Regularization in modern machine learning is crucial, and it can take various forms in algorithmic design: training set, model family, error function, regularization terms, and optimizations. In particular, the learning rate, which can be interpreted as a temperature-like parameter within the statistical mechanics of learning, plays a crucial role in neural network training. Indeed, many widely adopted training strategies basically just define the decay of the learning rate over time. This process can be interpreted as decreasing a temperature, using either a global learning rate (for the entire model) or a learning rate that varies for each parameter. This paper proposes TempBalance, a straightforward yet effective layer-wise learning rate method. TempBalance is based on Heavy-Tailed Self-Regularization (HT-SR) Theory, an approach which characterizes the implicit self-regularization of different layers in trained models. We demonstrate the efficacy of using HT-SR-motivated metrics to guide the scheduling and balancing of temperature across all network layers during model training, resulting in improved performance during testing. We implement TempBalance on CIFAR10, CIFAR100, SVHN, and TinyImageNet datasets using ResNets, VGGs, and WideResNets with various depths and widths. Our results show that TempBalance significantly outperforms ordinary SGD and carefully-tuned spectral norm regularization. We also show that TempBalance outperforms a number of state-of-the-art optimizers and learning rate schedulers.

Ray tracing (RT) is instrumental in 6G research in order to generate spatially-consistent and environment-specific channel impulse responses (CIRs). While acquiring accurate scene geometries is now relatively straightforward, determining material characteristics requires precise calibration using channel measurements. We therefore introduce a novel gradient-based calibration method, complemented by differentiable parametrizations of material properties, scattering and antenna patterns. Our method seamlessly integrates with differentiable ray tracers that enable the computation of derivatives of CIRs with respect to these parameters. Essentially, we approach field computation as a large computational graph wherein parameters are trainable akin to weights of a neural network (NN). We have validated our method using both synthetic data and real-world indoor channel measurements, employing a distributed multiple-input multiple-output (MIMO) channel sounder.

ZX-diagrams are a powerful graphical language for the description of quantum processes with applications in fundamental quantum mechanics, quantum circuit optimization, tensor network simulation, and many more. The utility of ZX-diagrams relies on a set of local transformation rules that can be applied to them without changing the underlying quantum process they describe. These rules can be exploited to optimize the structure of ZX-diagrams for a range of applications. However, finding an optimal sequence of transformation rules is generally an open problem. In this work, we bring together ZX-diagrams with reinforcement learning, a machine learning technique designed to discover an optimal sequence of actions in a decision-making problem and show that a trained reinforcement learning agent can significantly outperform other optimization techniques like a greedy strategy or simulated annealing. The use of graph neural networks to encode the policy of the agent enables generalization to diagrams much bigger than seen during the training phase.

This paper proposes a novel, data-agnostic, model poisoning attack on Federated Learning (FL), by designing a new adversarial graph autoencoder (GAE)-based framework. The attack requires no knowledge of FL training data and achieves both effectiveness and undetectability. By listening to the benign local models and the global model, the attacker extracts the graph structural correlations among the benign local models and the training data features substantiating the models. The attacker then adversarially regenerates the graph structural correlations while maximizing the FL training loss, and subsequently generates malicious local models using the adversarial graph structure and the training data features of the benign ones. A new algorithm is designed to iteratively train the malicious local models using GAE and sub-gradient descent. The convergence of FL under attack is rigorously proved, with a considerably large optimality gap. Experiments show that the FL accuracy drops gradually under the proposed attack and existing defense mechanisms fail to detect it. The attack can give rise to an infection across all benign devices, making it a serious threat to FL.

Machine learning models are known to memorize private data to reduce their training loss, which can be inadvertently exploited by privacy attacks such as model inversion and membership inference. To protect against these attacks, differential privacy (DP) has become the de facto standard for privacy-preserving machine learning, particularly those popular training algorithms using stochastic gradient descent, such as DPSGD. Nonetheless, DPSGD still suffers from severe utility loss due to its slow convergence. This is partially caused by the random sampling, which brings bias and variance to the gradient, and partially by the Gaussian noise, which leads to fluctuation of gradient updates. Our key idea to address these issues is to apply selective updates to the model training, while discarding those useless or even harmful updates. Motivated by this, this paper proposes DPSUR, a Differentially Private training framework based on Selective Updates and Release, where the gradient from each iteration is evaluated based on a validation test, and only those updates leading to convergence are applied to the model. As such, DPSUR ensures the training in the right direction and thus can achieve faster convergence than DPSGD. The main challenges lie in two aspects -- privacy concerns arising from gradient evaluation, and gradient selection strategy for model update. To address the challenges, DPSUR introduces a clipping strategy for update randomization and a threshold mechanism for gradient selection. Experiments conducted on MNIST, FMNIST, CIFAR-10, and IMDB datasets show that DPSUR significantly outperforms previous works in terms of convergence speed and model utility.

