In this work, we offer a theoretical analysis of two modern optimization techniques for training large and complex models: (i) adaptive optimization algorithms, such as Adam, and (ii) the model exponential moving average (EMA). Specifically, we demonstrate that a clipped version of Adam with model EMA achieves the optimal convergence rates in various nonconvex optimization settings, both smooth and nonsmooth. Moreover, when the scale varies significantly across different coordinates, we demonstrate that the coordinate-wise adaptivity of Adam is provably advantageous. Notably, unlike previous analyses of Adam, our analysis crucially relies on its core elements -- momentum and discounting factors -- as well as model EMA, motivating their wide applications in practice.

Intelligent agents must be generalists, capable of quickly adapting to various tasks. In reinforcement learning (RL), model-based RL learns a dynamics model of the world, in principle enabling transfer to arbitrary reward functions through planning. However, autoregressive model rollouts suffer from compounding error, making model-based RL ineffective for long-horizon problems. Successor features offer an alternative by modeling a policy's long-term state occupancy, reducing policy evaluation under new tasks to linear reward regression. Yet, policy improvement with successor features can be challenging. This work proposes a novel class of models, i.e., generalized occupancy models (GOMs), that learn a distribution of successor features from a stationary dataset, along with a policy that acts to realize different successor features. These models can quickly select the optimal action for arbitrary new tasks. By directly modeling long-term outcomes in the dataset, GOMs avoid compounding error while enabling rapid transfer across reward functions. We present a practical instantiation of GOMs using diffusion models and show their efficacy as a new class of transferable models, both theoretically and empirically across various simulated robotics problems.

Institute for Particle Physics Phenomenology, Department of Physics, Durham University, Durham DH1 3LE, U.K. We propose symbolic regression as a powerful tool for studying Beyond the Standard Model physics. As a benchmark model, we consider the so-called Constrained Minimal Supersymmetric Standard Model, which has a four-dimensional parameter space defined at the GUT scale. We provide a set of analytical expressions that reproduce three low-energy observables of interest in terms of the parameters of the theory: the Higgs mass, the contribution to the anomalous magnetic moment of the muon, and the cold dark matter relic density. To demonstrate the power of the approach, we employ the symbolic expressions in a global fits analysis to derive the posterior probability densities of the parameters, which are obtained extremely rapidly in comparison with conventional methods. The chief test of any proposal for Beyond the Standard To avoid this bottleneck, it is natural to turn to Model (BSM) physics is to confront it with experimental machine learning to bypass the computation chain or data.

Continual Test-Time Adaptation (CTTA) is an emerging and challenging task where a model trained in a source domain must adapt to continuously changing conditions during testing, without access to the original source data. CTTA is prone to error accumulation due to uncontrollable domain shifts, leading to blurred decision boundaries between categories. Existing CTTA methods primarily focus on suppressing domain shifts, which proves inadequate during the unsupervised test phase. In contrast, we introduce a novel approach that guides rather than suppresses these shifts. Specifically, we propose $\textbf{C}$ontrollable $\textbf{Co}$ntinual $\textbf{T}$est-$\textbf{T}$ime $\textbf{A}$daptation (C-CoTTA), which explicitly prevents any single category from encroaching on others, thereby mitigating the mutual influence between categories caused by uncontrollable shifts. Moreover, our method reduces the sensitivity of model to domain transformations, thereby minimizing the magnitude of category shifts. Extensive quantitative experiments demonstrate the effectiveness of our method, while qualitative analyses, such as t-SNE plots, confirm the theoretical validity of our approach.

Existing first-order optimizers mainly include two branches: classical optimizers represented by Stochastic Gradient Descent (SGD) and adaptive optimizers represented by Adam, along with their many derivatives. The debate over the merits and demerits of these two types of optimizers has persisted for a decade. In practical experience, it is generally considered that SGD is more suitable for tasks like Computer Vision(CV), while adaptive optimizers are widely used in tasks with sparse gradients, such as Large Language Models(LLM). Although adaptive optimizers always offer better convergence speeds in almost all tasks, they can lead to over-fitting in some cases, resulting in poorer generalization performance compared to SGD in certain tasks. Even in Large Language Models, Adam continues to face challenges, and its original strategy may not always have an advantage due to the introduction of improvements such as gradient clipping. With a wide variety of optimization methods available, it is essential to introduce a unified, interpretable theory. This paper will discuss under the framework of first-order optimizers and, through the intervention of the balance theory, will for the first time propose a unified strategy to integrate all first-order optimization methods.

