture learning with (stochastic) gradient descent by showing it correctly describes the complexity of learning with a two-layer neural network in the mean field regime and linear scaling.

Click-through rate (CTR) prediction is a crucial area of research in online advertising. While binary cross entropy (BCE) has been widely used as the optimization objective for treating CTR prediction as a binary classification problem, recent advancements have shown that combining BCE loss with an auxiliary ranking loss can significantly improve performance. However, the full effectiveness of this combination loss is not yet fully understood. In this paper, we uncover a new challenge associated with the BCE loss in scenarios where positive feedback is sparse: the issue of gradient vanishing for negative samples. We introduce a novel perspective on the effectiveness of the auxiliary ranking loss in CTR prediction: it generates larger gradients on negative samples, thereby mitigating the optimization difficulties when using the BCE loss only and resulting in improved classification ability. To validate our perspective, we conduct theoretical analysis and extensive empirical evaluations on public datasets. Additionally, we successfully integrate the ranking loss into Tencent's online advertising system, achieving notable lifts of 0.70% and 1.26% in Gross Merchandise Value (GMV) for two main scenarios. The code is openly accessible at: //github.com/SkylerLinn/Understanding-the-Ranking-Loss.

We consider the problem of determining the manifold $n$-widths of Sobolev and Besov spaces with error measured in the $L_p$-norm. The manifold widths control how efficiently these spaces can be approximated by general non-linear parametric methods with the restriction that the parameter selection and parameterization maps must be continuous. Existing upper and lower bounds only match when the Sobolev or Besov smoothness index $q$ satisfies $q\leq p$ or $1 \leq p \leq 2$. We close this gap and obtain sharp lower bounds for all $1 \leq p,q \leq \infty$ for which a compact embedding holds. A key part of our analysis is to determine the exact value of the manifold widths of finite dimensional $\ell^M_q$-balls in the $\ell_p$-norm when $p\leq q$. Although this result is not new, we provide a new proof and apply it to lower bounding the manifold widths of Sobolev and Besov spaces. Our results show that the Bernstein widths, which are typically used to lower bound the manifold widths, decay asymptotically faster than the manifold widths in many cases.

Evaluating the generalisation capabilities of multimodal models based solely on their performance on out-of-distribution data fails to capture their true robustness. This work introduces a comprehensive evaluation framework that systematically examines the role of instructions and inputs in the generalisation abilities of such models, considering architectural design, input perturbations across language and vision modalities, and increased task complexity. The proposed framework uncovers the resilience of multimodal models to extreme instruction perturbations and their vulnerability to observational changes, raising concerns about overfitting to spurious correlations. By employing this evaluation framework on current Transformer-based multimodal models for robotic manipulation tasks, we uncover limitations and suggest future advancements should focus on architectural and training innovations that better integrate multimodal inputs, enhancing a model's generalisation prowess by prioritising sensitivity to input content over incidental correlations.

Performance evaluation of particular channel coding has been a significant topic in coding theory, often involving the use of bounding techniques. This paper focuses on the new family of capacity-achieving codes, Spinal codes, to provide a comprehensive analysis framework to tightly upper bound the block error rate (BLER) of Spinal codes in the finite block length (FBL) regime. First, we resort to a variant of the Gallager random coding bound to upper bound the BLER of Spinal codes over the fading channel. Then, this paper derives a new bound without resorting to the use of Gallager random coding bound, achieving provable tightness over the wide range of signal-to-noise ratios (SNR). The derived BLER upper bounds in this paper are generalized, facilitating the performance evaluations of Spinal codes over different types of fast fading channels. Over the Rayleigh, Nakagami-m, and Rician fading channels, this paper explicitly derived the BLER upper bounds on Spinal codes as case studies. Based on the bounds, we theoretically reveal that the tail transmission pattern (TTP) for ML-decoded Spinal codes remains optimal in terms of reliability performance. Simulations verify the tightness of the bounds and the insights obtained.

Many organizations use algorithms that have a disparate impact, i.e., the benefits or harms of the algorithm fall disproportionately on certain social groups. Addressing an algorithm's disparate impact can be challenging, however, because it is often unclear whether it is possible to reduce this impact without sacrificing other objectives of the organization, such as accuracy or profit. Establishing the improvability of algorithms with respect to multiple criteria is of both conceptual and practical interest: in many settings, disparate impact that would otherwise be prohibited under US federal law is permissible if it is necessary to achieve a legitimate business interest. The question is how a policy-maker can formally substantiate, or refute, this "necessity" defense. In this paper, we provide an econometric framework for testing the hypothesis that it is possible to improve on the fairness of an algorithm without compromising on other pre-specified objectives. Our proposed test is simple to implement and can be applied under any exogenous constraint on the algorithm space. We establish the large-sample validity and consistency of our test, and illustrate its practical application by evaluating a healthcare algorithm originally considered by Obermeyer et al. (2019). In this application, we reject the null hypothesis that it is not possible to reduce the algorithm's disparate impact without compromising the accuracy of its predictions.

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