The emergence of In-Context Learning (ICL) in LLMs remains a significant phenomenon with little understanding. To explain ICL, recent studies try to shed light on ICL by connecting it to Gradient Descent (GD). However, the question is, do these hold up in practice in actual pre-trained models? We highlight the limiting assumptions in prior works that make their context considerably different from the practical context in which language models are trained. For example, the theoretical hand-constructed weights used in these studies have properties that don't match those of real LLMs. Furthermore, their experimental verification uses \emph{ICL objective} (training models explicitly for ICL), which differs from the emergent ICL in the wild. We also look for evidence in real models. We observe that ICL and GD have different sensitivity to the order in which they observe demonstrations. Finally, we probe and compare the ICL vs. GD hypothesis in a natural setting. We conduct comprehensive empirical analyses on language models pre-trained on natural data (LLaMa-7B). Our comparisons of three performance metrics highlight the inconsistent behavior of ICL and GD as a function of various factors such as datasets, models, and the number of demonstrations. We observe that ICL and GD modify the output distribution of language models differently. These results indicate that the equivalence between ICL and GD remains an open hypothesis and calls for further studies.

Model-agnostic meta-learning (MAML) is one of the most successful meta-learning algorithms. It has a bi-level optimization structure where the outer-loop process learns a shared initialization and the inner-loop process optimizes task-specific weights. Although MAML relies on the standard gradient descent in the inner-loop, recent studies have shown that controlling the inner-loop's gradient descent with a meta-learned preconditioner can be beneficial. Existing preconditioners, however, cannot simultaneously adapt in a task-specific and path-dependent way. Additionally, they do not satisfy the Riemannian metric condition, which can enable the steepest descent learning with preconditioned gradient. In this study, we propose Geometry-Adaptive Preconditioned gradient descent (GAP) that can overcome the limitations in MAML; GAP can efficiently meta-learn a preconditioner that is dependent on task-specific parameters, and its preconditioner can be shown to be a Riemannian metric. Thanks to the two properties, the geometry-adaptive preconditioner is effective for improving the inner-loop optimization. Experiment results show that GAP outperforms the state-of-the-art MAML family and preconditioned gradient descent-MAML (PGD-MAML) family in a variety of few-shot learning tasks. Code is available at: https://github.com/Suhyun777/CVPR23-GAP.

Federated Learning (FL) has become an emerging norm for distributed model training, which enables multiple devices cooperatively to train a shared model utilizing their own datasets scheduled by a central server while keeping private data localized. However, during the training process, the non-independent-and-identically-distributed (Non-IID) data generated on heterogeneous clients and frequent communication across participants may significantly influence the training performance, slow down the convergent rate, and increase communication consumption. In this paper, we ameliorate the standard stochastic gradient descent approach by introducing the aggregated gradients at each local update epoch and propose an adaptive learning rate iterative algorithm that further takes the deviation between the local parameter and global parameter into account. The aforementioned adaptive learning rate design mechanism requires local information of all clients, which is challenging as there is no communication during the local update epochs. To obtain a decentralized adaptive learning rate for each client, we introduce the mean-field approach by utilizing two mean-field terms to estimate the average local parameters and gradients respectively without exchanging clients' local information with each other over time. Through theoretical analysis, we prove that our method can provide the convergence guarantee for model training and derive a convergent upper bound for the client drifting term. Extensive numerical results show that our proposed framework is superior to the state-of-the-art FL schemes in both model accuracy and convergent rate on real-world datasets with IID and Non-IID data distribution.

We prove closed-form equations for the exact high-dimensional asymptotics of a family of first order gradient-based methods, learning an estimator (e.g. M-estimator, shallow neural network, ...) from observations on Gaussian data with empirical risk minimization. This includes widely used algorithms such as stochastic gradient descent (SGD) or Nesterov acceleration. The obtained equations match those resulting from the discretization of dynamical mean-field theory (DMFT) equations from statistical physics when applied to gradient flow. Our proof method allows us to give an explicit description of how memory kernels build up in the effective dynamics, and to include non-separable update functions, allowing datasets with non-identity covariance matrices. Finally, we provide numerical implementations of the equations for SGD with generic extensive batch-size and with constant learning rates.

The graduated optimization approach is a heuristic method for finding globally optimal solutions for nonconvex functions and has been theoretically analyzed in several studies. This paper defines a new family of nonconvex functions for graduated optimization, discusses their sufficient conditions, and provides a convergence analysis of the graduated optimization algorithm for them. It shows that stochastic gradient descent (SGD) with mini-batch stochastic gradients has the effect of smoothing the function, the degree of which is determined by the learning rate and batch size. This finding provides theoretical insights on why large batch sizes fall into sharp local minima, why decaying learning rates and increasing batch sizes are superior to fixed learning rates and batch sizes, and what the optimal learning rate scheduling is. To the best of our knowledge, this is the first paper to provide a theoretical explanation for these aspects. Moreover, a new graduated optimization framework that uses a decaying learning rate and increasing batch size is analyzed and experimental results of image classification that support our theoretical findings are reported.