Recent empirical evidence indicates that many machine learning applications involve heavy-tailed gradient noise, which challenges the standard assumptions of bounded variance in stochastic optimization. Gradient clipping has emerged as a popular tool to handle this heavy-tailed noise, as it achieves good performance in this setting both theoretically and practically. However, our current theoretical understanding of non-convex gradient clipping has three main shortcomings. First, the theory hinges on large, increasing clipping thresholds, which are in stark contrast to the small constant clipping thresholds employed in practice. Second, clipping thresholds require knowledge of problem-dependent parameters to guarantee convergence. Lastly, even with this knowledge, current sampling complexity upper bounds for the method are sub-optimal in nearly all parameters. To address these issues, we study convergence of Normalized SGD (NSGD). First, we establish a parameter-free sample complexity for NSGD of $\mathcal{O}\left(\varepsilon^{-\frac{2p}{p-1}}\right)$ to find an $\varepsilon$-stationary point. Furthermore, we prove tightness of this result, by providing a matching algorithm-specific lower bound. In the setting where all problem parameters are known, we show this complexity is improved to $\mathcal{O}\left(\varepsilon^{-\frac{3p-2}{p-1}}\right)$, matching the previously known lower bound for all first-order methods in all problem dependent parameters. Finally, we establish high-probability convergence of NSGD with a mild logarithmic dependence on the failure probability. Our work complements the studies of gradient clipping under heavy tailed noise improving the sample complexities of existing algorithms and offering an alternative mechanism to achieve high probability convergence.

Model merging has gained significant attention as a cost-effective approach to integrate multiple single-task fine-tuned models into a unified one that can perform well on multiple tasks. However, existing model merging techniques primarily focus on resolving conflicts between task-specific models, they often overlook potential security threats, particularly the risk of backdoor attacks in the open-source model ecosystem. In this paper, we first investigate the vulnerabilities of existing model merging methods to backdoor attacks, identifying two critical challenges: backdoor succession and backdoor transfer. To address these issues, we propose a novel Defense-Aware Merging (DAM) approach that simultaneously mitigates task interference and backdoor vulnerabilities. Specifically, DAM employs a meta-learning-based optimization method with dual masks to identify a shared and safety-aware subspace for model merging. These masks are alternately optimized: the Task-Shared mask identifies common beneficial parameters across tasks, aiming to preserve task-specific knowledge while reducing interference, while the Backdoor-Detection mask isolates potentially harmful parameters to neutralize security threats. This dual-mask design allows us to carefully balance the preservation of useful knowledge and the removal of potential vulnerabilities. Compared to existing merging methods, DAM achieves a more favorable balance between performance and security, reducing the attack success rate by 2-10 percentage points while sacrificing only about 1% in accuracy. Furthermore, DAM exhibits robust performance and broad applicability across various types of backdoor attacks and the number of compromised models involved in the merging process. We will release the codes and models soon.

Traditional molecule generation methods often rely on sequence or graph-based representations, which can limit their expressive power or require complex permutation-equivariant architectures. This paper introduces a novel paradigm for learning molecule generative models based on functional representations. Specifically, we propose Molecular Implicit Neural Generation (MING), a diffusion-based model that learns molecular distributions in function space. Unlike standard diffusion processes in data space, MING employs a novel functional denoising probabilistic process, which jointly denoises the information in both the function's input and output spaces by leveraging an expectation-maximization procedure for latent implicit neural representations of data. This approach allows for a simple yet effective model design that accurately captures underlying function distributions. Experimental results on molecule-related datasets demonstrate MING's superior performance and ability to generate plausible molecular samples, surpassing state-of-the-art data-space methods while offering a more streamlined architecture and significantly faster generation times.

Black-box optimization algorithms have been widely used in various machine learning problems, including reinforcement learning and prompt fine-tuning. However, directly optimizing the training loss value, as commonly done in existing black-box optimization methods, could lead to suboptimal model quality and generalization performance. To address those problems in black-box optimization, we propose a novel Sharpness-Aware Black-box Optimization (SABO) algorithm, which applies a sharpness-aware minimization strategy to improve the model generalization. Specifically, the proposed SABO method first reparameterizes the objective function by its expectation over a Gaussian distribution. Then it iteratively updates the parameterized distribution by approximated stochastic gradients of the maximum objective value within a small neighborhood around the current solution in the Gaussian distribution space. Theoretically, we prove the convergence rate and generalization bound of the proposed SABO algorithm. Empirically, extensive experiments on the black-box prompt fine-tuning tasks demonstrate the effectiveness of the proposed SABO method in improving model generalization performance.

Search-based software testing (SBST) is a widely adopted technique for testing complex systems with large input spaces, such as Deep Learning-enabled (DL-enabled) systems. Many SBST techniques focus on Pareto-based optimization, where multiple objectives are optimized in parallel to reveal failures. However, it is important to ensure that identified failures are spread throughout the entire failure-inducing area of a search domain and not clustered in a sub-region. This ensures that identified failures are semantically diverse and reveal a wide range of underlying causes. In this paper, we present a theoretical argument explaining why testing based on Pareto optimization is inadequate for covering failure-inducing areas within a search domain. We support our argument with empirical results obtained by applying two widely used types of Pareto-based optimization techniques, namely NSGA-II (an evolutionary algorithm) and OMOPSO (a swarm-based Pareto-optimization algorithm), to two DL-enabled systems: an industrial Automated Valet Parking (AVP) system and a system for classifying handwritten digits. We measure the coverage of failure-revealing test inputs in the input space using a metric that we refer to as the Coverage Inverted Distance quality indicator. Our results show that NSGA-II-based search and OMOPSO are not more effective than a na\"ive random search baseline in covering test inputs that reveal failures. The replication package for this study is available in a GitHub repository.