Graph Prompt Learning (GPL) bridges significant disparities between pretraining and downstream applications to alleviate the knowledge transfer bottleneck in real-world graph learning. While GPL offers superior effectiveness in graph knowledge transfer and computational efficiency, the security risks posed by backdoor poisoning effects embedded in pretrained models remain largely unexplored. Our study provides a comprehensive analysis of GPL's vulnerability to backdoor attacks. We introduce \textit{CrossBA}, the first cross-context backdoor attack against GPL, which manipulates only the pretraining phase without requiring knowledge of downstream applications. Our investigation reveals both theoretically and empirically that tuning trigger graphs, combined with prompt transformations, can seamlessly transfer the backdoor threat from pretrained encoders to downstream applications. Through extensive experiments involving 3 representative GPL methods across 5 distinct cross-context scenarios and 5 benchmark datasets of node and graph classification tasks, we demonstrate that \textit{CrossBA} consistently achieves high attack success rates while preserving the functionality of downstream applications over clean input. We also explore potential countermeasures against \textit{CrossBA} and conclude that current defenses are insufficient to mitigate \textit{CrossBA}. Our study highlights the persistent backdoor threats to GPL systems, raising trustworthiness concerns in the practices of GPL techniques.

We consider a semi-supervised classification problem with non-stationary label-shift in which we observe a labelled data set followed by a sequence of unlabelled covariate vectors in which the marginal probabilities of the class labels may change over time. Our objective is to predict the corresponding class-label for each covariate vector, without ever observing the ground-truth labels, beyond the initial labelled data set. Previous work has demonstrated the potential of sophisticated variants of online gradient descent to perform competitively with the optimal dynamic strategy (Bai et al. 2022). In this work we explore an alternative approach grounded in statistical methods for adaptive transfer learning. We demonstrate the merits of this alternative methodology by establishing a high-probability regret bound on the test error at any given individual test-time, which adapt automatically to the unknown dynamics of the marginal label probabilities. Further more, we give bounds on the average dynamic regret which match the average guarantees of the online learning perspective for any given time interval.

Adaptive moment estimation (Adam), as a Stochastic Gradient Descent (SGD) variant, has gained widespread popularity in federated learning (FL) due to its fast convergence. However, federated Adam (FedAdam) algorithms suffer from a threefold increase in uplink communication overhead compared to federated SGD (FedSGD) algorithms, which arises from the necessity to transmit both local model updates and first and second moment estimates from distributed devices to the centralized server for aggregation. Driven by this issue, we propose a novel sparse FedAdam algorithm called FedAdam-SSM, wherein distributed devices sparsify the updates of local model parameters and moment estimates and subsequently upload the sparse representations to the centralized server. To further reduce the communication overhead, the updates of local model parameters and moment estimates incorporate a shared sparse mask (SSM) into the sparsification process, eliminating the need for three separate sparse masks. Theoretically, we develop an upper bound on the divergence between the local model trained by FedAdam-SSM and the desired model trained by centralized Adam, which is related to sparsification error and imbalanced data distribution. By minimizing the divergence bound between the model trained by FedAdam-SSM and centralized Adam, we optimize the SSM to mitigate the learning performance degradation caused by sparsification error. Additionally, we provide convergence bounds for FedAdam-SSM in both convex and non-convex objective function settings, and investigate the impact of local epoch, learning rate and sparsification ratio on the convergence rate of FedAdam-SSM. Experimental results show that FedAdam-SSM outperforms baselines in terms of convergence rate (over 1.1$\times$ faster than the sparse FedAdam baselines) and test accuracy (over 14.5\% ahead of the quantized FedAdam baselines).

Reinforcement learning has traditionally focused on learning state-dependent policies to solve optimal control problems in a closed-loop fashion. In this work, we introduce the paradigm of open-loop reinforcement learning where a fixed action sequence is learned instead. We present three new algorithms: one robust model-based method and two sample-efficient model-free methods. Rather than basing our algorithms on Bellman's equation from dynamic programming, our work builds on Pontryagin's principle from the theory of open-loop optimal control. We provide convergence guarantees and evaluate all methods empirically on a pendulum swing-up task, as well as on two high-dimensional MuJoCo tasks, demonstrating remarkable performance compared to existing baselines.

Machine unlearning (MU) addresses privacy concerns by removing information of `forgetting data' samples from trained models. Typically, evaluating MU methods involves comparing unlearned models to those retrained from scratch without forgetting data, using metrics such as membership inference attacks (MIA) and accuracy measurements. These evaluations implicitly assume that if the output logits of the unlearned and retrained models are similar, the unlearned model has successfully forgotten the data. Here, we challenge if this assumption is valid. In particular, we conduct a simple experiment of training only the last layer of a given original model using a novel masked-distillation technique while keeping the rest fixed. Surprisingly, simply altering the last layer yields favorable outcomes in the existing evaluation metrics, while the model does not successfully unlearn the samples or classes. For better evaluating the MU methods, we propose a metric that quantifies the residual information about forgetting data samples in intermediate features using mutual information, called information difference index or IDI for short. The IDI provides a comprehensive evaluation of MU methods by efficiently analyzing the internal structure of DNNs. Our metric is scalable to large datasets and adaptable to various model architectures. Additionally, we present COLapse-and-Align (COLA), a simple contrastive-based method that effectively unlearns intermediate features.