The content selection problem of digital services is often modeled as a decision-process where a service chooses, over multiple rounds, an arm to pull from a set of arms that each return a certain reward. This classical model does not account for the possibility that users disengage when dissatisfied and thus fails to capture an important trade-off between choosing content that promotes future engagement versus immediate reward. In this work, we introduce a model for the content selection problem where dissatisfied users may disengage and where the content that maximizes immediate reward does not necessarily maximize the odds of future user engagement. We show that when the relationship between each arm's expected reward and effect on user satisfaction are linearly related, an optimal content selection policy can be computed efficiently with dynamic programming under natural assumptions about the complexity of the users' engagement patterns. Moreover, we show that in an online learning setting where users with unknown engagement patterns arrive, there is a variant of Hedge that attains a $\tfrac 12$-competitive ratio regret bound. We also use our model to identify key primitives that determine how digital services should weigh engagement against revenue. For example, when it is more difficult for users to rejoin a service they are disengaged from, digital services naturally see a reduced payoff but user engagement may -- counterintuitively -- increase.

Partial-differential-equation (PDE)-constrained optimization is a well-worn technique for acquiring optimal parameters of systems governed by PDEs. However, this approach is limited to providing a single set of optimal parameters per optimization. Given a differentiable PDE solver, if the free parameters are reparameterized as the output of a neural network, that neural network can be trained to learn a map from a probability distribution to the distribution of optimal parameters. This proves useful in the case where there are many well performing local minima for the PDE. We apply this technique to train a neural network that generates optimal parameters that minimize laser-plasma instabilities relevant to laser fusion and show that the neural network generates many well performing and diverse minima.

Real-time aerial image segmentation plays an important role in the environmental perception of Uncrewed Aerial Vehicles (UAVs). We introduce BlabberSeg, an optimized Vision-Language Model built on CLIPSeg for on-board, real-time processing of aerial images by UAVs. BlabberSeg improves the efficiency of CLIPSeg by reusing prompt and model features, reducing computational overhead while achieving real-time open-vocabulary aerial segmentation. We validated BlabberSeg in a safe landing scenario using the Dynamic Open-Vocabulary Enhanced SafE-Landing with Intelligence (DOVESEI) framework, which uses visual servoing and open-vocabulary segmentation. BlabberSeg reduces computational costs significantly, with a speed increase of 927.41% (16.78 Hz) on a NVIDIA Jetson Orin AGX (64GB) compared with the original CLIPSeg (1.81Hz), achieving real-time aerial segmentation with negligible loss in accuracy (2.1% as the ratio of the correctly segmented area with respect to CLIPSeg). BlabberSeg's source code is open and available online.

Developing efficient traffic models is essential for optimizing transportation systems, yet current approaches remain time-intensive and susceptible to human errors due to their reliance on manual processes. Traditional workflows involve exhaustive literature reviews, formula optimization, and iterative testing, leading to inefficiencies in research. In response, we introduce the Traffic Research Agent (TR-Agent), an AI-driven system designed to autonomously develop and refine traffic models through an iterative, closed-loop process. Specifically, we divide the research pipeline into four key stages: idea generation, theory formulation, theory evaluation, and iterative optimization; and construct TR-Agent with four corresponding modules: Idea Generator, Code Generator, Evaluator, and Analyzer. Working in synergy, these modules retrieve knowledge from external resources, generate novel ideas, implement and debug models, and finally assess them on the evaluation datasets. Furthermore, the system continuously refines these models based on iterative feedback, enhancing research efficiency and model performance. Experimental results demonstrate that TR-Agent achieves significant performance improvements across multiple traffic models, including the Intelligent Driver Model (IDM) for car following, the MOBIL lane-changing model, and the Lighthill-Whitham-Richards (LWR) traffic flow model. Additionally, TR-Agent provides detailed explanations for its optimizations, allowing researchers to verify and build upon its improvements easily. This flexibility makes the framework a powerful tool for researchers in transportation and beyond. To further support research and collaboration, we have open-sourced both the code and data used in our experiments, facilitating broader access and enabling continued advancements in the field.

RL-based techniques can be employed to search for prompts that, when fed into a target language model, maximize a set of user-specified reward functions. However, in many target applications, the natural reward functions are in tension with one another -- for example, content preservation vs. style matching in style transfer tasks. Current techniques focus on maximizing the average of reward functions, which does not necessarily lead to prompts that achieve balance across rewards -- an issue that has been well-studied in the multi-objective and robust optimization literature. In this paper, we conduct an empirical comparison of several existing multi-objective optimization techniques adapted to this new setting: RL-based discrete prompt optimization. We compare two methods optimizing the volume of the Pareto reward surface and one method that chooses an update direction that benefits all rewards simultaneously. We evaluate performance on two NLP tasks: style transfer and machine translation, each using three competing reward functions. Our experiments demonstrate that multi-objective methods that directly optimize the volume of the Pareto reward surface perform better and achieve a better balance of all rewards than those that attempt to find monotonic update directions.